Questions like these are not able to be answered in 1 short reply. It took me quite sometime to think through whether I should write a topic solely on Taoist Thunder Gods Series，because it is very long topic of dicussion.
1st - Nowadays folks who are seeking for Taoist Sorcery Help are more concern about immediate help from taoist talismans or rituals, and have no interest to understand about the heavenly structure of Taoist Gods. Folks like these have no interest to get too deep into understanding Taoist Gods.
2nd - There is too little information on Pure Religious Taoism and Folk Taoism, written in English. Folks from Western Countries and also the English Educated Chinese, who wish to know more and understand deeper into Taoist Gods / Deities can't get much infomation online. Therefore, if I don't spend the time to write and share, many folks interested in Religious Taoism can't get the much needed information.
3rd - Worst case - some western folks who are Taoist-Master-Wannabes, without full knowledge of Taoist Deities nor the proper Spiritual / Magical Training, not even able to read and write Chinese Characters and not even know the secret chants, hand seals and full ritual to create and empower the talismans, are trying to copy blindly on the Taoist Talismans they happen to see online.
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Since someone asked about Thunder Gods, I shall share as much details as possible for Your understanding of the Taoist Thunder Gods. Read only if You are interested.
Many ordinally Chinese Folks, and some Western Folks who are interested in Taoist Magic, would have only heard about 五雷 (Wu Lei) - Five Thunders, or have seen some different types of "Five Thunder Talismans" (五雷符). Many folks don't know who are the Five Thunder Gods.
*The Taoist Thunder Series written here are just brief introduction to the Structure of different groups and departments of Taoist Thunder Gods. To fully understand the full details about Taoist Thunder Topics, You have to read up several Taoist Thunder Related Scriptures , such as 《無上九霄玉清大梵紫微玄都雷庭玉經》 (Wu Shang Jiu Xiao Yu Qing Da Fan Zi Wei Xuan Du Lei Ting Yu Jing).
Even before getting to know who are the 5 thunder gods, lets start from the highest top ranking - The Thunder Patriarch (雷祖 - Lei Zu) in Pure (Orthodox) Taoist Religion.
The Thunder Patriarch (雷祖 Lei Zu) is also called:
1) 九天應元雷聲普化天尊 （Jiu Tian Ying Yuan Lei Sheng Pu Hua Tian Zun) - The 'Heavenly Lord of Universal Transformation Whose Voice of Thunder Resonates from the Origin of the Nine Heavens'
2) 九天應元雷聲普化真王 （Jiu Tian Ying Yuan Lei Sheng Pu Hua Zhen Wang) - The 'Perfect King of Universal Transformation Whose Voice of Thunder Resonates with the Origin of the Nine Heavens' .
According to Taoist Scripture - ( 《無上九霄玉清大梵紫微玄都雷庭玉經》 Wu Shang Jiu Xiao Yu Qing Da Fan Zi Wei Xuan Du Lei Ting Yu Jing): Thunder Patriarch (雷祖 Lei Zu) is the avatar of the NINTH SON of 'Fu Li Primeval Lord of Heaven' (浮黎元始天尊 - Fu Li Yuan Shi Tian Zun), known as The Perfect King of Jade Clarity - Yu Qing Zhen Wang (玉清真王).
The Thunder Patriarch lives in the 'Jade Mansion of Divine Heaven' (神霄玉府 - Shen Xiao Yu Fu), in the midst of the Pure Vital Breath of the Azure Heaven ( 碧霄梵氣 Bi Xiao Fan Qi), 2300 miles from the Thunder City (雷城 - Lei Cheng). The '81 Zhang' high Thunder City is the place where the Heavenly Court administers thunders, to the left of which is the Jade Pivot Five Thunder Agency (玉樞五雷使 Yu Shu Wu Lei Shi) and to the right of which is the Jade Mansion Five Thunder Agency (玉府五雷使 - Yu Fu Wu Lei Shi). *雷祖居于神霄玉府，在碧霄梵气之中，去雷城有二千三百里。雷城是天庭行雷之所，高八十一丈，左有玉枢五雷使院，右有玉府五雷使院*
In front of the Heavenly Lord, there are thirty-six thunder drums, in charge by thirty-six thunder spirits. When it is time for thunders, the Thunder Patriarch beats the drum once; and Grandpa Thunder ( 雷公 Lei Gong ) and the Master of Thunder ( 雷師 Lei Shi) throw out thunder bolts. The thirty-six spirits of the Thunder Agency are all meritorious ministers of the time. *天尊前有雷鼓三十六面，由三十六神司之。行雷之时，雷祖击鼓一下，即时雷公雷师兴发雷声。雷部有神三十六名，皆当时辅相有功之臣*
Base on 'The investiture of the gods' ( 封神演義 Feng Shen Yan Yi ), a fiction of the Ming Dynasty:
Wen Zhong (闻仲) is the 'Heavenly Lord of Universal Transformation Whose Voice of Thunder Resonates with the Origin of the Nine Heavens", who leads 24 Law-Protecting Heavenly Sovereigns Who Bring Wind and Rain (催雲助雨護法天君 Cui Yun ZhuYu Hu Fa Tian Jun).
*明代小说《封神演义》则称闻仲为九天应元雷声普化天尊，其率领之雷部催云助雨护法天君共有二十四名*
Among the 24 of them, there is Deng Zhong （鄧元帥， 名忠） - the Great Spirit of Statutes and Ordinances (律令大神 Lu ling Da Shen), who is often worshipped in Folk Taoist temples.
Functions of Thunder Agency:
Since ancient times in China, Grandpa Thunder (雷公) / Thunder Deity (雷神) had already been worshipped.
But it was at the end of the Northern Song that the Thunder Agency (雷部 Lei Bu), in the charge of the 'Heavenly Lord of Universal Transformation Whose Voice of Thunder Resonates with the Origin of the Nine Heavens' (九天应元雷声普化天尊), was incorporated into the Daoist divinity system.
In the Northern Song period, Daoist sects such as the Divine Heaven Tradition ( 神霄派 Shen Xiao Pai) and the Pristine Subtlety Tradition ( 清微派 Qing Wei Pai), emphasized Thunder Skills ( 雷法 Lei Fa).
Thus, the functions of thunder expanded from providing rain to announcing fortune or misfortune, and even to conferring life or death after the inspection and evaluation of people.
The Jade Pivot Precious Book of the Heavenly Lord of Universal Transformation Whose Voice of Thunder Resonates with the Origin of the Nine Heavens ( 《九天應元雷聲普化天尊玉樞寶經》 Jiu Tian Ying Yuan Lei Sheng Pu Hua Tian Zun Yu Shu Bao Jing) stated that "Those who are Disloyal to the emperor, infilial to parents, disrespect to teachers" will be killed by the Five Thunders Inspection and Execution Agency. The impious are killed first in the spirit and then in the body, and even beaten into pieces by thunder bolts.
Worshipping of Thunder Deities in Temples:
According to the 'Records of Rites" in the History of the Ming Dynasty ( 明史 Ming Shi), 'the Heavenly Lord of Universal Transformation Whose Voice of Thunder Resonates with the Origin of the Nine Heavens' is in charge of the Five Thunders Marshals.
The 24th day of the sixth lunar month is considered by Daoists as the day of his manifestation. On this day every year, Taoist temples that worship the Thunder Patriarch (雷祖 - Lei Zu) will have Taoist Priests and Taoist Followers doing prayer and burn incense in temples to pray for gook luck.
Interesting Point to take note: Lei Zu (雷祖) has a 3rd eye. The third eye can see all things in the world, in charge of yin and yang, good and evil, thunder agency, five elements, descendants, etc.
Important point to take note: Thunder Rituals and Thunder Talismans are sometime used in extreme exorcism - To destroy the evil spirits and demons from a person or place.
Continue to Article:
*Below are the different departnments of 'Jade Mansion of Divine Heaven' (神霄玉府 - Shen Xiao Yu Fu), base on the Taoist Scripture - ( 《無上九霄玉清大梵紫微玄都雷庭玉經》 Wu Shang Jiu Xiao Yu Qing Da Fan Zi Wei Xuan Du Lei Ting Yu Jing) : *For reference only, so no English Translation
据《无上九霄玉清大梵紫微玄都雷霆玉经》称:
The Four Thunder Mansions are: 'Jiu Xiao Yu Qing' Mansion, 'Dong Ji Qing Xuan' Mansion, 'Jiu Tian Ying Yuan' Mansion, 'Dong Yuan Jade' Mansion
四府为：九霄玉清府、东极青玄府、九天应元府、洞渊玉府
The 6 Thunder Institutions (院 -Yuan) are: 'Tai Yi Nei' Yuan, 'Yu Shu' Yuan, 'Wu Lei' Yuan, 'Dou Shu' Yuan, 'Shi Yang' Yuan, 'Xian Du Huo Lei' Yuan
六院为：太一内院、玉枢院、五雷院、斗枢院、氏阳院、仙都火雷院
There are Several Thunder Departments (司 - Si): Tian Bu Ting Si, Peng Lai Du Shui Si, Tai Yi Lei Ting Si, Bei Di Lei Ting Si, Bei Dou Fang Wei Si, Yu Fu Lei Ting Jiu Si, Zhu Cao Yuan Zi Si.
诸有司为：天部廷司、蓬莱都水司、太乙雷霆四司, 北帝雷霆司、北斗征伐司、北斗防卫司、玉府雷霆九司及诸曹院子司。
In each institutions / departments, there are sevreal groups of thunder spiritual assistants: "Yu Fu Zuo Xuan, You Xuan, Jin Shu Shi Zhong, Shu She, Shang Xiang Zhen Xian, Zhen Bo, Qing Jian, Xian Lang, Yu Lang, Yu Tong, Yu Nu Zuo You, Si Hui Zhu Bu Lei Shen, officials, Guan Li, Jiang Li".
并称每个机构中均有“玉府左玄、右玄、金阀侍中、仆射、上相真仙、真伯、卿监、恃宸、仙郎、玉郎、玉童、玉女左右，司麾诸部雷神、官吏、将吏”。
Also known as "Jiu Tian Lei Gong Jiang Jun, Ba Fang Yun Lei Jiang Jun, Wu Fang Man Lei Shi Zhe, Lei Bu Zong Bing Shi Zhe, under the command of 九天應元雷聲普化天尊 （Jiu Tian Ying Yuan Lei Sheng Pu Hua Tian Zun).
且称“九天雷公将军、八方云雷将军、五方蛮雷使者、雷部总兵使者”，均在九天应元雷声普化天尊麾下听令。
There are36 thunder gods among the divisions, divided into 3 categories: Heaven, Earth, and Human, with 12 in each category.
是经称诸司中有三十六雷公，分天、地、人三类，每类十二名。
天雷十二为 (12 Thunder spirits of the Sky)：神霄雷公、五方雷公、行风雷公、行雨雷公、行云雷公、布泽雷公、行冰雷公、行霄雷公、飞砂雷公、食粜雷公、伏魔雷公、吞鬼雷公。
地雷十二为 (12 Thunder spirits of the ground)：纠善雷公、罚恶雷公、社令雷公、发稻雷公、四序雷公、却灾雷公、收毒雷公、扶危雷公、救病雷公、太升雷公、巡天雷公、察地雷公。
人雷十二为 (12 Thunder spirits of human)：收瘟雷公、摄毒雷公、却祸雷公、除祸雷公、破祸雷公、破庙雷公、封山雷公、伏虎雷公、打虎雷公、灭尸雷公、破障雷公、管魄雷公、荡怪雷公。
These 36 Thunder Spirits (Lei Gongs) take charge of thirty-six types of heavenly laws, strictly abiding by the order of 九天應元雷聲普化天尊 （Jiu Tian Ying Yuan Lei Sheng Pu Hua Tian Zun) , and imposing punishment on behalf of the Heaven. It is said that “The orders are as fast as wind and fire, as if raining spears everywhere and sounds of thunder. It can be bring drought or rain, and the decrees must be issued." 九天應元雷聲普化天尊 （Jiu Tian Ying Yuan Lei Sheng Pu Hua Tian Zun) is in charge of the Five Thunderials , Ten Thunderials, and 36 Thunderials.
这三十六雷公掌三十六天曹刑律，严格遵照九天应元雷声普化天尊的命令，代天实施刑罚，经称“雷司布令行至疾如风火，不可留停，降泽之处有矛，震雷之声有数，可旱即旱，可雨即雨，必奉帝令”。是经还称九天应元雷声普化天尊执掌五雷、十雷、三十六雷霆。
The meaning of 5 Types Of Thunders : Sky Thunder, Ground Thunder, Water Thunder, God Thunder, Spirit (Of the land) Thunder.
五雷为：天雷、地雷、水雷、神雷、社雷。
The meaning of 10 Types Of Thunders: Yu Shu Thunder, Shen Xiao Thunder, Da Dong Thunder, Xian Du Thunder, Bei Ji Thunder, Tai Yi Thunder, Zi Fu Thunder, Yu Chen Thunder, Tai Xiao Thunder, Taiji Thunder.
十雷为：玉枢雷、神霄雷、大洞雷、仙都雷、北极雷、太乙雷、紫府雷、玉晨雷、太霄雷、太极雷。
The meaning of 36 types of Thunders: Yu Shu Thunder, Yu Fu Thunder, Yu Zhu Thunder, Shang Qing Da Dong Thunder, Fire Wheel Thunder, Guan Dou Thunder, Feng Huo Thunder, Fei Jie Thunder, Bei Dou Thunder, Zi Wei Xuan Shu Thunder, Shen Xiao Thunder, Xian Du Thunder, Tai Yi Hong Tian Thunder, Zi Fu Thunder, Tie Jia Thunder, Shao Yang Thunder, Chu Huo Thunder, She Ling Man Thunder, De Zhi Ming Thunder, San Jie Thunder, Zhan Kuang Thunder, Da Wei Thunder, Liu Bo Thunder, Qing Cao Thunder, Bagua Thunder, Hun Yuan Ying Quan Thunder, Xiao Ming Feng Lei, Huo Yun Thunder, Yu Bu Da Tong She Thunder, Tai Ji Thunder, Jian Huo Thunder, Wai Jian Thunder, Nei Jian Thunder, Shen Fu Tian Shu Thunder, Da Fan Dou Shu Thunder, Yu Chen Thunder.
三十六雷为 ：玉枢雷、玉府雷、玉柱雷，上清大洞雷、火轮雷、灌斗雷、风火雷、飞捷雷、北极雷、紫微璇枢雷、神霄雷、仙都雷、太乙轰天雷、紫府雷、铁甲雷、邵阳雷、欻火雷、社令蛮雷、地祗鸣雷、三界雷、斩圹雷、大威雷、六波雷、青草雷、八卦雷、混元鹰犬雷、啸命风雷、火云雷、禹步大统摄雷、太极雷、剑火雷、外鉴雷、内鉴雷、神府天枢雷、大梵斗枢雷、玉晨雷。