The Officio Assassinorum was a concept created and pushed by a handful of Incubators, led by Kyuubey, in order to bring a semblance of formalization and organization to contractees all over the world. This was mainly to keep territorial disputes and infighting to a minimum. It was also a way to legitimize the operation as a whole, raise it from its clandestine underground status, and basically make the entire thing a well-greased machine running on tangible resources and adequate support rather than counting on the mettle of a few bright, but still decidedly fragile magical girls. To prevent the heat death of the universe requires more than just a clean heart, a pure Soul Gem and a handful of grief seeds - one also needs synergy. Bureaucracy. Zazz. With the Officio Assassinorum came the classification of Magical Girls.
The Officios work mostly like huge businesses with their respective Incubator as CEO. Some formed international alliances, some are rivals and some sworn enemies. But while their employees might consider each other enemies, the Incubators themselves still see themselves as brothers. 
The best. The brightest. The Ultramarines of the setting. They only induct Warmasters and Magical Girls of note.
Location: The Moon
Warmaster: Hazuki Amane
It is said that a candidate for the First needs the combat prowess of Kharn and the heart of Mami to be half as good as what it takes to get in. The First Incubator is confirmed to be the leader of the Incubator operations on Earth. While each of them acts mostly independently, he has the right to intervene when seen fit and can invite magical girls from all Officios to join his forces without repercussions.
The First Officio always has twenty Magical Girls, with five always in reserve. Those 'reserve' five are the strongest of the First, along with the Warmaster.
The Holy Inquisition of the setting. Witch Hunters and seekers of Magical Girls turned rogue. Abhors heresy. Has a division called the Black Templars.
Location: Unknown castle in Britain
Warmaster: Gertrude von Egisheim
This organization is largely responsible for the spread of the Blessed Lady religion. They worked for this even before the Officio system was established and were known as the Ordos.
Dissolved. Incubator Status Unknown. Folded into the Ninth.
Last Known Location: Mitakihara, Japan
Last Acting Warmaster: Ahriman
Former Incubator: Sanbey
The Third Incubator arrived on Earth long before Kyubey and helped him get started. They shared friendly relations until the Third Warmaster, Ahriman, sacrificed a large number of magical girls in a plot to gain the Blessed Lady's favor. She was struck down by the Ninth Warmaster at the time, Kharn Valnikov, and the Third's contracts were transferred to the Ninth.
It has recently been revealed that not all of the Third's contracts were transferred over to the Ninth Officio. Several rogue squads broke off in a rebellion which nearly cost Murderface her life.
Warmaster: Petra Dammekos
Girls of the Fourth Officio are infamous for fully exchanging their flesh bodies for ones made out of metal, aka “Ironforms”. Tiny Pete was first developed here.
Barbara Falko is a member of the Fourth.
Non-canon events concerning the Fourth are depicted in side-stories in TwiceBorn's The Iron Circle and in Dimunsis's “An Irish Girl's Wish”.
Monster Hunters, the Space Wolves of the setting. Specialize in anti-Officio and Witch hunting tactics. The Warmaster is rumored to be a monster herself.
Location: Sydney, Australia
Warmaster: Leman Russ
Girls that originally contract with the Sixth tend to have some sort of animalistic trait or affinity. Suzi Berry, for instance, has been shown to control spiders, while Leman Russ has wolf ears and a tail. They seem more laid back about discipline and order than other Officios, and are mostly looked down upon as savages; the fact that most of them have tattoos of their kills, trophies of some kind taken from their battles, or both, does not help with this image. They do take their training seriously, though, and 90% of them are Eversors. In fact, every girl at the Sixth is expected to master at least three things : the ability to adapt to any environment or situation; the ability to treat the injuries of themselves and others; and the ability to cook their own meals with a portable barbecue pit.
Formerly the Officio of Risa Schrodinger.
The Peacekeepers. An Officio centered around peace and spirituality. The Incubator contracts Magical Girls seemingly at random, and gladly provides refuge for Magical Girls who want to escape from their Officio.
Warmaster: Xiaomei Baocun
Formerly the Officio of Yuu Kotarou
The Assassins. A very powerful Officio powered with the funding and technology of the most hamburger nation in the world, America. The Incubator is a strange one.
Location: Santa Destroy, California
Warmaster: Mary Sue Springfield
An Officio filled with bloodthirsty lunatics, even by magical girl standards. They are in competition with the United Assassins Association. The Eighth Officio is home to Wendy Cooldown, a mysterious character occasionally appearing in Chiaki's dreams. A party of the Ninth visited their HQ in a flashback featuring Sayaka. Other events concerning the Eighth Officio take place in side-stories written by Wendy Cooldown and -That- Guy.
The Murderers. Equal to the Eighth in power, funding and technology through its shrewd Incubator, this Officio in Japan always gets the most lucrative of assignments, along with the Eighth. It also owns quite a lot of business ventures all over the world, and a mysterious R&D facility in Siberia.
Location: Mitakihara, Japan
Warmaster: Chiaki Matsuda
Home to the quest protagonists, the Ninth Officio and its Incubator are one of the most important resources at the players disposal, even more so since Chiaki Matsuda's promotion to Warmaster. It is the biggest and most efficient Officio, even the other Incubators admit to Kyubey's skill despite their rivalries.
The Thugs. An Officio that had taken to underground dealings to expand its power. Hires out its Magical Girls to criminal organizations.
Location: Mitakihara, Japan
Warmaster: Saki Asami
Previously home to Midori Hanegawa, the Tenth Officio uses underhanded tactics in a ruthless manner to achieve its goals. They are suspected of actively working against the Ninth. The Tenth Incubator Jyuubey is sort of an outcast among his brothers. Their elite members are collectively known as The Pleiades Saints.
The Witchmakers. Comprised primarily of Vanus rank magical girls.
An Officio dedicated primarily to data collection and analysis, especially concerning Witches. It has recently been revealed that it also serves as a backup cell for energy harvest. More than seventy percent of Juunibey's contractees turn into Witches.
Very magically active and competent. Their combat ranks are constantly understaffed, and known for being tomboyish.
The Twelfth Offico has yet to appear in any main thread, and only figures in The Riddle of Witch Flesh by Ratmie. Everything about it can therefore be assumed to be non-canon.
The Chemists. Comprised primarily of Venenum rank magical girls.
Location: Iowa class battleship - SS Rafflesia, unknown home base in Germany
Chief Director: Fran Madaraki
An Officio of scientists, the Thirteenth primarily focus on research rather than direct combat. To this end, the Thirteenth have subdivided their Venenum into further specializations, of which only the Carnicula rank is currently known, led by Fabulous Billie. The Thirteenth is also known for being primarily seaborne, possessing several large ships, two of which have been named thus far: the SS Rafflesia and the MS Pulchritudinous.
Their first Warmaster, Doctor Emma Strauss, was a ruthless woman who did everything she deemed necessary to further her scientific progress. Following the kidnapping of a magical girl of the Ninth Officio, Dr. Strauss was deposed and replaced by Chief Director Madaraki.
The Soldiers of Faith. An Officio installed in the Vatican. Its Warmaster is a hedonist. Allied to the Second.
Location: The Holy See.
This Officio is largely responsible for the spread of the Blessed Lady as a religion, alongside the Second.
Mentioned to have been wiped out some years prior to the events of MGNQ. Current details unknown.
Working in the Middle-East. Their HQ is a heavily stealthed aircraft carrier.
Location: Mobile, stealthed aircraft carrier
Warmaster: Sofiya Pavlovena
Events revolving around the Sixteenth are depicted in side-stories by Rin, Saga of the Sixteenth.
Their technology consists of Incubator-tech and the most advanced human technologies resulting in a Metal Gear Solid level.
The Underdogs. Often considered the weakest of the 'conventional' Officios.
Location: Toronto, Canada
Warmaster: Odette Brighton
Despite being looked upon with distaste by most other Incubators, the Seventeenth Officio has two major strengths. First, they have the largest Culexus division of any Officio, coming in at just over two dozen. Their Culexus also tend to live at least a year longer than those of other Officios. Their second strength is their longevity and tenacity; the magical girls of the Seventeenth are notoriously resistant to Witching Out compared to girls from other Officios. As a result, the Seventeenth has one of the highest numbers of retired magical girls. Much of this is due partly to the fact that their incubator, Fubey, is one of few that places the well-being of his magical girls over the collection of grief seeds. He is often shunned by other incubators because of this, but it has also made him best friends with the incubator of the Seventh, Kelzang.
In thread 234, it was the revealed in a letter that Odette Brighton is once again the Warmaster of the Seventeenth as of Chiaki's ratification. The letter also cryptically states that the Seventeenth is no longer able to act openly.
Rumored to be an organization made up completely of Callidus.
Spymaster: Satou Yuri
Events within the Twentieth Officio are depicted in side-stories by Shibuya Rin.
Each Officio has their own variation of predicting witch events and other relevant things. The Second uses prayers and seer visions, the Fourth uses statistical analysis, the Seventh reads from tea leaves. The Ninth utilizes its Culexus prognostications which gives the most accurate results.