1-3

Space Marine Chapter: The Inquisitor has contact with a chapter of the Adeptus Astartes, and can call upon them when in need of a favour, which often involves a large amount of brute force.

4-15

Adeptus Mechanicus: Useful to aid in the identification and use of alien or ancient technology, an Inquisitor with ties to the Mechanicus must be careful their position is not compromised by agents of the Machine God.

16-30

Administratum: Bureaucrats, archivists, and logisters, the staff of the Administratum possess a great deal of information; they simply need to be told where to look.

31-40

Adeptus Arbites: Good for the detention of heretics, as well as tracking criminals and providing a decent amount of firepower when necessary.

41-55

Ecclesiarchy: The Imperial Church possesses vast wealth and resources, as well as a presence on almost all Imperial worlds.

56-57

Assassinorum Temple: The Inquisitor has a powerful contact, possibly to do with the Ordo Sicarius, and can gain access to a deadly Assassin of one of the six temples.

58-63

Criminal Organisation: Anything from a xeno-trading cartel to narcotics barons, having access to a criminal gang can be very useful in some places where Imperial justice does not hold so much sway.

64-70

Noble House: Ideal for those of aristocratic birth, ties with the nobility can often lead to use of House ships, troops and funds, as well as bolt-holes and spies. This could also be a Navigator House.

71-76

Adeptus Astra Telepathica: Due to investigations into psykers or being a psyker themselves, the Inquisitor has ties with the body that deals with all sanctioned psykers in the Imperium. Can be taken by default even if Ties With wasn't hit on the previous table or on top of rolls here if the Inquisitor is psychic, rerolling if you hit this.

77-88

Imperial Government: The Inquisitor has friends in high places within a particular region's government, be it a Sub-Sector, Sector or even a Segmentum.

89-98

Imperial Military: Naval or Imperial Guard assets are available to the Inquisitor due to a martial background or contacts within the organization.

99-100

Exotic: For Radicals, this could be aliens or even a daemon, whilst for Puritans it's more likely to be a particularly holy figure (possibly on the verge of Sainthood), a Rogue Trader, etc.