system
Given the following post, respond as if you're commenting on Reddit:
human
[{40k}]Who's running the show?

so the emperor is dead, the primarchs are missing, who's in charge now?  is it a chaotic morass of competing interests or does humanity have a hierarchy that is fairly constant.  is there a class of space nobles?
gpt
The 13 High Lords of Terra rule the Imperium in the Emperor's Stead. Though the occupants of each seat are not set, common inclusions into the council are;

The Fabricator General (leader of the Machine Cult)
The head of the Departmento Munitorum (Probably spelled that wrong, essentially the head of the Imperial armies)
The head of the Administratum (the bureaucrats) 
The head of the Ministorum (theeee Space Pope!)
Someone from the House of Navigators.