From Halopedia, the Halo wiki
Ministries were a political and military subdivision of the Covenant Empire.
Each ministry acted as a governing body of the Covenant, directing vital religious and secular activites within the empire. The power and prestige of their groups waxed and waned as they waged bloody internal wars for bureaucratic dominance and promotion of their particular brand of orthodoxy. Ministries controlled a large number of independent martial organisations, with the empire as a whole not having one strict standing military. During the Human-Covenant War, three ministries served as the primary military force encountered by humans.
A given ministry is led by a San'Shyuum minister, with a vice minister under him. Some ministries may also employ a Minor Minister. The ministries employed senior and junior staffers below these leadership positions.
Known ministries of the Covenant