United States government

According to United States Constitution the President may require the Opinion of the principal Officer in each of the executive Departments, upon any subject relating to the Duties of their respective Offices (Article Two, Section 2, Clause 1).

Before the War
The Enclave was covert branch of the government and even a shadow government. Federal executive departments and its branches mentioned Fallout games:
 * War Department - mentioned in Maxson Log (Department of Defence - according to van Buren screenshot concerning HERMES armor and according to Fallout 3 "Faction Profile – the Brotherhood of Steel"), its seat was Pentagon; in real world subsumed by Department of Defense in 1947 (renamed Department of the Army),
 * Department of Energy (mentioned in Fallout Bible timeline); in real world created in 1977,
 * department or departments responsible for war bonds and Unamerican Activities Force supervision (if latter one was government executive branch dependent organization),
 * Environmental Protection Agency.

Possible Cabinet positions:
 * Secretary of War,
 * Secretary of Energy,
 * Secretary of Treasure,
 * Administrator of the Environmental Protection Agency (cabinet level administration officer).

Afrer the War - the Enclave
The Cabinet was addresse of the Project report from United States Chemical Corps and Power Plant Operations report from Atomic Energy Commision. Its seat was Executive Office on the oil rig.
 * The only known cabinet level administration officer in the Enclave was Vice-President (President of the Senate also), the first person in the presidential line of succession (declaring to be republican).
 * Secret Service (USSS) was present there also - if existed before the War, because of Divergence in Fallout world it could be overseen by Department of Treasure. It is not certain, if USSS was an official part of the Enclave armed forces however.
 * Atomic Energy Commision with unknown exact status, it reported to the Cabinet (Department of Energy not mentioned). In real world the same name body existed in 1946-1974 period (see: Atomic Energy Commision).
 * National Aeronautics and Space Administration (NASA) mentioned by Vice-President Bird (however he was only an drolling idiot talking about martian canals); the Enclave was present at Bloomfield Space Center before the War; in real world NASA was created in 1958 and was supervised by the President.

Very likely Cabinet present in the Enclave was minimally staffed (eg. the first American President appointed a Cabinet of four people).

The destruction of the Enclave erased all trace of President Dick Richardson from history. According to one of Fallout 2 endings eventually the survivors of the Enclave find a home in the ranks of NCR. In that case it can be said, that there didn't survive any the USA President succesor.

However survived the broken remnants of the Enclave following the Chosen One’s assassination of the Enclave’s U.S. President and the destruction of their Poseidon oil tanker headquarters off of the California coast (according to J.E.Sawyer's Fallout PnP).

See also: USA, Enclave.