Not sure it this is the type of info you are interested in but:
I was in the Marine Corps in Vietnam. The following is a rough breakdown of how we were set up. Starting at the smallest unit:
A fireteam. From 2-4 riflemen.
A squad. 2-4 fireteams.
A platoon. 3 squads plus the platoon commander (usually a lieutenant), platoon sergeant, radio man, and a Corpsman. A platoon generally had between 35-45 men.
A company. 3 rifle platoons and a weapons platoon. Weapons platoon had the machine guns, rockets, and 60mm mortars, though most of these were sprinkled out among the 3 rifle platoons. A company was generally commanded by a Captain and ran around 175-210 men. The command group might have 2-3 FO’s (forward observers for artillery and airsupport, though liason might have been a better word.), the captain, the gunnery sergeant, 2 radio men.
A battalion. 3 rifle (or line) companies and a H&S (Headquarters and Support) company. A battalion might run around 1,000 men and was usually commanded by a Lt. colonel. H&S company had the 106 recoiless rifles, larger, less transportable, mortars, an attached artillery company, etc.
A regiment. 3 battalions plus an H&S. Commanded by a colonel and had around 3,500 men. It might have it’s own attached helicopter unit and larger artillery such as 175mm and 8" cannons. I think a tank battalion was attached also.
A division. 3 or 4 regiments. 10-15,000 men and was commanded by a general.
In the Marine Corps that was about as far as we went. The Army, I understand, uses brigades which are of 2-3 division strength. So obviously we are getting into some major size here.
I think brigades are combined to make armies.