A REGIMENT was made up of 10 companies, usually commanded by Colonel. The regiments were numbered in the order their states organized them.
A BRIGADE was made up of 3 to 5 regiments, usually commanded by a Brigadier General. The brigades were named for their commanders (CSA) or numbered (USA).
A DIVISION was made up of 3 to five brigades, usually commanded by a Major General. The divisions were named for their commanders (CSA) or numbered (USA).
A CORPS was made up of 3 or 4 divisions, usually commanded by a Lieutenant General (CSA) or a Major General (USA). The corps were usually named for their commanders, but in some instances also had numbers (CSA), or were just numbered (USA).
An ARMY was made up of 2 to 4 corps, usually commanded by a General (CSA), or a Major General (USA). Confederate armies were named for the regions in which they fought. Union armies were usually named for principal rivers in their zones.
CAVALRY was organized as a separate corps of horse soldiers.
ARILLERY was organized as follows: