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Military units

Military organization is the structuring of the armed forces of a state so as to offer military capability required by the national defence policy. In some countries paramilitary forces are included in a nation's armed forces. Armed forces that are not a part of the military or paramilitary organizations, such as insurgent forces, often mimic military organizations, or use ad hoc structures. 
Military organization is hierarchical. The use of formalized ranks in a hierarchical structure came into widespread use with the Roman Army. In modern times, executive control, management and administration of military organizations is typically undertaken by the government through a government department within the structure of public administration, often known as a Department of Defense, Department of War, or Ministry of Defence. These in turn manage Armed Services that themselves command combat, combat support and service support formations and units. (wiki)

It is common, at least in the European and North American militaries, to refer to the building blocks of a military as commands, formations and units. In a military context, a command is a collection of units and formations under the control of a single officer. In general it is an administrative and executive strategic headquarters which is responsible to the national government or the national military headquarters. 
It is not uncommon for a nation's services to each consist of their own command (such as Land Force Command, Air Command, and Maritime Command in the Canadian Forces), but this does not preclude the existence of commands which are not service-based.

formation is a composite military organization that includes a mixture of integrated and operationally attached sub-units, and is usually combat-capable. A formation is defined by the US Department of Defense as 'two or more aircraft, ships, or units proceeding together under a commander.'[wiki
The Shorter Oxford English Dictionary describes a formation as an 'arrangement or disposition of troops.' Formations include brigades, divisions, wings, etc.

A typical unit is a homogeneous military organization, either combat, combat support or non-combat in capability, that includes service personnel predominantly from a single Arm of Service, or a Branch of Service, and its administrative and command functions are integrated (self-contained). Anything smaller than a unit is considered a "sub-unit" or "minor unit".

Please note that for simplicity purpose we included descriptions only of the infantry units and we did not include support aviation and strategic weaponry units.

 Unit  /
 Number of soldiers and officers Basic tasks / Description Consist of  Commanded by
 Soldier 1 soldier Smallest unit to perform certain independent tasks (such as driver, signals, etc.) or part of a larger formation (group, squad, etc.)
 One soldier

 Pair     2 soldiers

 Fire and maneuver team Two
soldiers, one in subordination to another. 
 Usually led by a Specialist or Efreitor   
 Group 3-5 soldiers 
Smallest unit (fire-team) to perform military / combat tasks. Part of Squad

 Usually 3 soldiers and 1 corporal

 Squad or
 10-14 soldiers 
 3 groups + 1 soldier + 1 sergeant
 Senior corporal or
 Platoon 33-60 soldiers,
 1 officer or warrant-officer
 3-4 sections + 1 group +
 commanding officer
 Warrant Officer or
 Company 100-200 soldiers,
 2-3 warrant-officers,
 2-4 officers
 Smallest tactical unit to perform military/combat tasks 3-4 platoons (including 1 fire platoon) + 1 section + 1 headquarters group (not always) + commanding officer and his deputy (second-in-command) Captain

 Battalion 400-1000 soldiers,
 Could be a part of larger unit (regiment or brigade), or could be an independent entity
 3 line companies + 1 combat support company + 1 mixed artillery / weaponry company (battery) +
1 signal/support platoon + 1 headquarters squad + number of officers and warrant-officers (3-5) in headquarters + battalion commander and his deputy (second-in-command)

 Regiment 1,500-3,000 
 3-4 line battalions + 1 combat support battalion + 1 mixed artillery battalion (div) + 1 signal/support company + headquarters platoon + number of commanding officers in headquarters + Regiment commander with several deputies (second-in-command) Colonel

 Brigade 2,000-5,000   Brigade-General or
 Division 8,000-12,000   Major-General

 Corps 20,000-40,000 A composite military organization that includes different military types of combat forces (artillery, cavalry, heavy tanks, aviation, etc.) and support elements (hospitals, logistics, maintenance, etc.)

 Army 50,000-100,000  Includes aviation, tactical and strategic weapons
 Group of
 over 100,000
   General of the Army or
 Front /
 Block /
Task Force
 up to 1 million

 Army, /
 Protection of the country from external enemies. Includes all the Military Forces (army, navy, air force, strategic missile and space forces) of the country Royal Marshal

Example: fire-team in action.

Example: Russian / Soviet platoon near barracks (circa 1988)