The numbers change as you go up because of support personel as well. A rifle company(Army) will have 130 or so trigger pullers, but you also have folks like motor pool, admin, supply etc. As the units get bigger, the logistics slice gets bigger, because the more the unit is self-sustaining. So in the next higher unit, (Battalion), you could have a whole company of support (the Headquarters and Headquarters Company, or HHC) in addition to the company's, and some will have another company for service, (Headquarters Service Company, or HSC) in addition to that.
As the unit grows to the Division size, the division has it's three line Brigades, but other brigade sized units such as DIVARTY (Divisional Artillery), CAB (Combat Aviaiton Brigade, the 101st has two of them), DISCOM (Division support command), MP, ADA, Chem, Engineer, Signal, Medical, and on and on.
Generally speaking, the bigger the unit, the longer it's "logistics tail", because it has to provide that support for it's smaller units.
Also a line unit often won't fight as a "pure" company. Units in the US Army can "task organize" as required. So company sized and larger will swap platoons/companies, etc to get the right mix for the mission. When you see a tank and a Brad working together, they are almost always a "task force" where some of the platoons have been traded, so the rifle company now has a tank platoon, and the tank company now has a rifle platoon. As long as that "company sized task force" exists, the commander has what is in effect a mixed company. It allows a great deal more firepower and flexibility at a lower level.
This task organizing, is also done with support units to maintian support of those units that are task organized.
So in the end, the size of a company from one operation to the next can vary greatly just due to how it's organized for that particular fight.
One way to remember the approximate numbers though is 10-100-1000-10,000. Squad-company-battalion-division. This was actually the way many acient armies were organized, and where terms like "Centurion" (for the leader of a century or 100) in the Roman Army come from. While not completely the same number wise, the organization isn't too far off from today.
Ross