US Army organization and leadership

My understanding of the organization of WW2 US Army infantry structures is as follows:

Division lead by major general, consisted of about 10 battalions Brigade lead by brigadier general, consisted of 2-5 battalions Regiment lead by colonel, consisted of 3 battalions Battalion lead by lt. colonel, consisted of 5 companies (hq, weapons, and 3 rifle) Company lead by captain consisted of 3 rifle platoons, 1 weapons platoon and hq. Platoon lead by lieutenant divided into 2 or more squad.

First question-any errors with the above? Second-where does a major fit in to the command structure? third-if the above is correct, how do brigades and regiments relate as they seem to overlap in size? Thanks in advance.

Re Brigades: no, wrong; you are stirring in British practice. An INFANTRY Brigade, up until 1942, consisted of two Inf Regiments, and was nearly always subordinate to a Division