The phrase "main branch" refers to the primary or central location of a company, organization, or institution. It is the biggest or most important place where activities are coordinated and decisions are made. Full definition
I noted that in the 1970s the three main branches came to acknowledge that they could learn from one another. (religion-online.org)
The other main branch of the field uses a nickel - hydrogen setup, which can produce greater than 400 times as much energy as it uses. (scientificamerican.com)