"main branches of" is correct and usable in written English.
It is usually used to introduce two or more related topics. For example: "The main branches of mathematics are algebra, geometry, and calculus."
There are two main branches of Bell Laboratories.
There are two main branches of sedimentary petrology.
Communication, transport, information communications, main branches of industry will grow.
Shiites and Sunnis represent the two main branches of Islam.
Serious skaters are concerned with 3 main branches of their art: School figures, free skating, & dancing.
The goal is to give students a thorough introduction to the main branches of mathematics.
Other main branches of the Volga delta are the Bakhtemir, Kamyzyak, Staraya (Old) Volga, and Bolda.
The main branches of industry are engineering, metalworking, and paper-pulp making.
The two main branches of formal logic are the propositional calculus and the predicate calculus.
Catfish farming is pond based, along two main branches of the Lower Mekong and associated waterways.
The redundancy allocation problem is one of the main branches of reliability optimization problems.
