there are five branches: inorganic, organic, analytical, physical, and biochemistry. they could be further broken down into sub-branches such as organometallic chemistry, physical organic chemistry, electroanalytical chemistry, and so on and so forth.

Journal of Physical Organic Chemistry was created in 1988.

Organic Chemistry.

For non-carbon containing compounds it is INORGANIC CHemistry

For the calculations, equations, physical changes, it is PHYSICAL CHEMISTRY .

Yes all chemistry comes from physical chemistry. Organic chemistry is the reaction of organic molecules (those with C-H bonds). How those reactions happen is physical chemistry i.e. think thermodynamics.

Organic, inorganic, analytical, physical, and your guess is as good as mine.

Biochemistry? Polymer chemistry? Surface chemistry? Theoretical chemistry? Nuclear chemistry? Depending on your bias any of those might be regarded as a subdivision of one of the Big Four or as a largely independent field of study.

According to my textbook (Grade 11 Chem) they are Organic, Inorganic, Analytical, Physical and Biochemistry.