It is long since the last person commented on this post. And I think the sub topics of mathematics are still not available yet?
I am going to suggest a new list.
List:
Algebra
Geometry
Logics
Statistics
Trigonometry
Pre-calculus
Calculus
This list is much shorter and I can't think of anything that isn't in the area of the list.
Differential Eq.s are in calculus.
Financial Maths are in Algebra due to the percentages and indices.
Surds are in Algebra.
Complex numbers are in Algebra or Geometry because there are various kinds of complex numbers question. Some involves Pythagoras Theorem.
Coordinates are in Geometry.
Pythagoras Theorem is in Geometry or Trigonometry.
I think we don't need so much categories.