Conjugacy Class of symmetry group $S_{10}$

Question

Let $X=\{a\in S_{10} | ~~\text{order}(a)=8\}$. Determine how many conjugacy classes are in $X$.

How to do this question in general?

Answer 1

Hint: Consider cycle decompositions.

Answer 2

Hint #2: It suffices to consider disjoint cycle decompositions for which every cycle is of length 2,4 or 8.