Conjugacy and the Class Equation · Superchallenge problem

How many conjugacy classes does $GL(2,\mathbb{Z}_5)$ (the general linear group of $2\times2$ invertible matrices over $\mathbb{Z}_5$) have? $GL(2,5)$ has order $(5^2-1)(5^2-5) = 24 \times 20 = 480$.