Conjugacy Classes of Completely Reducible Cube-Free Solvable p′-Subgroups of GL(2,q)

Let m be a cube-free positive integer and let p be a prime such that p does not divide m. In this paper we find the number of conjugacy classes of completely reducible solvable cube-free subgroups in GL(2, q) of order m, where q is a power of p.