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 ∤ 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. [ABSTRACT FROM AUTHOR]