Groups of order 5^2.2^n

This article discusses the groups of order $$5^2 \cdot 2^n$$, where $$n$$ varies over nonnegative integers. Note that any such group has a 5-Sylow subgroup of order $$5^2 = 25$$, and a 2-Sylow subgroup, which is of order $$2^n$$. Further, because order has only two prime factors implies solvable, any such group is a solvable group and in particular a finite solvable group.