A note on finite groups with few conjugacy classes of subgroups

Abstract

In this note, we give some conditions of solvability of a finite group $G$ based on its number of conjugacy classes of subgroups $Con(G)$. We classify all finite groups $G$ with $Con(G)\le 5$. A new characterization of $A_5$ is also given.

Accepted for publication in Comm. Algebra