Detecting solvability, supersolvability and CLT properties via an invariant based on conjugacy classes of subgroups

Mihai-Silviu Lazorec

For a finite group $G$, denote by $k^{\prime }(G)$ and $L(G)$ the number of conjugacy classes of subgroups and the subgroup lattice of $G$, respectively. Let $d^{\prime }(G)=\frac{k^{\prime }(G)}{|L(G)|}$ an…