Subgroups of simple groups are as diverse as possible

Martin Kassabov, Brady A. Tyburski, James B. Wilson

For a finite group $G$, let $\sigma (G)$ be the number of subgroups of $G$ and ${\sigma }_{\iota }(G)$ the number of isomorphism types of subgroups of $G$. Let $L=L_r(p^e)$ denote a simple group of Lie…