Characterization by intersection graph of some families of finite nonsimple groups

summary:For a finite group $G$, $\Gamma (G)$, the intersection graph of $G$, is a simple graph whose vertices are all nontrivial proper subgroups of $G$ and two distinct vertices $H$ and $K$ are adjacent when $H\cap K\neq 1$. In this paper, we classify all finite nonsimple groups whose intersection graphs have a leaf and also we discuss the characterizability of them using their intersection graphs