Let $G$ be a finite group. $H \leq G$ is a component of $G$ if $H$ is quasisimple and subnormal in $G$. $E(G)$ is the group generated by all the components of $G$.
What can be said about the structure of a group $G$ if $E(G)=1$? (i.e $G$ has no components) I know that finite solvable groups and simple groups have no components, but are those the only cases?
Thank you in advance for the help.