classification of semisimple groups

For every semisimple group $G$ there is a normal subgroup $H$ of $G$, (called the centerlesscompetely reducible radical) which isomorphic to a direct product of nonabelian simple groupssuch that conjugation on $H$ gives an injection into $\mathrm{Aut}(H)$. Thus $G$ is isomorphic to asubgroup of $\mathrm{Aut}(H)$ containing the inner automorphisms, and for every group $H$ isomorphicto a direct product of non-abelian simple groups, every such subgroup is semisimple.