Finite simple groups of section 2 with rank at least 5 have
Sylow 2-subgroups with a self-centralizing
normal subgroup of rank at least 3, which implies that they have to be of either
component type or of
characteristic 2 type. Therefore, the Gorenstein–Harada theorem splits the problem of classifying finite simple groups into these two sub-cases.
Gorenstein, D.; Harada, Koichiro (1973), "Finite groups of sectional 2-rank at most 4", in Gagen, Terrence; Hale, Mark P. Jr.; Shult, Ernest E. (eds.), Finite groups '72. Proceedings of the Gainesville Conference on Finite Groups, March 23-24, 1972, North-Holland Math. Studies, vol. 7, Amsterdam: North-Holland, pp. 57–67,
ISBN978-0-444-10451-9,
MR0352243