Section FrobeniusProperties.
Variables G H K : {group gT}.
Hypothesis frobG : [Frobenius G = K ><| H].
End FrobeniusProperties.

Lemma Frobenius_subl G K K1 H :
K1 :!=: 1 -> K1 \subset K -> H \subset 'N(K1) -> [Frobenius G = K ><| H] ->
[Frobenius K1 <*> H = K1 ><| H].