Subgroup for which the transfer to its quotient by the intersection with the derived subgroup is surjective

Definition
Suppose $$G$$ is a group and $$H$$ is a subgroup of finite index in $$G$$. We say that $$H$$ is a subgroup for which the transfer to its quotient by the intersection with the commutator subgroup is surjective if the transfer homomorphism $$G \to H/(H \cap [G,G])$$ is a surjective homomorphism of groups.

Stronger properties

 * Weaker than::Sylow subgroup