Normal subgroup of Sylow subgroup

Definition
A subgroup of a finite group is termed a normal subgroup of Sylow subgroup if it can be expressed as a normal subgroup of a $$p$$-Sylow subgroup of the whole for some prime $$p$$.

Stronger properties

 * Weaker than::Normal subgroup of prime power order: Any normal $$p$$-subgroup for a prime $$p$$ is contained in a $$p$$-Sylow subgroup, and is also normal in that.
 * Weaker than::Sylow subgroup of normal subgroup

Weaker properties

 * Subgroup of prime power order