Normal subgroup having no common composition factor with its quotient group

Definition
A subgroup $$N$$ of a group of finite composition length $$G$$ is termed a normal subgroup having no common composition factor with its quotient group if $$N$$ is a normal subgroup of $$G$$ and no composition factor of $$N$$ is isomorphic to any composition factor of the quotient group $$G/N$$.

Stronger properties

 * Weaker than::Normal Sylow subgroup
 * Weaker than::Normal Hall subgroup

Weaker properties

 * Stronger than::Normal-homomorph-containing subgroup
 * Stronger than::Characteristic subgroup
 * Stronger than::Normal subgroup

Incomparable properties

 * Complemented normal subgroup:
 * Normal subgroup having no nontrivial homomorphism to its quotient group:
 * Fully invariant subgroup