Quotient-isomorph-free subgroup

Definition
A subgroup $$H$$ of a group $$G$$ is termed quotient-isomorph-free if $$H$$ is normal in $$G$$, and there is no other normal subgroup $$K$$ of $$G$$ such that $$G/H$$ is isomorphic to $$G/K$$.

Stronger properties

 * Quotient-subisomorph-containing subgroup when the quotient is a Hopfian group.

Weaker properties

 * Stronger than::Series-isomorph-free subgroup
 * Stronger than::Characteristic subgroup
 * Stronger than::Normal subgroup

Related properties

 * Isomorph-free subgroup