Fully invariant-potentially fully invariant subgroup

Definition
A subgroup $$H$$ of a group $$K$$ is termed a strongly potentially fully characteristic subgroup if there exists a group $$G$$ containing $$K$$ such that both $$H$$ and $$K$$ are defining ingredient::fully invariant subgroups of $$G$$.

Stronger properties

 * Weaker than::Fully invariant subgroup

Weaker properties

 * Stronger than::Potentially fully invariant subgroup
 * Stronger than::Normal subgroup