Right-transitively isomorph-containing subgroup

Definition
A subgroup $$H$$ of a group $$G$$ is termed a right-transitively isomorph-containing subgroup if, for any isomorph-containing subgroup $$K$$ of $$H$$, $$K$$ is also an isomorph-containing subgroup of $$G$$.

Stronger properties

 * Weaker than::Subisomorph-containing subgroup
 * Weaker than::Subhomomorph-containing subgroup
 * Weaker than::Variety-containing subgroup

Weaker properties

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