Order-dominated subgroup

Definition
A subgroup $$H$$ of a finite group $$G$$ is termed order-dominated in $$G$$ if, given any finite subgroup $$K$$ of $$G$$ such that the order of $$H$$ divides the order of $$K$$, there exists $$g \in G$$ such that $$gHg^{-1} \le K$$.

Stronger properties

 * Weaker than::Sylow subgroup:

Weaker properties

 * Stronger than::Order-conjugate subgroup
 * Stronger than::Isomorph-conjugate subgroup
 * Stronger than::Prehomomorph-dominated subgroup (when the whole group is finite)