Order-dominating subgroup

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof.
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RANDOM TIP:The metaproperties section lists important facts about the subgroup property, and addresses many of the natural questions that arise about it. It has links to proofs.

Definition

Symbol-free definition

A finite subgroup of a group is termed order-dominating if every other subgroup whose order divides its order, is conjugate to a subgroup contained in it.

Definition with symbols

Let $G$ be a group and $H$ be a finite subgroup. Then, $H$ is termed order-dominating in $G$ if, for any subgroup $K \le G$ such that the order of $K$ divides the order of $G$ , there exists $g \in G$ such that $gKg^{-1} \le H$ .