Conjugate-join-closed subgroup property

Symbol-free definition
A subgroup property $$p$$ is termed conjugate-join-closed if the join of a nonempty collection of conjugate subgroups satisfying $$p$$, also satisfies $$p$$. Note that any two subgroups in the collection must be conjugate; however, the collection need not include all members of that conjugacy class of subgroups.

Stronger metaproperties

 * Join-closed subgroup property
 * Automorph-join-closed subgroup property

Weaker metaproperties

 * Normal closure-closed subgroup property