Conjugation-invariantly relatively normal subgroup

Definition
Suppose $$H \le K \le G$$. We say that $$H$$ is conjugation-invariantly relatively normal in $$K$$ with respect to $$G$$ if $$H$$ is a normal subgroup in every conjugate of $$K$$ in $$G$$ that contains $$H$$.

Stronger properties

 * Weaker than::Strongly closed subgroup
 * Weaker than::Weakly closed subgroup:

Weaker properties

 * Stronger than::Relatively normal subgroup