Middle-characteristic subgroup

Definition
Suppose $$H \le K \le G$$ are groups. We say that $$H$$ is middle-characteristic if $$H$$ is a defining ingredient::characteristic subgroup of $$K$$.

Stronger properties

 * Weaker than::Relatively characteristic subgroup

Weaker properties

 * Stronger than::Normalizer-relatively normal subgroup
 * Stronger than::Relatively normal subgroup