Subgroup not contained in a proper central factor

Definition
A subgroup $$H$$ of a group $$G$$ is termed a subgroup not contained in a proper central factor if the only defining ingredient::central factor of $$G$$ that contains $$H$$ is $$G$$ itself.

Stronger properties

 * Weaker than::Self-centralizing subgroup
 * Weaker than::Self-normalizing subgroup
 * Weaker than::Contranormal subgroup

Weaker properties

 * Stronger than::Subgroup not contained in a proper direct factor