Subgroup not contained in a proper direct factor

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

Stronger properties

 * Weaker than::Contranormal subgroup
 * Weaker than::Subgroup not contained in a proper central factor
 * Weaker than::Self-centralizing subgroup
 * Normal subgroup such that the quotient is a directly indecomposable group