Subgroup not contained in a proper direct factor

This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

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VIEW FACTS THAT:use, or start with, a subgroup satisfying the property|prove, or show that, a subgroup satisfies the property

Definition

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

Relation with other properties

Stronger properties

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