Group in which every proper subgroup is contained in a maximal subgroup

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This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions
This is a variation of finiteness (groups)|Find other variations of finiteness (groups) |

Definition

Symbol-free definition

A group in which every proper subgroup is contained in a maximal subgroup is a group for which every proper subgroup (subgroup that is not the whole group) is contained in a maximal subgroup (a proper subgroup not contained in any other proper subgroup).

Relation with other properties

Stronger properties

Facts

For such a group, the Frattini subgroup is indeed the largest Frattini-embedded normal subgroup.