Linked from

The 23 pages that link to Subgroup, each with the reason it gives.

• Group theoryBroader topic: Subgroups reveal smaller structures contained within a group.

• GroupBroader topic: Subgroups identify collections of elements closed under the group’s operations.

• Group homomorphismNarrower topic: A homomorphism maps subgroups to subgroups, including its image.

• Finite groupRelated: Subgroups reveal how a finite group decomposes into smaller groups.

• Quotient groupNarrower topic: The subgroup being collapsed must first be a subgroup of the original group.

• Cyclic groupRelated: Every subgroup of a cyclic group is cyclic, linking generators to the group’s internal structure.

• Normal subgroupNarrower topic: Normal subgroups are distinguished from ordinary subgroups by an additional invariance condition.

• Abelian groupRelated: Every subgroup of an Abelian group is Abelian under the inherited operation.

• CosetNarrower topic: The subgroup supplies the elements being translated to form a coset.

• Fission–fusion societyRelated: Temporary subgroups are the units that split off and later rejoin.

• Orbit-stabilizer theoremRelated: Every point stabilizer is a subgroup of the acting group.

• Lagrange's theoremNarrower topic: The theorem relates each subgroup’s size to the size of its containing group.

• Simple groupNarrower topic: A simple group can have many proper subgroups; only its normal subgroups are restricted.

• Sylow theoremsNarrower topic: Each object classified by the theorems is a subgroup of the ambient finite group.

• Composition seriesNarrower topic: The series is a nested chain of subgroups inside one group.

• Finite simple groupCompared with: A simple group may have proper subgroups; only proper normal subgroups are forbidden.

• Finite cyclic groupNarrower topic: Every subgroup of a finite cyclic group is cyclic, with one subgroup for each divisor of its order.

• Erlangen programRelated: Relations among transformation groups organize geometries by how much structure they preserve.

• CentralizerRelated: The elements commuting with a fixed subset always form a subgroup.

• Zassenhaus lemmaBroader topic: The lemma begins with two subgroups and their intersections.

• Closed-subgroup theoremNarrower topic: The theorem concerns subgroups before establishing their smooth structure.

• Frattini's argumentNarrower topic: The theorem relates a normal subgroup to a Sylow subgroup contained within it.

• Herzog–Schönheim conjectureRelated: Each coset in the conjecture is defined by a subgroup.