KnowraSubgroupLinked fromLinked fromThe 23 pages that link to Subgroup, each with the reason it gives.All 23Broader topic 3Related 8Narrower topic 11Compared with 1Group homomorphismNarrower topic: A homomorphism maps subgroups to subgroups, including its image.Quotient groupNarrower topic: The subgroup being collapsed must first be a subgroup of the original group.Normal subgroupNarrower topic: Normal subgroups are distinguished from ordinary subgroups by an additional invariance condition.CosetNarrower topic: The subgroup supplies the elements being translated to form a coset.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 cyclic groupNarrower topic: Every subgroup of a finite cyclic group is cyclic, with one subgroup for each divisor of its order.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.