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The 18 pages that link to Normal subgroup, each with the reason it gives.

• Congruence relationRelated: Normal subgroups correspond exactly to congruences on groups.

• Group homomorphismRelated: Every group homomorphism's kernel is a normal subgroup.

• Quotient groupBroader topic: Normality ensures coset multiplication does not depend on the chosen representatives.

• SubgroupBroader topic: Normality adds a conjugation condition that enables quotient groups.

• CosetRelated: A subgroup is normal exactly when all its left and right cosets coincide.

• Conjugacy classRelated: A subgroup is normal exactly when it is a union of conjugacy classes.

• Simple groupBroader topic: Simplicity is defined by allowing only the trivial subgroup and the whole group to be normal.

• Sylow theoremsCompared with: A unique Sylow p-subgroup is normal, but Sylow subgroups need not be unique.

• Composition seriesNarrower topic: Each term must be normal in the next for the successive quotient to be a group.

• Finite simple groupRelated: Normality is the exact condition used to define simplicity.

• Jordan–Hölder theoremRelated: Composition series require each subgroup to be normal in the next.

• Fundamental theorem of Galois theoryRelated: Normal subgroups correspond precisely to intermediate fields that are Galois over the base field.

• Normal extensionRelated: Under the Galois correspondence, normal intermediate extensions correspond to normal subgroups.

• Isomorphism theoremsRelated: Normality is what permits the quotient groups used throughout the theorems.

• Zassenhaus lemmaBroader topic: The quotient groups in the lemma require normal subgroups.

• Brauer–Suzuki theoremRelated: The structural argument forces central behavior incompatible with nonabelian simplicity.

• Frattini's argumentBroader topic: Normality allows conjugates of the chosen Sylow subgroup to remain inside the subgroup.

• Fundamental theorem on homomorphismsRelated: A homomorphism's kernel is normal, so its cosets form a quotient group.