Linked from

The 16 pages that link to Lagrange's theorem, each with the reason it gives.

• Group theoryRelated: Coset partitioning yields this fundamental restriction on finite group sizes.

• GroupRelated: It constrains subgroup sizes and the possible orders of elements in finite groups.

• Fermat's little theoremRelated: Applied to the multiplicative group modulo p, it forces each element's order to divide p−1.

• Finite groupRelated: It is the basic divisibility constraint on finite subgroup structure.

• Quotient groupRelated: Coset sizes explain why finite quotient groups have order equal to an index.

• SubgroupRelated: It constrains the possible sizes of finite subgroups.

• CosetRelated: Equal-sized cosets partition finite groups, yielding this divisibility result.

• Orbit-stabilizer theoremRelated: It ensures the stabilizer’s size divides the acting group’s order.

• Sylow theoremsRelated: It bounds possible subgroup orders and identifies the largest power of a chosen prime that can occur.

• Multiplicative orderRelated: It forces every element’s order in a finite group to divide the group order.

• Wedderburn's little theoremRelated: Finite multiplicative subgroups constrain element orders in the proof.

• Artin's conjecture on primitive rootsRelated: It explains why multiplicative orders divide p−1.

• Carmichael's theoremRelated: It constrains the possible orders of elements in the finite subgroup.

• Herzog–Schönheim conjectureRelated: It relates subgroup indices to subgroup sizes in finite groups.