Abstract Algebra/Group Theory/Subgroup/Lagrange's Theorem


Let H be a subgroup of group G.

Let o(H), o(G), be orders of H, G respectively

o(H) divides o(G)


As H is Subgroup of G,

1. All Left Cosets of H partitions G.
2. Each of such partitions is one of the Cosets of H.
3. Any coset of H has the same order as H does.
4. Thus, o(H) divides o(G)