Lagrange's Theorem, One of the Most Important Results Infinite Group Theory, States That the Order of a Subgroup Must Divide the Orderof the Group. This Theorem Provides a Powerful Tool For Analyzing Finitegroups; It Gives Us an Idea of Exactly What Type of Subgroups We Might Expect Afinite Group to Possess. Central to Understanding Lagrange’S Theorem Is Thenotion of a Coset.