A left coset of a subgroup H of a group G is a set of the form gH for some element g of G; a right coset is of the form Hg If the group happens to be Abelian, or if H is a normal subgroup of G, then the left and right cosets coincide and we simply speak of "cosets" In any case, the numbers of left and right cosets are equal; this number is the index of H in G Distinct left cosets are disjoint, and each has the same cardinality as the subgroup H; so they form a partition of the group The same applies to right cosets This is the basis of Lagrange's Theorem