1. The problem statement, all variables and given/known data Consider the cyclic group Cn = <g> of order n and let H=<gm> where m|n. How many distinct H cosets are there? Describe these cosets explicitly. 2. Relevant equations Lagrange's Theorem: |G| = |H| x number of distinct H cosets 3. The attempt at a solution |G| = n I'm unsure if I have interpreted H correctly, I think it is the cyclic group generated by gm so contains gmk for integers k. I don't know how I can work out the order of H from this, or how to describe the cosets.