Let H be a cyclic group of order 36 under the addition operation.

a) Identify all subgroups of order 9. Explain how these groups are obtained.

b) Construct a subgroup lattice diagram for H

c) Give a group G that is isomorphic to H. Explain how to show that G  is isomorphic to H.

d) Up to isomorphism, describe all finitely generated abelian groups of order 36. Then, explain why they are not isomorphic to each other.