Find all subgroups of Z60 and draw a lattice diagram for them.
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- Let be a group of order , where and are distinct prime integers. If has only one subgroup of order and only one subgroup of order , prove that is cyclic.34. Suppose that and are subgroups of the group . Prove that is a subgroup of .16. Let be a subgroup of and assume that every left coset of in is equal to a right coset of in . Prove that is a normal subgroup of .