MHB Find All Subgroups of U(14) in $\mathbb{Z}_{14}$

[alexmahone]

Find all subgroups of U(14), the group of units of $\mathbb{Z}_{14}$.

My attempt:

U(14)={1, 3, 5, 9, 11, 13} and the operation is multiplication modulo 14. Do I just find the subgroups generated by each of the elements in U(14)? What about subgroups generated by two elements?

 

[Deveno]

You have an abelian group of order $6$. There are, up to isomorphism, only two groups of order $6$, and only one of those is abelian. Thus, your group is cyclic.

This means you have exactly:

1 group of order 1
1 group of order 2
1 group of order 3
1 group of order 6

each of which will be generated by a single element. I suggest finding a generator (element) of order 6, first.