Let G be the group $\displaystyle (U(15), \times_{15})$. Find all distinct subgroup of G with exactly two elements.

Could anyone show me how to deal with this problem? So, I know that U(15)={1, 2, 4, 7, 8, 11, 13, 14} under multiplication modulo 15. I'm not sure if it helps, but I have constructed a Cayley table for G:

Any help is very appreciated.