Let G be the group . 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:

http://img534.imageshack.us/img534/6739/cayley.gif

Any help is very appreciated.