Let $\displaystyle G = U_{19}$. Write down the cosets of the subgroup of $\displaystyle G$ generated by $\displaystyle [7]$; by $\displaystyle [12]$; by $\displaystyle [8]$; by $\displaystyle [2]$. Verify Lagrange's theorm for each case.

Previously $\displaystyle G = U_m$ was the group (under multiplication) of units of $\displaystyle Z/mZ$

What are the subgroups and how do I find the cosets of those subgroups?

I really only need help getting started with one then I'm sure I'll be able to do the rest, I'm just not certain what the question is looking for.