I have been looking through my textbook and have noticed subgroup lattices. I understand the premise of them under addition, but this one example, in particular, I can't figure out. Let $G = Z^*_{26}$. I know the order of $G$ is $12$ with $7$ being a generator of $G$.
Am I just testing the length of every element when doing $(1,a,a^2,a^3,....)$ and whatever the length of the element is would be included in that particular level of the lattice?
Hopefully, that makes sense and I would appreciate any feedback