I am considering the normal subgroup $H=\langle[28]\rangle$ of the additive group $\mathbb{Z}_{220}$. I want to obtain the elements of the quotient group $\mathbb{Z_{220}}/H$.
Since $H=\langle14[2]\rangle$, we have that $|H|=\frac{220}{\gcd(220,14)}=55$. Therefore, by Lagrange's theorem, $|\mathbb{Z}_{220}/H|=\frac{|\mathbb{Z}_{220}|}{|H|}=\frac{220}{55}=4$. So, I know that $\mathbb{Z}_{220}/H$ has four elements and one of them is $[0]+H$.
The problem I encounter is that, for example, $[0]+H$ is the same as $[28]+H$. Because of this, I have to be careful when writing the other three elements to make sure that I am not making the mistake of writing twice the same element because it is written in two ways that "look different".
If I wrote explicitly all $55$ elements of each element (maybe I should call it class or coset) of the quotient group then I would be sure I am not making that mistake. But this does not look very efficient. I was wondering if there might be some clever way of choosing the representative of each class so as to make sure there are no hidden repetitions.
Thanks in advance.