Suppose I have a factor group $\mathbb{Z}^{*}_{175} /\mathbb{Z}_{2}$. What is it? $$\mathbb{Z}^{*}_{175}=\mathbb{Z}^*_{25}\times \mathbb{Z}^*_{7}=\mathbb{Z}_{20}\times \mathbb{Z}_{6}.$$ $(\mathbb{Z}_{20}\times \mathbb{Z}_{6})/\mathbb{Z}_2=\mathbb{Z}_{10}\times \mathbb{Z}_{6}$ or $\mathbb{Z}_{20}\times \mathbb{Z}_{3}$?
Thank you for any help!