I am trying to find all of the subgroups of a given group. To do this, I follow the following steps:
- Look at the order of the group. For example, if it is $15$, the subgroups can only be of order $1,3,5,15$.
- Then find the cyclic groups.
- Then find the non cyclic groups.
But i do not know how to find the non cyclic groups. For example, let us consider the dihedral group $D_4$, then the subgroups are of the orders $1,2,4$ or $8$. I find all cyclic groups. Then, I saw that there are non-cyclic groups of order $4$. How can I find them? I appreciate any help. Thanks.