First Question: I was asked, "Find a group that has a subgroup of order $n$ for each positive integer $n$. I considered the nonzero complex numbers under multiplication, and noticed that the roots of the polynomial $x^n-1$ will generate a group. Is this right?
Second Question: I asked myself, "does there exist a group $G$ that has every subgroup up to isomorphism for each positive integer $n$?" For example, if we let $n=24$, there are $15$ different groups up to isomorphism. So I want the group $G$ to have $15$ subgroups of order $24$ that none of them are pairwise isomorphic. If anyone can phrase this question better, please edit my post.