For a group $G$. let $F(G)$ denote the collection of all subgroups of $G$. Which of the following situation can occur?
A) $G$ is finite but $F(G)$ is infinite.
B)$G$ is infinite but $F(G)$ is finite.
C)$G$ is countable but $F(G)$ is uncountable.
D)$G$ is uncountable but $F(G)$ is countable.
I don't know how i approach this problem. I think any group $G$ of infinite order has an infinite of subgroups as i can take this group generated by power of these elements. But i don't know how i go through this problem. I can sure that A is not true as $G$ is finite the power set of $G$is also finite .