Difficult# Isomorphism Theorems: Subgroup Property from Order & Intersection

ABSALG-VX1KRY

Let $G$ be a group and let $H$ and $K$ be subgroups of $G$.

Suppose the orders $|G|$, $|H|$, and $|K|$ of these groups satisfy:

$15$ divides $|G|$ and $\cfrac1{15}|G|\le 15$, $\qquad|H|=4$, $\quad|K|=8$, $\quad |H\cap K|=2$

Which of the following are true?

Select **ALL** that apply.