Example of Two Groups and a Subgroup of the Direct Product that is Not of the Form of Direct Product
Problem 467
Give an example of two groups $G$ and $H$ and a subgroup $K$ of the direct product $G\times H$ such that $K$ cannot be written as $K=G_1\times H_1$, where $G_1$ and $H_1$ are subgroups of $G$ and $H$, respectively.
Add to solve later 
