A problem asks me to find all the covering spaces of a Klein bottle. This needs to calculate all the subgroups of the fundamental group of the Klein bottle. But I don't have any idea how to do it.
I googled it and an article says
The subgroups of the fundamental group of the Klein bottle are either trivial, free of rank one, free Abelian of rank two, or non-Abelian of rank two.
I don't know how to get the result and what is the concrete form of the subgroups (which is needed to calculate the covering spaces.)
Can you please help? Thank you.