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Is there a general method to find all subgroups in a given abstract group?? Many Thanks!!

This question came into my classmates' mind when he wants to find a 2 sheet covering of the Klein Bottle. This question is equivalent to find a subgroup of index 2 in Z free product Z/2Z. When n = 2, this question is sovalble using homology method according to my tutor, since the subgroup of index 2 is always regular, but when it comes to the general case, he says he suspected it has been solved.

PS: I'm sorry for my poor English. (I'm not a native speaker.) Hope I've expained it clearly.

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# How to find subgroup of index n in a given group

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