Hi,

Suppose you have a group of order 130, and suppose you were able to prove that it has exactly 13 different subgroups of order 2. Can you conclude that there are exactly 13 elements of order 2 (since they have the identity in common) or is it possible that another subgroup, say the subgroup of order 10 (which exists) contains an element of order 2 different than the 13?

i.e. are they exactly 13 or more?

Thanks very much