1. The problem statement, all variables and given/known data Prove that G cannot have a subgroup H with |H| = n - 1, where n = |G| > 2. 2. Relevant equations 3. The attempt at a solution Counter-example, the multiplicative group R and its subgroup, multiplicative group R+. Or, the additive group Z, and its subgroup of integer multiples of 2. What am I missing here? I think this is trivial for finite groups, but they don't say finite groups, they don't say anything.