Prove that A5 is a group of order 60 having no subgroup of order 30.

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- Nov 15th 2009, 08:30 AMjohnt4335Alternating Group A5
Prove that A5 is a group of order 60 having no subgroup of order 30.

- Nov 16th 2009, 12:58 AMSwlabr
Have you covered the fact that $\displaystyle A_5$ is simple yet? As if so, you can apply the fact that a subgroup of order 30 would have index 2, and so is normal, a contradiction.

Otherwise, I am sorry but I can't think of a neat way of doing it. I keep wanting to prove that $\displaystyle A_5$ is simple...