# Alternating Group A5

• Nov 15th 2009, 09:30 AM
johnt4335
Alternating Group A5
Prove that A5 is a group of order 60 having no subgroup of order 30.
• Nov 16th 2009, 01:58 AM
Swlabr
Quote:

Originally Posted by johnt4335
Prove that A5 is a group of order 60 having no subgroup of order 30.

Have you covered the fact that $A_5$ 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 $A_5$ is simple...