The problem is that: How to check, if $A_{4}$ is normal (or not) subgroup of $A_{5}$? We know that $|A_{5}|=60$ - i suppose that we shouldn't find all left and right conjugate classes, because it's a bit tough job, anyway.
How can i cope with it?
2026-03-29 15:14:47.1774797287
A4 is a normal subgroup of A5
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$(1,2,5)\in A_5$ and $(1,2,3)\in A_4$ but $$(1,2,5)^{-1}(1,2,3)(1,2,5)\notin A_4$$