Prove that a group of order 120 is not simple.

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Posting 31061
Prove that a group of order 120 is not simple.

Solution :- 120 = 23.3.5 Let G be a group of order 120.
The number of Sylow 5-subgroup in G is 1 + 5k and 1 + 5k│24,
then k = 0 , 1
If k = 0, then then Sylow 5-subgroup is normal in G.
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