# Sylow 5-subgroup

Suppose that G is a group of order 30 and has a Sylow 5-subgroup that is not normal. Find the number (not what they are) of elements of order 1, of order 2, of order 3, of order 5. Justify your answer.

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Proof: Suppose that G is a group of order and has a Sylow 5-subgroup that is not normal. Now the number of Sylow 5-subgroups must satisfy and Since a unique Sylow 5-subgroup of G would be normal, it follows that Note ...

#### Solution Summary

Suppose that G is a group of order 30 and has a Sylow 5-subgroup that is not normal.

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