Question: Please provide each step and Theorems used. Let N be a finite group and let H be a subgroup of N. If |H| is odd

Please provide each step and Theorems used.

Let N be a finite group and let H be a subgroup of N. If |H| is odd and [N:H] = 2, prove that the product of all of the elements of N, in any order, cannot belong to H.

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