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Why must a group of order 98 contain a subgroup of order 7?

I would think that Sylow's 1st theorem implies there exists at least one Sylow-7-subgroup of order 49 and at least one Sylow-2-subgroup of order 2 (since 98=2x7x7).

Thanks

Ray Veldkamp

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# Sylow's Theorems question

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