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Let $G$ be a group of order $56$. Then which of the following are true

  1. All $7$-sylow subgroups of $G$ are normal
  2. All $2$-Sylow Subgroups of $G$ are normal
  3. Either a $7$-Sylow subgroup or a $2$-Sylow subgroup of $G$ is normal
  4. There is a proper normal subgroup of $G$.

How would I able to solve this problem and which theorem(s) would be required to solve this? Thanks for your time.

3 Answers 3