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  "body": "\n## Statement\n\nLet $G$ be a finite [[group|G5S1M9]] and let $p$ be a prime number.\nThen any two [[Sylow p-subgroups|0053CQE9Y2]] $P$ and $Q$ of $G$ are [[conjugate|0H11ZPX4ND]]: there is a $g \\in G$ with $Q = gPg^{-1}$.\nMoreover, each $p$-subgroup of $G$ is contained in some Sylow $p$-subgroup of $G$.\n\n## Remarks\n\nSo all Sylow $p$-subgroups of $G$ are [[isomorphic|08MG7H8JW5]].\nA Sylow $p$-subgroup is [[normal|0CB0DX5BVV]] in $G$ if and only if $n_p = 1$.\nThe proof lets a $p$-subgroup $H$ act on the left cosets of $P$ and uses the [[fixed point lemma|098D2E7DEH]].\n\n## Explanations\n\n### L1 human\n\nThe Sylow $p$-subgroups of a group can look different as subsets.\nBut each one can be moved onto each other one by a conjugation.\nSo, up to a renaming, there is only one Sylow $p$-subgroup.\n",
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