= Solution
Write the <cardinality> of the finite <group> as $|G|=p^am$, where $p$ is <prime> and $p\nmid m$. The <Sylow theorems> say that a <Sylow subgroup> of order $p^a$ exists; every <p-group> is contained in a <Sylow subgroup>; and all <Sylow subgroups> are <conjugate subgroups>. If $n_p$ is their number, then
$$
\boxed{n_p\equiv1\pmod p,\qquad n_p\mid m.}
$$
Equivalently, for a <Sylow subgroup> $P$, conjugation and the <orbit-stabilizer theorem> give $n_p=[G:N_G(P)]$, where $N_G(P)$ is the <normalizer>. The containment statement is often included in the conjugacy form: every <p-group> lies in a conjugate of any fixed <Sylow subgroup>.
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