Sylow system of a group

Question

Let $G$ be a finite group with distinct prime divisors $p_1, p_2, \ldots, p_k$. If $Q_i$ is the Hall $p_i'$-subgroup of $G$, then the set $\sum = \{Q_1, Q_2, \ldots, Q_k\}$ is a Sylow System of $G$.

Suppose that $H\leq G$. Then $\sum \cap H := \{K \cap H \,|\, K \in \sum \}$ is not necessarily a Sylow system of $H$. I need to find a counterexample to show this.

Answer 1

Let $H$ be a conjugate of $Q_1$ that is not equal to $Q_1$.

Answer 2

suppose G ia finite group and o(G)=(p^m)n where p is prime .If p^m|o(G) and p^(m+1) is not a divisor of o(G) then G is a subgroup of p^m