Let G be a finite group and S be the set of Sylow p-subgroups of G for a prime p dividing the order of G. Assume that |S|>1.

Let U and V be two disjoint non-empty subsets of S such that,

$$\bigcup_{P\in U}P=\bigcup_{P\in V}P=\bigcup_{P\in S}P$$ and

$$\bigcap_{P\in U}P=\bigcap_{P\in V}P=\bigcap_{P\in S}P$$ .

Is there any group with this property ?