The Sylow subgroups are unique? Sorry, I'm new on this subject. I faced a question which let me confused with the concept of a Sylow p-subgroup. The p-subgroups of a group are all contained in the Sylow p-subgroup? In another words, the Sylow p-subgroups are unique?
Thanks 

No, a Sylow subgroup needs not be unique: it is by definition a maximal element in the lattice of $p$-subgroups but it need not be a maximum element. Since all Sylow $p$-subgroups for the same prime are conjugate, a Sylow subgroup is unique iff it is normal.
For example, when $n$ is odd, the dihedral group of the $n$-gon has $n$ 2-Sylow subgroups.
