Sylow Theorems/Examples/Sylow 2-Subgroups in Group of Order 32

Example of Use of Sylow Theorems
The Sylow Theorems tell us nothing about the Sylow $2$-subgroups in a group of order $32$.

Proof
We have that $32 = 2^5$.

Hence the only Sylow $2$-subgroup in $G$ is $G$ itself.