Those structures are always conjugate to each other, implying that when one of them is normal, it is also unique.  
The Abhyankar problem uses structures named for this man in order to show the existance of Galois group for a projective curve.  The Alperin-Braer-Gorenstein theorem is about classifying structures with a property named for this man that are quasi-dihedral. Structures named for this man are central to Frattini's Argument. One theorem named for this man states that the number of subgroups whose order has prime divisor p is equal to 1 mod p. Those structures are always conjugate to each other, implying that when one of them is normal, it is also unique.  His namesake theorems state that for a group of order p to the n times q, specific subgroups exist. FTP, name this man who names particular p-subgroups, a partial converse to Lagrange's theorem.
The Abhyankar problem uses structures named for this man in order to show the existance of Galois group for a projective curve.  
Peter Ludwig Mejdell {Sylow}