 Lagrange's theorem states that for any finite group "G" the order (number of elements) of every subgroup of "G" divides the order of "G".The Sylow theorems state that for every prime factor "p" of the order of a finite group "G", there exists a Sylow "p"-subgroup of "G" of order "pn", the highest power of "p" that divides the order of "G".Moreover, every subgroup of order "pn" is a Sylow "p"-subgroup of "G", and the Sylow "p"-subgroups of a group (for a given prime "p") are conjugate to each other.