Let p and q be odd primes such that (Formula presented.) Let F be the field with p elements and (Formula presented.) be a group, where A is an abelian group of order (Formula presented.) In this article, we prove that if (Formula presented.) then G does not have a normal complement in (Formula presented.) Further, for any integer (Formula presented.) we prove that if F is a finite field such that (Formula presented.) then (Formula presented.) and (Formula presented.) do not have a normal complement in (Formula presented.) and (Formula presented.) respectively.