According to Möhres’s Theorem an arbitrary group whose proper subgroups are all subnormal (or a group without non-subnormal proper subgroups) is solvable. In this paper we generalize Möhres’s Theorem, by proving that every group with at most 56 nonsubnormal subgroups is solvable. Also we show that the derived length of a solvable group with a finite number k of non-n-subnormal subgroups is bounded in terms of n and k.
