Mohres's Theorem says that an arbitrary group whose proper subgroups are all subnormal is solvable. Here we generalize Mohres's Theorem, by proving that every group with at most 56 non-subnormal 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.
