  For a finite group $G$, we study the probability $sp(G)$ that, given two
elements $x,y \in G$, the cyclic subgroup $\langle x \rangle$ is subnormal in
the subgroup $\langle x, y \rangle$. This can be seen as an intermediate
invariant between the probability that two elements generate a nilpotent
subgroup and the probability that two elements generate a solvable subgroup. We
prove that $sp(G) \leq 1/6$ for every nonsolvable group $G$.
