Subgroup permutability degree criterion for nonsimplicity

Let $G$ be a finite group, and let $\mathfrak{p}(G)$ denote its subgroup permutability degree. Subgroup permutability degree criterion. If

$$\mathfrak{p}(G)>\mathfrak{p}(A_5),$$

then $G$ is not simple. This is presented as a weaker version of the preceding conjecture and is motivated by the empirical observation that a high subgroup permutability degree forces normality; the source does not establish the criterion.