  In 1962, V.A. Belonogov proved that if a finite group $G$ contains two
maximal subgroups of coprime orders, then either $G$ is one of known solvable
groups or $G$ is simple. In this short note based on results by M. Liebeck and
J. Saxl on odd order maximal subgroups in finite simple groups we determine
possibilities for triples $(G,H,M)$, where $G$ is a finite nonabelian simple
group, $H$ and $M$ are maximal subgroups of $G$ with $(|H|,|M|)=1$.
