Finite almost simple groups whose Gruenberg–Kegel graphs as abstract graphs are isomorphic to subgraphs of the Gruenberg–Kegel graph of the alternating group $A_{10}$

We consider the problem of describing finite groups whose the Gruenberg-Kegel graphs as abstract graphs are isomorphic to the Gruenberg–Kegel graph of the alternating group $A_{10}$. In the given paper, we prove that if such group is non-solvable then its quotient group by solvable radical is almost simple and classify all finite almost simple groups whose the Gruenberg-Kegel graphs as abstract graphs are isomorphic to subgraphs of the Gruenberg–Kegel graph of $A_{10}$.