Conjugacy of alternating groups of degree 5 and SL(2,5) subgroups of the complex Lie group of type E(,8)

Let G be the complex Lie group of type E;Clearly, if L;The first question has been completely settled for both Alt;Reference. (1) Cohen, A. M. and Griess, R., Jr., 'On finite simple subgroups of the complex Lie group of type E...