Conjugacy ofAlt5andSL(2, 5) Subgroups ofE6( ),F4( ), and a Subgroup ofE8( ) of TypeA2E6

We classifyAlt5andSL(2, 5) subgroups ofE6( ) andF4( ) up to conjugacy. We then use our results to answer conjugacy questions aboutAlt5andSL(2, 5) subgroups ofE8( ) which were not resolved in earlier work.