Conjugacy of \(\text{Alt}_5\) and \(\text{SL}(2,5)\) subgroups of \(E_7(\mathbb{C})\) (Q2747315)

Many mathematicians solved the embedding and conjugacy problems of finite quasisimple subgroups of exceptional Lie groups (see, for example, the survey of \textit{R. L. Griess}, jun. and \textit{A. J. E. Ryba} [Bull. Am. Math. Soc., New Ser. 36, No. 1, 75-93 (1999; Zbl 0916.22008)]). The author considers the problem of classification of the \(\text{Alt}_5\) and \(\text{SL}(2,5)\) subgroups of exceptional complex Lie groups up to conjugacy. This conjugacy problem was solved by \textit{R. L. Griess}, jun. [in Invent. Math. 121, No. 2, 257-277 (1995; Zbl 0832.22013)] for \(G_2(\mathbb{C})\) and by the author [in Mem. Am. Math. Soc. 634, 1-162 (1998; Zbl 0907.22013)] for \(E_8(\mathbb{C})\) and [in J. Algebra 202, No. 2, 414-454 (1998; Zbl 0908.20036)] for \(E_6(\mathbb{C})\) and \(F_4(\mathbb{C})\). The purpose of this paper is to finish the conjugacy problem in exceptional groups (modulo a few unresolved zero-dimensional-centralizer cases) by classifying the \(\text{Alt}_5\) and \(\text{SL}(2,5)\) subgroups of \(E_7(\mathbb{C})\).