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The Maximal Subgroups Of The Orthogonal Group P + (10, 2)Keywords: Finite groups , linear groups , matrix groups , maximal subgroups Abstract: The main result of this work is called "the main theorem” which is a list of maximal subgroups of the orthogonal groupP +(10, 2) which has been proved by using Aschbacher’s Theorem ([1]). So, this work is divided into two main parts: Part (1): In this part, we will find the maximal subgroups in the classes C1 – C8 of Aschbacher’s Theorem ([1]). Part (2): In this part, we will find the maximal subgroups in the class C9 of Aschbacher’s Theorem ([1]), which are the maximal primitive subgroups H of G that have the property that the minimal normal subgroup M of H is not abelian group and simple, thus, we divided this part into two cases: Case (1): M is generated by transvections: In this case, we will use result of Kantor ([2]). Case (2): M is a finite primitive subgroup of rank three: In this case, we will use the classification of Kantor and Liebler ([3]). Mathematics Subject Classification: 20B05; 20G40, 20H30, 20E28
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