This paper studies subgroups of the split spinor groupG=Spin (n, k), n ≥6, over a field K containing a maximal split torus T=T(n,K)assuming that charK≠2 and ||K ||≥7. The main result of the first pan of the paper is the reduction of the proof that subgroups containing T are standard to the study of subgroups not containing root unipotent elements.