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Resolution of singularities of vector fields (see [6,12,5]) generates vector fields on manifolds with pointed divisors. It is useful to consider the stationary subgroup of this pointed divisor and to study the action of this subgroup on the space of vector fields.The simplest kind of this situations in this paper is considered: the covering manifold is the plane, and the divisor -the line or two transversal lines on the plane. Our consideration is local: we consider germs of vector fields, which have a singularity in the point of the divisor. We give the complete list of nonequivalent finite C~-sufficient jets of vector fields in this situations. Here the equivalence means orbital equivalence of vector fields, that is diffeomorphism of the phase portrait of one vector field to the phase portrait of another which preserves the direction of motion on the phase curves.