  We study non-Abelian Chern-Simon BPS-saturated vortices enjoying N=2
supersymmetry in d=2+1 dimensions, with generic gauge groups of the form U(1) x
G', with G' being a simple group, allowing for orientational modes in the
solutions. We will keep the group as general as possible and utilizing the
powerful moduli matrix formalism to provide the moduli spaces of vortices and
derive the corresponding master equations. Furthermore, we study numerically
the vortices applying a radial Ansatz to solve the obtained master equations
and we find especially a splitting of the magnetic fields, when the coupling
constants for the trace-part and the traceless part of the Chern-Simons term
are varied, such that the Abelian magnetic field density can become negative
near the origin of the vortex while the non-Abelian part stays positive, and
vice versa.
