Homogeneous Spaces of the Lorentz Group

We present a classification, up to isomorphisms, of all the homogeneous spaces of the Lorentz group with dimension lower than six. At the same time, we classify, up to conjugation, all the non-discrete closed subgroup of the Lorentz group and all the subalgebras of the Lorentz Lie algebra. We also study the covariant mappings between some pairs of homogeneous spaces. This exercise is done without any claim of originality, but with the hope of providing a useful instrument for the investigation of the Lorentz transformation properties of some physical quantities.