Why does one separately study the representation of the Lorentz group instead of directly and only studying the representations of the Poincare group? After all, the Lagrangians of field theory should be not only be Lorentz invariant but should also be Poincare invariant.

Why does one separately study the representations of the Lorentz group and the Poincaré group, instead of directly and only studying the representations of the Poincaré group? After all, the Lagrangians of field theory should not only be Lorentz invariant but should also be Poincaré invariant.