  We give the classification of T-duals of the flat background in four
dimensions with respect to one-, two-, and three-dimensional subgroups of the
Poincar\'e group using non-Abelian T-duality with spectators. As duals we find
backgrounds for sigma models in the form of plane-parallel waves or
diagonalizable curved metrics often with torsion. Among others, we find exactly
solvable time-dependent isotropic pp-wave, singular pp-waves, or generalized
plane wave (K-model).
