First, it is shown that there is no (intrinsic) topological order in 1D (ie all 1D gapped states are short-range entangled). Thus, if the Hamiltonians have no symmetry, all their 1D gapped quantum states belong to one phase—the phase of trivial product states. On the other hand, if the Hamiltonians do have a symmetry, their 1D gapped quantum states are either symmetry-breaking phases, SPT phases, and their mix.