  We study two-legged spin-1 ladder systems with $D_2\times \sigma$ symmetry
group, where $D_2$ is discrete spin rotational symmetry and $\sigma$ means
interchain reflection symmetry. The system has one trivial phase and seven
nontrivial symmetry protected topological (SPT) phases. We construct
Hamiltonians to realize all of these SPT phases and study the phase transitions
between them. Our numerical results indicate that there is no direct continuous
transition between any two SPT phases we studied. We interpret our results via
topological nonlinear sigma model effective field theory, and further
conjecture that generally there is no direct continuous transition between two
SPT phases in one dimension if the symmetry group is discrete at all length
scales.
