  We analyze a model demonstrating the co-existence of subsystem symmetry
breaking (SSB) and symmetry-protected topological (SPT) order, or subsystem
LSPT order for short. Its mathematical origin is the existence of both a
subsystem and a local operator, both of which commute with the Hamiltonian but
anti-commute between themselves. The reason for the exponential growth of the
ground state degeneracy is attributed to the existence of subsystem symmetries,
which allows one to define both the Landau order parameter and the SPT-like
order for each independent loop.
