Liquid helium becomes a superfluid and flows with zero viscosity at low temperatures. Superfluidity is manifested by a failure to rotate, as its mass is decoupled from the rotation of the containing cell. Supersolid helium should show similar behaviour; apparent rotational inertia decreases when the solid helium is set into torsional oscillation below 200 mK (refs 1,2). However, a number of later experiments(3-7) revealed characteristics unexpected within a conventional superfluid framework. Recent observations include hysteresis in the resonant period(8,9) and relaxation dynamics(10). To account for the inconsistencies, there are various proposals that include superfluid grain boundaries(11), glassy behaviour(12,13), viscoelasticity(14), a vortex fluid(15) and a superglass(16). Here we systematically investigate the hysteresis and relaxation processes with a set of temperature and velocity sweeps. We unveil two hidden states associated with pinning of low-temperature excitations and construct a new phase diagram.