  We measure the charge periodicity of Coulomb blockade conductance
oscillations of a hybrid InSb-Al island as a function of gate voltage and
parallel magnetic field. The periodicity changes from $2e$ to $1e$ at a
gate-dependent value of the magnetic field, $B^*$, decreasing from a high to a
low limit upon increasing the gate voltage. In the gate voltage region between
the two limits, which our numerical simulations indicate to be the most
promising for locating Majorana zero modes, we observe correlated oscillations
of peak spacings and heights. For positive gate voltages, the $2e$-$1e$
transition with low $B^*$ is due to the presence of non-topological states
whose energy quickly disperses below the charging energy due to the orbital
effect of the magnetic field. Our measurements demonstrate the importance of a
careful exploration of the entire available phase space of a proximitized
nanowire as a prerequisite to define future topological qubits.
