  We employ a magnetocapacitance technique to study the spectrum of the soft
two-subband (or double-layer) electron system in a parabolic quantum well with
a narrow tunnel barrier in the centre. In this system unbalanced by gate
depletion, at temperatures $T\agt 30$ mK we observe two sets of quantum
oscillations: one originates from the upper electron subband in the
closer-to-the-gate part of the well and the other indicates the existence of
common gaps in the spectrum at integer fillings. For the lowest filling factors
$\nu=1$ and $\nu=2$, both the common gap presence down to the point of one- to
two-subband transition and their non-trivial magnetic field dependences point
to magnetic-field-induced hybridization of electron subbands.
