  First-ascent red giants with masses below about $2\,M_\odot$ ignite helium in
their degenerate core as a flash. Stellar evolution codes predict that the He
flash consists of a series of consecutive subflashes. The detection of mixed
modes in red giants from space missions CoRoT and Kepler has opened new
opportunities to search for stars in this evolution stage. During a subflash,
the He burning shell is convective, which splits the cavity of gravity modes in
two. We here investigate how this additional cavity modifies the oscillation
spectrum of the star. We calculate the asymptotic mode frequencies of stellar
models going through a He subflash using the JWKB approximation. To predict the
detectability of the modes, we estimate their expected heights, taking into
account the effects of radiative damping in the core. Our results are then
compared to the oscillation spectra obtained by calculating numerically the
mode frequencies during a He subflash. We show that during a He subflash, the
detectable oscillation spectrum mainly consists of modes trapped in the
acoustic cavity and in the outer g-mode cavity. The spectrum should thus
resemble that of a core-helium-burning giant. However, we find a list of clear,
detectable features that could enable us to identify red giants passing through
a He subflash. In particular, during a He subflash, several modes that are
trapped in the innermost g-mode cavity are expected to be detectable. We show
that these modes could be identified by their frequencies or by their
rotational splittings. Other features, such as the measured period spacing of
gravity modes or the location of the H-burning shell within the g-mode cavity
could also be used to identify stars going through a He subflash. The features
derived in this study can now be searched for in the large datasets provided by
the CoRoT and Kepler missions.
