  Recently a correspondence between non-propagating degrees of freedom in
maximal supergravity and the very extended algebra E_11 has been found. We
perform a similar analysis for a supergravity theory with eight supercharges
and very extended G_2. In particular, in the context of d=5 minimal
supergravity, we study whether supersymmetry can be realised on higher-rank
tensors with no propagating degrees of freedom. We find that in this case the
very extended algebra fails to capture these possibilities.
