Non-propagating degrees of freedom in supergravity and very extended G₂

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.