To avoid or mitigate runaway electron (RE) beams in ITER, RE-driven instabilities are actively studied as a complimentary technique to massive material injection. In this work we report experimental dependencies of Alfvénic instabilities driven by REs during the current quench in DIII-D on plasma and material injection parameters. These instabilities, observed in the frequency range of 0.1–3 MHz, correlate with increased RE loss and thus may play a role in non-sustained RE beams. It was found that as the toroidal magnetic field (BT) decreases, the RE population becomes more energetic, the energy of instabilities increases, and no RE beam is observed when the maximum energy of REs exceeds 15 MeV (or when BT is below 1.8 T). Analysis of disruptions at plasma core temperature (Te) of 1 keV and 8 keV shows that the RE population is much less energetic (with the maximum energy of only about 3 MeV) when Te is high, and no instabilities are observed in this case. Besides disruptions above caused by Ar injection, cases with Ne and D2 injections were also studied. Both Ne and D2 injections cause no sustained RE beams, however, by different reasons. Measurements of the instability polarization indicates that it is of predominantly compressional nature at the edge which is consistent with modeling suggesting excitation of compressional Alfvén eigenmodes. However, drive of global Alfvén eigenmodes is also possible at low frequencies.