  We exhaustively search quaternary metal hydrides based on the (13-2-1) and
(13-3-1) structures that are the two of the putative densest ternary sphere
packings in cubic systems [R. Koshoji \textit{et al.}, Phys. Rev. E
\textbf{104}, 024101 (2021)]. The 73304 candidate hydrides are generated by
substituting the small spheres with hydrogen atoms, the medium, large, and
fourth spheres with metallic atoms. Especially, the substitution of the small
spheres with hydrogen atoms gives the unconventional hydrogen sublattices. We
screen unstable hydrides in the candidates through geometrical optimizations,
constant pressure molecular dynamics simulations, and phonon calculations under
hydrostatic pressure of $10$ GPa, and identify 23 hydrides with static and
dynamic stability, including $\mathrm{H}_{12} \mathrm{Sc} \mathrm{Y}_{2}
\mathrm{La}$ and $\mathrm{H}_{12} \mathrm{Ti} \mathrm{Ni}_{3} \mathrm{Ba}$. We
expect that the 23 candidates of hydrides screened by the exhaustive search for
73304 hydrides provide a guideline to narrow down the search space for trials
in the experimental synthesis of quaternary metal hydrides.
