Supersolvable
A matroid is supersolvable if its lattice of flats has a maximal chain $F_0 \subset F_1 \subset \dots \subset F_r$ consisting of modular flats, one of each rank. A flat $F$ is modular if $r(F) + r(G) = r(F \vee G) + r(F \wedge G)$ for every flat $G$.
Computed by scripts/is_supersolvable.jl, which searches for such a chain.