Gassmann equivalence (reviewed)

Two subgroups $H_1$ and $H_2$ of a finite group $G$ are Gassmann equivalent if, for every conjugacy class $C$ of $G$, the sets $C \cap H_1$ and $C \cap H_2$ have the same size. An ordering of the conjugacy classes of $G$ then induces an ordering of the Gassmann equivalence classes of subgroups of $G$, just by lexicographically ordering the vectors of intersection counts.