| Graph | No. of vertices | Diameter |
| Doubled Grassmann graph $\mathrm{DJ}_2(5,2)$ | 310 | 5 |
| Hall–Janko/Cohen–Tits near octagon | 315 | 4 |
| Soicher's 3rd graph | 315 | 4 |
| $H(2,18)$ | 324 | 2 |
| $J(26,2)$ | 325 | 2 |
| $\mathrm{K}(26,2)$ | 325 | 2 |
| $\mathrm{NO}_5^+(5)$ graph | 325 | 2 |
| $\mathrm{NO}_5^{+ \perp}(5)$ graph | 325 | 2 |
| Point graph of $\mathrm{GQ}(4,16) \cong \mathrm{O}_6^-(4)$ graph | 325 | 2 |
| Merged Johnson graph $J(11,4)$ | 330 | 2 |
| Doubly truncated Witt graph | 330 | 4 |
| $J(11,4)$ | 330 | 4 |
| Incidence graph of $AG(2,13)$ minus a parallel class | 338 | 4 |
| $H(3,7)$ | 343 | 3 |
| $J(27,2)$ | 351 | 2 |
| $\mathrm{K}(27,2)$ | 351 | 2 |
| $\mathrm{NO}_7^{- \perp}(3)$ graph | 351 | 2 |
| Incidence graph of Higman's symmetric design | 352 | 3 |
| Taylor graphs from Higman–Sims group (2 graphs) | 352 | 3 |
| $\mathrm{O}_6^+(4)$ graph | 357 | 2 |
| $H(2,19)$ | 361 | 2 |
| Paley graph $P_{361}$ | 361 | 2 |
| Peisert graph on 361 vertices | 361 | 2 |
| Rank-3 $\mathrm{SRG}(361,144,59,56)$ | 361 | 2 |
| $J(14,3)$ | 364 | 3 |
| $\mathrm{O}_7(3)$ graph | 364 | 2 |
| Point graph of $GH(3,3)$ | 364 | 3 |
| $\mathrm{Sp}_6(3)$ graph | 364 | 2 |
| Antipodal 3-cover of Zara graph | 378 | 4 |
| $J(28,2)$ | 378 | 2 |
| $\mathrm{K}(28,2)$ | 378 | 2 |
| $\mathrm{NO}_7^{+ \perp}(3)$ graph | 378 | 2 |
| $H(2,20)$ | 400 | 2 |
| Point graphs of $\mathrm{GQ}(7,7)$s | 400 | 2 |
| $J(29,2)$ | 406 | 2 |
| $\mathrm{K}(29,2)$ | 406 | 2 |
| $\mathrm{G}_2(4)$ graph | 416 | 2 |
| Flag graph of $GQ(4,4)$ | 425 | 4 |
| $J(30,2)$ | 435 | 2 |
| $\mathrm{K}(30,2)$ | 435 | 2 |
| $H(2,21)$ | 441 | 2 |
| $J(15,3)$ | 455 | 3 |
| Folded Johnson graph $J(12,6)$ | 462 | 3 |
| $J(11,5)$ | 462 | 5 |
| Odd graph $O_6$ | 462 | 5 |
| $J(31,2)$ | 465 | 2 |
| $\mathrm{K}(31,2)$ | 465 | 2 |
| $H(2,22)$ | 484 | 2 |
| Koolen–Riebeek graph | 486 | 4 |
| Soicher's 2nd graph | 486 | 4 |
| $J(12,4)$ | 495 | 4 |
| $\mathrm{O}_{10}^-(2)$ graph | 495 | 2 |
| $J(32,2)$ | 496 | 2 |
| $\mathrm{K}(32,2)$ | 496 | 2 |
| $\mathrm{NO}_{10}^+(2)$ graph | 496 | 2 |
| $\overline{\mathrm{NO}_{10}^+(2)}$ graph | 496 | 2 |