| 1 | C31×#3416 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C31×#3415 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C31×#3292 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C31×#3290 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C31×#2250 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C31×#2223 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C31×#2221 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C31×#2213 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C31×#2212 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C31×#2194 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C31×#2193 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C31×#2192 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | C31×#2192 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C31×#2179 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C31×#2171 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C31×#578 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | C31×#577 | — | 2 | 1 | no | — |
| 18 | C31×#576 | — | 2 | 1 | no | — |
| 19 | C31×#576 | C22 | 1 | 1 | yes | characteristic |
| 20 | C31×#576 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | C31×#576 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | C31×#510 | — | 2 | 1 | no | — |
| 23 | C31×#510 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | C31×#509 | — | 2 | 1 | no | — |
| 25 | C31×#509 | — | 2 | 1 | no | — |
| 26 | C31×#509 | — | 2 | 1 | no | — |
| 27 | C31×#509 | C22 | 1 | 1 | yes | characteristic |
| 28 | C31×#509 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | C31×#509 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | C31×#508 | — | 2 | 1 | no | — |
| 31 | C31×#508 | — | 2 | 1 | no | — |
| 32 | C31×#508 | C22 | 1 | 1 | yes | characteristic |
| 33 | C2×C31×SD32 | — | 2 | 1 | no | — |
| 34 | C2×C31×SD32 | C22 | 1 | 1 | yes | characteristic, complemented |
| 35 | C2×C31×SD32 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | C2×C31×D16 | — | 2 | 1 | no | — |
| 37 | C2×C31×D16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | C2×C31×D16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | C31×#504 | C22 | 1 | 1 | yes | characteristic, complemented |
| 40 | C31×#504 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | C31×#495 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | C31×#493 | C22 | 1 | 1 | yes | characteristic, complemented |
| 43 | C31×#473 | C22 | 1 | 1 | yes | characteristic, complemented |
| 44 | C31×#472 | — | 2 | 1 | no | — |
| 45 | C31×#472 | C22 | 1 | 1 | yes | characteristic |
| 46 | C31×#472 | C22 | 1 | 1 | yes | characteristic, complemented |
| 47 | C31×#472 | C22 | 1 | 1 | yes | characteristic, complemented |
| 48 | C31×#471 | — | 2 | 1 | no | — |
| 49 | C31×#455 | — | 2 | 1 | no | — |
| 50 | C31×#454 | — | 2 | 1 | no | — |
| 51 | C31×#453 | — | 2 | 1 | no | — |
| 52 | C31×#453 | — | 2 | 1 | no | — |
| 53 | C31×#443 | C22 | 1 | 1 | yes | characteristic |
| 54 | C31×#443 | C22 | 1 | 1 | yes | characteristic, complemented |
| 55 | C31×#443 | C22 | 1 | 1 | yes | characteristic, complemented |
| 56 | C31×#368 | C22 | 1 | 1 | yes | characteristic, complemented |
| 57 | C31×#364 | C22 | 1 | 1 | yes | characteristic, complemented |
| 58 | C31×#362 | C22 | 1 | 1 | yes | characteristic, complemented |
| 59 | C31×#361 | C22 | 1 | 1 | yes | characteristic, complemented |
| 60 | C31×#361 | C22 | 1 | 1 | yes | characteristic, complemented |
| 61 | C31×#361 | C22 | 1 | 1 | yes | characteristic, complemented |
| 62 | C31×#359 | C22 | 1 | 1 | yes | characteristic, complemented |
| 63 | C31×#359 | C22 | 1 | 1 | yes | characteristic, complemented |
| 64 | C31×#350 | C22 | 1 | 1 | yes | characteristic, complemented |
| 65 | C31×#350 | C22 | 1 | 1 | yes | characteristic, complemented |
| 66 | C31×#346 | C22 | 1 | 1 | yes | characteristic, complemented |
| 67 | C31×2−1+4 | — | 2 | 1 | no | — |
| 68 | C31×H(5,𝔽2) | — | 2 | 1 | no | — |
| 69 | C31×H(5,𝔽2) | — | 2 | 1 | no | — |
| 70 | C31×H(5,𝔽2) | — | 2 | 1 | no | — |
| 71 | C31×#137 | — | 2 | 1 | no | — |
| 72 | C31×#137 | — | 2 | 1 | no | — |
| 73 | C31×#137 | — | 4 | 1 | no | — |
| 74 | C31×#137 | — | 4 | 1 | no | — |
| 75 | C31×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 76 | C31×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 77 | C31×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 78 | C31×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 79 | C31×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 80 | C31×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 81 | C31×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 82 | C31×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 83 | C31×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 84 | C31×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 85 | C31×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 86 | C31×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 87 | C31×#135 | — | 2 | 1 | no | — |
| 88 | C31×#135 | — | 2 | 1 | no | — |
| 89 | C31×#135 | — | 2 | 1 | no | — |
| 90 | C31×#135 | — | 2 | 1 | no | — |
| 91 | C31×#135 | — | 4 | 1 | no | — |
| 92 | C31×#135 | — | 4 | 1 | no | — |
| 93 | C31×#135 | D4 | 1 | 1 | yes | characteristic |
| 94 | C31×#135 | C23 | 1 | 1 | yes | characteristic |
| 95 | C31×#135 | C23 | 1 | 1 | yes | characteristic |
| 96 | C2×Q16×C31 | — | 2 | 1 | no | — |
| 97 | C2×Q16×C31 | C23 | 1 | 1 | yes | characteristic |
| 98 | C2×SD16×C31 | — | 2 | 1 | no | — |
| 99 | C2×SD16×C31 | — | 4 | 1 | no | — |
| 100 | C2×D8×C31 | — | 2 | 1 | no | — |
| 101 | C2×D8×C31 | — | 2 | 1 | no | — |
| 102 | C2×D8×C31 | — | 2 | 1 | no | — |
| 103 | C2×D8×C31 | — | 2 | 1 | no | — |
| 104 | C2×D8×C31 | — | 4 | 1 | no | — |
| 105 | C2×D8×C31 | C23 | 1 | 1 | yes | characteristic |
| 106 | C2×D8×C31 | C23 | 1 | 1 | yes | characteristic |
| 107 | C2×D8×C31 | C23 | 1 | 1 | yes | characteristic |
| 108 | C31×#131 | — | 2 | 1 | no | — |
| 109 | C31×#131 | — | 2 | 1 | no | — |
| 110 | C31×#131 | C23 | 1 | 1 | yes | characteristic |
| 111 | C31×#131 | C23 | 1 | 1 | yes | characteristic |
| 112 | C31×#127 | — | 2 | 1 | no | — |
| 113 | C31×#124 | — | 2 | 1 | no | — |
| 114 | C31×Q32 | — | 2 | 1 | no | — |
| 115 | C31×Q32 | D4 | 1 | 1 | yes | characteristic, complemented |
| 116 | C31×SD32 | — | 2 | 1 | no | — |
| 117 | C31×SD32 | — | 2 | 1 | no | — |
| 118 | C31×SD32 | — | 2 | 1 | no | — |
| 119 | C31×SD32 | — | 2 | 1 | no | — |
| 120 | C31×SD32 | — | 2 | 1 | no | — |
| 121 | C31×SD32 | — | 2 | 1 | no | — |
| 122 | C31×SD32 | — | 4 | 1 | no | — |
| 123 | C31×SD32 | D4 | 1 | 1 | yes | characteristic, complemented |
| 124 | C31×SD32 | D4 | 1 | 1 | yes | characteristic, complemented |
| 125 | C31×D16 | — | 2 | 1 | no | — |
| 126 | C31×D16 | — | 2 | 1 | no | — |
| 127 | C31×D16 | — | 2 | 1 | no | — |
| 128 | C31×D16 | — | 2 | 1 | no | — |
| 129 | C31×D16 | — | 2 | 1 | no | — |
| 130 | C31×D16 | — | 4 | 1 | no | — |
| 131 | C31×D16 | D4 | 1 | 1 | yes | characteristic, complemented |
| 132 | C31×M32 | — | 2 | 1 | no | — |
| 133 | C31×M32 | — | 2 | 1 | no | — |
| 134 | C31×M32 | C23 | 1 | 1 | yes | characteristic |
| 135 | C31×M32 | C23 | 1 | 1 | yes | characteristic |
| 136 | C2×C16×C31 | — | 2 | 1 | no | — |
| 137 | C2×C16×C31 | — | 2 | 1 | no | — |
| 138 | C2×C16×C31 | C23 | 1 | 1 | yes | characteristic |
| 139 | C2×C16×C31 | C23 | 1 | 1 | yes | characteristic |
| 140 | C31×#108 | D4 | 1 | 1 | yes | characteristic |
| 141 | C31×#108 | C23 | 1 | 1 | yes | characteristic |
| 142 | C31×#108 | C23 | 1 | 1 | yes | characteristic |
| 143 | C31×#104 | — | 2 | 1 | no | — |
| 144 | C31×#104 | — | 2 | 1 | no | — |
| 145 | C31×#104 | D4 | 1 | 1 | yes | characteristic |
| 146 | C31×#104 | D4 | 1 | 1 | yes | characteristic |
| 147 | C31×#101 | — | 2 | 1 | no | — |
| 148 | C31×#100 | — | 2 | 1 | no | — |
| 149 | C31×#100 | — | 2 | 1 | no | — |
| 150 | C31×#100 | — | 2 | 1 | no | — |
| 151 | C4×C8×C31 | C23 | 1 | 1 | yes | characteristic |
| 152 | #41×C31 | — | 2 | 1 | no | — |
| 153 | #41×C31 | — | 2 | 1 | no | — |
| 154 | #41×C31 | — | 4 | 1 | no | — |
| 155 | #41×C31 | — | 4 | 1 | no | — |
| 156 | #41×C31 | — | 4 | 1 | no | — |
| 157 | #41×C31 | — | 4 | 1 | no | — |
| 158 | #41×C31 | — | 4 | 1 | no | — |
| 159 | #41×C31 | — | 4 | 1 | no | — |
| 160 | #41×C31 | — | 4 | 1 | no | — |
| 161 | #41×C31 | — | 4 | 1 | no | — |
| 162 | #41×C31 | — | 8 | 1 | no | — |
| 163 | #41×C31 | C2×D4 | 1 | 1 | yes | characteristic |
| 164 | #41×C31 | C2×D4 | 1 | 1 | yes | characteristic |
| 165 | C2×Q8×C31 | — | 2 | 1 | no | — |
| 166 | C2×Q8×C31 | — | 4 | 1 | no | — |
| 167 | C2×Q8×C31 | — | 4 | 1 | no | — |
| 168 | C2×D4×C31 | — | 2 | 1 | no | — |
| 169 | C2×D4×C31 | — | 2 | 1 | no | — |
| 170 | C2×D4×C31 | — | 2 | 1 | no | — |
| 171 | C2×D4×C31 | — | 4 | 1 | no | — |
| 172 | C2×D4×C31 | — | 4 | 1 | no | — |
| 173 | C2×D4×C31 | — | 4 | 1 | no | — |
| 174 | C2×D4×C31 | — | 4 | 1 | no | — |
| 175 | C2×D4×C31 | — | 4 | 1 | no | — |
| 176 | C2×D4×C31 | — | 4 | 1 | no | — |
| 177 | C2×D4×C31 | — | 8 | 1 | no | — |
| 178 | C2×D4×C31 | — | 8 | 1 | no | — |
| 179 | C2×D4×C31 | — | 8 | 1 | no | — |
| 180 | C2×D4×C31 | — | 8 | 1 | no | — |
| 181 | Q16×C31 | — | 2 | 1 | no | — |
| 182 | Q16×C31 | — | 2 | 1 | no | — |
| 183 | Q16×C31 | — | 4 | 1 | no | — |
| 184 | Q16×C31 | — | 4 | 1 | no | — |
| 185 | Q16×C31 | D8 | 1 | 1 | yes | characteristic |
| 186 | Q16×C31 | C2×D4 | 1 | 1 | yes | characteristic |
| 187 | Q16×C31 | C2×D4 | 1 | 1 | yes | characteristic |
| 188 | SD16×C31 | — | 2 | 1 | no | — |
| 189 | SD16×C31 | — | 2 | 1 | no | — |
| 190 | SD16×C31 | — | 4 | 1 | no | — |
| 191 | SD16×C31 | — | 4 | 1 | no | — |
| 192 | SD16×C31 | — | 4 | 1 | no | — |
| 193 | SD16×C31 | — | 4 | 1 | no | — |
| 194 | SD16×C31 | — | 4 | 1 | no | — |
| 195 | SD16×C31 | — | 4 | 1 | no | — |
| 196 | SD16×C31 | — | 4 | 1 | no | — |
| 197 | SD16×C31 | — | 4 | 1 | no | — |
| 198 | SD16×C31 | — | 4 | 1 | no | — |
| 199 | SD16×C31 | — | 4 | 1 | no | — |
| 200 | SD16×C31 | D8 | 1 | 1 | yes | characteristic |
| 201 | SD16×C31 | D8 | 1 | 1 | yes | characteristic |
| 202 | D8×C31 | — | 2 | 1 | no | — |
| 203 | D8×C31 | — | 2 | 1 | no | — |
| 204 | D8×C31 | — | 2 | 1 | no | — |
| 205 | D8×C31 | — | 2 | 1 | no | — |
| 206 | D8×C31 | — | 2 | 1 | no | — |
| 207 | D8×C31 | — | 2 | 1 | no | — |
| 208 | D8×C31 | — | 4 | 1 | no | — |
| 209 | D8×C31 | — | 4 | 1 | no | — |
| 210 | D8×C31 | — | 4 | 1 | no | — |
| 211 | D8×C31 | — | 4 | 1 | no | — |
| 212 | D8×C31 | — | 4 | 1 | no | — |
| 213 | D8×C31 | — | 4 | 1 | no | — |
| 214 | D8×C31 | — | 4 | 1 | no | — |
| 215 | D8×C31 | — | 4 | 1 | no | — |
| 216 | D8×C31 | D8 | 1 | 1 | yes | characteristic |
| 217 | D8×C31 | C2×D4 | 1 | 1 | yes | characteristic |
| 218 | D8×C31 | C2×D4 | 1 | 1 | yes | characteristic |
| 219 | M16×C31 | — | 2 | 1 | no | — |
| 220 | M16×C31 | — | 2 | 1 | no | — |
| 221 | M16×C31 | — | 2 | 1 | no | — |
| 222 | M16×C31 | — | 2 | 1 | no | — |
| 223 | M16×C31 | — | 4 | 1 | no | — |
| 224 | M16×C31 | — | 4 | 1 | no | — |
| 225 | M16×C31 | C2×D4 | 1 | 1 | yes | characteristic |
| 226 | M16×C31 | C2×D4 | 1 | 1 | yes | characteristic |
| 227 | C2×C8×C31 | — | 2 | 1 | no | — |
| 228 | C2×C8×C31 | — | 2 | 1 | no | — |
| 229 | C2×C8×C31 | — | 4 | 1 | no | — |
| 230 | C2×C8×C31 | — | 4 | 1 | no | — |
| 231 | C2×C8×C31 | C2×D4 | 1 | 1 | yes | characteristic |
| 232 | C2×C8×C31 | C24 | 1 | 1 | yes | characteristic |
| 233 | C22⋊C4×C31 | — | 8 | 1 | no | — |
| 234 | C42×C31 | C2×D4 | 1 | 1 | yes | characteristic |
| 235 | C16×C31 | — | 2 | 1 | no | — |
| 236 | C16×C31 | — | 2 | 1 | no | — |
| 237 | C16×C31 | — | 2 | 1 | no | — |
| 238 | C16×C31 | C2×D4 | 1 | 1 | yes | characteristic |
| 239 | C16×C31 | C2×D4 | 1 | 1 | yes | characteristic |
| 240 | #33854 | C31 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 241 | C23×C31 | — | 4 | 1 | no | — |
| 242 | C23×C31 | — | 4 | 1 | no | — |
| 243 | C23×C31 | — | 4 | 1 | no | — |
| 244 | C23×C31 | — | 8 | 1 | no | — |
| 245 | C23×C31 | — | 8 | 1 | no | — |
| 246 | C23×C31 | — | 8 | 1 | no | — |
| 247 | Q8×C31 | — | 2 | 1 | no | — |
| 248 | Q8×C31 | — | 2 | 1 | no | — |
| 249 | Q8×C31 | — | 4 | 1 | no | — |
| 250 | Q8×C31 | — | 4 | 1 | no | — |
| 251 | Q8×C31 | — | 8 | 1 | no | — |
| 252 | Q8×C31 | C2×D8 | 1 | 1 | yes | characteristic |
| 253 | Q8×C31 | C2×D8 | 1 | 1 | yes | characteristic |
| 254 | D4×C31 | — | 2 | 1 | no | — |
| 255 | D4×C31 | — | 2 | 1 | no | — |
| 256 | D4×C31 | — | 2 | 1 | no | — |
| 257 | D4×C31 | — | 2 | 1 | no | — |
| 258 | D4×C31 | — | 4 | 1 | no | — |
| 259 | D4×C31 | — | 4 | 1 | no | — |
| 260 | D4×C31 | — | 4 | 1 | no | — |
| 261 | D4×C31 | — | 4 | 1 | no | — |
| 262 | D4×C31 | — | 4 | 1 | no | — |
| 263 | D4×C31 | — | 4 | 1 | no | — |
| 264 | D4×C31 | — | 4 | 1 | no | — |
| 265 | D4×C31 | — | 4 | 1 | no | — |
| 266 | D4×C31 | — | 8 | 1 | no | — |
| 267 | D4×C31 | — | 8 | 1 | no | — |
| 268 | D4×C31 | — | 8 | 1 | no | — |
| 269 | D4×C31 | — | 8 | 1 | no | — |
| 270 | D4×C31 | — | 8 | 1 | no | — |
| 271 | D4×C31 | — | 8 | 1 | no | — |
| 272 | D4×C31 | — | 8 | 1 | no | — |
| 273 | D4×C31 | — | 16 | 2 | no | — |
| 274 | D4×C31 | C2×D8 | 1 | 1 | yes | characteristic |
| 275 | D4×C31 | C2×D8 | 1 | 1 | yes | characteristic |
| 276 | C2×C4×C31 | — | 2 | 1 | no | — |
| 277 | C2×C4×C31 | — | 2 | 1 | no | — |
| 278 | C2×C4×C31 | — | 2 | 1 | no | — |
| 279 | C2×C4×C31 | — | 4 | 1 | no | — |
| 280 | C2×C4×C31 | — | 4 | 1 | no | — |
| 281 | C2×C4×C31 | — | 4 | 1 | no | — |
| 282 | C2×C4×C31 | — | 8 | 1 | no | — |
| 283 | C2×C4×C31 | — | 8 | 1 | no | — |
| 284 | C2×C4×C31 | — | 8 | 1 | no | — |
| 285 | C2×C4×C31 | — | 8 | 1 | no | — |
| 286 | C2×C4×C31 | — | 8 | 1 | no | — |
| 287 | C2×C4×C31 | C22×D4 | 1 | 1 | yes | characteristic |
| 288 | C8×C31 | — | 2 | 1 | no | — |
| 289 | C8×C31 | — | 2 | 1 | no | — |
| 290 | C8×C31 | — | 4 | 1 | no | — |
| 291 | C8×C31 | — | 4 | 1 | no | — |
| 292 | C8×C31 | C2×D8 | 1 | 1 | yes | characteristic |
| 293 | C8×C31 | C2×D8 | 1 | 1 | yes | characteristic |
| 294 | C8×C31 | C22×D4 | 1 | 1 | yes | characteristic |
| 295 | C8×C31 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 296 | #3416 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 297 | #3415 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 298 | #3292 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 299 | #3290 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 300 | #2250 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 301 | #2223 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 302 | #2221 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 303 | #2213 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 304 | #2212 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 305 | #2194 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 306 | #2193 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 307 | #2192 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 308 | #2192 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 309 | #2179 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 310 | #2171 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 311 | C22×C31 | — | 2 | 1 | no | — |
| 312 | C22×C31 | — | 2 | 1 | no | — |
| 313 | C22×C31 | — | 4 | 1 | no | — |
| 314 | C22×C31 | — | 4 | 1 | no | — |
| 315 | C22×C31 | — | 8 | 1 | no | — |
| 316 | C22×C31 | — | 8 | 1 | no | — |
| 317 | C22×C31 | — | 8 | 1 | no | — |
| 318 | C22×C31 | — | 16 | 1 | no | — |
| 319 | C22×C31 | — | 16 | 1 | no | — |
| 320 | C22×C31 | — | 16 | 1 | no | — |
| 321 | C22×C31 | — | 32 | 1 | no | — |
| 322 | C22×C31 | — | 32 | 1 | no | — |
| 323 | C22×C31 | — | 32 | 1 | no | — |
| 324 | C22×C31 | #576 | 1 | 1 | yes | characteristic |
| 325 | C4×C31 | — | 2 | 1 | no | — |
| 326 | C4×C31 | — | 2 | 1 | no | — |
| 327 | C4×C31 | — | 4 | 1 | no | — |
| 328 | C4×C31 | — | 4 | 1 | no | — |
| 329 | C4×C31 | — | 4 | 1 | no | — |
| 330 | C4×C31 | — | 8 | 1 | no | — |
| 331 | C4×C31 | D42 | 1 | 1 | yes | characteristic |
| 332 | C4×C31 | C22×D8 | 1 | 1 | yes | characteristic |
| 333 | #578 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 334 | #577 | — | 2 | 1 | no | — |
| 335 | #576 | — | 2 | 1 | no | — |
| 336 | #576 | C22×C31 | 1 | 1 | yes | characteristic |
| 337 | #576 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 338 | #576 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 339 | #510 | — | 2 | 1 | no | — |
| 340 | #510 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 341 | #509 | — | 2 | 1 | no | — |
| 342 | #509 | — | 2 | 1 | no | — |
| 343 | #509 | — | 2 | 1 | no | — |
| 344 | #509 | C22×C31 | 1 | 1 | yes | characteristic |
| 345 | #509 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 346 | #509 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 347 | #508 | — | 2 | 1 | no | — |
| 348 | #508 | — | 2 | 1 | no | — |
| 349 | #508 | C22×C31 | 1 | 1 | yes | characteristic |
| 350 | C2×SD32 | — | 2 | 1 | no | — |
| 351 | C2×SD32 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 352 | C2×SD32 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 353 | C2×D16 | — | 2 | 1 | no | — |
| 354 | C2×D16 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 355 | C2×D16 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 356 | #504 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 357 | #504 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 358 | #495 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 359 | #493 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 360 | #473 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 361 | #472 | — | 2 | 1 | no | — |
| 362 | #472 | C22×C31 | 1 | 1 | yes | characteristic |
| 363 | #472 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 364 | #472 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 365 | #471 | — | 2 | 1 | no | — |
| 366 | #455 | — | 2 | 1 | no | — |
| 367 | #454 | — | 2 | 1 | no | — |
| 368 | #453 | — | 2 | 1 | no | — |
| 369 | #453 | — | 2 | 1 | no | — |
| 370 | #443 | C22×C31 | 1 | 1 | yes | characteristic |
| 371 | #443 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 372 | #443 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 373 | #368 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 374 | #364 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 375 | #362 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 376 | #361 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 377 | #361 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 378 | #361 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 379 | #359 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 380 | #359 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 381 | #350 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 382 | #350 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 383 | #346 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 384 | C2×C31 | — | 2 | 1 | no | — |
| 385 | C2×C31 | — | 4 | 1 | no | — |
| 386 | C2×C31 | — | 4 | 1 | no | — |
| 387 | C2×C31 | — | 8 | 1 | no | — |
| 388 | C2×C31 | — | 8 | 1 | no | — |
| 389 | C2×C31 | — | 16 | 1 | no | — |
| 390 | C2×C31 | — | 16 | 1 | no | — |
| 391 | C2×C31 | — | 16 | 1 | no | — |
| 392 | C2×C31 | D4×D8 | 1 | 1 | yes | characteristic |
| 393 | 2−1+4 | — | 2 | 1 | no | — |
| 394 | H(5,𝔽2) | — | 2 | 1 | no | — |
| 395 | H(5,𝔽2) | — | 2 | 1 | no | — |
| 396 | H(5,𝔽2) | — | 2 | 1 | no | — |
| 397 | #137 | — | 2 | 1 | no | — |
| 398 | #137 | — | 2 | 1 | no | — |
| 399 | #137 | — | 4 | 1 | no | — |
| 400 | #137 | — | 4 | 1 | no | — |
| 401 | AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 402 | AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 403 | AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 404 | AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 405 | AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 406 | AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 407 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 408 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 409 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 410 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 411 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 412 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 413 | #135 | — | 2 | 1 | no | — |
| 414 | #135 | — | 2 | 1 | no | — |
| 415 | #135 | — | 2 | 1 | no | — |
| 416 | #135 | — | 2 | 1 | no | — |
| 417 | #135 | — | 4 | 1 | no | — |
| 418 | #135 | — | 4 | 1 | no | — |
| 419 | #135 | D4×C31 | 1 | 1 | yes | characteristic |
| 420 | #135 | C23×C31 | 1 | 1 | yes | characteristic |
| 421 | #135 | C23×C31 | 1 | 1 | yes | characteristic |
| 422 | C2×Q16 | — | 2 | 1 | no | — |
| 423 | C2×Q16 | C23×C31 | 1 | 1 | yes | characteristic |
| 424 | C2×SD16 | — | 2 | 1 | no | — |
| 425 | C2×SD16 | — | 4 | 1 | no | — |
| 426 | C2×D8 | — | 2 | 1 | no | — |
| 427 | C2×D8 | — | 2 | 1 | no | — |
| 428 | C2×D8 | — | 2 | 1 | no | — |
| 429 | C2×D8 | — | 2 | 1 | no | — |
| 430 | C2×D8 | — | 4 | 1 | no | — |
| 431 | C2×D8 | C23×C31 | 1 | 1 | yes | characteristic |
| 432 | C2×D8 | C23×C31 | 1 | 1 | yes | characteristic |
| 433 | C2×D8 | C23×C31 | 1 | 1 | yes | characteristic |
| 434 | #131 | — | 2 | 1 | no | — |
| 435 | #131 | — | 2 | 1 | no | — |
| 436 | #131 | C23×C31 | 1 | 1 | yes | characteristic |
| 437 | #131 | C23×C31 | 1 | 1 | yes | characteristic |
| 438 | #127 | — | 2 | 1 | no | — |
| 439 | #124 | — | 2 | 1 | no | — |
| 440 | Q32 | — | 2 | 1 | no | — |
| 441 | Q32 | D4×C31 | 1 | 1 | yes | characteristic, complemented |
| 442 | SD32 | — | 2 | 1 | no | — |
| 443 | SD32 | — | 2 | 1 | no | — |
| 444 | SD32 | — | 2 | 1 | no | — |
| 445 | SD32 | — | 2 | 1 | no | — |
| 446 | SD32 | — | 2 | 1 | no | — |
| 447 | SD32 | — | 2 | 1 | no | — |
| 448 | SD32 | — | 4 | 1 | no | — |
| 449 | SD32 | D4×C31 | 1 | 1 | yes | characteristic, complemented |
| 450 | SD32 | D4×C31 | 1 | 1 | yes | characteristic, complemented |
| 451 | D16 | — | 2 | 1 | no | — |
| 452 | D16 | — | 2 | 1 | no | — |
| 453 | D16 | — | 2 | 1 | no | — |
| 454 | D16 | — | 2 | 1 | no | — |
| 455 | D16 | — | 2 | 1 | no | — |
| 456 | D16 | — | 4 | 1 | no | — |
| 457 | D16 | D4×C31 | 1 | 1 | yes | characteristic, complemented |
| 458 | M32 | — | 2 | 1 | no | — |
| 459 | M32 | — | 2 | 1 | no | — |
| 460 | M32 | C23×C31 | 1 | 1 | yes | characteristic |
| 461 | M32 | C23×C31 | 1 | 1 | yes | characteristic |
| 462 | C2×C16 | — | 2 | 1 | no | — |
| 463 | C2×C16 | — | 2 | 1 | no | — |
| 464 | C2×C16 | C23×C31 | 1 | 1 | yes | characteristic |
| 465 | C2×C16 | C23×C31 | 1 | 1 | yes | characteristic |
| 466 | #108 | D4×C31 | 1 | 1 | yes | characteristic |
| 467 | #108 | C23×C31 | 1 | 1 | yes | characteristic |
| 468 | #108 | C23×C31 | 1 | 1 | yes | characteristic |
| 469 | #104 | — | 2 | 1 | no | — |
| 470 | #104 | — | 2 | 1 | no | — |
| 471 | #104 | D4×C31 | 1 | 1 | yes | characteristic |
| 472 | #104 | D4×C31 | 1 | 1 | yes | characteristic |
| 473 | #101 | — | 2 | 1 | no | — |
| 474 | #100 | — | 2 | 1 | no | — |
| 475 | #100 | — | 2 | 1 | no | — |
| 476 | #100 | — | 2 | 1 | no | — |
| 477 | C4×C8 | C23×C31 | 1 | 1 | yes | characteristic |
| 478 | C31 | #33854 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 479 | #41 | — | 2 | 1 | no | — |
| 480 | #41 | — | 2 | 1 | no | — |
| 481 | #41 | — | 4 | 1 | no | — |
| 482 | #41 | — | 4 | 1 | no | — |
| 483 | #41 | — | 4 | 1 | no | — |
| 484 | #41 | — | 4 | 1 | no | — |
| 485 | #41 | — | 4 | 1 | no | — |
| 486 | #41 | — | 4 | 1 | no | — |
| 487 | #41 | — | 4 | 1 | no | — |
| 488 | #41 | — | 4 | 1 | no | — |
| 489 | #41 | — | 8 | 1 | no | — |
| 490 | #41 | C2×D4×C31 | 1 | 1 | yes | characteristic |
| 491 | #41 | C2×D4×C31 | 1 | 1 | yes | characteristic |
| 492 | C2×Q8 | — | 2 | 1 | no | — |
| 493 | C2×Q8 | — | 4 | 1 | no | — |
| 494 | C2×Q8 | — | 4 | 1 | no | — |
| 495 | C2×D4 | — | 2 | 1 | no | — |
| 496 | C2×D4 | — | 2 | 1 | no | — |
| 497 | C2×D4 | — | 2 | 1 | no | — |
| 498 | C2×D4 | — | 4 | 1 | no | — |
| 499 | C2×D4 | — | 4 | 1 | no | — |
| 500 | C2×D4 | — | 4 | 1 | no | — |
| 501 | C2×D4 | — | 4 | 1 | no | — |
| 502 | C2×D4 | — | 4 | 1 | no | — |
| 503 | C2×D4 | — | 4 | 1 | no | — |
| 504 | C2×D4 | — | 8 | 1 | no | — |
| 505 | C2×D4 | — | 8 | 1 | no | — |
| 506 | C2×D4 | — | 8 | 1 | no | — |
| 507 | C2×D4 | — | 8 | 1 | no | — |
| 508 | Q16 | — | 2 | 1 | no | — |
| 509 | Q16 | — | 2 | 1 | no | — |
| 510 | Q16 | — | 4 | 1 | no | — |
| 511 | Q16 | — | 4 | 1 | no | — |
| 512 | Q16 | D8×C31 | 1 | 1 | yes | characteristic |
| 513 | Q16 | C2×D4×C31 | 1 | 1 | yes | characteristic |
| 514 | Q16 | C2×D4×C31 | 1 | 1 | yes | characteristic |
| 515 | SD16 | — | 2 | 1 | no | — |
| 516 | SD16 | — | 2 | 1 | no | — |
| 517 | SD16 | — | 4 | 1 | no | — |
| 518 | SD16 | — | 4 | 1 | no | — |
| 519 | SD16 | — | 4 | 1 | no | — |
| 520 | SD16 | — | 4 | 1 | no | — |
| 521 | SD16 | — | 4 | 1 | no | — |
| 522 | SD16 | — | 4 | 1 | no | — |
| 523 | SD16 | — | 4 | 1 | no | — |
| 524 | SD16 | — | 4 | 1 | no | — |
| 525 | SD16 | — | 4 | 1 | no | — |
| 526 | SD16 | — | 4 | 1 | no | — |
| 527 | SD16 | D8×C31 | 1 | 1 | yes | characteristic |
| 528 | SD16 | D8×C31 | 1 | 1 | yes | characteristic |
| 529 | D8 | — | 2 | 1 | no | — |
| 530 | D8 | — | 2 | 1 | no | — |
| 531 | D8 | — | 2 | 1 | no | — |
| 532 | D8 | — | 2 | 1 | no | — |
| 533 | D8 | — | 2 | 1 | no | — |
| 534 | D8 | — | 2 | 1 | no | — |
| 535 | D8 | — | 4 | 1 | no | — |
| 536 | D8 | — | 4 | 1 | no | — |
| 537 | D8 | — | 4 | 1 | no | — |
| 538 | D8 | — | 4 | 1 | no | — |
| 539 | D8 | — | 4 | 1 | no | — |
| 540 | D8 | — | 4 | 1 | no | — |
| 541 | D8 | — | 4 | 1 | no | — |
| 542 | D8 | — | 4 | 1 | no | — |
| 543 | D8 | D8×C31 | 1 | 1 | yes | characteristic |
| 544 | D8 | C2×D4×C31 | 1 | 1 | yes | characteristic |
| 545 | D8 | C2×D4×C31 | 1 | 1 | yes | characteristic |
| 546 | M16 | — | 2 | 1 | no | — |
| 547 | M16 | — | 2 | 1 | no | — |
| 548 | M16 | — | 2 | 1 | no | — |
| 549 | M16 | — | 2 | 1 | no | — |
| 550 | M16 | — | 4 | 1 | no | — |
| 551 | M16 | — | 4 | 1 | no | — |
| 552 | M16 | C2×D4×C31 | 1 | 1 | yes | characteristic |
| 553 | M16 | C2×D4×C31 | 1 | 1 | yes | characteristic |
| 554 | C2×C8 | — | 2 | 1 | no | — |
| 555 | C2×C8 | — | 2 | 1 | no | — |
| 556 | C2×C8 | — | 4 | 1 | no | — |
| 557 | C2×C8 | — | 4 | 1 | no | — |
| 558 | C2×C8 | C2×D4×C31 | 1 | 1 | yes | characteristic |
| 559 | C2×C8 | C24×C31 | 1 | 1 | yes | characteristic |
| 560 | C22⋊C4 | — | 8 | 1 | no | — |
| 561 | C42 | C2×D4×C31 | 1 | 1 | yes | characteristic |
| 562 | C16 | — | 2 | 1 | no | — |
| 563 | C16 | — | 2 | 1 | no | — |
| 564 | C16 | — | 2 | 1 | no | — |
| 565 | C16 | C2×D4×C31 | 1 | 1 | yes | characteristic |
| 566 | C16 | C2×D4×C31 | 1 | 1 | yes | characteristic |
| 567 | C23 | — | 4 | 1 | no | — |
| 568 | C23 | — | 4 | 1 | no | — |
| 569 | C23 | — | 4 | 1 | no | — |
| 570 | C23 | — | 8 | 1 | no | — |
| 571 | C23 | — | 8 | 1 | no | — |
| 572 | C23 | — | 8 | 1 | no | — |
| 573 | Q8 | — | 2 | 1 | no | — |
| 574 | Q8 | — | 2 | 1 | no | — |
| 575 | Q8 | — | 4 | 1 | no | — |
| 576 | Q8 | — | 4 | 1 | no | — |
| 577 | Q8 | — | 8 | 1 | no | — |
| 578 | Q8 | C2×D8×C31 | 1 | 1 | yes | characteristic |
| 579 | Q8 | C2×D8×C31 | 1 | 1 | yes | characteristic |
| 580 | D4 | — | 2 | 1 | no | — |
| 581 | D4 | — | 2 | 1 | no | — |
| 582 | D4 | — | 2 | 1 | no | — |
| 583 | D4 | — | 2 | 1 | no | — |
| 584 | D4 | — | 4 | 1 | no | — |
| 585 | D4 | — | 4 | 1 | no | — |
| 586 | D4 | — | 4 | 1 | no | — |
| 587 | D4 | — | 4 | 1 | no | — |
| 588 | D4 | — | 4 | 1 | no | — |
| 589 | D4 | — | 4 | 1 | no | — |
| 590 | D4 | — | 4 | 1 | no | — |
| 591 | D4 | — | 4 | 1 | no | — |
| 592 | D4 | — | 8 | 1 | no | — |
| 593 | D4 | — | 8 | 1 | no | — |
| 594 | D4 | — | 8 | 1 | no | — |
| 595 | D4 | — | 8 | 1 | no | — |
| 596 | D4 | — | 8 | 1 | no | — |
| 597 | D4 | — | 8 | 1 | no | — |
| 598 | D4 | — | 8 | 1 | no | — |
| 599 | D4 | — | 16 | 2 | no | — |
| 600 | D4 | C2×D8×C31 | 1 | 1 | yes | characteristic |
| 601 | D4 | C2×D8×C31 | 1 | 1 | yes | characteristic |
| 602 | C2×C4 | — | 2 | 1 | no | — |
| 603 | C2×C4 | — | 2 | 1 | no | — |
| 604 | C2×C4 | — | 2 | 1 | no | — |
| 605 | C2×C4 | — | 4 | 1 | no | — |
| 606 | C2×C4 | — | 4 | 1 | no | — |
| 607 | C2×C4 | — | 4 | 1 | no | — |
| 608 | C2×C4 | — | 8 | 1 | no | — |
| 609 | C2×C4 | — | 8 | 1 | no | — |
| 610 | C2×C4 | — | 8 | 1 | no | — |
| 611 | C2×C4 | — | 8 | 1 | no | — |
| 612 | C2×C4 | — | 8 | 1 | no | — |
| 613 | C2×C4 | C22×D4×C31 | 1 | 1 | yes | characteristic |
| 614 | C8 | — | 2 | 1 | no | — |
| 615 | C8 | — | 2 | 1 | no | — |
| 616 | C8 | — | 4 | 1 | no | — |
| 617 | C8 | — | 4 | 1 | no | — |
| 618 | C8 | C2×D8×C31 | 1 | 1 | yes | characteristic |
| 619 | C8 | C2×D8×C31 | 1 | 1 | yes | characteristic |
| 620 | C8 | C22×D4×C31 | 1 | 1 | yes | characteristic |
| 621 | C8 | C31×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 622 | C22 | — | 2 | 1 | no | — |
| 623 | C22 | — | 2 | 1 | no | — |
| 624 | C22 | — | 4 | 1 | no | — |
| 625 | C22 | — | 4 | 1 | no | — |
| 626 | C22 | — | 8 | 1 | no | — |
| 627 | C22 | — | 8 | 1 | no | — |
| 628 | C22 | — | 8 | 1 | no | — |
| 629 | C22 | — | 16 | 1 | no | — |
| 630 | C22 | — | 16 | 1 | no | — |
| 631 | C22 | — | 16 | 1 | no | — |
| 632 | C22 | — | 32 | 1 | no | — |
| 633 | C22 | — | 32 | 1 | no | — |
| 634 | C22 | — | 32 | 1 | no | — |
| 635 | C22 | C31×#576 | 1 | 1 | yes | characteristic |
| 636 | C4 | — | 2 | 1 | no | — |
| 637 | C4 | — | 2 | 1 | no | — |
| 638 | C4 | — | 4 | 1 | no | — |
| 639 | C4 | — | 4 | 1 | no | — |
| 640 | C4 | — | 4 | 1 | no | — |
| 641 | C4 | — | 8 | 1 | no | — |
| 642 | C4 | D42×C31 | 1 | 1 | yes | characteristic |
| 643 | C4 | C22×D8×C31 | 1 | 1 | yes | characteristic |
| 644 | C2 | — | 2 | 1 | no | — |
| 645 | C2 | — | 4 | 1 | no | — |
| 646 | C2 | — | 4 | 1 | no | — |
| 647 | C2 | — | 8 | 1 | no | — |
| 648 | C2 | — | 8 | 1 | no | — |
| 649 | C2 | — | 16 | 1 | no | — |
| 650 | C2 | — | 16 | 1 | no | — |
| 651 | C2 | — | 16 | 1 | no | — |
| 652 | C2 | D4×D8×C31 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta