| 1 | C31×#3067 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×C31×#368 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C31×#2148 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×C31×#359 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×C31×#350 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C31×#1813 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C31×#1385 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C31×#575 | — | 2 | 1 | no | — |
| 9 | C2×C31×#135 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×C31×#131 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×C31×M32 | C22 | 1 | 1 | yes | characteristic |
| 12 | C22×C16×C31 | C22 | 1 | 1 | yes | characteristic |
| 13 | C31×#473 | — | 2 | 1 | no | — |
| 14 | C31×#472 | — | 2 | 1 | no | — |
| 15 | C31×#471 | — | 2 | 2 | no | — |
| 16 | C2×C31×#108 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×C31×#108 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×C31×#108 | C22 | 1 | 1 | yes | characteristic |
| 19 | C31×#413 | — | 2 | 1 | no | — |
| 20 | C31×#413 | — | 2 | 1 | no | — |
| 21 | C31×#368 | — | 2 | 2 | no | — |
| 22 | C31×#362 | — | 2 | 1 | no | — |
| 23 | C31×#361 | — | 2 | 1 | no | — |
| 24 | C31×#359 | — | 2 | 2 | no | — |
| 25 | C31×#350 | — | 2 | 2 | no | — |
| 26 | C31×#338 | — | 2 | 1 | no | — |
| 27 | C2×#41×C31 | — | 2 | 1 | no | — |
| 28 | C2×#41×C31 | D4 | 1 | 1 | yes | characteristic |
| 29 | C31×#137 | — | 2 | 2 | no | — |
| 30 | C31×#137 | — | 4 | 1 | no | — |
| 31 | C31×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 32 | C31×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 33 | C31×#135 | — | 2 | 1 | no | — |
| 34 | C31×#135 | — | 2 | 1 | no | — |
| 35 | C31×#135 | — | 2 | 1 | no | — |
| 36 | C31×#135 | — | 2 | 1 | no | — |
| 37 | C31×#135 | — | 4 | 2 | no | — |
| 38 | C2×Q16×C31 | D4 | 1 | 1 | yes | characteristic |
| 39 | C2×SD16×C31 | — | 2 | 1 | no | — |
| 40 | C2×D8×C31 | D4 | 1 | 1 | yes | characteristic |
| 41 | C31×#131 | — | 2 | 1 | no | — |
| 42 | C31×#131 | — | 2 | 1 | no | — |
| 43 | C31×#131 | — | 2 | 1 | no | — |
| 44 | C31×#131 | — | 2 | 1 | no | — |
| 45 | C2×M16×C31 | — | 2 | 1 | no | — |
| 46 | C2×M16×C31 | — | 2 | 1 | no | — |
| 47 | C2×M16×C31 | — | 2 | 1 | no | — |
| 48 | C2×M16×C31 | — | 2 | 1 | no | — |
| 49 | C2×M16×C31 | D4 | 1 | 1 | yes | characteristic |
| 50 | C22×C8×C31 | — | 2 | 1 | no | — |
| 51 | C22×C8×C31 | C23 | 1 | 1 | yes | characteristic |
| 52 | C31×M32 | — | 2 | 1 | no | — |
| 53 | C31×M32 | — | 2 | 1 | no | — |
| 54 | C2×C16×C31 | — | 2 | 1 | no | — |
| 55 | C2×C16×C31 | — | 2 | 1 | no | — |
| 56 | C2×C16×C31 | — | 2 | 1 | no | — |
| 57 | C2×C16×C31 | D4 | 1 | 2 | yes | — |
| 58 | C31×#108 | — | 2 | 1 | no | — |
| 59 | C31×#108 | — | 2 | 1 | no | — |
| 60 | C31×#108 | — | 2 | 1 | no | — |
| 61 | C31×#108 | — | 2 | 1 | no | — |
| 62 | C31×#108 | — | 2 | 1 | no | — |
| 63 | C31×#108 | D4 | 1 | 2 | yes | — |
| 64 | C31×#101 | — | 2 | 2 | no | — |
| 65 | C31×#101 | — | 4 | 1 | no | — |
| 66 | C31×#100 | — | 2 | 2 | no | — |
| 67 | C31×#100 | — | 4 | 1 | no | — |
| 68 | #41×C31 | — | 2 | 1 | no | — |
| 69 | #41×C31 | — | 2 | 1 | no | — |
| 70 | #41×C31 | — | 2 | 1 | no | — |
| 71 | #41×C31 | — | 2 | 1 | no | — |
| 72 | #41×C31 | — | 4 | 1 | no | — |
| 73 | #41×C31 | — | 4 | 1 | no | — |
| 74 | #41×C31 | — | 4 | 1 | no | — |
| 75 | #41×C31 | — | 4 | 1 | no | — |
| 76 | C2×Q8×C31 | — | 2 | 1 | no | — |
| 77 | C2×Q8×C31 | D8 | 1 | 1 | yes | characteristic |
| 78 | C2×D4×C31 | — | 2 | 1 | no | — |
| 79 | C2×D4×C31 | — | 2 | 1 | no | — |
| 80 | C2×D4×C31 | — | 4 | 1 | no | — |
| 81 | C2×D4×C31 | D8 | 1 | 1 | yes | characteristic |
| 82 | C22×C4×C31 | — | 2 | 1 | no | — |
| 83 | C22×C4×C31 | — | 4 | 1 | no | — |
| 84 | C22×C4×C31 | C2×D4 | 1 | 1 | yes | characteristic |
| 85 | Q16×C31 | — | 2 | 1 | no | — |
| 86 | Q16×C31 | — | 2 | 1 | no | — |
| 87 | Q16×C31 | — | 4 | 2 | no | — |
| 88 | SD16×C31 | — | 4 | 2 | no | — |
| 89 | SD16×C31 | — | 4 | 2 | no | — |
| 90 | SD16×C31 | — | 4 | 1 | no | — |
| 91 | SD16×C31 | — | 4 | 1 | no | — |
| 92 | D8×C31 | — | 2 | 1 | no | — |
| 93 | D8×C31 | — | 2 | 1 | no | — |
| 94 | D8×C31 | — | 4 | 2 | no | — |
| 95 | M16×C31 | — | 2 | 1 | no | — |
| 96 | M16×C31 | — | 2 | 2 | no | — |
| 97 | M16×C31 | — | 2 | 1 | no | — |
| 98 | M16×C31 | — | 4 | 1 | no | — |
| 99 | M16×C31 | — | 4 | 1 | no | — |
| 100 | M16×C31 | — | 4 | 1 | no | — |
| 101 | M16×C31 | — | 4 | 1 | no | — |
| 102 | M16×C31 | — | 4 | 1 | no | — |
| 103 | M16×C31 | — | 4 | 1 | no | — |
| 104 | M16×C31 | — | 4 | 1 | no | — |
| 105 | C2×C8×C31 | — | 2 | 1 | no | — |
| 106 | C2×C8×C31 | — | 4 | 1 | no | — |
| 107 | C2×C8×C31 | — | 4 | 1 | no | — |
| 108 | C2×C8×C31 | — | 4 | 1 | no | — |
| 109 | C2×C8×C31 | — | 4 | 1 | no | — |
| 110 | C2×C8×C31 | — | 4 | 1 | no | — |
| 111 | C2×C8×C31 | C2×D4 | 1 | 1 | yes | characteristic |
| 112 | C2×C8×C31 | C2×D4 | 1 | 1 | yes | characteristic |
| 113 | C2×C8×C31 | C2×D4 | 1 | 1 | yes | characteristic |
| 114 | C2×C8×C31 | #41 | 1 | 1 | yes | characteristic |
| 115 | C2×C8×C31 | #41 | 1 | 1 | yes | characteristic |
| 116 | C2×C8×C31 | #41 | 1 | 1 | yes | characteristic |
| 117 | C16×C31 | — | 2 | 2 | no | — |
| 118 | C16×C31 | — | 4 | 1 | no | — |
| 119 | #13392 | C31 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 120 | C23×C31 | — | 2 | 1 | no | — |
| 121 | C23×C31 | — | 4 | 1 | no | — |
| 122 | C23×C31 | #137 | 1 | 1 | yes | characteristic |
| 123 | Q8×C31 | — | 2 | 1 | no | — |
| 124 | Q8×C31 | — | 2 | 1 | no | — |
| 125 | Q8×C31 | — | 4 | 1 | no | — |
| 126 | Q8×C31 | — | 4 | 1 | no | — |
| 127 | D4×C31 | — | 2 | 1 | no | — |
| 128 | D4×C31 | — | 2 | 1 | no | — |
| 129 | D4×C31 | — | 4 | 1 | no | — |
| 130 | D4×C31 | — | 4 | 1 | no | — |
| 131 | D4×C31 | — | 4 | 1 | no | — |
| 132 | D4×C31 | — | 4 | 1 | no | — |
| 133 | D4×C31 | — | 8 | 1 | no | — |
| 134 | D4×C31 | — | 8 | 1 | no | — |
| 135 | C2×C4×C31 | — | 2 | 1 | no | — |
| 136 | C2×C4×C31 | — | 4 | 1 | no | — |
| 137 | C2×C4×C31 | — | 4 | 1 | no | — |
| 138 | C2×C4×C31 | — | 4 | 1 | no | — |
| 139 | C2×C4×C31 | — | 8 | 1 | no | — |
| 140 | C2×C4×C31 | — | 8 | 1 | no | — |
| 141 | C2×C4×C31 | #120 | 1 | 1 | yes | characteristic |
| 142 | C2×C4×C31 | #121 | 1 | 1 | yes | characteristic |
| 143 | C2×C4×C31 | #123 | 1 | 1 | yes | characteristic |
| 144 | C2×C4×C31 | C2×D8 | 1 | 1 | yes | characteristic |
| 145 | C2×C4×C31 | #135 | 1 | 1 | yes | characteristic |
| 146 | C2×C4×C31 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 147 | C8×C31 | — | 4 | 1 | no | — |
| 148 | C8×C31 | — | 4 | 2 | no | — |
| 149 | C8×C31 | — | 8 | 1 | no | — |
| 150 | C8×C31 | — | 8 | 1 | no | — |
| 151 | C8×C31 | #121 | 1 | 1 | yes | characteristic |
| 152 | C8×C31 | #121 | 1 | 1 | yes | characteristic |
| 153 | C8×C31 | #123 | 1 | 1 | yes | characteristic |
| 154 | C8×C31 | #124 | 1 | 1 | yes | characteristic |
| 155 | #3067 | C2×C31 | 1 | 1 | yes | characteristic |
| 156 | C2×#368 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 157 | #2148 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 158 | C2×#359 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 159 | C2×#350 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 160 | #1813 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 161 | #1385 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 162 | C22×C31 | — | 4 | 1 | no | — |
| 163 | C22×C31 | — | 4 | 1 | no | — |
| 164 | C22×C31 | — | 8 | 1 | no | — |
| 165 | C22×C31 | — | 8 | 1 | no | — |
| 166 | C22×C31 | — | 16 | 1 | no | — |
| 167 | C22×C31 | #452 | 1 | 1 | yes | characteristic |
| 168 | C22×C31 | #468 | 1 | 1 | yes | characteristic |
| 169 | C22×C31 | #480 | 1 | 1 | yes | characteristic |
| 170 | C4×C31 | — | 4 | 1 | no | — |
| 171 | C4×C31 | — | 8 | 1 | no | — |
| 172 | C4×C31 | #394 | 1 | 1 | yes | characteristic |
| 173 | C4×C31 | #447 | 1 | 1 | yes | characteristic |
| 174 | C4×C31 | #466 | 1 | 1 | yes | characteristic |
| 175 | C4×C31 | #482 | 1 | 1 | yes | characteristic |
| 176 | #575 | — | 2 | 1 | no | — |
| 177 | C2×#135 | C22×C31 | 1 | 1 | yes | characteristic |
| 178 | C2×#131 | C22×C31 | 1 | 1 | yes | characteristic |
| 179 | C2×M32 | C22×C31 | 1 | 1 | yes | characteristic |
| 180 | C22×C16 | C22×C31 | 1 | 1 | yes | characteristic |
| 181 | #473 | — | 2 | 1 | no | — |
| 182 | #472 | — | 2 | 1 | no | — |
| 183 | #471 | — | 2 | 2 | no | — |
| 184 | C2×#108 | C22×C31 | 1 | 1 | yes | characteristic |
| 185 | C2×#108 | C22×C31 | 1 | 1 | yes | characteristic |
| 186 | C2×#108 | C22×C31 | 1 | 1 | yes | characteristic |
| 187 | #413 | — | 2 | 1 | no | — |
| 188 | #413 | — | 2 | 1 | no | — |
| 189 | #368 | — | 2 | 2 | no | — |
| 190 | #362 | — | 2 | 1 | no | — |
| 191 | #361 | — | 2 | 1 | no | — |
| 192 | #359 | — | 2 | 2 | no | — |
| 193 | #350 | — | 2 | 2 | no | — |
| 194 | #338 | — | 2 | 1 | no | — |
| 195 | C2×C31 | — | 2 | 1 | no | — |
| 196 | C2×C31 | — | 2 | 1 | no | — |
| 197 | C2×C31 | — | 2 | 1 | no | — |
| 198 | C2×C31 | — | 8 | 1 | no | — |
| 199 | C2×C31 | — | 16 | 1 | no | — |
| 200 | C2×C31 | #2033 | 1 | 1 | yes | characteristic |
| 201 | C2×#41 | — | 2 | 1 | no | — |
| 202 | C2×#41 | D4×C31 | 1 | 1 | yes | characteristic |
| 203 | #137 | — | 2 | 2 | no | — |
| 204 | #137 | — | 4 | 1 | no | — |
| 205 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 206 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 207 | #135 | — | 2 | 1 | no | — |
| 208 | #135 | — | 2 | 1 | no | — |
| 209 | #135 | — | 2 | 1 | no | — |
| 210 | #135 | — | 2 | 1 | no | — |
| 211 | #135 | — | 4 | 2 | no | — |
| 212 | C2×Q16 | D4×C31 | 1 | 1 | yes | characteristic |
| 213 | C2×SD16 | — | 2 | 1 | no | — |
| 214 | C2×D8 | D4×C31 | 1 | 1 | yes | characteristic |
| 215 | #131 | — | 2 | 1 | no | — |
| 216 | #131 | — | 2 | 1 | no | — |
| 217 | #131 | — | 2 | 1 | no | — |
| 218 | #131 | — | 2 | 1 | no | — |
| 219 | C2×M16 | — | 2 | 1 | no | — |
| 220 | C2×M16 | — | 2 | 1 | no | — |
| 221 | C2×M16 | — | 2 | 1 | no | — |
| 222 | C2×M16 | — | 2 | 1 | no | — |
| 223 | C2×M16 | D4×C31 | 1 | 1 | yes | characteristic |
| 224 | C22×C8 | — | 2 | 1 | no | — |
| 225 | C22×C8 | C23×C31 | 1 | 1 | yes | characteristic |
| 226 | M32 | — | 2 | 1 | no | — |
| 227 | M32 | — | 2 | 1 | no | — |
| 228 | C2×C16 | — | 2 | 1 | no | — |
| 229 | C2×C16 | — | 2 | 1 | no | — |
| 230 | C2×C16 | — | 2 | 1 | no | — |
| 231 | C2×C16 | D4×C31 | 1 | 2 | yes | — |
| 232 | #108 | — | 2 | 1 | no | — |
| 233 | #108 | — | 2 | 1 | no | — |
| 234 | #108 | — | 2 | 1 | no | — |
| 235 | #108 | — | 2 | 1 | no | — |
| 236 | #108 | — | 2 | 1 | no | — |
| 237 | #108 | D4×C31 | 1 | 2 | yes | — |
| 238 | #101 | — | 2 | 2 | no | — |
| 239 | #101 | — | 4 | 1 | no | — |
| 240 | #100 | — | 2 | 2 | no | — |
| 241 | #100 | — | 4 | 1 | no | — |
| 242 | C31 | #13392 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 243 | #41 | — | 2 | 1 | no | — |
| 244 | #41 | — | 2 | 1 | no | — |
| 245 | #41 | — | 2 | 1 | no | — |
| 246 | #41 | — | 2 | 1 | no | — |
| 247 | #41 | — | 4 | 1 | no | — |
| 248 | #41 | — | 4 | 1 | no | — |
| 249 | #41 | — | 4 | 1 | no | — |
| 250 | #41 | — | 4 | 1 | no | — |
| 251 | C2×Q8 | — | 2 | 1 | no | — |
| 252 | C2×Q8 | D8×C31 | 1 | 1 | yes | characteristic |
| 253 | C2×D4 | — | 2 | 1 | no | — |
| 254 | C2×D4 | — | 2 | 1 | no | — |
| 255 | C2×D4 | — | 4 | 1 | no | — |
| 256 | C2×D4 | D8×C31 | 1 | 1 | yes | characteristic |
| 257 | C22×C4 | — | 2 | 1 | no | — |
| 258 | C22×C4 | — | 4 | 1 | no | — |
| 259 | C22×C4 | C2×D4×C31 | 1 | 1 | yes | characteristic |
| 260 | Q16 | — | 2 | 1 | no | — |
| 261 | Q16 | — | 2 | 1 | no | — |
| 262 | Q16 | — | 4 | 2 | no | — |
| 263 | SD16 | — | 4 | 2 | no | — |
| 264 | SD16 | — | 4 | 2 | no | — |
| 265 | SD16 | — | 4 | 1 | no | — |
| 266 | SD16 | — | 4 | 1 | no | — |
| 267 | D8 | — | 2 | 1 | no | — |
| 268 | D8 | — | 2 | 1 | no | — |
| 269 | D8 | — | 4 | 2 | no | — |
| 270 | M16 | — | 2 | 1 | no | — |
| 271 | M16 | — | 2 | 2 | no | — |
| 272 | M16 | — | 2 | 1 | no | — |
| 273 | M16 | — | 4 | 1 | no | — |
| 274 | M16 | — | 4 | 1 | no | — |
| 275 | M16 | — | 4 | 1 | no | — |
| 276 | M16 | — | 4 | 1 | no | — |
| 277 | M16 | — | 4 | 1 | no | — |
| 278 | M16 | — | 4 | 1 | no | — |
| 279 | M16 | — | 4 | 1 | no | — |
| 280 | C2×C8 | — | 2 | 1 | no | — |
| 281 | C2×C8 | — | 4 | 1 | no | — |
| 282 | C2×C8 | — | 4 | 1 | no | — |
| 283 | C2×C8 | — | 4 | 1 | no | — |
| 284 | C2×C8 | — | 4 | 1 | no | — |
| 285 | C2×C8 | — | 4 | 1 | no | — |
| 286 | C2×C8 | C2×D4×C31 | 1 | 1 | yes | characteristic |
| 287 | C2×C8 | C2×D4×C31 | 1 | 1 | yes | characteristic |
| 288 | C2×C8 | C2×D4×C31 | 1 | 1 | yes | characteristic |
| 289 | C2×C8 | #41×C31 | 1 | 1 | yes | characteristic |
| 290 | C2×C8 | #41×C31 | 1 | 1 | yes | characteristic |
| 291 | C2×C8 | #41×C31 | 1 | 1 | yes | characteristic |
| 292 | C16 | — | 2 | 2 | no | — |
| 293 | C16 | — | 4 | 1 | no | — |
| 294 | C23 | — | 2 | 1 | no | — |
| 295 | C23 | — | 4 | 1 | no | — |
| 296 | C23 | C31×#137 | 1 | 1 | yes | characteristic |
| 297 | Q8 | — | 2 | 1 | no | — |
| 298 | Q8 | — | 2 | 1 | no | — |
| 299 | Q8 | — | 4 | 1 | no | — |
| 300 | Q8 | — | 4 | 1 | no | — |
| 301 | D4 | — | 2 | 1 | no | — |
| 302 | D4 | — | 2 | 1 | no | — |
| 303 | D4 | — | 4 | 1 | no | — |
| 304 | D4 | — | 4 | 1 | no | — |
| 305 | D4 | — | 4 | 1 | no | — |
| 306 | D4 | — | 4 | 1 | no | — |
| 307 | D4 | — | 8 | 1 | no | — |
| 308 | D4 | — | 8 | 1 | no | — |
| 309 | C2×C4 | — | 2 | 1 | no | — |
| 310 | C2×C4 | — | 4 | 1 | no | — |
| 311 | C2×C4 | — | 4 | 1 | no | — |
| 312 | C2×C4 | — | 4 | 1 | no | — |
| 313 | C2×C4 | — | 8 | 1 | no | — |
| 314 | C2×C4 | — | 8 | 1 | no | — |
| 315 | C2×C4 | C31×#120 | 1 | 1 | yes | characteristic |
| 316 | C2×C4 | C31×#121 | 1 | 1 | yes | characteristic |
| 317 | C2×C4 | C31×#123 | 1 | 1 | yes | characteristic |
| 318 | C2×C4 | C2×D8×C31 | 1 | 1 | yes | characteristic |
| 319 | C2×C4 | C31×#135 | 1 | 1 | yes | characteristic |
| 320 | C2×C4 | C31×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 321 | C8 | — | 4 | 2 | no | — |
| 322 | C8 | — | 4 | 1 | no | — |
| 323 | C8 | — | 8 | 1 | no | — |
| 324 | C8 | — | 8 | 1 | no | — |
| 325 | C8 | C31×#121 | 1 | 1 | yes | characteristic |
| 326 | C8 | C31×#121 | 1 | 1 | yes | characteristic |
| 327 | C8 | C31×#123 | 1 | 1 | yes | characteristic |
| 328 | C8 | C31×#124 | 1 | 1 | yes | characteristic |
| 329 | C22 | — | 4 | 1 | no | — |
| 330 | C22 | — | 4 | 1 | no | — |
| 331 | C22 | — | 8 | 1 | no | — |
| 332 | C22 | — | 8 | 1 | no | — |
| 333 | C22 | — | 16 | 1 | no | — |
| 334 | C22 | C31×#452 | 1 | 1 | yes | characteristic |
| 335 | C22 | C31×#468 | 1 | 1 | yes | characteristic |
| 336 | C22 | C31×#480 | 1 | 1 | yes | characteristic |
| 337 | C4 | — | 4 | 1 | no | — |
| 338 | C4 | — | 8 | 1 | no | — |
| 339 | C4 | C31×#394 | 1 | 1 | yes | characteristic |
| 340 | C4 | C31×#447 | 1 | 1 | yes | characteristic |
| 341 | C4 | C31×#466 | 1 | 1 | yes | characteristic |
| 342 | C4 | C31×#482 | 1 | 1 | yes | characteristic |
| 343 | C2 | — | 2 | 1 | no | — |
| 344 | C2 | — | 2 | 1 | no | — |
| 345 | C2 | — | 2 | 1 | no | — |
| 346 | C2 | — | 8 | 1 | no | — |
| 347 | C2 | — | 16 | 1 | no | — |
| 348 | C2 | C31×#2033 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta