| 1 | C31×#3175 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C31×#3155 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C31×#2250 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C31×#2249 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C31×#2243 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C31×#2240 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C31×#2211 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C31×#2210 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C31×#2207 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C31×#2206 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C31×#2189 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C31×#2187 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | C31×#2186 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C31×#2184 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C31×#2164 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C2×C31×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 17 | C2×C31×#135 | C22 | 1 | 1 | yes | characteristic |
| 18 | C22×D8×C31 | C22 | 1 | 1 | yes | characteristic |
| 19 | C31×#542 | — | 2 | 1 | no | — |
| 20 | C31×#535 | — | 2 | 1 | no | — |
| 21 | C2×C31×Q32 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | C2×C31×SD32 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×C31×SD32 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×C31×SD32 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | C2×C31×SD32 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | C2×C31×D16 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×C31×D16 | C22 | 1 | 1 | yes | characteristic |
| 28 | C2×C31×D16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | C31×#500 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | C31×#496 | — | 2 | 1 | no | — |
| 31 | C31×#496 | — | 2 | 1 | no | — |
| 32 | C31×#495 | C22 | 1 | 1 | yes | characteristic |
| 33 | C31×#495 | C22 | 1 | 1 | yes | characteristic |
| 34 | C31×#495 | C22 | 1 | 1 | yes | characteristic, complemented |
| 35 | C31×#493 | C22 | 1 | 1 | yes | characteristic |
| 36 | C31×#493 | C22 | 1 | 1 | yes | characteristic |
| 37 | C31×#489 | — | 2 | 1 | no | — |
| 38 | C31×#468 | — | 2 | 1 | no | — |
| 39 | C31×#467 | C22 | 1 | 1 | yes | characteristic |
| 40 | C31×#466 | C22 | 1 | 1 | yes | characteristic |
| 41 | C31×#440 | — | 2 | 1 | no | — |
| 42 | C4×Q16×C31 | C22 | 1 | 1 | yes | characteristic, complemented |
| 43 | C4×D8×C31 | C22 | 1 | 1 | yes | characteristic, complemented |
| 44 | C31×#405 | C22 | 1 | 1 | yes | characteristic |
| 45 | C31×C4⋊C16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 46 | C31×C4⋊C16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 47 | C31×#358 | C22 | 1 | 1 | yes | characteristic, complemented |
| 48 | C31×#358 | C22 | 1 | 1 | yes | characteristic, complemented |
| 49 | C31×#357 | C22 | 1 | 1 | yes | characteristic |
| 50 | C31×#357 | C22 | 1 | 1 | yes | characteristic |
| 51 | C31×#357 | C22 | 1 | 1 | yes | characteristic |
| 52 | C31×#357 | C22 | 1 | 1 | yes | characteristic |
| 53 | C31×#357 | C22 | 1 | 1 | yes | characteristic, complemented |
| 54 | C31×#357 | C22 | 1 | 1 | yes | characteristic, complemented |
| 55 | C31×C22⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 56 | C31×C22⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 57 | C31×#346 | C22 | 1 | 1 | yes | characteristic, complemented |
| 58 | C4×C16×C31 | C22 | 1 | 1 | yes | characteristic, complemented |
| 59 | C2×#41×C31 | — | 2 | 1 | no | — |
| 60 | C22×D4×C31 | — | 2 | 1 | no | — |
| 61 | C31×AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 62 | C31×#135 | — | 4 | 1 | no | — |
| 63 | C31×#135 | — | 4 | 1 | no | — |
| 64 | C2×Q16×C31 | C23 | 1 | 1 | yes | characteristic |
| 65 | C2×Q16×C31 | C23 | 1 | 1 | yes | characteristic |
| 66 | C2×SD16×C31 | — | 2 | 1 | no | — |
| 67 | C2×SD16×C31 | — | 2 | 1 | no | — |
| 68 | C2×SD16×C31 | — | 2 | 1 | no | — |
| 69 | C2×SD16×C31 | — | 2 | 1 | no | — |
| 70 | C2×D8×C31 | — | 2 | 1 | no | — |
| 71 | C2×D8×C31 | — | 2 | 1 | no | — |
| 72 | C2×D8×C31 | — | 2 | 1 | no | — |
| 73 | C2×D8×C31 | — | 4 | 1 | no | — |
| 74 | C2×D8×C31 | — | 4 | 1 | no | — |
| 75 | C2×D8×C31 | C23 | 1 | 1 | yes | characteristic |
| 76 | C2×D8×C31 | C23 | 1 | 1 | yes | characteristic |
| 77 | C2×D8×C31 | C23 | 1 | 1 | yes | characteristic |
| 78 | C2×D8×C31 | C23 | 1 | 1 | yes | characteristic |
| 79 | C2×M16×C31 | D4 | 1 | 1 | yes | characteristic |
| 80 | C22×C8×C31 | C23 | 1 | 1 | yes | characteristic |
| 81 | C31×C4⋊Q8 | — | 2 | 1 | no | — |
| 82 | C31×#127 | — | 2 | 1 | no | — |
| 83 | C31×#127 | — | 2 | 1 | no | — |
| 84 | C31×#126 | — | 4 | 1 | no | — |
| 85 | C31×#124 | — | 2 | 1 | no | — |
| 86 | C31×#124 | — | 2 | 1 | no | — |
| 87 | C31×#124 | — | 2 | 1 | no | — |
| 88 | C31×#124 | — | 4 | 1 | no | — |
| 89 | C31×#123 | — | 4 | 1 | no | — |
| 90 | C31×C22⋊Q8 | — | 2 | 1 | no | — |
| 91 | C31×C22⋊Q8 | — | 4 | 1 | no | — |
| 92 | C31×#121 | — | 2 | 1 | no | — |
| 93 | C31×#121 | — | 4 | 1 | no | — |
| 94 | C31×#121 | — | 4 | 1 | no | — |
| 95 | C31×#120 | — | 4 | 1 | no | — |
| 96 | C31×#120 | — | 4 | 1 | no | — |
| 97 | C4×Q8×C31 | — | 2 | 1 | no | — |
| 98 | C4×D4×C31 | — | 2 | 1 | no | — |
| 99 | C31×#117 | D4 | 1 | 1 | yes | characteristic |
| 100 | C31×Q32 | — | 4 | 1 | no | — |
| 101 | C31×SD32 | — | 4 | 1 | no | — |
| 102 | C31×SD32 | — | 4 | 1 | no | — |
| 103 | C31×SD32 | — | 4 | 1 | no | — |
| 104 | C31×SD32 | — | 4 | 1 | no | — |
| 105 | C31×D16 | — | 4 | 1 | no | — |
| 106 | C31×D16 | — | 4 | 1 | no | — |
| 107 | C31×D16 | — | 4 | 1 | no | — |
| 108 | C2×C16×C31 | C23 | 1 | 1 | yes | characteristic |
| 109 | C2×C16×C31 | C23 | 1 | 1 | yes | characteristic |
| 110 | C2×C16×C31 | C23 | 1 | 1 | yes | characteristic |
| 111 | C2×C16×C31 | C23 | 1 | 1 | yes | characteristic |
| 112 | C31×#107 | — | 2 | 1 | no | — |
| 113 | C31×#107 | C23 | 1 | 1 | yes | characteristic |
| 114 | C31×#107 | C23 | 1 | 1 | yes | characteristic |
| 115 | C31×#103 | — | 2 | 1 | no | — |
| 116 | C31×#103 | — | 2 | 1 | no | — |
| 117 | C31×#102 | — | 2 | 1 | no | — |
| 118 | C31×#102 | — | 2 | 1 | no | — |
| 119 | C31×#97 | D4 | 1 | 1 | yes | characteristic |
| 120 | C31×#97 | D4 | 1 | 1 | yes | characteristic |
| 121 | C4×C8×C31 | C23 | 1 | 1 | yes | characteristic |
| 122 | C4×C8×C31 | C23 | 1 | 1 | yes | characteristic |
| 123 | C24×C31 | — | 4 | 1 | no | — |
| 124 | #41×C31 | — | 4 | 2 | no | — |
| 125 | #41×C31 | — | 4 | 2 | no | — |
| 126 | C2×Q8×C31 | — | 2 | 1 | no | — |
| 127 | C2×Q8×C31 | — | 2 | 1 | no | — |
| 128 | C2×Q8×C31 | — | 4 | 1 | no | — |
| 129 | C2×D4×C31 | — | 2 | 1 | no | — |
| 130 | C2×D4×C31 | — | 2 | 1 | no | — |
| 131 | C2×D4×C31 | — | 2 | 1 | no | — |
| 132 | C2×D4×C31 | — | 2 | 1 | no | — |
| 133 | C2×D4×C31 | — | 4 | 2 | no | — |
| 134 | C2×D4×C31 | — | 4 | 2 | no | — |
| 135 | C2×D4×C31 | — | 4 | 1 | no | — |
| 136 | C2×D4×C31 | — | 4 | 1 | no | — |
| 137 | C2×D4×C31 | — | 4 | 1 | no | — |
| 138 | C2×D4×C31 | — | 4 | 1 | no | — |
| 139 | C2×D4×C31 | — | 4 | 1 | no | — |
| 140 | C2×D4×C31 | — | 4 | 1 | no | — |
| 141 | C2×D4×C31 | — | 4 | 1 | no | — |
| 142 | C22×C4×C31 | — | 4 | 1 | no | — |
| 143 | C22×C4×C31 | — | 4 | 1 | no | — |
| 144 | C22×C4×C31 | C2×D4 | 1 | 1 | yes | characteristic |
| 145 | Q16×C31 | — | 2 | 1 | no | — |
| 146 | Q16×C31 | — | 2 | 1 | no | — |
| 147 | Q16×C31 | — | 2 | 1 | no | — |
| 148 | Q16×C31 | — | 2 | 1 | no | — |
| 149 | SD16×C31 | — | 4 | 2 | no | — |
| 150 | SD16×C31 | — | 4 | 2 | no | — |
| 151 | SD16×C31 | — | 4 | 2 | no | — |
| 152 | SD16×C31 | — | 4 | 2 | no | — |
| 153 | D8×C31 | — | 2 | 1 | no | — |
| 154 | D8×C31 | — | 2 | 1 | no | — |
| 155 | D8×C31 | — | 2 | 1 | no | — |
| 156 | D8×C31 | — | 2 | 1 | no | — |
| 157 | D8×C31 | — | 2 | 1 | no | — |
| 158 | D8×C31 | — | 2 | 1 | no | — |
| 159 | D8×C31 | — | 2 | 1 | no | — |
| 160 | D8×C31 | — | 2 | 1 | no | — |
| 161 | D8×C31 | — | 4 | 2 | no | — |
| 162 | D8×C31 | — | 4 | 2 | no | — |
| 163 | D8×C31 | — | 4 | 2 | no | — |
| 164 | M16×C31 | — | 2 | 2 | no | — |
| 165 | C2×C8×C31 | — | 2 | 1 | no | — |
| 166 | C2×C8×C31 | — | 2 | 1 | no | — |
| 167 | C2×C8×C31 | C2×D4 | 1 | 1 | yes | characteristic |
| 168 | C2×C8×C31 | C2×D4 | 1 | 1 | yes | characteristic |
| 169 | C2×C8×C31 | C2×D4 | 1 | 1 | yes | characteristic |
| 170 | C2×C8×C31 | C24 | 1 | 1 | yes | characteristic |
| 171 | C4⋊C4×C31 | — | 2 | 1 | no | — |
| 172 | C4⋊C4×C31 | — | 2 | 1 | no | — |
| 173 | C4⋊C4×C31 | — | 4 | 1 | no | — |
| 174 | C4⋊C4×C31 | — | 4 | 1 | no | — |
| 175 | C4⋊C4×C31 | — | 4 | 1 | no | — |
| 176 | C4⋊C4×C31 | D8 | 1 | 1 | yes | characteristic |
| 177 | C4⋊C4×C31 | D8 | 1 | 1 | yes | characteristic |
| 178 | C22⋊C4×C31 | — | 4 | 1 | no | — |
| 179 | C22⋊C4×C31 | — | 4 | 1 | no | — |
| 180 | C22⋊C4×C31 | — | 4 | 1 | no | — |
| 181 | C22⋊C4×C31 | — | 4 | 1 | no | — |
| 182 | C22⋊C4×C31 | — | 4 | 1 | no | — |
| 183 | C22⋊C4×C31 | — | 4 | 1 | no | — |
| 184 | C22⋊C4×C31 | — | 4 | 1 | no | — |
| 185 | C22⋊C4×C31 | — | 4 | 1 | no | — |
| 186 | C22⋊C4×C31 | — | 4 | 1 | no | — |
| 187 | C22⋊C4×C31 | D8 | 1 | 1 | yes | characteristic |
| 188 | C22⋊C4×C31 | D8 | 1 | 1 | yes | characteristic |
| 189 | C42×C31 | — | 4 | 1 | no | — |
| 190 | C42×C31 | C2×D4 | 1 | 1 | yes | characteristic |
| 191 | C42×C31 | C2×D4 | 1 | 1 | yes | characteristic |
| 192 | C16×C31 | — | 2 | 1 | no | — |
| 193 | C16×C31 | — | 2 | 1 | no | — |
| 194 | C16×C31 | — | 2 | 1 | no | — |
| 195 | C16×C31 | — | 2 | 1 | no | — |
| 196 | #33790 | C31 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 197 | C23×C31 | — | 4 | 1 | no | — |
| 198 | C23×C31 | — | 4 | 1 | no | — |
| 199 | C23×C31 | — | 4 | 1 | no | — |
| 200 | C23×C31 | — | 4 | 1 | no | — |
| 201 | C23×C31 | — | 8 | 2 | no | — |
| 202 | C23×C31 | — | 16 | 1 | no | — |
| 203 | C23×C31 | — | 16 | 1 | no | — |
| 204 | C23×C31 | C2×D8 | 1 | 1 | yes | characteristic |
| 205 | Q8×C31 | — | 4 | 1 | no | — |
| 206 | Q8×C31 | — | 4 | 1 | no | — |
| 207 | Q8×C31 | — | 4 | 1 | no | — |
| 208 | Q8×C31 | — | 4 | 1 | no | — |
| 209 | Q8×C31 | — | 16 | 1 | no | — |
| 210 | D4×C31 | — | 4 | 1 | no | — |
| 211 | D4×C31 | — | 4 | 1 | no | — |
| 212 | D4×C31 | — | 4 | 1 | no | — |
| 213 | D4×C31 | — | 4 | 1 | no | — |
| 214 | D4×C31 | — | 4 | 1 | no | — |
| 215 | D4×C31 | — | 4 | 1 | no | — |
| 216 | D4×C31 | — | 4 | 1 | no | — |
| 217 | D4×C31 | — | 4 | 1 | no | — |
| 218 | D4×C31 | — | 8 | 2 | no | — |
| 219 | D4×C31 | — | 8 | 2 | no | — |
| 220 | D4×C31 | — | 16 | 1 | no | — |
| 221 | D4×C31 | — | 16 | 1 | no | — |
| 222 | D4×C31 | — | 16 | 1 | no | — |
| 223 | D4×C31 | — | 16 | 1 | no | — |
| 224 | D4×C31 | — | 16 | 1 | no | — |
| 225 | C2×C4×C31 | — | 2 | 1 | no | — |
| 226 | C2×C4×C31 | — | 2 | 1 | no | — |
| 227 | C2×C4×C31 | — | 4 | 1 | no | — |
| 228 | C2×C4×C31 | — | 4 | 1 | no | — |
| 229 | C2×C4×C31 | — | 4 | 1 | no | — |
| 230 | C2×C4×C31 | — | 4 | 1 | no | — |
| 231 | C2×C4×C31 | — | 8 | 2 | no | — |
| 232 | C2×C4×C31 | — | 16 | 1 | no | — |
| 233 | C2×C4×C31 | C2×D8 | 1 | 1 | yes | characteristic |
| 234 | C2×C4×C31 | C2×D8 | 1 | 1 | yes | characteristic |
| 235 | C2×C4×C31 | C2×D8 | 1 | 1 | yes | characteristic |
| 236 | C2×C4×C31 | C2×D8 | 1 | 1 | yes | characteristic |
| 237 | C2×C4×C31 | C2×D8 | 1 | 1 | yes | characteristic |
| 238 | C2×C4×C31 | C22×D4 | 1 | 1 | yes | characteristic |
| 239 | C8×C31 | — | 2 | 1 | no | — |
| 240 | C8×C31 | — | 2 | 1 | no | — |
| 241 | C8×C31 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 242 | C8×C31 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 243 | C8×C31 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 244 | #3175 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 245 | #3155 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 246 | #2250 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 247 | #2249 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 248 | #2243 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 249 | #2240 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 250 | #2211 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 251 | #2210 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 252 | #2207 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 253 | #2206 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 254 | #2189 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 255 | #2187 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 256 | #2186 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 257 | #2184 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 258 | #2164 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 259 | C22×C31 | — | 2 | 1 | no | — |
| 260 | C22×C31 | — | 2 | 1 | no | — |
| 261 | C22×C31 | — | 2 | 1 | no | — |
| 262 | C22×C31 | — | 8 | 1 | no | — |
| 263 | C22×C31 | — | 8 | 1 | no | — |
| 264 | C22×C31 | — | 8 | 1 | no | — |
| 265 | C22×C31 | — | 8 | 1 | no | — |
| 266 | C22×C31 | — | 8 | 1 | no | — |
| 267 | C22×C31 | — | 8 | 1 | no | — |
| 268 | C22×C31 | — | 8 | 1 | no | — |
| 269 | C22×C31 | — | 8 | 1 | no | — |
| 270 | C22×C31 | — | 8 | 1 | no | — |
| 271 | C22×C31 | — | 8 | 1 | no | — |
| 272 | C22×C31 | — | 8 | 1 | no | — |
| 273 | C22×C31 | — | 8 | 1 | no | — |
| 274 | C22×C31 | — | 16 | 4 | no | — |
| 275 | C22×C31 | C22×D8 | 1 | 1 | yes | characteristic |
| 276 | C4×C31 | — | 2 | 1 | no | — |
| 277 | C4×C31 | — | 2 | 1 | no | — |
| 278 | C4×C31 | — | 2 | 1 | no | — |
| 279 | C4×C31 | — | 2 | 1 | no | — |
| 280 | C4×C31 | — | 2 | 1 | no | — |
| 281 | C4×C31 | — | 8 | 1 | no | — |
| 282 | C4×C31 | — | 8 | 1 | no | — |
| 283 | C4×C31 | — | 8 | 1 | no | — |
| 284 | C4×C31 | — | 8 | 1 | no | — |
| 285 | C4×C31 | #535 | 1 | 1 | yes | characteristic |
| 286 | C4×C31 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 287 | C2×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 288 | C2×#135 | C22×C31 | 1 | 1 | yes | characteristic |
| 289 | C22×D8 | C22×C31 | 1 | 1 | yes | characteristic |
| 290 | #542 | — | 2 | 1 | no | — |
| 291 | #535 | — | 2 | 1 | no | — |
| 292 | C2×Q32 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 293 | C2×SD32 | C22×C31 | 1 | 1 | yes | characteristic |
| 294 | C2×SD32 | C22×C31 | 1 | 1 | yes | characteristic |
| 295 | C2×SD32 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 296 | C2×SD32 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 297 | C2×D16 | C22×C31 | 1 | 1 | yes | characteristic |
| 298 | C2×D16 | C22×C31 | 1 | 1 | yes | characteristic |
| 299 | C2×D16 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 300 | #500 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 301 | #496 | — | 2 | 1 | no | — |
| 302 | #496 | — | 2 | 1 | no | — |
| 303 | #495 | C22×C31 | 1 | 1 | yes | characteristic |
| 304 | #495 | C22×C31 | 1 | 1 | yes | characteristic |
| 305 | #495 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 306 | #493 | C22×C31 | 1 | 1 | yes | characteristic |
| 307 | #493 | C22×C31 | 1 | 1 | yes | characteristic |
| 308 | #489 | — | 2 | 1 | no | — |
| 309 | #468 | — | 2 | 1 | no | — |
| 310 | #467 | C22×C31 | 1 | 1 | yes | characteristic |
| 311 | #466 | C22×C31 | 1 | 1 | yes | characteristic |
| 312 | #440 | — | 2 | 1 | no | — |
| 313 | C4×Q16 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 314 | C4×D8 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 315 | #405 | C22×C31 | 1 | 1 | yes | characteristic |
| 316 | C4⋊C16 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 317 | C4⋊C16 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 318 | #358 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 319 | #358 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 320 | #357 | C22×C31 | 1 | 1 | yes | characteristic |
| 321 | #357 | C22×C31 | 1 | 1 | yes | characteristic |
| 322 | #357 | C22×C31 | 1 | 1 | yes | characteristic |
| 323 | #357 | C22×C31 | 1 | 1 | yes | characteristic |
| 324 | #357 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 325 | #357 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 326 | C22⋊C16 | C22×C31 | 1 | 1 | yes | characteristic |
| 327 | C22⋊C16 | C22×C31 | 1 | 1 | yes | characteristic |
| 328 | #346 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 329 | C4×C16 | C22×C31 | 1 | 1 | yes | characteristic, complemented |
| 330 | C2×C31 | — | 4 | 1 | no | — |
| 331 | C2×C31 | — | 16 | 1 | no | — |
| 332 | C2×C31 | — | 16 | 1 | no | — |
| 333 | C2×C31 | — | 16 | 1 | no | — |
| 334 | C2×C31 | — | 16 | 1 | no | — |
| 335 | C2×C31 | #3205 | 1 | 1 | yes | characteristic |
| 336 | C2×C31 | #3415 | 1 | 1 | yes | characteristic |
| 337 | C2×C31 | #3416 | 1 | 1 | yes | characteristic |
| 338 | C2×#41 | — | 2 | 1 | no | — |
| 339 | C22×D4 | — | 2 | 1 | no | — |
| 340 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 341 | #135 | — | 4 | 1 | no | — |
| 342 | #135 | — | 4 | 1 | no | — |
| 343 | C2×Q16 | C23×C31 | 1 | 1 | yes | characteristic |
| 344 | C2×Q16 | C23×C31 | 1 | 1 | yes | characteristic |
| 345 | C2×SD16 | — | 2 | 1 | no | — |
| 346 | C2×SD16 | — | 2 | 1 | no | — |
| 347 | C2×SD16 | — | 2 | 1 | no | — |
| 348 | C2×SD16 | — | 2 | 1 | no | — |
| 349 | C2×D8 | — | 2 | 1 | no | — |
| 350 | C2×D8 | — | 2 | 1 | no | — |
| 351 | C2×D8 | — | 2 | 1 | no | — |
| 352 | C2×D8 | — | 4 | 1 | no | — |
| 353 | C2×D8 | — | 4 | 1 | no | — |
| 354 | C2×D8 | C23×C31 | 1 | 1 | yes | characteristic |
| 355 | C2×D8 | C23×C31 | 1 | 1 | yes | characteristic |
| 356 | C2×D8 | C23×C31 | 1 | 1 | yes | characteristic |
| 357 | C2×D8 | C23×C31 | 1 | 1 | yes | characteristic |
| 358 | C2×M16 | D4×C31 | 1 | 1 | yes | characteristic |
| 359 | C22×C8 | C23×C31 | 1 | 1 | yes | characteristic |
| 360 | C4⋊Q8 | — | 2 | 1 | no | — |
| 361 | #127 | — | 2 | 1 | no | — |
| 362 | #127 | — | 2 | 1 | no | — |
| 363 | #126 | — | 4 | 1 | no | — |
| 364 | #124 | — | 2 | 1 | no | — |
| 365 | #124 | — | 2 | 1 | no | — |
| 366 | #124 | — | 2 | 1 | no | — |
| 367 | #124 | — | 4 | 1 | no | — |
| 368 | #123 | — | 4 | 1 | no | — |
| 369 | C22⋊Q8 | — | 2 | 1 | no | — |
| 370 | C22⋊Q8 | — | 4 | 1 | no | — |
| 371 | #121 | — | 2 | 1 | no | — |
| 372 | #121 | — | 4 | 1 | no | — |
| 373 | #121 | — | 4 | 1 | no | — |
| 374 | #120 | — | 4 | 1 | no | — |
| 375 | #120 | — | 4 | 1 | no | — |
| 376 | C4×Q8 | — | 2 | 1 | no | — |
| 377 | C4×D4 | — | 2 | 1 | no | — |
| 378 | #117 | D4×C31 | 1 | 1 | yes | characteristic |
| 379 | Q32 | — | 4 | 1 | no | — |
| 380 | SD32 | — | 4 | 1 | no | — |
| 381 | SD32 | — | 4 | 1 | no | — |
| 382 | SD32 | — | 4 | 1 | no | — |
| 383 | SD32 | — | 4 | 1 | no | — |
| 384 | D16 | — | 4 | 1 | no | — |
| 385 | D16 | — | 4 | 1 | no | — |
| 386 | D16 | — | 4 | 1 | no | — |
| 387 | C2×C16 | C23×C31 | 1 | 1 | yes | characteristic |
| 388 | C2×C16 | C23×C31 | 1 | 1 | yes | characteristic |
| 389 | C2×C16 | C23×C31 | 1 | 1 | yes | characteristic |
| 390 | C2×C16 | C23×C31 | 1 | 1 | yes | characteristic |
| 391 | #107 | — | 2 | 1 | no | — |
| 392 | #107 | C23×C31 | 1 | 1 | yes | characteristic |
| 393 | #107 | C23×C31 | 1 | 1 | yes | characteristic |
| 394 | #103 | — | 2 | 1 | no | — |
| 395 | #103 | — | 2 | 1 | no | — |
| 396 | #102 | — | 2 | 1 | no | — |
| 397 | #102 | — | 2 | 1 | no | — |
| 398 | #97 | D4×C31 | 1 | 1 | yes | characteristic |
| 399 | #97 | D4×C31 | 1 | 1 | yes | characteristic |
| 400 | C4×C8 | C23×C31 | 1 | 1 | yes | characteristic |
| 401 | C4×C8 | C23×C31 | 1 | 1 | yes | characteristic |
| 402 | C31 | #33790 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 403 | C24 | — | 4 | 1 | no | — |
| 404 | #41 | — | 4 | 2 | no | — |
| 405 | #41 | — | 4 | 2 | no | — |
| 406 | C2×Q8 | — | 2 | 1 | no | — |
| 407 | C2×Q8 | — | 2 | 1 | no | — |
| 408 | C2×Q8 | — | 4 | 1 | no | — |
| 409 | C2×D4 | — | 2 | 1 | no | — |
| 410 | C2×D4 | — | 2 | 1 | no | — |
| 411 | C2×D4 | — | 2 | 1 | no | — |
| 412 | C2×D4 | — | 2 | 1 | no | — |
| 413 | C2×D4 | — | 4 | 2 | no | — |
| 414 | C2×D4 | — | 4 | 2 | no | — |
| 415 | C2×D4 | — | 4 | 1 | no | — |
| 416 | C2×D4 | — | 4 | 1 | no | — |
| 417 | C2×D4 | — | 4 | 1 | no | — |
| 418 | C2×D4 | — | 4 | 1 | no | — |
| 419 | C2×D4 | — | 4 | 1 | no | — |
| 420 | C2×D4 | — | 4 | 1 | no | — |
| 421 | C2×D4 | — | 4 | 1 | no | — |
| 422 | C22×C4 | — | 4 | 1 | no | — |
| 423 | C22×C4 | — | 4 | 1 | no | — |
| 424 | C22×C4 | C2×D4×C31 | 1 | 1 | yes | characteristic |
| 425 | Q16 | — | 2 | 1 | no | — |
| 426 | Q16 | — | 2 | 1 | no | — |
| 427 | Q16 | — | 2 | 1 | no | — |
| 428 | Q16 | — | 2 | 1 | no | — |
| 429 | SD16 | — | 4 | 2 | no | — |
| 430 | SD16 | — | 4 | 2 | no | — |
| 431 | SD16 | — | 4 | 2 | no | — |
| 432 | SD16 | — | 4 | 2 | no | — |
| 433 | D8 | — | 2 | 1 | no | — |
| 434 | D8 | — | 2 | 1 | no | — |
| 435 | D8 | — | 2 | 1 | no | — |
| 436 | D8 | — | 2 | 1 | no | — |
| 437 | D8 | — | 2 | 1 | no | — |
| 438 | D8 | — | 2 | 1 | no | — |
| 439 | D8 | — | 2 | 1 | no | — |
| 440 | D8 | — | 2 | 1 | no | — |
| 441 | D8 | — | 4 | 2 | no | — |
| 442 | D8 | — | 4 | 2 | no | — |
| 443 | D8 | — | 4 | 2 | no | — |
| 444 | M16 | — | 2 | 2 | no | — |
| 445 | C2×C8 | — | 2 | 1 | no | — |
| 446 | C2×C8 | — | 2 | 1 | no | — |
| 447 | C2×C8 | C2×D4×C31 | 1 | 1 | yes | characteristic |
| 448 | C2×C8 | C2×D4×C31 | 1 | 1 | yes | characteristic |
| 449 | C2×C8 | C2×D4×C31 | 1 | 1 | yes | characteristic |
| 450 | C2×C8 | C24×C31 | 1 | 1 | yes | characteristic |
| 451 | C4⋊C4 | — | 2 | 1 | no | — |
| 452 | C4⋊C4 | — | 2 | 1 | no | — |
| 453 | C4⋊C4 | — | 4 | 1 | no | — |
| 454 | C4⋊C4 | — | 4 | 1 | no | — |
| 455 | C4⋊C4 | — | 4 | 1 | no | — |
| 456 | C4⋊C4 | D8×C31 | 1 | 1 | yes | characteristic |
| 457 | C4⋊C4 | D8×C31 | 1 | 1 | yes | characteristic |
| 458 | C22⋊C4 | — | 4 | 1 | no | — |
| 459 | C22⋊C4 | — | 4 | 1 | no | — |
| 460 | C22⋊C4 | — | 4 | 1 | no | — |
| 461 | C22⋊C4 | — | 4 | 1 | no | — |
| 462 | C22⋊C4 | — | 4 | 1 | no | — |
| 463 | C22⋊C4 | — | 4 | 1 | no | — |
| 464 | C22⋊C4 | — | 4 | 1 | no | — |
| 465 | C22⋊C4 | — | 4 | 1 | no | — |
| 466 | C22⋊C4 | — | 4 | 1 | no | — |
| 467 | C22⋊C4 | D8×C31 | 1 | 1 | yes | characteristic |
| 468 | C22⋊C4 | D8×C31 | 1 | 1 | yes | characteristic |
| 469 | C42 | — | 4 | 1 | no | — |
| 470 | C42 | C2×D4×C31 | 1 | 1 | yes | characteristic |
| 471 | C42 | C2×D4×C31 | 1 | 1 | yes | characteristic |
| 472 | C16 | — | 2 | 1 | no | — |
| 473 | C16 | — | 2 | 1 | no | — |
| 474 | C16 | — | 2 | 1 | no | — |
| 475 | C16 | — | 2 | 1 | no | — |
| 476 | C23 | — | 4 | 1 | no | — |
| 477 | C23 | — | 4 | 1 | no | — |
| 478 | C23 | — | 4 | 1 | no | — |
| 479 | C23 | — | 4 | 1 | no | — |
| 480 | C23 | — | 8 | 2 | no | — |
| 481 | C23 | — | 16 | 1 | no | — |
| 482 | C23 | — | 16 | 1 | no | — |
| 483 | C23 | C2×D8×C31 | 1 | 1 | yes | characteristic |
| 484 | Q8 | — | 4 | 1 | no | — |
| 485 | Q8 | — | 4 | 1 | no | — |
| 486 | Q8 | — | 4 | 1 | no | — |
| 487 | Q8 | — | 4 | 1 | no | — |
| 488 | Q8 | — | 16 | 1 | no | — |
| 489 | D4 | — | 4 | 1 | no | — |
| 490 | D4 | — | 4 | 1 | no | — |
| 491 | D4 | — | 4 | 1 | no | — |
| 492 | D4 | — | 4 | 1 | no | — |
| 493 | D4 | — | 4 | 1 | no | — |
| 494 | D4 | — | 4 | 1 | no | — |
| 495 | D4 | — | 4 | 1 | no | — |
| 496 | D4 | — | 4 | 1 | no | — |
| 497 | D4 | — | 8 | 2 | no | — |
| 498 | D4 | — | 8 | 2 | no | — |
| 499 | D4 | — | 16 | 1 | no | — |
| 500 | D4 | — | 16 | 1 | no | — |
| 501 | D4 | — | 16 | 1 | no | — |
| 502 | D4 | — | 16 | 1 | no | — |
| 503 | D4 | — | 16 | 1 | no | — |
| 504 | C2×C4 | — | 2 | 1 | no | — |
| 505 | C2×C4 | — | 2 | 1 | no | — |
| 506 | C2×C4 | — | 4 | 1 | no | — |
| 507 | C2×C4 | — | 4 | 1 | no | — |
| 508 | C2×C4 | — | 4 | 1 | no | — |
| 509 | C2×C4 | — | 4 | 1 | no | — |
| 510 | C2×C4 | — | 8 | 2 | no | — |
| 511 | C2×C4 | — | 16 | 1 | no | — |
| 512 | C2×C4 | C2×D8×C31 | 1 | 1 | yes | characteristic |
| 513 | C2×C4 | C2×D8×C31 | 1 | 1 | yes | characteristic |
| 514 | C2×C4 | C2×D8×C31 | 1 | 1 | yes | characteristic |
| 515 | C2×C4 | C2×D8×C31 | 1 | 1 | yes | characteristic |
| 516 | C2×C4 | C2×D8×C31 | 1 | 1 | yes | characteristic |
| 517 | C2×C4 | C22×D4×C31 | 1 | 1 | yes | characteristic |
| 518 | C8 | — | 2 | 1 | no | — |
| 519 | C8 | — | 2 | 1 | no | — |
| 520 | C8 | C31×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 521 | C8 | C31×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 522 | C8 | C31×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 523 | C22 | — | 2 | 1 | no | — |
| 524 | C22 | — | 2 | 1 | no | — |
| 525 | C22 | — | 2 | 1 | no | — |
| 526 | C22 | — | 8 | 1 | no | — |
| 527 | C22 | — | 8 | 1 | no | — |
| 528 | C22 | — | 8 | 1 | no | — |
| 529 | C22 | — | 8 | 1 | no | — |
| 530 | C22 | — | 8 | 1 | no | — |
| 531 | C22 | — | 8 | 1 | no | — |
| 532 | C22 | — | 8 | 1 | no | — |
| 533 | C22 | — | 8 | 1 | no | — |
| 534 | C22 | — | 8 | 1 | no | — |
| 535 | C22 | — | 8 | 1 | no | — |
| 536 | C22 | — | 8 | 1 | no | — |
| 537 | C22 | — | 8 | 1 | no | — |
| 538 | C22 | — | 16 | 4 | no | — |
| 539 | C22 | C22×D8×C31 | 1 | 1 | yes | characteristic |
| 540 | C4 | — | 2 | 1 | no | — |
| 541 | C4 | — | 2 | 1 | no | — |
| 542 | C4 | — | 2 | 1 | no | — |
| 543 | C4 | — | 2 | 1 | no | — |
| 544 | C4 | — | 2 | 1 | no | — |
| 545 | C4 | — | 8 | 1 | no | — |
| 546 | C4 | — | 8 | 1 | no | — |
| 547 | C4 | — | 8 | 1 | no | — |
| 548 | C4 | — | 8 | 1 | no | — |
| 549 | C4 | C31×#535 | 1 | 1 | yes | characteristic |
| 550 | C4 | C2×C31×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 551 | C2 | — | 4 | 1 | no | — |
| 552 | C2 | — | 16 | 1 | no | — |
| 553 | C2 | — | 16 | 1 | no | — |
| 554 | C2 | — | 16 | 1 | no | — |
| 555 | C2 | — | 16 | 1 | no | — |
| 556 | C2 | C31×#3205 | 1 | 1 | yes | characteristic |
| 557 | C2 | C31×#3415 | 1 | 1 | yes | characteristic |
| 558 | C2 | C31×#3416 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta