| 1 | #22598299 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22597877 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #22597224 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22596935 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22589872 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22589852 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #22589785 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #22589549 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #22589003 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #22588940 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #22588848 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #22588714 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #22588568 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #22588568 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C71×#1876 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C2×#14556153 | C22 | 1 | 1 | yes | characteristic |
| 17 | #17986563 | C22 | 1 | 1 | yes | characteristic |
| 18 | #17986482 | C22 | 1 | 1 | yes | characteristic |
| 19 | #17986482 | C22 | 1 | 1 | yes | characteristic |
| 20 | #17986482 | C22 | 1 | 1 | yes | characteristic |
| 21 | #17986324 | — | 2 | 1 | no | — |
| 22 | #17986324 | — | 2 | 1 | no | — |
| 23 | #17986318 | — | 2 | 1 | no | — |
| 24 | #17986313 | — | 2 | 1 | no | — |
| 25 | #17986223 | — | 2 | 1 | no | — |
| 26 | #17986216 | — | 2 | 1 | no | — |
| 27 | #17986197 | — | 2 | 1 | no | — |
| 28 | #17986192 | — | 2 | 1 | no | — |
| 29 | #17986111 | — | 2 | 1 | no | — |
| 30 | #17986106 | — | 2 | 1 | no | — |
| 31 | SD16×Dic71 | — | 2 | 1 | no | — |
| 32 | SD16×Dic71 | — | 2 | 1 | no | — |
| 33 | #17986041 | — | 2 | 1 | no | — |
| 34 | #17986041 | — | 2 | 1 | no | — |
| 35 | #17986041 | C22 | 1 | 1 | yes | characteristic |
| 36 | #17986041 | C22 | 1 | 1 | yes | characteristic |
| 37 | #17986041 | C22 | 1 | 1 | yes | characteristic |
| 38 | #17986037 | — | 2 | 1 | no | — |
| 39 | #17986037 | C22 | 1 | 1 | yes | characteristic |
| 40 | C2×#14556060 | — | 2 | 1 | no | — |
| 41 | C2×#14556060 | C22 | 1 | 1 | yes | characteristic |
| 42 | C2×#14556060 | C22 | 1 | 1 | yes | characteristic |
| 43 | #17986025 | C22 | 1 | 1 | yes | characteristic |
| 44 | #17986005 | C22 | 1 | 1 | yes | characteristic |
| 45 | #17986000 | C22 | 1 | 1 | yes | characteristic |
| 46 | #17986000 | C22 | 1 | 1 | yes | characteristic |
| 47 | #17986000 | C22 | 1 | 1 | yes | characteristic |
| 48 | C2×#14556050 | C22 | 1 | 1 | yes | characteristic |
| 49 | C2×#14556050 | C22 | 1 | 1 | yes | characteristic |
| 50 | C2×#14556044 | C22 | 1 | 1 | yes | characteristic |
| 51 | #17985954 | C22 | 1 | 1 | yes | characteristic |
| 52 | #17985901 | C22 | 1 | 1 | yes | characteristic |
| 53 | #17985869 | C22 | 1 | 1 | yes | characteristic |
| 54 | #17985767 | C22 | 1 | 1 | yes | characteristic |
| 55 | #17985767 | C22 | 1 | 1 | yes | characteristic |
| 56 | #17985767 | C22 | 1 | 1 | yes | characteristic |
| 57 | #17985764 | C22 | 1 | 1 | yes | characteristic |
| 58 | #17985759 | C22 | 1 | 1 | yes | characteristic |
| 59 | #17985759 | C22 | 1 | 1 | yes | characteristic |
| 60 | C2×#135×C71 | C22 | 1 | 1 | yes | characteristic |
| 61 | C2×#131×C71 | C22 | 1 | 1 | yes | characteristic |
| 62 | C2×#104×C71 | C22 | 1 | 1 | yes | characteristic |
| 63 | C2×#104×C71 | C22 | 1 | 1 | yes | characteristic |
| 64 | #408×C71 | C22 | 1 | 1 | yes | characteristic |
| 65 | #341×C71 | C22 | 1 | 1 | yes | characteristic |
| 66 | #336×C71 | C22 | 1 | 1 | yes | characteristic |
| 67 | C22×D284 | C23 | 1 | 1 | yes | characteristic |
| 68 | #14556153 | — | 2 | 2 | no | — |
| 69 | #14556153 | — | 2 | 2 | no | — |
| 70 | C2×#11765852 | — | 2 | 1 | no | — |
| 71 | C2×#11765850 | — | 2 | 1 | no | — |
| 72 | C2×#11765849 | C23 | 1 | 1 | yes | characteristic |
| 73 | C2×#11765849 | C23 | 1 | 1 | yes | characteristic |
| 74 | #14556124 | — | 2 | 1 | no | — |
| 75 | #14556117 | — | 2 | 1 | no | — |
| 76 | #14556102 | — | 2 | 1 | no | — |
| 77 | #14556102 | — | 2 | 1 | no | — |
| 78 | #14556096 | — | 4 | 1 | no | — |
| 79 | Q8×Dic71 | — | 2 | 1 | no | — |
| 80 | Q8×Dic71 | — | 2 | 1 | no | — |
| 81 | Q8×Dic71 | — | 2 | 1 | no | — |
| 82 | D4×Dic71 | — | 2 | 1 | no | — |
| 83 | D4×Dic71 | — | 2 | 1 | no | — |
| 84 | D4×Dic71 | — | 2 | 1 | no | — |
| 85 | D4×Dic71 | — | 4 | 1 | no | — |
| 86 | D4×Dic71 | — | 4 | 1 | no | — |
| 87 | D4×Dic71 | — | 4 | 1 | no | — |
| 88 | #14556087 | — | 2 | 1 | no | — |
| 89 | #14556087 | — | 2 | 1 | no | — |
| 90 | #14556087 | — | 2 | 1 | no | — |
| 91 | #14556087 | C23 | 1 | 1 | yes | characteristic |
| 92 | #14556087 | C23 | 1 | 1 | yes | characteristic |
| 93 | C2×C4⋊Dic71 | — | 2 | 1 | no | — |
| 94 | C2×C4⋊Dic71 | — | 2 | 1 | no | — |
| 95 | C2×C4⋊Dic71 | — | 2 | 1 | no | — |
| 96 | C2×C4⋊Dic71 | — | 4 | 1 | no | — |
| 97 | C2×C4⋊Dic71 | C23 | 1 | 1 | yes | characteristic |
| 98 | C2×C4⋊Dic71 | C23 | 1 | 1 | yes | characteristic |
| 99 | C2×C4⋊Dic71 | C23 | 1 | 1 | yes | characteristic |
| 100 | C2×(C2×D71)⋊C4 | — | 4 | 1 | no | — |
| 101 | #14556062 | — | 2 | 1 | no | — |
| 102 | #14556062 | — | 2 | 1 | no | — |
| 103 | #14556062 | — | 2 | 1 | no | — |
| 104 | #14556062 | D4 | 1 | 1 | yes | characteristic |
| 105 | #14556062 | D4 | 1 | 1 | yes | characteristic |
| 106 | #14556060 | — | 2 | 1 | no | — |
| 107 | #14556060 | — | 2 | 1 | no | — |
| 108 | #14556060 | — | 2 | 1 | no | — |
| 109 | #14556060 | — | 2 | 1 | no | — |
| 110 | #14556060 | — | 2 | 1 | no | — |
| 111 | #14556060 | — | 2 | 1 | no | — |
| 112 | #14556060 | — | 2 | 1 | no | — |
| 113 | #14556060 | D4 | 1 | 1 | yes | characteristic |
| 114 | #14556060 | D4 | 1 | 1 | yes | characteristic |
| 115 | Dic71⋊C8 | — | 2 | 1 | no | — |
| 116 | Dic71⋊C8 | — | 2 | 1 | no | — |
| 117 | #14556052 | — | 2 | 1 | no | — |
| 118 | #14556052 | — | 2 | 1 | no | — |
| 119 | #14556052 | — | 2 | 1 | no | — |
| 120 | #14556050 | — | 2 | 1 | no | — |
| 121 | #14556050 | — | 2 | 1 | no | — |
| 122 | #14556050 | — | 2 | 1 | no | — |
| 123 | #14556050 | — | 2 | 1 | no | — |
| 124 | #14556050 | — | 2 | 1 | no | — |
| 125 | #14556050 | — | 2 | 1 | no | — |
| 126 | #14556049 | — | 2 | 1 | no | — |
| 127 | #14556049 | — | 2 | 1 | no | — |
| 128 | #14556049 | — | 2 | 1 | no | — |
| 129 | #14556044 | — | 2 | 2 | no | — |
| 130 | #14556038 | — | 2 | 1 | no | — |
| 131 | C8×Dic71 | — | 2 | 1 | no | — |
| 132 | C2×#41×C71 | C23 | 1 | 1 | yes | characteristic |
| 133 | C2×#41×C71 | C23 | 1 | 1 | yes | characteristic |
| 134 | #135×C71 | — | 2 | 2 | no | — |
| 135 | #135×C71 | — | 2 | 2 | no | — |
| 136 | C2×Q16×C71 | D4 | 1 | 1 | yes | characteristic |
| 137 | C2×SD16×C71 | D4 | 1 | 1 | yes | characteristic |
| 138 | C2×SD16×C71 | D4 | 1 | 1 | yes | characteristic |
| 139 | C2×D8×C71 | D4 | 1 | 1 | yes | characteristic |
| 140 | #131×C71 | — | 2 | 2 | no | — |
| 141 | #131×C71 | — | 2 | 2 | no | — |
| 142 | C2×M16×C71 | — | 2 | 1 | no | — |
| 143 | C2×M16×C71 | C23 | 1 | 1 | yes | characteristic |
| 144 | C2×M16×C71 | C23 | 1 | 1 | yes | characteristic |
| 145 | C22×C8×C71 | — | 2 | 1 | no | — |
| 146 | C22×C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 147 | C22×C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 148 | C2×C42×C71 | C23 | 1 | 1 | yes | characteristic |
| 149 | #104×C71 | — | 2 | 2 | no | — |
| 150 | #104×C71 | — | 2 | 2 | no | — |
| 151 | C22⋊C8×C71 | — | 2 | 1 | no | — |
| 152 | C22⋊C8×C71 | — | 2 | 1 | no | — |
| 153 | C23×D71 | — | 2 | 1 | no | — |
| 154 | C2×D284 | — | 2 | 1 | no | — |
| 155 | C2×D284 | — | 2 | 1 | no | — |
| 156 | C2×D284 | — | 2 | 1 | no | — |
| 157 | C2×D284 | — | 2 | 1 | no | — |
| 158 | C2×D284 | — | 2 | 1 | no | — |
| 159 | C2×D284 | — | 2 | 1 | no | — |
| 160 | C2×C22⋊D71 | — | 4 | 1 | no | — |
| 161 | C2×C22⋊D71 | — | 4 | 1 | no | — |
| 162 | C22×Dic71 | — | 2 | 1 | no | — |
| 163 | C22×Dic71 | — | 2 | 1 | no | — |
| 164 | C22×Dic71 | — | 2 | 1 | no | — |
| 165 | C22×Dic71 | — | 4 | 1 | no | — |
| 166 | C22×Dic71 | — | 4 | 1 | no | — |
| 167 | C22×Dic71 | — | 4 | 1 | no | — |
| 168 | #11765852 | — | 4 | 2 | no | — |
| 169 | #11765850 | — | 4 | 2 | no | — |
| 170 | #11765849 | — | 2 | 1 | no | — |
| 171 | #11765849 | — | 2 | 1 | no | — |
| 172 | #11765849 | — | 2 | 1 | no | — |
| 173 | #11765849 | — | 2 | 1 | no | — |
| 174 | C2×C71⋊C8 | — | 2 | 1 | no | — |
| 175 | C2×C71⋊C8 | — | 2 | 1 | no | — |
| 176 | C4⋊Dic71 | — | 2 | 1 | no | — |
| 177 | C4⋊Dic71 | — | 2 | 1 | no | — |
| 178 | C4⋊Dic71 | — | 2 | 1 | no | — |
| 179 | C4⋊Dic71 | — | 2 | 1 | no | — |
| 180 | C4⋊Dic71 | — | 2 | 1 | no | — |
| 181 | C4⋊Dic71 | — | 2 | 1 | no | — |
| 182 | C4⋊Dic71 | — | 4 | 1 | no | — |
| 183 | C4⋊Dic71 | — | 4 | 1 | no | — |
| 184 | C4⋊Dic71 | — | 4 | 1 | no | — |
| 185 | C4⋊Dic71 | — | 8 | 2 | no | — |
| 186 | C4⋊Dic71 | C2×D4 | 1 | 1 | yes | characteristic |
| 187 | C4⋊Dic71 | C2×D4 | 1 | 1 | yes | characteristic |
| 188 | C4⋊Dic71 | C2×D4 | 1 | 1 | yes | characteristic |
| 189 | C4⋊Dic71 | C2×D4 | 1 | 1 | yes | characteristic |
| 190 | C22⋊Dic71 | — | 2 | 1 | no | — |
| 191 | C22⋊Dic71 | — | 2 | 1 | no | — |
| 192 | C22⋊Dic71 | — | 4 | 1 | no | — |
| 193 | C22⋊Dic71 | — | 4 | 1 | no | — |
| 194 | C22⋊Dic71 | — | 4 | 1 | no | — |
| 195 | (C2×D71)⋊C4 | — | 4 | 1 | no | — |
| 196 | (C2×D71)⋊C4 | — | 4 | 1 | no | — |
| 197 | (C2×D71)⋊C4 | — | 8 | 2 | no | — |
| 198 | C4×Dic71 | — | 2 | 1 | no | — |
| 199 | C4×Dic71 | — | 2 | 1 | no | — |
| 200 | C4×Dic71 | — | 4 | 1 | no | — |
| 201 | C4×Dic71 | — | 4 | 1 | no | — |
| 202 | C4×Dic71 | — | 4 | 1 | no | — |
| 203 | #41×C71 | — | 2 | 1 | no | — |
| 204 | #41×C71 | — | 2 | 1 | no | — |
| 205 | #41×C71 | — | 2 | 1 | no | — |
| 206 | #41×C71 | — | 2 | 1 | no | — |
| 207 | #41×C71 | — | 2 | 1 | no | — |
| 208 | #41×C71 | — | 2 | 1 | no | — |
| 209 | #41×C71 | #41 | 1 | 2 | yes | — |
| 210 | #41×C71 | #41 | 1 | 2 | yes | — |
| 211 | C2×Q8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 212 | C2×Q8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 213 | C2×D4×C71 | — | 2 | 1 | no | — |
| 214 | C2×D4×C71 | — | 2 | 1 | no | — |
| 215 | C2×D4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 216 | C2×D4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 217 | C22×C4×C71 | — | 2 | 1 | no | — |
| 218 | C22×C4×C71 | — | 2 | 1 | no | — |
| 219 | C22×C4×C71 | — | 2 | 1 | no | — |
| 220 | C22×C4×C71 | C24 | 1 | 1 | yes | characteristic |
| 221 | Q16×C71 | — | 2 | 2 | no | — |
| 222 | SD16×C71 | — | 2 | 2 | no | — |
| 223 | SD16×C71 | — | 2 | 2 | no | — |
| 224 | D8×C71 | — | 2 | 2 | no | — |
| 225 | M16×C71 | — | 2 | 4 | no | — |
| 226 | M16×C71 | — | 2 | 1 | no | — |
| 227 | M16×C71 | — | 2 | 1 | no | — |
| 228 | M16×C71 | — | 2 | 1 | no | — |
| 229 | M16×C71 | #41 | 1 | 2 | yes | — |
| 230 | C2×C8×C71 | — | 2 | 4 | no | — |
| 231 | C2×C8×C71 | — | 2 | 1 | no | — |
| 232 | C2×C8×C71 | — | 2 | 1 | no | — |
| 233 | C2×C8×C71 | — | 2 | 1 | no | — |
| 234 | C2×C8×C71 | — | 2 | 1 | no | — |
| 235 | C2×C8×C71 | — | 2 | 1 | no | — |
| 236 | C2×C8×C71 | — | 2 | 1 | no | — |
| 237 | C2×C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 238 | C2×C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 239 | C2×C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 240 | C2×C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 241 | C42×C71 | — | 2 | 1 | no | — |
| 242 | C42×C71 | — | 2 | 1 | no | — |
| 243 | C23×C71 | — | 2 | 1 | no | — |
| 244 | C23×C71 | — | 2 | 1 | no | — |
| 245 | C23×C71 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 246 | C22×D71 | — | 4 | 1 | no | — |
| 247 | C22×D71 | — | 4 | 1 | no | — |
| 248 | C22×D71 | — | 4 | 1 | no | — |
| 249 | C22×D71 | — | 8 | 1 | no | — |
| 250 | C22×D71 | — | 8 | 1 | no | — |
| 251 | Q8×C71 | — | 2 | 1 | no | — |
| 252 | Q8×C71 | — | 2 | 1 | no | — |
| 253 | Q8×C71 | — | 2 | 1 | no | — |
| 254 | Q8×C71 | #123 | 1 | 2 | yes | — |
| 255 | D4×C71 | — | 2 | 2 | no | — |
| 256 | D4×C71 | — | 2 | 2 | no | — |
| 257 | D4×C71 | — | 2 | 1 | no | — |
| 258 | D4×C71 | — | 2 | 1 | no | — |
| 259 | D4×C71 | — | 2 | 1 | no | — |
| 260 | D4×C71 | — | 4 | 1 | no | — |
| 261 | D4×C71 | — | 4 | 1 | no | — |
| 262 | D4×C71 | #123 | 1 | 2 | yes | — |
| 263 | C2×C4×C71 | — | 2 | 1 | no | — |
| 264 | C2×C4×C71 | — | 2 | 2 | no | — |
| 265 | C2×C4×C71 | — | 2 | 2 | no | — |
| 266 | C2×C4×C71 | — | 2 | 2 | no | — |
| 267 | C2×C4×C71 | — | 2 | 1 | no | — |
| 268 | C2×C4×C71 | — | 4 | 1 | no | — |
| 269 | C2×C4×C71 | — | 4 | 1 | no | — |
| 270 | C2×C4×C71 | — | 4 | 1 | no | — |
| 271 | C2×C4×C71 | — | 4 | 1 | no | — |
| 272 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 273 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 274 | C2×C4×C71 | C2×#41 | 1 | 1 | yes | characteristic |
| 275 | C2×C4×C71 | C2×#41 | 1 | 1 | yes | characteristic |
| 276 | C2×C4×C71 | C2×#41 | 1 | 1 | yes | characteristic |
| 277 | C2×C4×C71 | 2−1+4 | 1 | 1 | yes | characteristic |
| 278 | C22⋊D71 | — | 16 | 1 | no | — |
| 279 | C22⋊D71 | — | 16 | 1 | no | — |
| 280 | C2×Dic71 | — | 2 | 1 | no | — |
| 281 | C2×Dic71 | — | 2 | 1 | no | — |
| 282 | C2×Dic71 | — | 2 | 1 | no | — |
| 283 | C2×Dic71 | — | 2 | 1 | no | — |
| 284 | C2×Dic71 | — | 4 | 1 | no | — |
| 285 | C2×Dic71 | — | 4 | 1 | no | — |
| 286 | C2×Dic71 | — | 4 | 1 | no | — |
| 287 | C2×Dic71 | — | 8 | 1 | no | — |
| 288 | C2×Dic71 | — | 8 | 1 | no | — |
| 289 | C2×Dic71 | — | 8 | 1 | no | — |
| 290 | C2×Dic71 | — | 16 | 1 | no | — |
| 291 | C2×Dic71 | — | 16 | 1 | no | — |
| 292 | C2×Dic71 | — | 16 | 1 | no | — |
| 293 | D284 | — | 4 | 1 | no | — |
| 294 | D284 | — | 4 | 1 | no | — |
| 295 | D284 | — | 4 | 1 | no | — |
| 296 | D284 | — | 4 | 1 | no | — |
| 297 | C8×C71 | — | 2 | 1 | no | — |
| 298 | C8×C71 | — | 2 | 1 | no | — |
| 299 | C8×C71 | — | 2 | 1 | no | — |
| 300 | C8×C71 | — | 2 | 2 | no | — |
| 301 | C8×C71 | — | 2 | 1 | no | — |
| 302 | C8×C71 | — | 4 | 1 | no | — |
| 303 | C71⋊C8 | — | 4 | 1 | no | — |
| 304 | C71⋊C8 | — | 4 | 1 | no | — |
| 305 | C22×C71 | — | 2 | 1 | no | — |
| 306 | C22×C71 | — | 2 | 1 | no | — |
| 307 | C22×C71 | — | 2 | 2 | no | — |
| 308 | C22×C71 | — | 4 | 1 | no | — |
| 309 | C22×C71 | — | 4 | 1 | no | — |
| 310 | C22×C71 | — | 4 | 1 | no | — |
| 311 | C22×C71 | — | 4 | 1 | no | — |
| 312 | C22×C71 | — | 4 | 1 | no | — |
| 313 | C22×C71 | #539 | 1 | 1 | yes | characteristic |
| 314 | C22×C71 | D42 | 1 | 1 | yes | characteristic |
| 315 | C22×C71 | #553 | 1 | 1 | yes | characteristic |
| 316 | C2×D71 | — | 8 | 2 | no | — |
| 317 | C2×D71 | — | 8 | 1 | no | — |
| 318 | C2×D71 | — | 8 | 1 | no | — |
| 319 | C2×D71 | — | 8 | 1 | no | — |
| 320 | C2×D71 | — | 16 | 1 | no | — |
| 321 | C4×C71 | — | 2 | 2 | no | — |
| 322 | C4×C71 | — | 4 | 2 | no | — |
| 323 | C4×C71 | — | 4 | 1 | no | — |
| 324 | C4×C71 | C2×#123 | 1 | 1 | yes | characteristic |
| 325 | C4×C71 | #525 | 1 | 1 | yes | characteristic |
| 326 | C4×C71 | #547 | 1 | 1 | yes | characteristic |
| 327 | C4×C71 | #548 | 1 | 1 | yes | characteristic |
| 328 | Dic71 | — | 4 | 1 | no | — |
| 329 | Dic71 | — | 4 | 1 | no | — |
| 330 | Dic71 | — | 4 | 1 | no | — |
| 331 | Dic71 | — | 4 | 1 | no | — |
| 332 | Dic71 | — | 8 | 1 | no | — |
| 333 | Dic71 | — | 8 | 1 | no | — |
| 334 | Dic71 | — | 8 | 1 | no | — |
| 335 | #26191 | — | 71 | 1 | no | maximal, Sylow |
| 336 | C2×C71 | — | 2 | 1 | no | — |
| 337 | C2×C71 | — | 2 | 1 | no | — |
| 338 | C2×C71 | — | 4 | 2 | no | — |
| 339 | C2×C71 | — | 8 | 1 | no | — |
| 340 | C2×C71 | #2443 | 1 | 1 | yes | characteristic |
| 341 | C2×C71 | #3288 | 1 | 1 | yes | characteristic |
| 342 | C2×C71 | #3291 | 1 | 1 | yes | characteristic |
| 343 | D71 | — | 16 | 1 | no | — |
| 344 | #3096 | — | 71 | 1 | no | — |
| 345 | #3045 | — | 71 | 1 | no | — |
| 346 | #2952 | — | 71 | 1 | no | — |
| 347 | #2912 | — | 71 | 1 | no | — |
| 348 | #2094 | — | 71 | 1 | no | — |
| 349 | #2090 | — | 71 | 1 | no | — |
| 350 | #2079 | — | 71 | 1 | no | — |
| 351 | #2037 | — | 71 | 1 | no | — |
| 352 | #1931 | — | 71 | 1 | no | — |
| 353 | #1922 | — | 71 | 1 | no | — |
| 354 | #1907 | — | 71 | 1 | no | — |
| 355 | #1883 | — | 71 | 1 | no | — |
| 356 | #1876 | D71 | 1 | 1 | yes | characteristic, complemented |
| 357 | #1859 | — | 71 | 1 | no | — |
| 358 | #1859 | — | 71 | 1 | no | — |
| 359 | C71 | #26191 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 360 | C2×AGL(1,ℤ/8) | — | 71 | 1 | no | — |
| 361 | C2×#135 | C2×D71 | 1 | 1 | yes | characteristic |
| 362 | C2×#131 | C2×D71 | 1 | 1 | yes | characteristic |
| 363 | #535 | — | 71 | 1 | no | — |
| 364 | #520 | — | 71 | 1 | no | — |
| 365 | #520 | — | 71 | 1 | no | — |
| 366 | #520 | — | 71 | 1 | no | — |
| 367 | #482 | — | 142 | 1 | no | — |
| 368 | #482 | — | 142 | 1 | no | — |
| 369 | #481 | — | 142 | 1 | no | — |
| 370 | #480 | — | 142 | 1 | no | — |
| 371 | #464 | — | 142 | 1 | no | — |
| 372 | #463 | — | 142 | 1 | no | — |
| 373 | #460 | — | 142 | 1 | no | — |
| 374 | #459 | — | 142 | 1 | no | — |
| 375 | #442 | — | 142 | 1 | no | — |
| 376 | #441 | — | 142 | 1 | no | — |
| 377 | C4×SD16 | — | 142 | 1 | no | — |
| 378 | C4×SD16 | — | 142 | 1 | no | — |
| 379 | #428 | — | 71 | 1 | no | — |
| 380 | #428 | — | 71 | 1 | no | — |
| 381 | #428 | — | 71 | 1 | no | — |
| 382 | #428 | — | 142 | 1 | no | — |
| 383 | #428 | — | 142 | 1 | no | — |
| 384 | #427 | — | 71 | 1 | no | — |
| 385 | #427 | — | 142 | 1 | no | — |
| 386 | C2×#106 | — | 71 | 1 | no | — |
| 387 | C2×#106 | — | 71 | 1 | no | — |
| 388 | C2×#106 | — | 142 | 1 | no | — |
| 389 | #424 | — | 71 | 1 | no | — |
| 390 | C2×#104 | C2×D71 | 1 | 1 | yes | characteristic |
| 391 | C2×#104 | C2×D71 | 1 | 1 | yes | characteristic |
| 392 | #418 | — | 71 | 1 | no | — |
| 393 | #417 | — | 71 | 1 | no | — |
| 394 | #417 | — | 71 | 1 | no | — |
| 395 | #417 | — | 71 | 1 | no | — |
| 396 | C2×#102 | — | 71 | 1 | no | — |
| 397 | C2×#102 | — | 71 | 1 | no | — |
| 398 | C2×#100 | — | 71 | 1 | no | — |
| 399 | #408 | C2×D71 | 1 | 1 | yes | characteristic |
| 400 | #405 | — | 71 | 1 | no | — |
| 401 | #390 | — | 71 | 1 | no | — |
| 402 | #384 | — | 71 | 1 | no | — |
| 403 | #343 | — | 71 | 1 | no | — |
| 404 | #343 | — | 71 | 1 | no | — |
| 405 | #343 | — | 71 | 1 | no | — |
| 406 | #341 | — | 71 | 1 | no | — |
| 407 | #341 | C2×D71 | 1 | 1 | yes | characteristic |
| 408 | #339 | — | 71 | 1 | no | — |
| 409 | #339 | — | 71 | 1 | no | — |
| 410 | #336 | C2×D71 | 1 | 1 | yes | characteristic |
| 411 | C2×#41 | C22×D71 | 1 | 1 | yes | characteristic |
| 412 | C2×#41 | C22×D71 | 1 | 1 | yes | characteristic |
| 413 | C22×D4 | — | 71 | 1 | no | — |
| 414 | AGL(1,ℤ/8) | — | 142 | 2 | no | — |
| 415 | AGL(1,ℤ/8) | — | 142 | 2 | no | — |
| 416 | #135 | — | 2 | 2 | no | — |
| 417 | #135 | — | 2 | 2 | no | — |
| 418 | C2×Q16 | D284 | 1 | 1 | yes | characteristic |
| 419 | C2×SD16 | — | 142 | 1 | no | — |
| 420 | C2×SD16 | D284 | 1 | 1 | yes | characteristic |
| 421 | C2×SD16 | D284 | 1 | 1 | yes | characteristic |
| 422 | C2×D8 | — | 142 | 1 | no | — |
| 423 | C2×D8 | D284 | 1 | 1 | yes | characteristic |
| 424 | #131 | — | 2 | 2 | no | — |
| 425 | #131 | — | 2 | 2 | no | — |
| 426 | C2×M16 | — | 2 | 1 | no | — |
| 427 | C2×M16 | — | 71 | 1 | no | — |
| 428 | C2×M16 | — | 71 | 1 | no | — |
| 429 | C2×M16 | C22×D71 | 1 | 1 | yes | characteristic |
| 430 | C2×M16 | C22×D71 | 1 | 1 | yes | characteristic |
| 431 | C22×C8 | — | 2 | 1 | no | — |
| 432 | C22×C8 | C22×D71 | 1 | 1 | yes | characteristic |
| 433 | C22×C8 | C22×D71 | 1 | 1 | yes | characteristic |
| 434 | #127 | — | 142 | 1 | no | — |
| 435 | #124 | — | 142 | 1 | no | — |
| 436 | #121 | — | 142 | 1 | no | — |
| 437 | #121 | — | 142 | 1 | no | — |
| 438 | #120 | — | 284 | 1 | no | — |
| 439 | C4×Q8 | — | 142 | 1 | no | — |
| 440 | C4×Q8 | — | 142 | 1 | no | — |
| 441 | C4×Q8 | — | 142 | 1 | no | — |
| 442 | C4×D4 | — | 284 | 1 | no | — |
| 443 | C4×D4 | — | 284 | 1 | no | — |
| 444 | C4×D4 | — | 284 | 1 | no | — |
| 445 | C4×D4 | — | 142 | 1 | no | — |
| 446 | C4×D4 | — | 142 | 1 | no | — |
| 447 | C4×D4 | — | 142 | 1 | no | — |
| 448 | #117 | — | 71 | 1 | no | — |
| 449 | #117 | — | 71 | 1 | no | — |
| 450 | #117 | — | 142 | 1 | no | — |
| 451 | #117 | — | 142 | 1 | no | — |
| 452 | #117 | — | 142 | 1 | no | — |
| 453 | C2×C4⋊C4 | — | 284 | 1 | no | — |
| 454 | C2×C4⋊C4 | — | 71 | 1 | no | — |
| 455 | C2×C4⋊C4 | — | 71 | 1 | no | — |
| 456 | C2×C4⋊C4 | — | 71 | 1 | no | — |
| 457 | C2×C4⋊C4 | — | 142 | 1 | no | — |
| 458 | C2×C4⋊C4 | — | 142 | 1 | no | — |
| 459 | C2×C4⋊C4 | — | 142 | 1 | no | — |
| 460 | C2×C22⋊C4 | — | 284 | 1 | no | — |
| 461 | C2×C42 | C22×D71 | 1 | 1 | yes | characteristic |
| 462 | #107 | — | 71 | 1 | no | — |
| 463 | #107 | — | 71 | 1 | no | — |
| 464 | #107 | — | 142 | 1 | no | — |
| 465 | #107 | — | 142 | 1 | no | — |
| 466 | #107 | — | 142 | 1 | no | — |
| 467 | #106 | — | 71 | 1 | no | — |
| 468 | #106 | — | 71 | 1 | no | — |
| 469 | #106 | — | 142 | 1 | no | — |
| 470 | #106 | — | 142 | 1 | no | — |
| 471 | #106 | — | 142 | 1 | no | — |
| 472 | #106 | — | 142 | 1 | no | — |
| 473 | #106 | — | 142 | 1 | no | — |
| 474 | #106 | — | 142 | 1 | no | — |
| 475 | #106 | — | 142 | 1 | no | — |
| 476 | C4⋊C8 | — | 142 | 1 | no | — |
| 477 | C4⋊C8 | — | 142 | 1 | no | — |
| 478 | #104 | — | 2 | 2 | no | — |
| 479 | #104 | — | 2 | 2 | no | — |
| 480 | #103 | — | 142 | 1 | no | — |
| 481 | #103 | — | 142 | 1 | no | — |
| 482 | #103 | — | 142 | 1 | no | — |
| 483 | #102 | — | 142 | 1 | no | — |
| 484 | #102 | — | 142 | 1 | no | — |
| 485 | #102 | — | 142 | 1 | no | — |
| 486 | #102 | — | 142 | 1 | no | — |
| 487 | #102 | — | 142 | 1 | no | — |
| 488 | #102 | — | 142 | 1 | no | — |
| 489 | #102 | — | 142 | 1 | no | — |
| 490 | #102 | — | 142 | 1 | no | — |
| 491 | #102 | — | 142 | 1 | no | — |
| 492 | #100 | — | 142 | 2 | no | — |
| 493 | C22⋊C8 | — | 2 | 1 | no | — |
| 494 | C22⋊C8 | — | 2 | 1 | no | — |
| 495 | #97 | — | 142 | 1 | no | — |
| 496 | C4×C8 | — | 142 | 1 | no | — |
| 497 | C24 | — | 142 | 1 | no | — |
| 498 | #41 | — | 2 | 1 | no | — |
| 499 | #41 | — | 2 | 1 | no | — |
| 500 | #41 | — | 2 | 1 | no | — |
| 501 | #41 | — | 2 | 1 | no | — |
| 502 | #41 | — | 2 | 1 | no | — |
| 503 | #41 | — | 2 | 1 | no | — |
| 504 | #41 | #11765864 | 1 | 2 | yes | — |
| 505 | #41 | #11765864 | 1 | 2 | yes | — |
| 506 | C2×Q8 | C2×D284 | 1 | 1 | yes | characteristic |
| 507 | C2×Q8 | C2×D284 | 1 | 1 | yes | characteristic |
| 508 | C2×D4 | — | 2 | 1 | no | — |
| 509 | C2×D4 | — | 2 | 1 | no | — |
| 510 | C2×D4 | — | 284 | 1 | no | — |
| 511 | C2×D4 | — | 284 | 1 | no | — |
| 512 | C2×D4 | — | 142 | 1 | no | — |
| 513 | C2×D4 | — | 142 | 1 | no | — |
| 514 | C2×D4 | — | 142 | 1 | no | — |
| 515 | C2×D4 | — | 142 | 1 | no | — |
| 516 | C2×D4 | — | 142 | 1 | no | — |
| 517 | C2×D4 | — | 142 | 1 | no | — |
| 518 | C2×D4 | C2×D284 | 1 | 1 | yes | characteristic |
| 519 | C2×D4 | C2×D284 | 1 | 1 | yes | characteristic |
| 520 | C22×C4 | — | 2 | 1 | no | — |
| 521 | C22×C4 | — | 2 | 1 | no | — |
| 522 | C22×C4 | — | 2 | 1 | no | — |
| 523 | C22×C4 | — | 284 | 1 | no | — |
| 524 | C22×C4 | — | 284 | 1 | no | — |
| 525 | C22×C4 | — | 284 | 1 | no | — |
| 526 | C22×C4 | — | 142 | 1 | no | — |
| 527 | C22×C4 | — | 142 | 1 | no | — |
| 528 | C22×C4 | — | 142 | 1 | no | — |
| 529 | C22×C4 | C23×D71 | 1 | 1 | yes | characteristic |
| 530 | Q16 | — | 2 | 2 | no | — |
| 531 | SD16 | — | 2 | 2 | no | — |
| 532 | SD16 | — | 2 | 2 | no | — |
| 533 | SD16 | — | 284 | 2 | no | — |
| 534 | D8 | — | 2 | 2 | no | — |
| 535 | D8 | — | 284 | 2 | no | — |
| 536 | M16 | — | 2 | 4 | no | — |
| 537 | M16 | — | 2 | 1 | no | — |
| 538 | M16 | — | 2 | 1 | no | — |
| 539 | M16 | — | 2 | 1 | no | — |
| 540 | M16 | — | 142 | 1 | no | — |
| 541 | M16 | — | 142 | 1 | no | — |
| 542 | M16 | — | 142 | 1 | no | — |
| 543 | M16 | — | 142 | 1 | no | — |
| 544 | M16 | #11765864 | 1 | 2 | yes | — |
| 545 | C2×C8 | — | 2 | 4 | no | — |
| 546 | C2×C8 | — | 2 | 1 | no | — |
| 547 | C2×C8 | — | 2 | 1 | no | — |
| 548 | C2×C8 | — | 2 | 1 | no | — |
| 549 | C2×C8 | — | 2 | 1 | no | — |
| 550 | C2×C8 | — | 2 | 1 | no | — |
| 551 | C2×C8 | — | 2 | 1 | no | — |
| 552 | C2×C8 | — | 142 | 1 | no | — |
| 553 | C2×C8 | — | 142 | 1 | no | — |
| 554 | C2×C8 | D4×D71 | 1 | 1 | yes | characteristic |
| 555 | C2×C8 | D4×D71 | 1 | 1 | yes | characteristic |
| 556 | C2×C8 | C2×D284 | 1 | 1 | yes | characteristic |
| 557 | C2×C8 | C2×D284 | 1 | 1 | yes | characteristic |
| 558 | C4⋊C4 | — | 284 | 1 | no | — |
| 559 | C4⋊C4 | — | 284 | 1 | no | — |
| 560 | C4⋊C4 | — | 284 | 1 | no | — |
| 561 | C4⋊C4 | — | 568 | 2 | no | — |
| 562 | C4⋊C4 | — | 71 | 1 | no | — |
| 563 | C4⋊C4 | — | 71 | 1 | no | — |
| 564 | C4⋊C4 | — | 71 | 1 | no | — |
| 565 | C4⋊C4 | — | 71 | 1 | no | — |
| 566 | C4⋊C4 | — | 142 | 1 | no | — |
| 567 | C4⋊C4 | — | 142 | 1 | no | — |
| 568 | C4⋊C4 | — | 142 | 1 | no | — |
| 569 | C4⋊C4 | — | 142 | 1 | no | — |
| 570 | C4⋊C4 | — | 142 | 1 | no | — |
| 571 | C4⋊C4 | — | 142 | 1 | no | — |
| 572 | C22⋊C4 | — | 284 | 1 | no | — |
| 573 | C22⋊C4 | — | 284 | 1 | no | — |
| 574 | C22⋊C4 | — | 284 | 1 | no | — |
| 575 | C22⋊C4 | — | 284 | 1 | no | — |
| 576 | C22⋊C4 | — | 284 | 1 | no | — |
| 577 | C22⋊C4 | — | 568 | 2 | no | — |
| 578 | C22⋊C4 | — | 142 | 1 | no | — |
| 579 | C22⋊C4 | — | 142 | 1 | no | — |
| 580 | C42 | — | 2 | 1 | no | — |
| 581 | C42 | — | 2 | 1 | no | — |
| 582 | C42 | — | 284 | 1 | no | — |
| 583 | C42 | — | 284 | 1 | no | — |
| 584 | C42 | — | 284 | 1 | no | — |
| 585 | C42 | — | 142 | 1 | no | — |
| 586 | C42 | — | 142 | 1 | no | — |
| 587 | C23 | — | 2 | 1 | no | — |
| 588 | C23 | — | 2 | 1 | no | — |
| 589 | C23 | — | 284 | 1 | no | — |
| 590 | C23 | — | 284 | 1 | no | — |
| 591 | C23 | — | 284 | 1 | no | — |
| 592 | C23 | — | 568 | 1 | no | — |
| 593 | C23 | — | 568 | 1 | no | — |
| 594 | C23 | #14556174 | 1 | 1 | yes | characteristic |
| 595 | Q8 | — | 2 | 1 | no | — |
| 596 | Q8 | — | 2 | 1 | no | — |
| 597 | Q8 | — | 2 | 1 | no | — |
| 598 | Q8 | #14556112 | 1 | 2 | yes | — |
| 599 | D4 | — | 2 | 2 | no | — |
| 600 | D4 | — | 2 | 2 | no | — |
| 601 | D4 | — | 2 | 1 | no | — |
| 602 | D4 | — | 2 | 1 | no | — |
| 603 | D4 | — | 2 | 1 | no | — |
| 604 | D4 | — | 4 | 1 | no | — |
| 605 | D4 | — | 4 | 1 | no | — |
| 606 | D4 | — | 284 | 1 | no | — |
| 607 | D4 | — | 284 | 1 | no | — |
| 608 | D4 | — | 284 | 1 | no | — |
| 609 | D4 | — | 284 | 1 | no | — |
| 610 | D4 | — | 1136 | 1 | no | — |
| 611 | D4 | — | 1136 | 1 | no | — |
| 612 | D4 | #14556112 | 1 | 2 | yes | — |
| 613 | C2×C4 | — | 2 | 1 | no | — |
| 614 | C2×C4 | — | 2 | 2 | no | — |
| 615 | C2×C4 | — | 2 | 2 | no | — |
| 616 | C2×C4 | — | 2 | 2 | no | — |
| 617 | C2×C4 | — | 2 | 1 | no | — |
| 618 | C2×C4 | — | 4 | 1 | no | — |
| 619 | C2×C4 | — | 4 | 1 | no | — |
| 620 | C2×C4 | — | 4 | 1 | no | — |
| 621 | C2×C4 | — | 4 | 1 | no | — |
| 622 | C2×C4 | — | 284 | 1 | no | — |
| 623 | C2×C4 | — | 284 | 1 | no | — |
| 624 | C2×C4 | — | 284 | 1 | no | — |
| 625 | C2×C4 | — | 568 | 1 | no | — |
| 626 | C2×C4 | — | 568 | 1 | no | — |
| 627 | C2×C4 | — | 568 | 1 | no | — |
| 628 | C2×C4 | — | 1136 | 1 | no | — |
| 629 | C2×C4 | — | 1136 | 1 | no | — |
| 630 | C2×C4 | — | 1136 | 1 | no | — |
| 631 | C2×C4 | — | 142 | 1 | no | — |
| 632 | C2×C4 | — | 142 | 1 | no | — |
| 633 | C2×C4 | — | 142 | 1 | no | — |
| 634 | C2×C4 | — | 142 | 1 | no | — |
| 635 | C2×C4 | C2×D4×D71 | 1 | 1 | yes | characteristic |
| 636 | C2×C4 | C22×D284 | 1 | 1 | yes | characteristic |
| 637 | C2×C4 | C2×#11765864 | 1 | 1 | yes | characteristic |
| 638 | C2×C4 | C2×#11765864 | 1 | 1 | yes | characteristic |
| 639 | C2×C4 | C2×#11765864 | 1 | 1 | yes | characteristic |
| 640 | C2×C4 | #14556175 | 1 | 1 | yes | characteristic |
| 641 | C8 | — | 2 | 1 | no | — |
| 642 | C8 | — | 2 | 1 | no | — |
| 643 | C8 | — | 2 | 1 | no | — |
| 644 | C8 | — | 2 | 2 | no | — |
| 645 | C8 | — | 2 | 1 | no | — |
| 646 | C8 | — | 4 | 1 | no | — |
| 647 | C8 | — | 284 | 1 | no | — |
| 648 | C8 | — | 284 | 1 | no | — |
| 649 | C22 | — | 2 | 1 | no | — |
| 650 | C22 | — | 2 | 1 | no | — |
| 651 | C22 | — | 2 | 2 | no | — |
| 652 | C22 | — | 4 | 1 | no | — |
| 653 | C22 | — | 4 | 1 | no | — |
| 654 | C22 | — | 4 | 1 | no | — |
| 655 | C22 | — | 4 | 1 | no | — |
| 656 | C22 | — | 4 | 1 | no | — |
| 657 | C22 | — | 568 | 2 | no | — |
| 658 | C22 | — | 568 | 1 | no | — |
| 659 | C22 | — | 568 | 1 | no | — |
| 660 | C22 | — | 568 | 1 | no | — |
| 661 | C22 | — | 1136 | 1 | no | — |
| 662 | C22 | #17986593 | 1 | 1 | yes | characteristic |
| 663 | C22 | D4×D284 | 1 | 1 | yes | characteristic |
| 664 | C22 | #17986701 | 1 | 1 | yes | characteristic |
| 665 | C4 | — | 2 | 2 | no | — |
| 666 | C4 | — | 4 | 2 | no | — |
| 667 | C4 | — | 4 | 1 | no | — |
| 668 | C4 | — | 284 | 1 | no | — |
| 669 | C4 | — | 284 | 1 | no | — |
| 670 | C4 | — | 284 | 1 | no | — |
| 671 | C4 | — | 284 | 1 | no | — |
| 672 | C4 | — | 568 | 1 | no | — |
| 673 | C4 | — | 568 | 1 | no | — |
| 674 | C4 | — | 568 | 1 | no | — |
| 675 | C4 | C2×#14556112 | 1 | 1 | yes | characteristic |
| 676 | C4 | #17986505 | 1 | 1 | yes | characteristic |
| 677 | C4 | #17986653 | 1 | 1 | yes | characteristic |
| 678 | C4 | #17986655 | 1 | 1 | yes | characteristic |
| 679 | C2 | — | 2 | 1 | no | — |
| 680 | C2 | — | 2 | 1 | no | — |
| 681 | C2 | — | 4 | 2 | no | — |
| 682 | C2 | — | 8 | 1 | no | — |
| 683 | C2 | — | 1136 | 1 | no | — |
| 684 | C2 | #22592073 | 1 | 1 | yes | characteristic |
| 685 | C2 | #22600107 | 1 | 1 | yes | characteristic |
| 686 | C2 | #22600134 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta