| 1 | C71×#3154 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#471×C71 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C71×#3063 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C71×#3062 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C71×#3061 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×#444×C71 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C71×#2038 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C71×#2037 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C71×#2007 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C71×#2006 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C71×#1973 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C71×#1952 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | C71×#1908 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C71×#1907 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C71×#1765 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C2×#137×C71 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#137×C71 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×AGL(1,ℤ/8)×C71 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×AGL(1,ℤ/8)×C71 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#135×C71 | C22 | 1 | 1 | yes | characteristic |
| 21 | C22×SD16×C71 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#131×C71 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#131×C71 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×#131×C71 | C22 | 1 | 1 | yes | characteristic |
| 25 | #537×C71 | C22 | 1 | 1 | yes | characteristic |
| 26 | #537×C71 | C22 | 1 | 1 | yes | characteristic |
| 27 | #536×C71 | C22 | 1 | 1 | yes | characteristic |
| 28 | #535×C71 | C22 | 1 | 1 | yes | characteristic |
| 29 | #497×C71 | — | 2 | 1 | no | — |
| 30 | #496×C71 | — | 2 | 1 | no | — |
| 31 | #495×C71 | — | 2 | 1 | no | — |
| 32 | #492×C71 | — | 2 | 1 | no | — |
| 33 | #471×C71 | — | 2 | 4 | no | — |
| 34 | #470×C71 | — | 2 | 1 | no | — |
| 35 | #469×C71 | — | 2 | 1 | no | — |
| 36 | #468×C71 | — | 2 | 1 | no | — |
| 37 | #468×C71 | — | 2 | 1 | no | — |
| 38 | #468×C71 | — | 2 | 1 | no | — |
| 39 | #468×C71 | — | 2 | 1 | no | — |
| 40 | #467×C71 | — | 2 | 1 | no | — |
| 41 | #467×C71 | — | 2 | 1 | no | — |
| 42 | #466×C71 | — | 2 | 1 | no | — |
| 43 | #466×C71 | — | 2 | 1 | no | — |
| 44 | #465×C71 | — | 2 | 1 | no | — |
| 45 | #465×C71 | — | 2 | 1 | no | — |
| 46 | #444×C71 | — | 2 | 4 | no | — |
| 47 | C2×#108×C71 | C22 | 1 | 1 | yes | characteristic |
| 48 | #428×C71 | C22 | 1 | 1 | yes | characteristic |
| 49 | #428×C71 | C22 | 1 | 1 | yes | characteristic |
| 50 | C2×#107×C71 | C22 | 1 | 1 | yes | characteristic |
| 51 | C2×#104×C71 | C22 | 1 | 1 | yes | characteristic |
| 52 | C2×#104×C71 | C22 | 1 | 1 | yes | characteristic |
| 53 | C2×#104×C71 | C22 | 1 | 1 | yes | characteristic |
| 54 | #417×C71 | C22 | 1 | 1 | yes | characteristic |
| 55 | #417×C71 | C22 | 1 | 1 | yes | characteristic |
| 56 | #416×C71 | C22 | 1 | 1 | yes | characteristic |
| 57 | C2×#103×C71 | C22 | 1 | 1 | yes | characteristic |
| 58 | C2×#102×C71 | C22 | 1 | 1 | yes | characteristic |
| 59 | C2×#101×C71 | C22 | 1 | 1 | yes | characteristic |
| 60 | C2×#100×C71 | C22 | 1 | 1 | yes | characteristic |
| 61 | #405×C71 | C22 | 1 | 1 | yes | characteristic |
| 62 | C2×#97×C71 | C22 | 1 | 1 | yes | characteristic |
| 63 | #391×C71 | C22 | 1 | 1 | yes | characteristic |
| 64 | #390×C71 | C22 | 1 | 1 | yes | characteristic |
| 65 | #343×C71 | C22 | 1 | 1 | yes | characteristic |
| 66 | #343×C71 | C22 | 1 | 1 | yes | characteristic |
| 67 | #341×C71 | C22 | 1 | 1 | yes | characteristic |
| 68 | #339×C71 | C22 | 1 | 1 | yes | characteristic |
| 69 | C2×#41×C71 | C23 | 1 | 1 | yes | characteristic |
| 70 | C2×#41×C71 | C23 | 1 | 1 | yes | characteristic |
| 71 | C2×#41×C71 | C23 | 1 | 1 | yes | characteristic |
| 72 | C22×Q8×C71 | C23 | 1 | 1 | yes | characteristic |
| 73 | C22×D4×C71 | C23 | 1 | 1 | yes | characteristic |
| 74 | #137×C71 | — | 2 | 2 | no | — |
| 75 | #137×C71 | — | 2 | 2 | no | — |
| 76 | #137×C71 | — | 4 | 1 | no | — |
| 77 | #137×C71 | — | 4 | 1 | no | — |
| 78 | AGL(1,ℤ/8)×C71 | — | 2 | 2 | no | — |
| 79 | AGL(1,ℤ/8)×C71 | — | 2 | 2 | no | — |
| 80 | AGL(1,ℤ/8)×C71 | — | 4 | 1 | no | — |
| 81 | AGL(1,ℤ/8)×C71 | — | 4 | 1 | no | — |
| 82 | #135×C71 | — | 2 | 2 | no | — |
| 83 | #135×C71 | — | 2 | 2 | no | — |
| 84 | C2×Q16×C71 | — | 2 | 1 | no | — |
| 85 | C2×Q16×C71 | — | 2 | 1 | no | — |
| 86 | C2×Q16×C71 | D4 | 1 | 1 | yes | characteristic |
| 87 | C2×SD16×C71 | — | 2 | 1 | no | — |
| 88 | C2×SD16×C71 | — | 2 | 1 | no | — |
| 89 | C2×SD16×C71 | — | 2 | 1 | no | — |
| 90 | C2×SD16×C71 | — | 2 | 1 | no | — |
| 91 | C2×SD16×C71 | — | 2 | 2 | no | — |
| 92 | C2×SD16×C71 | — | 2 | 1 | no | — |
| 93 | C2×SD16×C71 | — | 2 | 1 | no | — |
| 94 | C2×SD16×C71 | — | 2 | 2 | no | — |
| 95 | C2×SD16×C71 | D4 | 1 | 1 | yes | characteristic |
| 96 | C2×SD16×C71 | D4 | 1 | 1 | yes | characteristic |
| 97 | C2×D8×C71 | — | 2 | 1 | no | — |
| 98 | C2×D8×C71 | — | 2 | 1 | no | — |
| 99 | C2×D8×C71 | D4 | 1 | 1 | yes | characteristic |
| 100 | #131×C71 | — | 2 | 2 | no | — |
| 101 | #131×C71 | — | 2 | 2 | no | — |
| 102 | #131×C71 | — | 2 | 2 | no | — |
| 103 | #131×C71 | — | 2 | 2 | no | — |
| 104 | #131×C71 | — | 4 | 1 | no | — |
| 105 | #131×C71 | — | 4 | 1 | no | — |
| 106 | C2×M16×C71 | — | 2 | 1 | no | — |
| 107 | C2×M16×C71 | — | 2 | 1 | no | — |
| 108 | C2×M16×C71 | — | 2 | 1 | no | — |
| 109 | C2×M16×C71 | C23 | 1 | 1 | yes | characteristic |
| 110 | C2×M16×C71 | C23 | 1 | 1 | yes | characteristic |
| 111 | C2×M16×C71 | C23 | 1 | 1 | yes | characteristic |
| 112 | C2×M16×C71 | C23 | 1 | 1 | yes | characteristic |
| 113 | C22×C8×C71 | — | 2 | 1 | no | — |
| 114 | C22×C8×C71 | — | 2 | 1 | no | — |
| 115 | C22×C8×C71 | — | 2 | 1 | no | — |
| 116 | C22×C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 117 | C22×C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 118 | C4⋊Q8×C71 | — | 2 | 1 | no | — |
| 119 | #127×C71 | — | 2 | 1 | no | — |
| 120 | #124×C71 | — | 2 | 1 | no | — |
| 121 | #124×C71 | — | 2 | 1 | no | — |
| 122 | #123×C71 | — | 4 | 1 | no | — |
| 123 | C22⋊Q8×C71 | — | 2 | 1 | no | — |
| 124 | C22⋊Q8×C71 | — | 2 | 1 | no | — |
| 125 | C22⋊Q8×C71 | — | 2 | 1 | no | — |
| 126 | C22⋊Q8×C71 | — | 2 | 1 | no | — |
| 127 | C22⋊Q8×C71 | — | 2 | 1 | no | — |
| 128 | C22⋊Q8×C71 | — | 2 | 1 | no | — |
| 129 | #121×C71 | — | 2 | 1 | no | — |
| 130 | #121×C71 | — | 2 | 1 | no | — |
| 131 | #121×C71 | — | 2 | 1 | no | — |
| 132 | #121×C71 | — | 2 | 1 | no | — |
| 133 | #121×C71 | — | 2 | 1 | no | — |
| 134 | #121×C71 | — | 2 | 1 | no | — |
| 135 | #121×C71 | — | 4 | 1 | no | — |
| 136 | #121×C71 | — | 4 | 1 | no | — |
| 137 | #120×C71 | — | 4 | 1 | no | — |
| 138 | #117×C71 | C23 | 1 | 1 | yes | characteristic |
| 139 | C2×C4⋊C4×C71 | C23 | 1 | 1 | yes | characteristic |
| 140 | C2×C4⋊C4×C71 | C23 | 1 | 1 | yes | characteristic |
| 141 | C2×C22⋊C4×C71 | — | 4 | 1 | no | — |
| 142 | C2×C42×C71 | C23 | 1 | 1 | yes | characteristic |
| 143 | #108×C71 | D4 | 1 | 4 | yes | complemented |
| 144 | #107×C71 | — | 2 | 1 | no | — |
| 145 | #107×C71 | — | 2 | 1 | no | — |
| 146 | #107×C71 | — | 2 | 1 | no | — |
| 147 | #107×C71 | — | 2 | 1 | no | — |
| 148 | #106×C71 | — | 2 | 1 | no | — |
| 149 | #106×C71 | — | 2 | 1 | no | — |
| 150 | #104×C71 | — | 2 | 2 | no | — |
| 151 | #104×C71 | — | 2 | 2 | no | — |
| 152 | #104×C71 | — | 2 | 2 | no | — |
| 153 | #103×C71 | — | 2 | 1 | no | — |
| 154 | #103×C71 | — | 2 | 1 | no | — |
| 155 | #103×C71 | — | 2 | 1 | no | — |
| 156 | #103×C71 | — | 2 | 1 | no | — |
| 157 | #103×C71 | D4 | 1 | 1 | yes | characteristic |
| 158 | #103×C71 | D4 | 1 | 1 | yes | characteristic |
| 159 | #102×C71 | — | 2 | 1 | no | — |
| 160 | #102×C71 | — | 2 | 1 | no | — |
| 161 | #102×C71 | — | 2 | 1 | no | — |
| 162 | #102×C71 | — | 2 | 1 | no | — |
| 163 | #102×C71 | D4 | 1 | 1 | yes | characteristic |
| 164 | #102×C71 | D4 | 1 | 1 | yes | characteristic |
| 165 | #101×C71 | — | 2 | 2 | no | — |
| 166 | #100×C71 | — | 2 | 2 | no | — |
| 167 | #97×C71 | — | 2 | 1 | no | — |
| 168 | #97×C71 | — | 2 | 2 | no | — |
| 169 | C4×C8×C71 | — | 2 | 1 | no | — |
| 170 | #95×C71 | — | 4 | 1 | no | — |
| 171 | C24×C71 | — | 2 | 1 | no | — |
| 172 | #41×C71 | — | 2 | 1 | no | — |
| 173 | #41×C71 | — | 2 | 1 | no | — |
| 174 | #41×C71 | — | 2 | 1 | no | — |
| 175 | #41×C71 | — | 2 | 1 | no | — |
| 176 | #41×C71 | — | 2 | 1 | no | — |
| 177 | #41×C71 | — | 2 | 1 | no | — |
| 178 | #41×C71 | — | 2 | 1 | no | — |
| 179 | #41×C71 | — | 2 | 1 | no | — |
| 180 | #41×C71 | — | 2 | 1 | no | — |
| 181 | #41×C71 | — | 2 | 1 | no | — |
| 182 | #41×C71 | — | 2 | 1 | no | — |
| 183 | #41×C71 | — | 2 | 1 | no | — |
| 184 | C2×Q8×C71 | — | 2 | 1 | no | — |
| 185 | C2×Q8×C71 | — | 2 | 1 | no | — |
| 186 | C2×Q8×C71 | — | 2 | 1 | no | — |
| 187 | C2×Q8×C71 | — | 2 | 1 | no | — |
| 188 | C2×Q8×C71 | — | 2 | 1 | no | — |
| 189 | C2×Q8×C71 | — | 2 | 1 | no | — |
| 190 | C2×Q8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 191 | C2×Q8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 192 | C2×Q8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 193 | C2×D4×C71 | — | 2 | 1 | no | — |
| 194 | C2×D4×C71 | — | 2 | 1 | no | — |
| 195 | C2×D4×C71 | — | 2 | 1 | no | — |
| 196 | C2×D4×C71 | — | 2 | 1 | no | — |
| 197 | C2×D4×C71 | — | 2 | 1 | no | — |
| 198 | C2×D4×C71 | — | 2 | 1 | no | — |
| 199 | C2×D4×C71 | — | 2 | 1 | no | — |
| 200 | C2×D4×C71 | — | 2 | 1 | no | — |
| 201 | C2×D4×C71 | — | 2 | 1 | no | — |
| 202 | C2×D4×C71 | — | 4 | 1 | no | — |
| 203 | C2×D4×C71 | — | 4 | 1 | no | — |
| 204 | C2×D4×C71 | — | 4 | 1 | no | — |
| 205 | C2×D4×C71 | — | 4 | 1 | no | — |
| 206 | C2×D4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 207 | C2×D4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 208 | C2×D4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 209 | C22×C4×C71 | — | 2 | 1 | no | — |
| 210 | C22×C4×C71 | — | 2 | 1 | no | — |
| 211 | C22×C4×C71 | — | 2 | 1 | no | — |
| 212 | C22×C4×C71 | — | 2 | 1 | no | — |
| 213 | C22×C4×C71 | — | 2 | 1 | no | — |
| 214 | C22×C4×C71 | — | 2 | 1 | no | — |
| 215 | C22×C4×C71 | — | 2 | 1 | no | — |
| 216 | C22×C4×C71 | C24 | 1 | 1 | yes | characteristic |
| 217 | Q16×C71 | — | 2 | 2 | no | — |
| 218 | Q16×C71 | — | 4 | 2 | no | — |
| 219 | Q16×C71 | — | 4 | 2 | no | — |
| 220 | SD16×C71 | — | 2 | 2 | no | — |
| 221 | SD16×C71 | — | 2 | 2 | no | — |
| 222 | SD16×C71 | — | 4 | 2 | no | — |
| 223 | SD16×C71 | — | 4 | 2 | no | — |
| 224 | SD16×C71 | — | 4 | 2 | no | — |
| 225 | SD16×C71 | — | 4 | 2 | no | — |
| 226 | SD16×C71 | — | 4 | 2 | no | — |
| 227 | SD16×C71 | — | 4 | 2 | no | — |
| 228 | D8×C71 | — | 2 | 2 | no | — |
| 229 | D8×C71 | — | 4 | 2 | no | — |
| 230 | D8×C71 | — | 4 | 2 | no | — |
| 231 | M16×C71 | — | 2 | 1 | no | — |
| 232 | M16×C71 | — | 2 | 1 | no | — |
| 233 | M16×C71 | — | 2 | 1 | no | — |
| 234 | M16×C71 | — | 2 | 1 | no | — |
| 235 | M16×C71 | — | 2 | 1 | no | — |
| 236 | M16×C71 | — | 4 | 2 | no | — |
| 237 | M16×C71 | — | 4 | 2 | no | — |
| 238 | M16×C71 | — | 4 | 2 | no | — |
| 239 | M16×C71 | C2×D4 | 1 | 2 | yes | — |
| 240 | M16×C71 | C2×D4 | 1 | 2 | yes | — |
| 241 | M16×C71 | #41 | 1 | 2 | yes | — |
| 242 | C2×C8×C71 | — | 2 | 1 | no | — |
| 243 | C2×C8×C71 | — | 2 | 1 | no | — |
| 244 | C2×C8×C71 | — | 2 | 1 | no | — |
| 245 | C2×C8×C71 | — | 2 | 1 | no | — |
| 246 | C2×C8×C71 | — | 2 | 1 | no | — |
| 247 | C2×C8×C71 | — | 2 | 1 | no | — |
| 248 | C2×C8×C71 | — | 4 | 2 | no | — |
| 249 | C2×C8×C71 | — | 4 | 2 | no | — |
| 250 | C2×C8×C71 | — | 4 | 2 | no | — |
| 251 | C2×C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 252 | C2×C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 253 | C2×C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 254 | C2×C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 255 | C2×C8×C71 | C2×D4 | 1 | 2 | yes | — |
| 256 | C2×C8×C71 | #41 | 1 | 2 | yes | — |
| 257 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 258 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 259 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 260 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 261 | C4⋊C4×C71 | — | 4 | 1 | no | — |
| 262 | C4⋊C4×C71 | — | 4 | 1 | no | — |
| 263 | C4⋊C4×C71 | — | 4 | 1 | no | — |
| 264 | C4⋊C4×C71 | — | 4 | 1 | no | — |
| 265 | C4⋊C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 266 | C4⋊C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 267 | C22⋊C4×C71 | — | 2 | 1 | no | — |
| 268 | C22⋊C4×C71 | — | 4 | 1 | no | — |
| 269 | C22⋊C4×C71 | — | 4 | 1 | no | — |
| 270 | C22⋊C4×C71 | — | 4 | 1 | no | — |
| 271 | C22⋊C4×C71 | — | 4 | 1 | no | — |
| 272 | C22⋊C4×C71 | — | 4 | 1 | no | — |
| 273 | C22⋊C4×C71 | — | 4 | 1 | no | — |
| 274 | C22⋊C4×C71 | — | 4 | 1 | no | — |
| 275 | C22⋊C4×C71 | — | 4 | 1 | no | — |
| 276 | C22⋊C4×C71 | — | 8 | 2 | no | — |
| 277 | C42×C71 | — | 2 | 1 | no | — |
| 278 | C42×C71 | — | 2 | 1 | no | — |
| 279 | C42×C71 | — | 2 | 1 | no | — |
| 280 | C23×C71 | — | 2 | 1 | no | — |
| 281 | C23×C71 | — | 2 | 1 | no | — |
| 282 | C23×C71 | — | 2 | 1 | no | — |
| 283 | C23×C71 | — | 4 | 1 | no | — |
| 284 | C23×C71 | — | 4 | 1 | no | — |
| 285 | C23×C71 | — | 4 | 1 | no | — |
| 286 | C23×C71 | — | 8 | 1 | no | — |
| 287 | C23×C71 | — | 8 | 1 | no | — |
| 288 | C23×C71 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 289 | Q8×C71 | — | 2 | 1 | no | — |
| 290 | Q8×C71 | — | 2 | 1 | no | — |
| 291 | Q8×C71 | — | 2 | 1 | no | — |
| 292 | Q8×C71 | — | 2 | 1 | no | — |
| 293 | Q8×C71 | — | 2 | 1 | no | — |
| 294 | Q8×C71 | — | 2 | 1 | no | — |
| 295 | Q8×C71 | — | 4 | 1 | no | — |
| 296 | Q8×C71 | — | 4 | 1 | no | — |
| 297 | Q8×C71 | — | 4 | 1 | no | — |
| 298 | Q8×C71 | — | 4 | 1 | no | — |
| 299 | D4×C71 | — | 2 | 1 | no | — |
| 300 | D4×C71 | — | 2 | 1 | no | — |
| 301 | D4×C71 | — | 2 | 1 | no | — |
| 302 | D4×C71 | — | 2 | 1 | no | — |
| 303 | D4×C71 | — | 2 | 1 | no | — |
| 304 | D4×C71 | — | 2 | 1 | no | — |
| 305 | D4×C71 | — | 4 | 1 | no | — |
| 306 | D4×C71 | — | 4 | 1 | no | — |
| 307 | D4×C71 | — | 4 | 1 | no | — |
| 308 | D4×C71 | — | 4 | 1 | no | — |
| 309 | D4×C71 | — | 4 | 1 | no | — |
| 310 | D4×C71 | — | 4 | 1 | no | — |
| 311 | D4×C71 | — | 4 | 1 | no | — |
| 312 | D4×C71 | — | 4 | 1 | no | — |
| 313 | D4×C71 | — | 4 | 1 | no | — |
| 314 | D4×C71 | — | 4 | 1 | no | — |
| 315 | D4×C71 | — | 16 | 1 | no | — |
| 316 | D4×C71 | — | 16 | 1 | no | — |
| 317 | D4×C71 | — | 16 | 1 | no | — |
| 318 | D4×C71 | — | 16 | 1 | no | — |
| 319 | C2×C4×C71 | — | 2 | 1 | no | — |
| 320 | C2×C4×C71 | — | 2 | 1 | no | — |
| 321 | C2×C4×C71 | — | 2 | 1 | no | — |
| 322 | C2×C4×C71 | — | 2 | 1 | no | — |
| 323 | C2×C4×C71 | — | 2 | 1 | no | — |
| 324 | C2×C4×C71 | — | 4 | 1 | no | — |
| 325 | C2×C4×C71 | — | 4 | 1 | no | — |
| 326 | C2×C4×C71 | — | 4 | 1 | no | — |
| 327 | C2×C4×C71 | — | 4 | 1 | no | — |
| 328 | C2×C4×C71 | — | 4 | 1 | no | — |
| 329 | C2×C4×C71 | — | 4 | 1 | no | — |
| 330 | C2×C4×C71 | — | 4 | 1 | no | — |
| 331 | C2×C4×C71 | — | 4 | 1 | no | — |
| 332 | C2×C4×C71 | — | 4 | 1 | no | — |
| 333 | C2×C4×C71 | — | 4 | 1 | no | — |
| 334 | C2×C4×C71 | — | 4 | 1 | no | — |
| 335 | C2×C4×C71 | — | 4 | 1 | no | — |
| 336 | C2×C4×C71 | — | 4 | 1 | no | — |
| 337 | C2×C4×C71 | — | 4 | 1 | no | — |
| 338 | C2×C4×C71 | — | 8 | 1 | no | — |
| 339 | C2×C4×C71 | — | 8 | 1 | no | — |
| 340 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 341 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 342 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 343 | C2×C4×C71 | C2×#41 | 1 | 1 | yes | characteristic |
| 344 | C2×C4×C71 | C2×#41 | 1 | 1 | yes | characteristic |
| 345 | C2×C4×C71 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 346 | C8×C71 | — | 2 | 1 | no | — |
| 347 | C8×C71 | — | 2 | 1 | no | — |
| 348 | C8×C71 | — | 2 | 2 | no | — |
| 349 | C8×C71 | — | 2 | 2 | no | — |
| 350 | C8×C71 | — | 2 | 2 | no | — |
| 351 | C8×C71 | — | 4 | 1 | no | — |
| 352 | C8×C71 | #121 | 1 | 2 | yes | — |
| 353 | C8×C71 | #121 | 1 | 2 | yes | — |
| 354 | C22×C71 | — | 2 | 1 | no | — |
| 355 | C22×C71 | — | 2 | 1 | no | — |
| 356 | C22×C71 | — | 4 | 1 | no | — |
| 357 | C22×C71 | — | 4 | 1 | no | — |
| 358 | C22×C71 | — | 4 | 1 | no | — |
| 359 | C22×C71 | — | 4 | 1 | no | — |
| 360 | C22×C71 | — | 4 | 1 | no | — |
| 361 | C22×C71 | — | 4 | 1 | no | — |
| 362 | C22×C71 | — | 4 | 1 | no | — |
| 363 | C22×C71 | — | 4 | 1 | no | — |
| 364 | C22×C71 | — | 4 | 1 | no | — |
| 365 | C22×C71 | — | 8 | 2 | no | — |
| 366 | C22×C71 | — | 8 | 1 | no | — |
| 367 | C22×C71 | — | 8 | 1 | no | — |
| 368 | C22×C71 | — | 8 | 1 | no | — |
| 369 | C22×C71 | — | 16 | 1 | no | — |
| 370 | C22×C71 | #540 | 1 | 1 | yes | characteristic |
| 371 | C22×C71 | D42 | 1 | 1 | yes | characteristic |
| 372 | C22×C71 | #550 | 1 | 1 | yes | characteristic |
| 373 | C4×C71 | — | 4 | 1 | no | — |
| 374 | C4×C71 | — | 4 | 1 | no | — |
| 375 | C4×C71 | — | 4 | 1 | no | — |
| 376 | C4×C71 | — | 4 | 1 | no | — |
| 377 | C4×C71 | — | 4 | 1 | no | — |
| 378 | C4×C71 | — | 8 | 1 | no | — |
| 379 | C4×C71 | — | 8 | 1 | no | — |
| 380 | C4×C71 | — | 8 | 1 | no | — |
| 381 | C4×C71 | — | 8 | 1 | no | — |
| 382 | C4×C71 | C2×#121 | 1 | 1 | yes | characteristic |
| 383 | C4×C71 | #532 | 1 | 1 | yes | characteristic |
| 384 | C4×C71 | D42 | 1 | 1 | yes | characteristic |
| 385 | C4×C71 | #546 | 1 | 1 | yes | characteristic |
| 386 | #25443 | C71 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 387 | C2×C71 | — | 2 | 1 | no | — |
| 388 | C2×C71 | — | 2 | 1 | no | — |
| 389 | C2×C71 | — | 8 | 1 | no | — |
| 390 | C2×C71 | — | 8 | 1 | no | — |
| 391 | C2×C71 | — | 8 | 1 | no | — |
| 392 | C2×C71 | — | 16 | 1 | no | — |
| 393 | C2×C71 | #2428 | 1 | 1 | yes | characteristic |
| 394 | C2×C71 | #3288 | 1 | 1 | yes | characteristic |
| 395 | C2×C71 | #3289 | 1 | 1 | yes | characteristic |
| 396 | #3154 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 397 | C2×#471 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 398 | #3063 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 399 | #3062 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 400 | #3061 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 401 | C2×#444 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 402 | #2038 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 403 | #2037 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 404 | #2007 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 405 | #2006 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 406 | #1973 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 407 | #1952 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 408 | #1908 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 409 | #1907 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 410 | #1765 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 411 | C71 | #25443 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 412 | C2×#137 | C22×C71 | 1 | 1 | yes | characteristic |
| 413 | C2×#137 | C22×C71 | 1 | 1 | yes | characteristic |
| 414 | C2×AGL(1,ℤ/8) | C22×C71 | 1 | 1 | yes | characteristic |
| 415 | C2×AGL(1,ℤ/8) | C22×C71 | 1 | 1 | yes | characteristic |
| 416 | C2×#135 | C22×C71 | 1 | 1 | yes | characteristic |
| 417 | C22×SD16 | C22×C71 | 1 | 1 | yes | characteristic |
| 418 | C2×#131 | C22×C71 | 1 | 1 | yes | characteristic |
| 419 | C2×#131 | C22×C71 | 1 | 1 | yes | characteristic |
| 420 | C2×#131 | C22×C71 | 1 | 1 | yes | characteristic |
| 421 | #537 | C22×C71 | 1 | 1 | yes | characteristic |
| 422 | #537 | C22×C71 | 1 | 1 | yes | characteristic |
| 423 | #536 | C22×C71 | 1 | 1 | yes | characteristic |
| 424 | #535 | C22×C71 | 1 | 1 | yes | characteristic |
| 425 | #497 | — | 2 | 1 | no | — |
| 426 | #496 | — | 2 | 1 | no | — |
| 427 | #495 | — | 2 | 1 | no | — |
| 428 | #492 | — | 2 | 1 | no | — |
| 429 | #471 | — | 2 | 4 | no | — |
| 430 | #470 | — | 2 | 1 | no | — |
| 431 | #469 | — | 2 | 1 | no | — |
| 432 | #468 | — | 2 | 1 | no | — |
| 433 | #468 | — | 2 | 1 | no | — |
| 434 | #468 | — | 2 | 1 | no | — |
| 435 | #468 | — | 2 | 1 | no | — |
| 436 | #467 | — | 2 | 1 | no | — |
| 437 | #467 | — | 2 | 1 | no | — |
| 438 | #466 | — | 2 | 1 | no | — |
| 439 | #466 | — | 2 | 1 | no | — |
| 440 | #465 | — | 2 | 1 | no | — |
| 441 | #465 | — | 2 | 1 | no | — |
| 442 | #444 | — | 2 | 4 | no | — |
| 443 | C2×#108 | C22×C71 | 1 | 1 | yes | characteristic |
| 444 | #428 | C22×C71 | 1 | 1 | yes | characteristic |
| 445 | #428 | C22×C71 | 1 | 1 | yes | characteristic |
| 446 | C2×#107 | C22×C71 | 1 | 1 | yes | characteristic |
| 447 | C2×#104 | C22×C71 | 1 | 1 | yes | characteristic |
| 448 | C2×#104 | C22×C71 | 1 | 1 | yes | characteristic |
| 449 | C2×#104 | C22×C71 | 1 | 1 | yes | characteristic |
| 450 | #417 | C22×C71 | 1 | 1 | yes | characteristic |
| 451 | #417 | C22×C71 | 1 | 1 | yes | characteristic |
| 452 | #416 | C22×C71 | 1 | 1 | yes | characteristic |
| 453 | C2×#103 | C22×C71 | 1 | 1 | yes | characteristic |
| 454 | C2×#102 | C22×C71 | 1 | 1 | yes | characteristic |
| 455 | C2×#101 | C22×C71 | 1 | 1 | yes | characteristic |
| 456 | C2×#100 | C22×C71 | 1 | 1 | yes | characteristic |
| 457 | #405 | C22×C71 | 1 | 1 | yes | characteristic |
| 458 | C2×#97 | C22×C71 | 1 | 1 | yes | characteristic |
| 459 | #391 | C22×C71 | 1 | 1 | yes | characteristic |
| 460 | #390 | C22×C71 | 1 | 1 | yes | characteristic |
| 461 | #343 | C22×C71 | 1 | 1 | yes | characteristic |
| 462 | #343 | C22×C71 | 1 | 1 | yes | characteristic |
| 463 | #341 | C22×C71 | 1 | 1 | yes | characteristic |
| 464 | #339 | C22×C71 | 1 | 1 | yes | characteristic |
| 465 | C2×#41 | C23×C71 | 1 | 1 | yes | characteristic |
| 466 | C2×#41 | C23×C71 | 1 | 1 | yes | characteristic |
| 467 | C2×#41 | C23×C71 | 1 | 1 | yes | characteristic |
| 468 | C22×Q8 | C23×C71 | 1 | 1 | yes | characteristic |
| 469 | C22×D4 | C23×C71 | 1 | 1 | yes | characteristic |
| 470 | #137 | — | 2 | 2 | no | — |
| 471 | #137 | — | 2 | 2 | no | — |
| 472 | #137 | — | 4 | 1 | no | — |
| 473 | #137 | — | 4 | 1 | no | — |
| 474 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 475 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 476 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 477 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 478 | #135 | — | 2 | 2 | no | — |
| 479 | #135 | — | 2 | 2 | no | — |
| 480 | C2×Q16 | — | 2 | 1 | no | — |
| 481 | C2×Q16 | — | 2 | 1 | no | — |
| 482 | C2×Q16 | D4×C71 | 1 | 1 | yes | characteristic |
| 483 | C2×SD16 | — | 2 | 1 | no | — |
| 484 | C2×SD16 | — | 2 | 1 | no | — |
| 485 | C2×SD16 | — | 2 | 1 | no | — |
| 486 | C2×SD16 | — | 2 | 1 | no | — |
| 487 | C2×SD16 | — | 2 | 2 | no | — |
| 488 | C2×SD16 | — | 2 | 1 | no | — |
| 489 | C2×SD16 | — | 2 | 1 | no | — |
| 490 | C2×SD16 | — | 2 | 2 | no | — |
| 491 | C2×SD16 | D4×C71 | 1 | 1 | yes | characteristic |
| 492 | C2×SD16 | D4×C71 | 1 | 1 | yes | characteristic |
| 493 | C2×D8 | — | 2 | 1 | no | — |
| 494 | C2×D8 | — | 2 | 1 | no | — |
| 495 | C2×D8 | D4×C71 | 1 | 1 | yes | characteristic |
| 496 | #131 | — | 2 | 2 | no | — |
| 497 | #131 | — | 2 | 2 | no | — |
| 498 | #131 | — | 2 | 2 | no | — |
| 499 | #131 | — | 2 | 2 | no | — |
| 500 | #131 | — | 4 | 1 | no | — |
| 501 | #131 | — | 4 | 1 | no | — |
| 502 | C2×M16 | — | 2 | 1 | no | — |
| 503 | C2×M16 | — | 2 | 1 | no | — |
| 504 | C2×M16 | — | 2 | 1 | no | — |
| 505 | C2×M16 | C23×C71 | 1 | 1 | yes | characteristic |
| 506 | C2×M16 | C23×C71 | 1 | 1 | yes | characteristic |
| 507 | C2×M16 | C23×C71 | 1 | 1 | yes | characteristic |
| 508 | C2×M16 | C23×C71 | 1 | 1 | yes | characteristic |
| 509 | C22×C8 | — | 2 | 1 | no | — |
| 510 | C22×C8 | — | 2 | 1 | no | — |
| 511 | C22×C8 | — | 2 | 1 | no | — |
| 512 | C22×C8 | C23×C71 | 1 | 1 | yes | characteristic |
| 513 | C22×C8 | C23×C71 | 1 | 1 | yes | characteristic |
| 514 | C4⋊Q8 | — | 2 | 1 | no | — |
| 515 | #127 | — | 2 | 1 | no | — |
| 516 | #124 | — | 2 | 1 | no | — |
| 517 | #124 | — | 2 | 1 | no | — |
| 518 | #123 | — | 4 | 1 | no | — |
| 519 | C22⋊Q8 | — | 2 | 1 | no | — |
| 520 | C22⋊Q8 | — | 2 | 1 | no | — |
| 521 | C22⋊Q8 | — | 2 | 1 | no | — |
| 522 | C22⋊Q8 | — | 2 | 1 | no | — |
| 523 | C22⋊Q8 | — | 2 | 1 | no | — |
| 524 | C22⋊Q8 | — | 2 | 1 | no | — |
| 525 | #121 | — | 2 | 1 | no | — |
| 526 | #121 | — | 2 | 1 | no | — |
| 527 | #121 | — | 2 | 1 | no | — |
| 528 | #121 | — | 2 | 1 | no | — |
| 529 | #121 | — | 2 | 1 | no | — |
| 530 | #121 | — | 2 | 1 | no | — |
| 531 | #121 | — | 4 | 1 | no | — |
| 532 | #121 | — | 4 | 1 | no | — |
| 533 | #120 | — | 4 | 1 | no | — |
| 534 | #117 | C23×C71 | 1 | 1 | yes | characteristic |
| 535 | C2×C4⋊C4 | C23×C71 | 1 | 1 | yes | characteristic |
| 536 | C2×C4⋊C4 | C23×C71 | 1 | 1 | yes | characteristic |
| 537 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 538 | C2×C42 | C23×C71 | 1 | 1 | yes | characteristic |
| 539 | #108 | D4×C71 | 1 | 4 | yes | complemented |
| 540 | #107 | — | 2 | 1 | no | — |
| 541 | #107 | — | 2 | 1 | no | — |
| 542 | #107 | — | 2 | 1 | no | — |
| 543 | #107 | — | 2 | 1 | no | — |
| 544 | #106 | — | 2 | 1 | no | — |
| 545 | #106 | — | 2 | 1 | no | — |
| 546 | #104 | — | 2 | 2 | no | — |
| 547 | #104 | — | 2 | 2 | no | — |
| 548 | #104 | — | 2 | 2 | no | — |
| 549 | #103 | — | 2 | 1 | no | — |
| 550 | #103 | — | 2 | 1 | no | — |
| 551 | #103 | — | 2 | 1 | no | — |
| 552 | #103 | — | 2 | 1 | no | — |
| 553 | #103 | D4×C71 | 1 | 1 | yes | characteristic |
| 554 | #103 | D4×C71 | 1 | 1 | yes | characteristic |
| 555 | #102 | — | 2 | 1 | no | — |
| 556 | #102 | — | 2 | 1 | no | — |
| 557 | #102 | — | 2 | 1 | no | — |
| 558 | #102 | — | 2 | 1 | no | — |
| 559 | #102 | D4×C71 | 1 | 1 | yes | characteristic |
| 560 | #102 | D4×C71 | 1 | 1 | yes | characteristic |
| 561 | #101 | — | 2 | 2 | no | — |
| 562 | #100 | — | 2 | 2 | no | — |
| 563 | #97 | — | 2 | 2 | no | — |
| 564 | #97 | — | 2 | 1 | no | — |
| 565 | C4×C8 | — | 2 | 1 | no | — |
| 566 | #95 | — | 4 | 1 | no | — |
| 567 | C24 | — | 2 | 1 | no | — |
| 568 | #41 | — | 2 | 1 | no | — |
| 569 | #41 | — | 2 | 1 | no | — |
| 570 | #41 | — | 2 | 1 | no | — |
| 571 | #41 | — | 2 | 1 | no | — |
| 572 | #41 | — | 2 | 1 | no | — |
| 573 | #41 | — | 2 | 1 | no | — |
| 574 | #41 | — | 2 | 1 | no | — |
| 575 | #41 | — | 2 | 1 | no | — |
| 576 | #41 | — | 2 | 1 | no | — |
| 577 | #41 | — | 2 | 1 | no | — |
| 578 | #41 | — | 2 | 1 | no | — |
| 579 | #41 | — | 2 | 1 | no | — |
| 580 | C2×Q8 | — | 2 | 1 | no | — |
| 581 | C2×Q8 | — | 2 | 1 | no | — |
| 582 | C2×Q8 | — | 2 | 1 | no | — |
| 583 | C2×Q8 | — | 2 | 1 | no | — |
| 584 | C2×Q8 | — | 2 | 1 | no | — |
| 585 | C2×Q8 | — | 2 | 1 | no | — |
| 586 | C2×Q8 | C2×D4×C71 | 1 | 1 | yes | characteristic |
| 587 | C2×Q8 | C2×D4×C71 | 1 | 1 | yes | characteristic |
| 588 | C2×Q8 | C2×D4×C71 | 1 | 1 | yes | characteristic |
| 589 | C2×D4 | — | 2 | 1 | no | — |
| 590 | C2×D4 | — | 2 | 1 | no | — |
| 591 | C2×D4 | — | 2 | 1 | no | — |
| 592 | C2×D4 | — | 2 | 1 | no | — |
| 593 | C2×D4 | — | 2 | 1 | no | — |
| 594 | C2×D4 | — | 2 | 1 | no | — |
| 595 | C2×D4 | — | 2 | 1 | no | — |
| 596 | C2×D4 | — | 2 | 1 | no | — |
| 597 | C2×D4 | — | 2 | 1 | no | — |
| 598 | C2×D4 | — | 4 | 1 | no | — |
| 599 | C2×D4 | — | 4 | 1 | no | — |
| 600 | C2×D4 | — | 4 | 1 | no | — |
| 601 | C2×D4 | — | 4 | 1 | no | — |
| 602 | C2×D4 | C2×D4×C71 | 1 | 1 | yes | characteristic |
| 603 | C2×D4 | C2×D4×C71 | 1 | 1 | yes | characteristic |
| 604 | C2×D4 | C2×D4×C71 | 1 | 1 | yes | characteristic |
| 605 | C22×C4 | — | 2 | 1 | no | — |
| 606 | C22×C4 | — | 2 | 1 | no | — |
| 607 | C22×C4 | — | 2 | 1 | no | — |
| 608 | C22×C4 | — | 2 | 1 | no | — |
| 609 | C22×C4 | — | 2 | 1 | no | — |
| 610 | C22×C4 | — | 2 | 1 | no | — |
| 611 | C22×C4 | — | 2 | 1 | no | — |
| 612 | C22×C4 | C24×C71 | 1 | 1 | yes | characteristic |
| 613 | Q16 | — | 2 | 2 | no | — |
| 614 | Q16 | — | 4 | 2 | no | — |
| 615 | Q16 | — | 4 | 2 | no | — |
| 616 | SD16 | — | 2 | 2 | no | — |
| 617 | SD16 | — | 2 | 2 | no | — |
| 618 | SD16 | — | 4 | 2 | no | — |
| 619 | SD16 | — | 4 | 2 | no | — |
| 620 | SD16 | — | 4 | 2 | no | — |
| 621 | SD16 | — | 4 | 2 | no | — |
| 622 | SD16 | — | 4 | 2 | no | — |
| 623 | SD16 | — | 4 | 2 | no | — |
| 624 | D8 | — | 2 | 2 | no | — |
| 625 | D8 | — | 4 | 2 | no | — |
| 626 | D8 | — | 4 | 2 | no | — |
| 627 | M16 | — | 2 | 1 | no | — |
| 628 | M16 | — | 2 | 1 | no | — |
| 629 | M16 | — | 2 | 1 | no | — |
| 630 | M16 | — | 2 | 1 | no | — |
| 631 | M16 | — | 2 | 1 | no | — |
| 632 | M16 | — | 4 | 2 | no | — |
| 633 | M16 | — | 4 | 2 | no | — |
| 634 | M16 | — | 4 | 2 | no | — |
| 635 | M16 | C2×D4×C71 | 1 | 2 | yes | — |
| 636 | M16 | C2×D4×C71 | 1 | 2 | yes | — |
| 637 | M16 | #41×C71 | 1 | 2 | yes | — |
| 638 | C2×C8 | — | 2 | 1 | no | — |
| 639 | C2×C8 | — | 2 | 1 | no | — |
| 640 | C2×C8 | — | 2 | 1 | no | — |
| 641 | C2×C8 | — | 2 | 1 | no | — |
| 642 | C2×C8 | — | 2 | 1 | no | — |
| 643 | C2×C8 | — | 2 | 1 | no | — |
| 644 | C2×C8 | — | 4 | 2 | no | — |
| 645 | C2×C8 | — | 4 | 2 | no | — |
| 646 | C2×C8 | — | 4 | 2 | no | — |
| 647 | C2×C8 | C2×D4×C71 | 1 | 1 | yes | characteristic |
| 648 | C2×C8 | C2×D4×C71 | 1 | 1 | yes | characteristic |
| 649 | C2×C8 | C2×D4×C71 | 1 | 1 | yes | characteristic |
| 650 | C2×C8 | C2×D4×C71 | 1 | 1 | yes | characteristic |
| 651 | C2×C8 | C2×D4×C71 | 1 | 2 | yes | — |
| 652 | C2×C8 | #41×C71 | 1 | 2 | yes | — |
| 653 | C4⋊C4 | — | 2 | 1 | no | — |
| 654 | C4⋊C4 | — | 2 | 1 | no | — |
| 655 | C4⋊C4 | — | 2 | 1 | no | — |
| 656 | C4⋊C4 | — | 2 | 1 | no | — |
| 657 | C4⋊C4 | — | 4 | 1 | no | — |
| 658 | C4⋊C4 | — | 4 | 1 | no | — |
| 659 | C4⋊C4 | — | 4 | 1 | no | — |
| 660 | C4⋊C4 | — | 4 | 1 | no | — |
| 661 | C4⋊C4 | C2×D4×C71 | 1 | 1 | yes | characteristic |
| 662 | C4⋊C4 | C2×D4×C71 | 1 | 1 | yes | characteristic |
| 663 | C22⋊C4 | — | 2 | 1 | no | — |
| 664 | C22⋊C4 | — | 4 | 1 | no | — |
| 665 | C22⋊C4 | — | 4 | 1 | no | — |
| 666 | C22⋊C4 | — | 4 | 1 | no | — |
| 667 | C22⋊C4 | — | 4 | 1 | no | — |
| 668 | C22⋊C4 | — | 4 | 1 | no | — |
| 669 | C22⋊C4 | — | 4 | 1 | no | — |
| 670 | C22⋊C4 | — | 4 | 1 | no | — |
| 671 | C22⋊C4 | — | 4 | 1 | no | — |
| 672 | C22⋊C4 | — | 8 | 2 | no | — |
| 673 | C42 | — | 2 | 1 | no | — |
| 674 | C42 | — | 2 | 1 | no | — |
| 675 | C42 | — | 2 | 1 | no | — |
| 676 | C23 | — | 2 | 1 | no | — |
| 677 | C23 | — | 2 | 1 | no | — |
| 678 | C23 | — | 2 | 1 | no | — |
| 679 | C23 | — | 4 | 1 | no | — |
| 680 | C23 | — | 4 | 1 | no | — |
| 681 | C23 | — | 4 | 1 | no | — |
| 682 | C23 | — | 8 | 1 | no | — |
| 683 | C23 | — | 8 | 1 | no | — |
| 684 | C23 | H(5,𝔽2)×C71 | 1 | 1 | yes | characteristic |
| 685 | Q8 | — | 2 | 1 | no | — |
| 686 | Q8 | — | 2 | 1 | no | — |
| 687 | Q8 | — | 2 | 1 | no | — |
| 688 | Q8 | — | 2 | 1 | no | — |
| 689 | Q8 | — | 2 | 1 | no | — |
| 690 | Q8 | — | 2 | 1 | no | — |
| 691 | Q8 | — | 4 | 1 | no | — |
| 692 | Q8 | — | 4 | 1 | no | — |
| 693 | Q8 | — | 4 | 1 | no | — |
| 694 | Q8 | — | 4 | 1 | no | — |
| 695 | D4 | — | 2 | 1 | no | — |
| 696 | D4 | — | 2 | 1 | no | — |
| 697 | D4 | — | 2 | 1 | no | — |
| 698 | D4 | — | 2 | 1 | no | — |
| 699 | D4 | — | 2 | 1 | no | — |
| 700 | D4 | — | 2 | 1 | no | — |
| 701 | D4 | — | 4 | 1 | no | — |
| 702 | D4 | — | 4 | 1 | no | — |
| 703 | D4 | — | 4 | 1 | no | — |
| 704 | D4 | — | 4 | 1 | no | — |
| 705 | D4 | — | 4 | 1 | no | — |
| 706 | D4 | — | 4 | 1 | no | — |
| 707 | D4 | — | 4 | 1 | no | — |
| 708 | D4 | — | 4 | 1 | no | — |
| 709 | D4 | — | 4 | 1 | no | — |
| 710 | D4 | — | 4 | 1 | no | — |
| 711 | D4 | — | 16 | 1 | no | — |
| 712 | D4 | — | 16 | 1 | no | — |
| 713 | D4 | — | 16 | 1 | no | — |
| 714 | D4 | — | 16 | 1 | no | — |
| 715 | C2×C4 | — | 2 | 1 | no | — |
| 716 | C2×C4 | — | 2 | 1 | no | — |
| 717 | C2×C4 | — | 2 | 1 | no | — |
| 718 | C2×C4 | — | 2 | 1 | no | — |
| 719 | C2×C4 | — | 2 | 1 | no | — |
| 720 | C2×C4 | — | 4 | 1 | no | — |
| 721 | C2×C4 | — | 4 | 1 | no | — |
| 722 | C2×C4 | — | 4 | 1 | no | — |
| 723 | C2×C4 | — | 4 | 1 | no | — |
| 724 | C2×C4 | — | 4 | 1 | no | — |
| 725 | C2×C4 | — | 4 | 1 | no | — |
| 726 | C2×C4 | — | 4 | 1 | no | — |
| 727 | C2×C4 | — | 4 | 1 | no | — |
| 728 | C2×C4 | — | 4 | 1 | no | — |
| 729 | C2×C4 | — | 4 | 1 | no | — |
| 730 | C2×C4 | — | 4 | 1 | no | — |
| 731 | C2×C4 | — | 4 | 1 | no | — |
| 732 | C2×C4 | — | 4 | 1 | no | — |
| 733 | C2×C4 | — | 4 | 1 | no | — |
| 734 | C2×C4 | — | 8 | 1 | no | — |
| 735 | C2×C4 | — | 8 | 1 | no | — |
| 736 | C2×C4 | C22×D4×C71 | 1 | 1 | yes | characteristic |
| 737 | C2×C4 | C22×D4×C71 | 1 | 1 | yes | characteristic |
| 738 | C2×C4 | C22×D4×C71 | 1 | 1 | yes | characteristic |
| 739 | C2×C4 | C2×#41×C71 | 1 | 1 | yes | characteristic |
| 740 | C2×C4 | C2×#41×C71 | 1 | 1 | yes | characteristic |
| 741 | C2×C4 | H(5,𝔽2)×C71 | 1 | 1 | yes | characteristic |
| 742 | C8 | — | 2 | 1 | no | — |
| 743 | C8 | — | 2 | 1 | no | — |
| 744 | C8 | — | 2 | 2 | no | — |
| 745 | C8 | — | 2 | 2 | no | — |
| 746 | C8 | — | 2 | 2 | no | — |
| 747 | C8 | — | 4 | 1 | no | — |
| 748 | C8 | #121×C71 | 1 | 2 | yes | — |
| 749 | C8 | #121×C71 | 1 | 2 | yes | — |
| 750 | C22 | — | 2 | 1 | no | — |
| 751 | C22 | — | 2 | 1 | no | — |
| 752 | C22 | — | 4 | 1 | no | — |
| 753 | C22 | — | 4 | 1 | no | — |
| 754 | C22 | — | 4 | 1 | no | — |
| 755 | C22 | — | 4 | 1 | no | — |
| 756 | C22 | — | 4 | 1 | no | — |
| 757 | C22 | — | 4 | 1 | no | — |
| 758 | C22 | — | 4 | 1 | no | — |
| 759 | C22 | — | 4 | 1 | no | — |
| 760 | C22 | — | 4 | 1 | no | — |
| 761 | C22 | — | 8 | 2 | no | — |
| 762 | C22 | — | 8 | 1 | no | — |
| 763 | C22 | — | 8 | 1 | no | — |
| 764 | C22 | — | 8 | 1 | no | — |
| 765 | C22 | — | 16 | 1 | no | — |
| 766 | C22 | #540×C71 | 1 | 1 | yes | characteristic |
| 767 | C22 | D42×C71 | 1 | 1 | yes | characteristic |
| 768 | C22 | #550×C71 | 1 | 1 | yes | characteristic |
| 769 | C4 | — | 4 | 1 | no | — |
| 770 | C4 | — | 4 | 1 | no | — |
| 771 | C4 | — | 4 | 1 | no | — |
| 772 | C4 | — | 4 | 1 | no | — |
| 773 | C4 | — | 4 | 1 | no | — |
| 774 | C4 | — | 8 | 1 | no | — |
| 775 | C4 | — | 8 | 1 | no | — |
| 776 | C4 | — | 8 | 1 | no | — |
| 777 | C4 | — | 8 | 1 | no | — |
| 778 | C4 | C2×#121×C71 | 1 | 1 | yes | characteristic |
| 779 | C4 | #532×C71 | 1 | 1 | yes | characteristic |
| 780 | C4 | D42×C71 | 1 | 1 | yes | characteristic |
| 781 | C4 | #546×C71 | 1 | 1 | yes | characteristic |
| 782 | C2 | — | 2 | 1 | no | — |
| 783 | C2 | — | 2 | 1 | no | — |
| 784 | C2 | — | 8 | 1 | no | — |
| 785 | C2 | — | 8 | 1 | no | — |
| 786 | C2 | — | 8 | 1 | no | — |
| 787 | C2 | — | 16 | 1 | no | — |
| 788 | C2 | C71×#2428 | 1 | 1 | yes | characteristic |
| 789 | C2 | C71×#3288 | 1 | 1 | yes | characteristic |
| 790 | C2 | C71×#3289 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta