| 1 | C7×#3416 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C7×#3415 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C7×#3292 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C7×#3290 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C7×#2250 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C7×#2223 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C7×#2221 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C7×#2213 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C7×#2212 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C7×#2194 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C7×#2193 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C7×#2192 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | C7×#2192 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C7×#2179 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C7×#2171 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C7×#578 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | C7×#577 | — | 2 | 1 | no | — |
| 18 | C7×#576 | — | 2 | 1 | no | — |
| 19 | C7×#576 | C22 | 1 | 1 | yes | characteristic |
| 20 | C7×#576 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | C7×#576 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | C7×#510 | — | 2 | 1 | no | — |
| 23 | C7×#510 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | C7×#509 | — | 2 | 1 | no | — |
| 25 | C7×#509 | — | 2 | 1 | no | — |
| 26 | C7×#509 | — | 2 | 1 | no | — |
| 27 | C7×#509 | C22 | 1 | 1 | yes | characteristic |
| 28 | C7×#509 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | C7×#509 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | C7×#508 | — | 2 | 1 | no | — |
| 31 | C7×#508 | — | 2 | 1 | no | — |
| 32 | C7×#508 | C22 | 1 | 1 | yes | characteristic |
| 33 | C2×C7×SD32 | — | 2 | 1 | no | — |
| 34 | C2×C7×SD32 | C22 | 1 | 1 | yes | characteristic, complemented |
| 35 | C2×C7×SD32 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | C2×C7×D16 | — | 2 | 1 | no | — |
| 37 | C2×C7×D16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | C2×C7×D16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | C7×#504 | C22 | 1 | 1 | yes | characteristic, complemented |
| 40 | C7×#504 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | C7×#495 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | C7×#493 | C22 | 1 | 1 | yes | characteristic, complemented |
| 43 | C7×#473 | C22 | 1 | 1 | yes | characteristic, complemented |
| 44 | C7×#472 | — | 2 | 1 | no | — |
| 45 | C7×#472 | C22 | 1 | 1 | yes | characteristic |
| 46 | C7×#472 | C22 | 1 | 1 | yes | characteristic, complemented |
| 47 | C7×#472 | C22 | 1 | 1 | yes | characteristic, complemented |
| 48 | C7×#471 | — | 2 | 1 | no | — |
| 49 | C7×#455 | — | 2 | 1 | no | — |
| 50 | C7×#454 | — | 2 | 1 | no | — |
| 51 | C7×#453 | — | 2 | 1 | no | — |
| 52 | C7×#453 | — | 2 | 1 | no | — |
| 53 | C7×#443 | C22 | 1 | 1 | yes | characteristic |
| 54 | C7×#443 | C22 | 1 | 1 | yes | characteristic, complemented |
| 55 | C7×#443 | C22 | 1 | 1 | yes | characteristic, complemented |
| 56 | C7×#368 | C22 | 1 | 1 | yes | characteristic, complemented |
| 57 | C7×#364 | C22 | 1 | 1 | yes | characteristic, complemented |
| 58 | C7×#362 | C22 | 1 | 1 | yes | characteristic, complemented |
| 59 | C7×#361 | C22 | 1 | 1 | yes | characteristic, complemented |
| 60 | C7×#361 | C22 | 1 | 1 | yes | characteristic, complemented |
| 61 | C7×#361 | C22 | 1 | 1 | yes | characteristic, complemented |
| 62 | C7×#359 | C22 | 1 | 1 | yes | characteristic, complemented |
| 63 | C7×#359 | C22 | 1 | 1 | yes | characteristic, complemented |
| 64 | C7×#350 | C22 | 1 | 1 | yes | characteristic, complemented |
| 65 | C7×#350 | C22 | 1 | 1 | yes | characteristic, complemented |
| 66 | C7×#346 | C22 | 1 | 1 | yes | characteristic, complemented |
| 67 | #33854 | C7 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 68 | C7×2−1+4 | — | 2 | 1 | no | — |
| 69 | C7×H(5,𝔽2) | — | 2 | 1 | no | — |
| 70 | C7×H(5,𝔽2) | — | 2 | 1 | no | — |
| 71 | C7×H(5,𝔽2) | — | 2 | 1 | no | — |
| 72 | C7×#137 | — | 2 | 1 | no | — |
| 73 | C7×#137 | — | 2 | 1 | no | — |
| 74 | C7×#137 | — | 4 | 1 | no | — |
| 75 | C7×#137 | — | 4 | 1 | no | — |
| 76 | C7×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 77 | C7×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 78 | C7×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 79 | C7×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 80 | C7×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 81 | C7×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 82 | C7×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 83 | C7×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 84 | C7×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 85 | C7×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 86 | C7×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 87 | C7×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 88 | C7×#135 | — | 2 | 1 | no | — |
| 89 | C7×#135 | — | 2 | 1 | no | — |
| 90 | C7×#135 | — | 2 | 1 | no | — |
| 91 | C7×#135 | — | 2 | 1 | no | — |
| 92 | C7×#135 | — | 4 | 1 | no | — |
| 93 | C7×#135 | — | 4 | 1 | no | — |
| 94 | C7×#135 | D4 | 1 | 1 | yes | characteristic |
| 95 | C7×#135 | C23 | 1 | 1 | yes | characteristic |
| 96 | C7×#135 | C23 | 1 | 1 | yes | characteristic |
| 97 | C2×C7×Q16 | — | 2 | 1 | no | — |
| 98 | C2×C7×Q16 | C23 | 1 | 1 | yes | characteristic |
| 99 | C2×C7×SD16 | — | 2 | 1 | no | — |
| 100 | C2×C7×SD16 | — | 4 | 1 | no | — |
| 101 | C2×C7×D8 | — | 2 | 1 | no | — |
| 102 | C2×C7×D8 | — | 2 | 1 | no | — |
| 103 | C2×C7×D8 | — | 2 | 1 | no | — |
| 104 | C2×C7×D8 | — | 2 | 1 | no | — |
| 105 | C2×C7×D8 | — | 4 | 1 | no | — |
| 106 | C2×C7×D8 | C23 | 1 | 1 | yes | characteristic |
| 107 | C2×C7×D8 | C23 | 1 | 1 | yes | characteristic |
| 108 | C2×C7×D8 | C23 | 1 | 1 | yes | characteristic |
| 109 | C7×#131 | — | 2 | 1 | no | — |
| 110 | C7×#131 | — | 2 | 1 | no | — |
| 111 | C7×#131 | C23 | 1 | 1 | yes | characteristic |
| 112 | C7×#131 | C23 | 1 | 1 | yes | characteristic |
| 113 | C7×#127 | — | 2 | 1 | no | — |
| 114 | C7×#124 | — | 2 | 1 | no | — |
| 115 | C7×Q32 | — | 2 | 1 | no | — |
| 116 | C7×Q32 | D4 | 1 | 1 | yes | characteristic, complemented |
| 117 | C7×SD32 | — | 2 | 1 | no | — |
| 118 | C7×SD32 | — | 2 | 1 | no | — |
| 119 | C7×SD32 | — | 2 | 1 | no | — |
| 120 | C7×SD32 | — | 2 | 1 | no | — |
| 121 | C7×SD32 | — | 2 | 1 | no | — |
| 122 | C7×SD32 | — | 2 | 1 | no | — |
| 123 | C7×SD32 | — | 4 | 1 | no | — |
| 124 | C7×SD32 | D4 | 1 | 1 | yes | characteristic, complemented |
| 125 | C7×SD32 | D4 | 1 | 1 | yes | characteristic, complemented |
| 126 | C7×D16 | — | 2 | 1 | no | — |
| 127 | C7×D16 | — | 2 | 1 | no | — |
| 128 | C7×D16 | — | 2 | 1 | no | — |
| 129 | C7×D16 | — | 2 | 1 | no | — |
| 130 | C7×D16 | — | 2 | 1 | no | — |
| 131 | C7×D16 | — | 4 | 1 | no | — |
| 132 | C7×D16 | D4 | 1 | 1 | yes | characteristic, complemented |
| 133 | C7×M32 | — | 2 | 1 | no | — |
| 134 | C7×M32 | — | 2 | 1 | no | — |
| 135 | C7×M32 | C23 | 1 | 1 | yes | characteristic |
| 136 | C7×M32 | C23 | 1 | 1 | yes | characteristic |
| 137 | C2×C7×C16 | — | 2 | 1 | no | — |
| 138 | C2×C7×C16 | — | 2 | 1 | no | — |
| 139 | C2×C7×C16 | C23 | 1 | 1 | yes | characteristic |
| 140 | C2×C7×C16 | C23 | 1 | 1 | yes | characteristic |
| 141 | C7×#108 | D4 | 1 | 1 | yes | characteristic |
| 142 | C7×#108 | C23 | 1 | 1 | yes | characteristic |
| 143 | C7×#108 | C23 | 1 | 1 | yes | characteristic |
| 144 | C7×#104 | — | 2 | 1 | no | — |
| 145 | C7×#104 | — | 2 | 1 | no | — |
| 146 | C7×#104 | D4 | 1 | 1 | yes | characteristic |
| 147 | C7×#104 | D4 | 1 | 1 | yes | characteristic |
| 148 | C7×#101 | — | 2 | 1 | no | — |
| 149 | C7×#100 | — | 2 | 1 | no | — |
| 150 | C7×#100 | — | 2 | 1 | no | — |
| 151 | C7×#100 | — | 2 | 1 | no | — |
| 152 | C4×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 153 | #3416 | C2×C7 | 1 | 1 | yes | characteristic, complemented |
| 154 | #3415 | C2×C7 | 1 | 1 | yes | characteristic, complemented |
| 155 | #3292 | C2×C7 | 1 | 1 | yes | characteristic, complemented |
| 156 | #3290 | C2×C7 | 1 | 1 | yes | characteristic, complemented |
| 157 | #2250 | C2×C7 | 1 | 1 | yes | characteristic, complemented |
| 158 | #2223 | C2×C7 | 1 | 1 | yes | characteristic, complemented |
| 159 | #2221 | C2×C7 | 1 | 1 | yes | characteristic, complemented |
| 160 | #2213 | C2×C7 | 1 | 1 | yes | characteristic, complemented |
| 161 | #2212 | C2×C7 | 1 | 1 | yes | characteristic, complemented |
| 162 | #2194 | C2×C7 | 1 | 1 | yes | characteristic, complemented |
| 163 | #2193 | C2×C7 | 1 | 1 | yes | characteristic, complemented |
| 164 | #2192 | C2×C7 | 1 | 1 | yes | characteristic, complemented |
| 165 | #2192 | C2×C7 | 1 | 1 | yes | characteristic, complemented |
| 166 | #2179 | C2×C7 | 1 | 1 | yes | characteristic, complemented |
| 167 | #2171 | C2×C7 | 1 | 1 | yes | characteristic, complemented |
| 168 | C7×#41 | — | 2 | 1 | no | — |
| 169 | C7×#41 | — | 2 | 1 | no | — |
| 170 | C7×#41 | — | 4 | 1 | no | — |
| 171 | C7×#41 | — | 4 | 1 | no | — |
| 172 | C7×#41 | — | 4 | 1 | no | — |
| 173 | C7×#41 | — | 4 | 1 | no | — |
| 174 | C7×#41 | — | 4 | 1 | no | — |
| 175 | C7×#41 | — | 4 | 1 | no | — |
| 176 | C7×#41 | — | 4 | 1 | no | — |
| 177 | C7×#41 | — | 4 | 1 | no | — |
| 178 | C7×#41 | — | 8 | 1 | no | — |
| 179 | C7×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 180 | C7×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 181 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 182 | C2×C7×Q8 | — | 4 | 1 | no | — |
| 183 | C2×C7×Q8 | — | 4 | 1 | no | — |
| 184 | C2×C7×D4 | — | 2 | 1 | no | — |
| 185 | C2×C7×D4 | — | 2 | 1 | no | — |
| 186 | C2×C7×D4 | — | 2 | 1 | no | — |
| 187 | C2×C7×D4 | — | 4 | 1 | no | — |
| 188 | C2×C7×D4 | — | 4 | 1 | no | — |
| 189 | C2×C7×D4 | — | 4 | 1 | no | — |
| 190 | C2×C7×D4 | — | 4 | 1 | no | — |
| 191 | C2×C7×D4 | — | 4 | 1 | no | — |
| 192 | C2×C7×D4 | — | 4 | 1 | no | — |
| 193 | C2×C7×D4 | — | 8 | 1 | no | — |
| 194 | C2×C7×D4 | — | 8 | 1 | no | — |
| 195 | C2×C7×D4 | — | 8 | 1 | no | — |
| 196 | C2×C7×D4 | — | 8 | 1 | no | — |
| 197 | C7×Q16 | — | 2 | 1 | no | — |
| 198 | C7×Q16 | — | 2 | 1 | no | — |
| 199 | C7×Q16 | — | 4 | 1 | no | — |
| 200 | C7×Q16 | — | 4 | 1 | no | — |
| 201 | C7×Q16 | D8 | 1 | 1 | yes | characteristic |
| 202 | C7×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 203 | C7×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 204 | C7×SD16 | — | 2 | 1 | no | — |
| 205 | C7×SD16 | — | 2 | 1 | no | — |
| 206 | C7×SD16 | — | 4 | 1 | no | — |
| 207 | C7×SD16 | — | 4 | 1 | no | — |
| 208 | C7×SD16 | — | 4 | 1 | no | — |
| 209 | C7×SD16 | — | 4 | 1 | no | — |
| 210 | C7×SD16 | — | 4 | 1 | no | — |
| 211 | C7×SD16 | — | 4 | 1 | no | — |
| 212 | C7×SD16 | — | 4 | 1 | no | — |
| 213 | C7×SD16 | — | 4 | 1 | no | — |
| 214 | C7×SD16 | — | 4 | 1 | no | — |
| 215 | C7×SD16 | — | 4 | 1 | no | — |
| 216 | C7×SD16 | D8 | 1 | 1 | yes | characteristic |
| 217 | C7×SD16 | D8 | 1 | 1 | yes | characteristic |
| 218 | C7×D8 | — | 2 | 1 | no | — |
| 219 | C7×D8 | — | 2 | 1 | no | — |
| 220 | C7×D8 | — | 2 | 1 | no | — |
| 221 | C7×D8 | — | 2 | 1 | no | — |
| 222 | C7×D8 | — | 2 | 1 | no | — |
| 223 | C7×D8 | — | 2 | 1 | no | — |
| 224 | C7×D8 | — | 4 | 1 | no | — |
| 225 | C7×D8 | — | 4 | 1 | no | — |
| 226 | C7×D8 | — | 4 | 1 | no | — |
| 227 | C7×D8 | — | 4 | 1 | no | — |
| 228 | C7×D8 | — | 4 | 1 | no | — |
| 229 | C7×D8 | — | 4 | 1 | no | — |
| 230 | C7×D8 | — | 4 | 1 | no | — |
| 231 | C7×D8 | — | 4 | 1 | no | — |
| 232 | C7×D8 | D8 | 1 | 1 | yes | characteristic |
| 233 | C7×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 234 | C7×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 235 | C7×M16 | — | 2 | 1 | no | — |
| 236 | C7×M16 | — | 2 | 1 | no | — |
| 237 | C7×M16 | — | 2 | 1 | no | — |
| 238 | C7×M16 | — | 2 | 1 | no | — |
| 239 | C7×M16 | — | 4 | 1 | no | — |
| 240 | C7×M16 | — | 4 | 1 | no | — |
| 241 | C7×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 242 | C7×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 243 | C2×C7×C8 | — | 2 | 1 | no | — |
| 244 | C2×C7×C8 | — | 2 | 1 | no | — |
| 245 | C2×C7×C8 | — | 4 | 1 | no | — |
| 246 | C2×C7×C8 | — | 4 | 1 | no | — |
| 247 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 248 | C2×C7×C8 | C24 | 1 | 1 | yes | characteristic |
| 249 | C7×C22⋊C4 | — | 8 | 1 | no | — |
| 250 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 251 | C7×C16 | — | 2 | 1 | no | — |
| 252 | C7×C16 | — | 2 | 1 | no | — |
| 253 | C7×C16 | — | 2 | 1 | no | — |
| 254 | C7×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 255 | C7×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 256 | #578 | C22×C7 | 1 | 1 | yes | characteristic, complemented |
| 257 | #577 | — | 2 | 1 | no | — |
| 258 | #576 | — | 2 | 1 | no | — |
| 259 | #576 | C22×C7 | 1 | 1 | yes | characteristic |
| 260 | #576 | C22×C7 | 1 | 1 | yes | characteristic, complemented |
| 261 | #576 | C22×C7 | 1 | 1 | yes | characteristic, complemented |
| 262 | #510 | — | 2 | 1 | no | — |
| 263 | #510 | C22×C7 | 1 | 1 | yes | characteristic, complemented |
| 264 | #509 | — | 2 | 1 | no | — |
| 265 | #509 | — | 2 | 1 | no | — |
| 266 | #509 | — | 2 | 1 | no | — |
| 267 | #509 | C22×C7 | 1 | 1 | yes | characteristic |
| 268 | #509 | C22×C7 | 1 | 1 | yes | characteristic, complemented |
| 269 | #509 | C22×C7 | 1 | 1 | yes | characteristic, complemented |
| 270 | #508 | — | 2 | 1 | no | — |
| 271 | #508 | — | 2 | 1 | no | — |
| 272 | #508 | C22×C7 | 1 | 1 | yes | characteristic |
| 273 | C2×SD32 | — | 2 | 1 | no | — |
| 274 | C2×SD32 | C22×C7 | 1 | 1 | yes | characteristic, complemented |
| 275 | C2×SD32 | C22×C7 | 1 | 1 | yes | characteristic, complemented |
| 276 | C2×D16 | — | 2 | 1 | no | — |
| 277 | C2×D16 | C22×C7 | 1 | 1 | yes | characteristic, complemented |
| 278 | C2×D16 | C22×C7 | 1 | 1 | yes | characteristic, complemented |
| 279 | #504 | C22×C7 | 1 | 1 | yes | characteristic, complemented |
| 280 | #504 | C22×C7 | 1 | 1 | yes | characteristic, complemented |
| 281 | #495 | C22×C7 | 1 | 1 | yes | characteristic, complemented |
| 282 | #493 | C22×C7 | 1 | 1 | yes | characteristic, complemented |
| 283 | #473 | C22×C7 | 1 | 1 | yes | characteristic, complemented |
| 284 | #472 | — | 2 | 1 | no | — |
| 285 | #472 | C22×C7 | 1 | 1 | yes | characteristic |
| 286 | #472 | C22×C7 | 1 | 1 | yes | characteristic, complemented |
| 287 | #472 | C22×C7 | 1 | 1 | yes | characteristic, complemented |
| 288 | #471 | — | 2 | 1 | no | — |
| 289 | #455 | — | 2 | 1 | no | — |
| 290 | #454 | — | 2 | 1 | no | — |
| 291 | #453 | — | 2 | 1 | no | — |
| 292 | #453 | — | 2 | 1 | no | — |
| 293 | #443 | C22×C7 | 1 | 1 | yes | characteristic |
| 294 | #443 | C22×C7 | 1 | 1 | yes | characteristic, complemented |
| 295 | #443 | C22×C7 | 1 | 1 | yes | characteristic, complemented |
| 296 | #368 | C22×C7 | 1 | 1 | yes | characteristic, complemented |
| 297 | #364 | C22×C7 | 1 | 1 | yes | characteristic, complemented |
| 298 | #362 | C22×C7 | 1 | 1 | yes | characteristic, complemented |
| 299 | #361 | C22×C7 | 1 | 1 | yes | characteristic, complemented |
| 300 | #361 | C22×C7 | 1 | 1 | yes | characteristic, complemented |
| 301 | #361 | C22×C7 | 1 | 1 | yes | characteristic, complemented |
| 302 | #359 | C22×C7 | 1 | 1 | yes | characteristic, complemented |
| 303 | #359 | C22×C7 | 1 | 1 | yes | characteristic, complemented |
| 304 | #350 | C22×C7 | 1 | 1 | yes | characteristic, complemented |
| 305 | #350 | C22×C7 | 1 | 1 | yes | characteristic, complemented |
| 306 | #346 | C22×C7 | 1 | 1 | yes | characteristic, complemented |
| 307 | C23×C7 | — | 4 | 1 | no | — |
| 308 | C23×C7 | — | 4 | 1 | no | — |
| 309 | C23×C7 | — | 4 | 1 | no | — |
| 310 | C23×C7 | — | 8 | 1 | no | — |
| 311 | C23×C7 | — | 8 | 1 | no | — |
| 312 | C23×C7 | — | 8 | 1 | no | — |
| 313 | C7×Q8 | — | 2 | 1 | no | — |
| 314 | C7×Q8 | — | 2 | 1 | no | — |
| 315 | C7×Q8 | — | 4 | 1 | no | — |
| 316 | C7×Q8 | — | 4 | 1 | no | — |
| 317 | C7×Q8 | — | 8 | 1 | no | — |
| 318 | C7×Q8 | C2×D8 | 1 | 1 | yes | characteristic |
| 319 | C7×Q8 | C2×D8 | 1 | 1 | yes | characteristic |
| 320 | C7×D4 | — | 2 | 1 | no | — |
| 321 | C7×D4 | — | 2 | 1 | no | — |
| 322 | C7×D4 | — | 2 | 1 | no | — |
| 323 | C7×D4 | — | 2 | 1 | no | — |
| 324 | C7×D4 | — | 4 | 1 | no | — |
| 325 | C7×D4 | — | 4 | 1 | no | — |
| 326 | C7×D4 | — | 4 | 1 | no | — |
| 327 | C7×D4 | — | 4 | 1 | no | — |
| 328 | C7×D4 | — | 4 | 1 | no | — |
| 329 | C7×D4 | — | 4 | 1 | no | — |
| 330 | C7×D4 | — | 4 | 1 | no | — |
| 331 | C7×D4 | — | 4 | 1 | no | — |
| 332 | C7×D4 | — | 8 | 1 | no | — |
| 333 | C7×D4 | — | 8 | 1 | no | — |
| 334 | C7×D4 | — | 8 | 1 | no | — |
| 335 | C7×D4 | — | 8 | 1 | no | — |
| 336 | C7×D4 | — | 8 | 1 | no | — |
| 337 | C7×D4 | — | 8 | 1 | no | — |
| 338 | C7×D4 | — | 8 | 1 | no | — |
| 339 | C7×D4 | — | 16 | 2 | no | — |
| 340 | C7×D4 | C2×D8 | 1 | 1 | yes | characteristic |
| 341 | C7×D4 | C2×D8 | 1 | 1 | yes | characteristic |
| 342 | C2×C4×C7 | — | 2 | 1 | no | — |
| 343 | C2×C4×C7 | — | 2 | 1 | no | — |
| 344 | C2×C4×C7 | — | 2 | 1 | no | — |
| 345 | C2×C4×C7 | — | 4 | 1 | no | — |
| 346 | C2×C4×C7 | — | 4 | 1 | no | — |
| 347 | C2×C4×C7 | — | 4 | 1 | no | — |
| 348 | C2×C4×C7 | — | 8 | 1 | no | — |
| 349 | C2×C4×C7 | — | 8 | 1 | no | — |
| 350 | C2×C4×C7 | — | 8 | 1 | no | — |
| 351 | C2×C4×C7 | — | 8 | 1 | no | — |
| 352 | C2×C4×C7 | — | 8 | 1 | no | — |
| 353 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 354 | C7×C8 | — | 2 | 1 | no | — |
| 355 | C7×C8 | — | 2 | 1 | no | — |
| 356 | C7×C8 | — | 4 | 1 | no | — |
| 357 | C7×C8 | — | 4 | 1 | no | — |
| 358 | C7×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 359 | C7×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 360 | C7×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 361 | C7×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 362 | 2−1+4 | — | 2 | 1 | no | — |
| 363 | H(5,𝔽2) | — | 2 | 1 | no | — |
| 364 | H(5,𝔽2) | — | 2 | 1 | no | — |
| 365 | H(5,𝔽2) | — | 2 | 1 | no | — |
| 366 | #137 | — | 2 | 1 | no | — |
| 367 | #137 | — | 2 | 1 | no | — |
| 368 | #137 | — | 4 | 1 | no | — |
| 369 | #137 | — | 4 | 1 | no | — |
| 370 | AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 371 | AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 372 | AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 373 | AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 374 | AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 375 | AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 376 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 377 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 378 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 379 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 380 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 381 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 382 | #135 | — | 2 | 1 | no | — |
| 383 | #135 | — | 2 | 1 | no | — |
| 384 | #135 | — | 2 | 1 | no | — |
| 385 | #135 | — | 2 | 1 | no | — |
| 386 | #135 | — | 4 | 1 | no | — |
| 387 | #135 | — | 4 | 1 | no | — |
| 388 | #135 | C7×D4 | 1 | 1 | yes | characteristic |
| 389 | #135 | C23×C7 | 1 | 1 | yes | characteristic |
| 390 | #135 | C23×C7 | 1 | 1 | yes | characteristic |
| 391 | C2×Q16 | — | 2 | 1 | no | — |
| 392 | C2×Q16 | C23×C7 | 1 | 1 | yes | characteristic |
| 393 | C2×SD16 | — | 2 | 1 | no | — |
| 394 | C2×SD16 | — | 4 | 1 | no | — |
| 395 | C2×D8 | — | 2 | 1 | no | — |
| 396 | C2×D8 | — | 2 | 1 | no | — |
| 397 | C2×D8 | — | 2 | 1 | no | — |
| 398 | C2×D8 | — | 2 | 1 | no | — |
| 399 | C2×D8 | — | 4 | 1 | no | — |
| 400 | C2×D8 | C23×C7 | 1 | 1 | yes | characteristic |
| 401 | C2×D8 | C23×C7 | 1 | 1 | yes | characteristic |
| 402 | C2×D8 | C23×C7 | 1 | 1 | yes | characteristic |
| 403 | #131 | — | 2 | 1 | no | — |
| 404 | #131 | — | 2 | 1 | no | — |
| 405 | #131 | C23×C7 | 1 | 1 | yes | characteristic |
| 406 | #131 | C23×C7 | 1 | 1 | yes | characteristic |
| 407 | #127 | — | 2 | 1 | no | — |
| 408 | #124 | — | 2 | 1 | no | — |
| 409 | Q32 | — | 2 | 1 | no | — |
| 410 | Q32 | C7×D4 | 1 | 1 | yes | characteristic, complemented |
| 411 | SD32 | — | 2 | 1 | no | — |
| 412 | SD32 | — | 2 | 1 | no | — |
| 413 | SD32 | — | 2 | 1 | no | — |
| 414 | SD32 | — | 2 | 1 | no | — |
| 415 | SD32 | — | 2 | 1 | no | — |
| 416 | SD32 | — | 2 | 1 | no | — |
| 417 | SD32 | — | 4 | 1 | no | — |
| 418 | SD32 | C7×D4 | 1 | 1 | yes | characteristic, complemented |
| 419 | SD32 | C7×D4 | 1 | 1 | yes | characteristic, complemented |
| 420 | D16 | — | 2 | 1 | no | — |
| 421 | D16 | — | 2 | 1 | no | — |
| 422 | D16 | — | 2 | 1 | no | — |
| 423 | D16 | — | 2 | 1 | no | — |
| 424 | D16 | — | 2 | 1 | no | — |
| 425 | D16 | — | 4 | 1 | no | — |
| 426 | D16 | C7×D4 | 1 | 1 | yes | characteristic, complemented |
| 427 | M32 | — | 2 | 1 | no | — |
| 428 | M32 | — | 2 | 1 | no | — |
| 429 | M32 | C23×C7 | 1 | 1 | yes | characteristic |
| 430 | M32 | C23×C7 | 1 | 1 | yes | characteristic |
| 431 | C2×C16 | — | 2 | 1 | no | — |
| 432 | C2×C16 | — | 2 | 1 | no | — |
| 433 | C2×C16 | C23×C7 | 1 | 1 | yes | characteristic |
| 434 | C2×C16 | C23×C7 | 1 | 1 | yes | characteristic |
| 435 | #108 | C7×D4 | 1 | 1 | yes | characteristic |
| 436 | #108 | C23×C7 | 1 | 1 | yes | characteristic |
| 437 | #108 | C23×C7 | 1 | 1 | yes | characteristic |
| 438 | #104 | — | 2 | 1 | no | — |
| 439 | #104 | — | 2 | 1 | no | — |
| 440 | #104 | C7×D4 | 1 | 1 | yes | characteristic |
| 441 | #104 | C7×D4 | 1 | 1 | yes | characteristic |
| 442 | #101 | — | 2 | 1 | no | — |
| 443 | #100 | — | 2 | 1 | no | — |
| 444 | #100 | — | 2 | 1 | no | — |
| 445 | #100 | — | 2 | 1 | no | — |
| 446 | C4×C8 | C23×C7 | 1 | 1 | yes | characteristic |
| 447 | C22×C7 | — | 2 | 1 | no | — |
| 448 | C22×C7 | — | 2 | 1 | no | — |
| 449 | C22×C7 | — | 4 | 1 | no | — |
| 450 | C22×C7 | — | 4 | 1 | no | — |
| 451 | C22×C7 | — | 8 | 1 | no | — |
| 452 | C22×C7 | — | 8 | 1 | no | — |
| 453 | C22×C7 | — | 8 | 1 | no | — |
| 454 | C22×C7 | — | 16 | 1 | no | — |
| 455 | C22×C7 | — | 16 | 1 | no | — |
| 456 | C22×C7 | — | 16 | 1 | no | — |
| 457 | C22×C7 | — | 32 | 1 | no | — |
| 458 | C22×C7 | — | 32 | 1 | no | — |
| 459 | C22×C7 | — | 32 | 1 | no | — |
| 460 | C22×C7 | #576 | 1 | 1 | yes | characteristic |
| 461 | C4×C7 | — | 2 | 1 | no | — |
| 462 | C4×C7 | — | 2 | 1 | no | — |
| 463 | C4×C7 | — | 4 | 1 | no | — |
| 464 | C4×C7 | — | 4 | 1 | no | — |
| 465 | C4×C7 | — | 4 | 1 | no | — |
| 466 | C4×C7 | — | 8 | 1 | no | — |
| 467 | C4×C7 | D42 | 1 | 1 | yes | characteristic |
| 468 | C4×C7 | C22×D8 | 1 | 1 | yes | characteristic |
| 469 | #41 | — | 2 | 1 | no | — |
| 470 | #41 | — | 2 | 1 | no | — |
| 471 | #41 | — | 4 | 1 | no | — |
| 472 | #41 | — | 4 | 1 | no | — |
| 473 | #41 | — | 4 | 1 | no | — |
| 474 | #41 | — | 4 | 1 | no | — |
| 475 | #41 | — | 4 | 1 | no | — |
| 476 | #41 | — | 4 | 1 | no | — |
| 477 | #41 | — | 4 | 1 | no | — |
| 478 | #41 | — | 4 | 1 | no | — |
| 479 | #41 | — | 8 | 1 | no | — |
| 480 | #41 | C2×C7×D4 | 1 | 1 | yes | characteristic |
| 481 | #41 | C2×C7×D4 | 1 | 1 | yes | characteristic |
| 482 | C2×Q8 | — | 2 | 1 | no | — |
| 483 | C2×Q8 | — | 4 | 1 | no | — |
| 484 | C2×Q8 | — | 4 | 1 | no | — |
| 485 | C2×D4 | — | 2 | 1 | no | — |
| 486 | C2×D4 | — | 2 | 1 | no | — |
| 487 | C2×D4 | — | 2 | 1 | no | — |
| 488 | C2×D4 | — | 4 | 1 | no | — |
| 489 | C2×D4 | — | 4 | 1 | no | — |
| 490 | C2×D4 | — | 4 | 1 | no | — |
| 491 | C2×D4 | — | 4 | 1 | no | — |
| 492 | C2×D4 | — | 4 | 1 | no | — |
| 493 | C2×D4 | — | 4 | 1 | no | — |
| 494 | C2×D4 | — | 8 | 1 | no | — |
| 495 | C2×D4 | — | 8 | 1 | no | — |
| 496 | C2×D4 | — | 8 | 1 | no | — |
| 497 | C2×D4 | — | 8 | 1 | no | — |
| 498 | Q16 | — | 2 | 1 | no | — |
| 499 | Q16 | — | 2 | 1 | no | — |
| 500 | Q16 | — | 4 | 1 | no | — |
| 501 | Q16 | — | 4 | 1 | no | — |
| 502 | Q16 | C7×D8 | 1 | 1 | yes | characteristic |
| 503 | Q16 | C2×C7×D4 | 1 | 1 | yes | characteristic |
| 504 | Q16 | C2×C7×D4 | 1 | 1 | yes | characteristic |
| 505 | SD16 | — | 2 | 1 | no | — |
| 506 | SD16 | — | 2 | 1 | no | — |
| 507 | SD16 | — | 4 | 1 | no | — |
| 508 | SD16 | — | 4 | 1 | no | — |
| 509 | SD16 | — | 4 | 1 | no | — |
| 510 | SD16 | — | 4 | 1 | no | — |
| 511 | SD16 | — | 4 | 1 | no | — |
| 512 | SD16 | — | 4 | 1 | no | — |
| 513 | SD16 | — | 4 | 1 | no | — |
| 514 | SD16 | — | 4 | 1 | no | — |
| 515 | SD16 | — | 4 | 1 | no | — |
| 516 | SD16 | — | 4 | 1 | no | — |
| 517 | SD16 | C7×D8 | 1 | 1 | yes | characteristic |
| 518 | SD16 | C7×D8 | 1 | 1 | yes | characteristic |
| 519 | D8 | — | 2 | 1 | no | — |
| 520 | D8 | — | 2 | 1 | no | — |
| 521 | D8 | — | 2 | 1 | no | — |
| 522 | D8 | — | 2 | 1 | no | — |
| 523 | D8 | — | 2 | 1 | no | — |
| 524 | D8 | — | 2 | 1 | no | — |
| 525 | D8 | — | 4 | 1 | no | — |
| 526 | D8 | — | 4 | 1 | no | — |
| 527 | D8 | — | 4 | 1 | no | — |
| 528 | D8 | — | 4 | 1 | no | — |
| 529 | D8 | — | 4 | 1 | no | — |
| 530 | D8 | — | 4 | 1 | no | — |
| 531 | D8 | — | 4 | 1 | no | — |
| 532 | D8 | — | 4 | 1 | no | — |
| 533 | D8 | C7×D8 | 1 | 1 | yes | characteristic |
| 534 | D8 | C2×C7×D4 | 1 | 1 | yes | characteristic |
| 535 | D8 | C2×C7×D4 | 1 | 1 | yes | characteristic |
| 536 | M16 | — | 2 | 1 | no | — |
| 537 | M16 | — | 2 | 1 | no | — |
| 538 | M16 | — | 2 | 1 | no | — |
| 539 | M16 | — | 2 | 1 | no | — |
| 540 | M16 | — | 4 | 1 | no | — |
| 541 | M16 | — | 4 | 1 | no | — |
| 542 | M16 | C2×C7×D4 | 1 | 1 | yes | characteristic |
| 543 | M16 | C2×C7×D4 | 1 | 1 | yes | characteristic |
| 544 | C2×C8 | — | 2 | 1 | no | — |
| 545 | C2×C8 | — | 2 | 1 | no | — |
| 546 | C2×C8 | — | 4 | 1 | no | — |
| 547 | C2×C8 | — | 4 | 1 | no | — |
| 548 | C2×C8 | C2×C7×D4 | 1 | 1 | yes | characteristic |
| 549 | C2×C8 | C24×C7 | 1 | 1 | yes | characteristic |
| 550 | C22⋊C4 | — | 8 | 1 | no | — |
| 551 | C42 | C2×C7×D4 | 1 | 1 | yes | characteristic |
| 552 | C16 | — | 2 | 1 | no | — |
| 553 | C16 | — | 2 | 1 | no | — |
| 554 | C16 | — | 2 | 1 | no | — |
| 555 | C16 | C2×C7×D4 | 1 | 1 | yes | characteristic |
| 556 | C16 | C2×C7×D4 | 1 | 1 | yes | characteristic |
| 557 | C2×C7 | — | 2 | 1 | no | — |
| 558 | C2×C7 | — | 4 | 1 | no | — |
| 559 | C2×C7 | — | 4 | 1 | no | — |
| 560 | C2×C7 | — | 8 | 1 | no | — |
| 561 | C2×C7 | — | 8 | 1 | no | — |
| 562 | C2×C7 | — | 16 | 1 | no | — |
| 563 | C2×C7 | — | 16 | 1 | no | — |
| 564 | C2×C7 | — | 16 | 1 | no | — |
| 565 | C2×C7 | D4×D8 | 1 | 1 | yes | characteristic |
| 566 | C23 | — | 4 | 1 | no | — |
| 567 | C23 | — | 4 | 1 | no | — |
| 568 | C23 | — | 4 | 1 | no | — |
| 569 | C23 | — | 8 | 1 | no | — |
| 570 | C23 | — | 8 | 1 | no | — |
| 571 | C23 | — | 8 | 1 | no | — |
| 572 | Q8 | — | 2 | 1 | no | — |
| 573 | Q8 | — | 2 | 1 | no | — |
| 574 | Q8 | — | 4 | 1 | no | — |
| 575 | Q8 | — | 4 | 1 | no | — |
| 576 | Q8 | — | 8 | 1 | no | — |
| 577 | Q8 | C2×C7×D8 | 1 | 1 | yes | characteristic |
| 578 | Q8 | C2×C7×D8 | 1 | 1 | yes | characteristic |
| 579 | D4 | — | 2 | 1 | no | — |
| 580 | D4 | — | 2 | 1 | no | — |
| 581 | D4 | — | 2 | 1 | no | — |
| 582 | D4 | — | 2 | 1 | no | — |
| 583 | D4 | — | 4 | 1 | no | — |
| 584 | D4 | — | 4 | 1 | no | — |
| 585 | D4 | — | 4 | 1 | no | — |
| 586 | D4 | — | 4 | 1 | no | — |
| 587 | D4 | — | 4 | 1 | no | — |
| 588 | D4 | — | 4 | 1 | no | — |
| 589 | D4 | — | 4 | 1 | no | — |
| 590 | D4 | — | 4 | 1 | no | — |
| 591 | D4 | — | 8 | 1 | no | — |
| 592 | D4 | — | 8 | 1 | no | — |
| 593 | D4 | — | 8 | 1 | no | — |
| 594 | D4 | — | 8 | 1 | no | — |
| 595 | D4 | — | 8 | 1 | no | — |
| 596 | D4 | — | 8 | 1 | no | — |
| 597 | D4 | — | 8 | 1 | no | — |
| 598 | D4 | — | 16 | 2 | no | — |
| 599 | D4 | C2×C7×D8 | 1 | 1 | yes | characteristic |
| 600 | D4 | C2×C7×D8 | 1 | 1 | yes | characteristic |
| 601 | C2×C4 | — | 2 | 1 | no | — |
| 602 | C2×C4 | — | 2 | 1 | no | — |
| 603 | C2×C4 | — | 2 | 1 | no | — |
| 604 | C2×C4 | — | 4 | 1 | no | — |
| 605 | C2×C4 | — | 4 | 1 | no | — |
| 606 | C2×C4 | — | 4 | 1 | no | — |
| 607 | C2×C4 | — | 8 | 1 | no | — |
| 608 | C2×C4 | — | 8 | 1 | no | — |
| 609 | C2×C4 | — | 8 | 1 | no | — |
| 610 | C2×C4 | — | 8 | 1 | no | — |
| 611 | C2×C4 | — | 8 | 1 | no | — |
| 612 | C2×C4 | C22×C7×D4 | 1 | 1 | yes | characteristic |
| 613 | C8 | — | 2 | 1 | no | — |
| 614 | C8 | — | 2 | 1 | no | — |
| 615 | C8 | — | 4 | 1 | no | — |
| 616 | C8 | — | 4 | 1 | no | — |
| 617 | C8 | C2×C7×D8 | 1 | 1 | yes | characteristic |
| 618 | C8 | C2×C7×D8 | 1 | 1 | yes | characteristic |
| 619 | C8 | C22×C7×D4 | 1 | 1 | yes | characteristic |
| 620 | C8 | C7×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 621 | C7 | #33854 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 622 | C22 | — | 2 | 1 | no | — |
| 623 | C22 | — | 2 | 1 | no | — |
| 624 | C22 | — | 4 | 1 | no | — |
| 625 | C22 | — | 4 | 1 | no | — |
| 626 | C22 | — | 8 | 1 | no | — |
| 627 | C22 | — | 8 | 1 | no | — |
| 628 | C22 | — | 8 | 1 | no | — |
| 629 | C22 | — | 16 | 1 | no | — |
| 630 | C22 | — | 16 | 1 | no | — |
| 631 | C22 | — | 16 | 1 | no | — |
| 632 | C22 | — | 32 | 1 | no | — |
| 633 | C22 | — | 32 | 1 | no | — |
| 634 | C22 | — | 32 | 1 | no | — |
| 635 | C22 | C7×#576 | 1 | 1 | yes | characteristic |
| 636 | C4 | — | 2 | 1 | no | — |
| 637 | C4 | — | 2 | 1 | no | — |
| 638 | C4 | — | 4 | 1 | no | — |
| 639 | C4 | — | 4 | 1 | no | — |
| 640 | C4 | — | 4 | 1 | no | — |
| 641 | C4 | — | 8 | 1 | no | — |
| 642 | C4 | C7×D42 | 1 | 1 | yes | characteristic |
| 643 | C4 | C22×C7×D8 | 1 | 1 | yes | characteristic |
| 644 | C2 | — | 2 | 1 | no | — |
| 645 | C2 | — | 4 | 1 | no | — |
| 646 | C2 | — | 4 | 1 | no | — |
| 647 | C2 | — | 8 | 1 | no | — |
| 648 | C2 | — | 8 | 1 | no | — |
| 649 | C2 | — | 16 | 1 | no | — |
| 650 | C2 | — | 16 | 1 | no | — |
| 651 | C2 | — | 16 | 1 | no | — |
| 652 | C2 | C7×D4×D8 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta