← #28264697
Subgroups — #28264697
Order 13568.
1782 conjugacy classes of subgroups.
The subgroup lattice has 846 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #41×Dic106 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#16811353 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #20287651 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #20287642 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #20287629 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #20287620 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #20287596 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #20287570 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #20285259 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #20285257 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #20284526 | C2 | 1 | 2 | yes | maximal |
| 12 | #20284522 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #20284519 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | #20283666 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #20283539 | C2 | 1 | 2 | yes | maximal |
| 16 | C4×#13133247 | C2 | 1 | 1 | yes | maximal, characteristic |
| 17 | C53×#3079 | C2 | 1 | 1 | yes | maximal, characteristic |
| 18 | C2×#13133247 | C22 | 1 | 1 | yes | characteristic |
| 19 | Q8×Dic106 | C22 | 1 | 1 | yes | characteristic |
| 20 | #16811353 | — | 2 | 1 | no | — |
| 21 | #16811353 | — | 2 | 2 | no | — |
| 22 | #16811353 | — | 2 | 1 | no | — |
| 23 | #16811353 | C22 | 1 | 2 | yes | — |
| 24 | #16811353 | C22 | 1 | 4 | yes | — |
| 25 | #16811353 | C22 | 1 | 2 | yes | — |
| 26 | #16811352 | C22 | 1 | 1 | yes | characteristic |
| 27 | #16811349 | C22 | 1 | 2 | yes | — |
| 28 | #16811332 | — | 2 | 2 | no | — |
| 29 | #16811332 | C22 | 1 | 2 | yes | — |
| 30 | #16811330 | — | 2 | 1 | no | — |
| 31 | #16811330 | C22 | 1 | 1 | yes | characteristic |
| 32 | D4×Dic106 | — | 2 | 1 | no | — |
| 33 | D4×Dic106 | C22 | 1 | 1 | yes | characteristic |
| 34 | #16811180 | — | 2 | 1 | no | — |
| 35 | #16811180 | C22 | 1 | 1 | yes | characteristic |
| 36 | #16811176 | — | 2 | 2 | no | — |
| 37 | #16811176 | C22 | 1 | 2 | yes | — |
| 38 | C2×#13133216 | — | 2 | 1 | no | — |
| 39 | C2×#13133216 | C22 | 1 | 2 | yes | — |
| 40 | C2×#13133215 | — | 2 | 2 | no | — |
| 41 | #41×Dic53 | C22 | 1 | 2 | yes | — |
| 42 | C2×C4×Dic106 | — | 2 | 1 | no | — |
| 43 | C2×C4×Dic106 | C22 | 1 | 1 | yes | characteristic |
| 44 | C2×C4×Dic106 | C22 | 1 | 1 | yes | characteristic |
| 45 | C2×#13133182 | — | 2 | 1 | no | — |
| 46 | C2×#13133182 | C22 | 1 | 2 | yes | — |
| 47 | #16811031 | C22 | 1 | 4 | yes | — |
| 48 | #16811030 | C22 | 1 | 4 | yes | — |
| 49 | #16811029 | C22 | 1 | 4 | yes | — |
| 50 | #16811027 | C22 | 1 | 4 | yes | — |
| 51 | #16811026 | C22 | 1 | 2 | yes | — |
| 52 | #16811020 | C22 | 1 | 4 | yes | — |
| 53 | #16811019 | C22 | 1 | 2 | yes | — |
| 54 | #16810933 | C22 | 1 | 4 | yes | — |
| 55 | #16810931 | C22 | 1 | 4 | yes | — |
| 56 | #16810929 | C22 | 1 | 4 | yes | — |
| 57 | #16810919 | C22 | 1 | 2 | yes | — |
| 58 | #16810917 | C22 | 1 | 4 | yes | — |
| 59 | #16810916 | C22 | 1 | 4 | yes | — |
| 60 | #16810911 | C22 | 1 | 4 | yes | — |
| 61 | #16810909 | C22 | 1 | 2 | yes | — |
| 62 | #16810907 | C22 | 1 | 4 | yes | — |
| 63 | #16810906 | C22 | 1 | 4 | yes | — |
| 64 | #16810901 | C22 | 1 | 4 | yes | — |
| 65 | #16810752 | C22 | 1 | 4 | yes | — |
| 66 | #16810750 | C22 | 1 | 2 | yes | — |
| 67 | #16810747 | C22 | 1 | 2 | yes | — |
| 68 | #16810728 | C22 | 1 | 2 | yes | — |
| 69 | #16810727 | C22 | 1 | 4 | yes | — |
| 70 | #16810723 | C22 | 1 | 2 | yes | — |
| 71 | #16810720 | C22 | 1 | 4 | yes | — |
| 72 | C4×#11719925 | C22 | 1 | 2 | yes | — |
| 73 | #16810715 | C22 | 1 | 4 | yes | — |
| 74 | #16810714 | C22 | 1 | 4 | yes | — |
| 75 | C4×#11719923 | C22 | 1 | 2 | yes | — |
| 76 | #16810666 | C22 | 1 | 1 | yes | characteristic |
| 77 | #16810665 | C22 | 1 | 2 | yes | — |
| 78 | #16810663 | C22 | 1 | 2 | yes | — |
| 79 | #16810663 | C22 | 1 | 2 | yes | — |
| 80 | #16810646 | C22 | 1 | 2 | yes | — |
| 81 | #16810633 | C22 | 1 | 2 | yes | — |
| 82 | #16810631 | C22 | 1 | 1 | yes | characteristic |
| 83 | #16810624 | C22 | 1 | 1 | yes | characteristic |
| 84 | C4×#11719917 | C22 | 1 | 1 | yes | characteristic |
| 85 | M16×Dic53 | C22 | 1 | 2 | yes | — |
| 86 | C2×C4⋊Q8×C53 | C22 | 1 | 1 | yes | characteristic |
| 87 | C4×#41×C53 | C22 | 1 | 1 | yes | characteristic |
| 88 | C53×#477 | C22 | 1 | 2 | yes | — |
| 89 | C53×#476 | C22 | 1 | 2 | yes | — |
| 90 | C53×#475 | C22 | 1 | 2 | yes | — |
| 91 | C53×#474 | C22 | 1 | 2 | yes | — |
| 92 | C53×#428 | C22 | 1 | 2 | yes | — |
| 93 | C53×#423 | C22 | 1 | 1 | yes | characteristic |
| 94 | C53×#417 | C22 | 1 | 2 | yes | — |
| 95 | C22×Dic106 | — | 2 | 2 | no | — |
| 96 | C22×Dic106 | — | 2 | 1 | no | — |
| 97 | C22×Dic106 | D4 | 1 | 1 | yes | characteristic |
| 98 | C22×Dic106 | C23 | 1 | 1 | yes | characteristic |
| 99 | #13133247 | Q8 | 1 | 8 | yes | complemented |
| 100 | C2×#11719925 | C23 | 1 | 2 | yes | — |
| 101 | C2×#11719923 | C23 | 1 | 2 | yes | — |
| 102 | C2×#11719917 | C23 | 1 | 1 | yes | characteristic |
| 103 | C2×#11719917 | C23 | 1 | 1 | yes | characteristic |
| 104 | #13133217 | — | 2 | 1 | no | — |
| 105 | #13133217 | — | 2 | 1 | no | — |
| 106 | #13133217 | C23 | 1 | 1 | yes | characteristic |
| 107 | #13133217 | C23 | 1 | 1 | yes | characteristic |
| 108 | #13133216 | — | 2 | 2 | no | — |
| 109 | #13133216 | — | 2 | 4 | no | — |
| 110 | #13133216 | — | 2 | 2 | no | — |
| 111 | #13133216 | — | 2 | 2 | no | — |
| 112 | #13133216 | — | 2 | 2 | no | — |
| 113 | #13133216 | — | 2 | 2 | no | — |
| 114 | #13133216 | — | 2 | 2 | no | — |
| 115 | #13133216 | C23 | 1 | 2 | yes | — |
| 116 | #13133216 | C23 | 1 | 4 | yes | — |
| 117 | #13133216 | C23 | 1 | 2 | yes | — |
| 118 | #13133216 | C23 | 1 | 4 | yes | — |
| 119 | #13133215 | — | 2 | 4 | no | — |
| 120 | #13133215 | — | 2 | 4 | no | — |
| 121 | #13133215 | — | 2 | 4 | no | — |
| 122 | #13133215 | — | 2 | 4 | no | — |
| 123 | #13133209 | — | 2 | 2 | no | — |
| 124 | #13133209 | C23 | 1 | 2 | yes | — |
| 125 | #13133208 | — | 2 | 2 | no | — |
| 126 | #13133208 | — | 2 | 2 | no | — |
| 127 | #13133208 | C23 | 1 | 2 | yes | — |
| 128 | #13133208 | C23 | 1 | 2 | yes | — |
| 129 | #13133196 | — | 2 | 1 | no | — |
| 130 | #13133196 | — | 2 | 2 | no | — |
| 131 | #13133196 | — | 2 | 1 | no | — |
| 132 | #13133196 | — | 2 | 1 | no | — |
| 133 | #13133196 | — | 2 | 1 | no | — |
| 134 | #13133194 | — | 2 | 2 | no | — |
| 135 | #13133194 | — | 2 | 2 | no | — |
| 136 | #13133194 | — | 2 | 2 | no | — |
| 137 | #13133194 | — | 2 | 2 | no | — |
| 138 | #13133194 | — | 2 | 2 | no | — |
| 139 | #13133194 | — | 2 | 2 | no | — |
| 140 | Q8×Dic53 | C23 | 1 | 2 | yes | — |
| 141 | Q8×Dic53 | C23 | 1 | 2 | yes | — |
| 142 | C4×Dic106 | — | 2 | 1 | no | — |
| 143 | C4×Dic106 | — | 2 | 1 | no | — |
| 144 | C4×Dic106 | — | 2 | 1 | no | — |
| 145 | C4×Dic106 | — | 2 | 1 | no | — |
| 146 | C4×Dic106 | — | 2 | 1 | no | — |
| 147 | C4×Dic106 | — | 2 | 2 | no | — |
| 148 | C4×Dic106 | — | 2 | 2 | no | — |
| 149 | C4×Dic106 | — | 2 | 2 | no | — |
| 150 | C4×Dic106 | — | 2 | 1 | no | — |
| 151 | C4×Dic106 | D4 | 1 | 1 | yes | characteristic |
| 152 | C4×Dic106 | D4 | 1 | 2 | yes | — |
| 153 | C4×Dic106 | D4 | 1 | 1 | yes | characteristic |
| 154 | C4×Dic106 | C23 | 1 | 2 | yes | — |
| 155 | C4×Dic106 | C23 | 1 | 1 | yes | characteristic |
| 156 | C4×Dic106 | C23 | 1 | 1 | yes | characteristic |
| 157 | C4×Dic106 | C23 | 1 | 2 | yes | — |
| 158 | C4×Dic106 | C23 | 1 | 2 | yes | — |
| 159 | #13133182 | — | 2 | 2 | no | — |
| 160 | #13133182 | — | 2 | 2 | no | — |
| 161 | #13133182 | — | 2 | 4 | no | — |
| 162 | #13133182 | — | 2 | 2 | no | — |
| 163 | #13133182 | — | 2 | 2 | no | — |
| 164 | #13133182 | C23 | 1 | 4 | yes | — |
| 165 | #13133182 | C23 | 1 | 4 | yes | — |
| 166 | D4×Dic53 | — | 2 | 2 | no | — |
| 167 | D4×Dic53 | — | 2 | 2 | no | — |
| 168 | D4×Dic53 | C23 | 1 | 2 | yes | — |
| 169 | D4×Dic53 | C23 | 1 | 2 | yes | — |
| 170 | #13133176 | — | 2 | 2 | no | — |
| 171 | #13133176 | C23 | 1 | 2 | yes | — |
| 172 | C2×C4⋊Dic53 | — | 2 | 1 | no | — |
| 173 | C2×C4⋊Dic53 | D4 | 1 | 1 | yes | characteristic |
| 174 | C2×C4⋊Dic53 | C23 | 1 | 1 | yes | characteristic |
| 175 | C2×#11719919 | — | 2 | 2 | no | — |
| 176 | C2×#11719919 | — | 2 | 1 | no | — |
| 177 | C2×#11719919 | — | 2 | 2 | no | — |
| 178 | C2×#11719919 | — | 2 | 2 | no | — |
| 179 | C2×#11719919 | D4 | 1 | 2 | yes | — |
| 180 | C2×C4×Dic53 | — | 2 | 2 | no | — |
| 181 | C2×C4×Dic53 | — | 2 | 1 | no | — |
| 182 | C2×C4×Dic53 | — | 2 | 2 | no | — |
| 183 | C2×C4×Dic53 | C23 | 1 | 2 | yes | — |
| 184 | #13133151 | C23 | 1 | 4 | yes | — |
| 185 | #13133150 | C23 | 1 | 4 | yes | — |
| 186 | #13133150 | C23 | 1 | 4 | yes | — |
| 187 | #13133150 | C23 | 1 | 2 | yes | — |
| 188 | #13133149 | C23 | 1 | 4 | yes | — |
| 189 | #13133148 | C23 | 1 | 4 | yes | — |
| 190 | #13133148 | C23 | 1 | 4 | yes | — |
| 191 | #13133148 | C23 | 1 | 2 | yes | — |
| 192 | #13133146 | C23 | 1 | 4 | yes | — |
| 193 | #13133146 | C23 | 1 | 4 | yes | — |
| 194 | #13133142 | C23 | 1 | 4 | yes | — |
| 195 | #13133142 | C23 | 1 | 4 | yes | — |
| 196 | #13133141 | C23 | 1 | 2 | yes | — |
| 197 | #13133140 | C23 | 1 | 2 | yes | — |
| 198 | #13133140 | C23 | 1 | 2 | yes | — |
| 199 | #13133138 | C23 | 1 | 2 | yes | — |
| 200 | #13133128 | C23 | 1 | 2 | yes | — |
| 201 | #13133127 | C23 | 1 | 4 | yes | — |
| 202 | C4×#88322 | C23 | 1 | 2 | yes | — |
| 203 | C8×Dic53 | C23 | 1 | 4 | yes | — |
| 204 | C2×#41×C53 | C23 | 1 | 1 | yes | characteristic |
| 205 | C22×Q8×C53 | — | 2 | 1 | no | — |
| 206 | C2×M16×C53 | C23 | 1 | 2 | yes | — |
| 207 | C4⋊Q8×C53 | — | 2 | 1 | no | — |
| 208 | C4⋊Q8×C53 | — | 2 | 1 | no | — |
| 209 | C4⋊Q8×C53 | C23 | 1 | 2 | yes | — |
| 210 | C4⋊Q8×C53 | C23 | 1 | 2 | yes | — |
| 211 | C4×Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 212 | C4×Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 213 | C4×D4×C53 | — | 2 | 1 | no | — |
| 214 | C4×D4×C53 | — | 2 | 1 | no | — |
| 215 | C4×D4×C53 | C23 | 1 | 1 | yes | characteristic |
| 216 | C4×D4×C53 | C23 | 1 | 1 | yes | characteristic |
| 217 | #117×C53 | — | 2 | 1 | no | — |
| 218 | #117×C53 | C23 | 1 | 1 | yes | characteristic |
| 219 | C2×C4⋊C4×C53 | — | 2 | 1 | no | — |
| 220 | C2×C4⋊C4×C53 | C23 | 1 | 2 | yes | — |
| 221 | C2×C42×C53 | — | 2 | 1 | no | — |
| 222 | C2×C42×C53 | C23 | 1 | 1 | yes | characteristic |
| 223 | #107×C53 | C23 | 1 | 4 | yes | — |
| 224 | #106×C53 | C23 | 1 | 4 | yes | — |
| 225 | C4⋊C8×C53 | C23 | 1 | 2 | yes | — |
| 226 | C4⋊C8×C53 | C23 | 1 | 2 | yes | — |
| 227 | #103×C53 | C23 | 1 | 4 | yes | — |
| 228 | #102×C53 | C23 | 1 | 4 | yes | — |
| 229 | #41×C53 | — | 2 | 2 | no | — |
| 230 | #41×C53 | C2×Q8 | 1 | 4 | yes | — |
| 231 | C2×Q8×C53 | — | 2 | 2 | no | — |
| 232 | C2×Q8×C53 | — | 2 | 2 | no | — |
| 233 | C2×Q8×C53 | — | 8 | 2 | no | — |
| 234 | C2×Q8×C53 | C24 | 1 | 1 | yes | characteristic |
| 235 | C2×D4×C53 | — | 2 | 1 | no | — |
| 236 | C2×D4×C53 | C24 | 1 | 1 | yes | characteristic |
| 237 | C22×C4×C53 | — | 2 | 1 | no | — |
| 238 | C22×C4×C53 | — | 2 | 2 | no | — |
| 239 | C22×C4×C53 | — | 2 | 1 | no | — |
| 240 | C22×C4×C53 | — | 2 | 1 | no | — |
| 241 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 242 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 243 | C22×C4×C53 | C24 | 1 | 1 | yes | characteristic |
| 244 | C22×Dic53 | — | 2 | 1 | no | — |
| 245 | C22×Dic53 | — | 2 | 1 | no | — |
| 246 | C22×Dic53 | — | 2 | 2 | no | — |
| 247 | C22×Dic53 | — | 2 | 2 | no | — |
| 248 | C22×Dic53 | C2×D4 | 1 | 2 | yes | — |
| 249 | C22×Dic53 | C2×D4 | 1 | 2 | yes | — |
| 250 | C2×Dic106 | — | 2 | 1 | no | — |
| 251 | C2×Dic106 | — | 2 | 2 | no | — |
| 252 | C2×Dic106 | — | 2 | 4 | no | — |
| 253 | C2×Dic106 | — | 2 | 1 | no | — |
| 254 | C2×Dic106 | — | 2 | 2 | no | — |
| 255 | C2×Dic106 | — | 2 | 1 | no | — |
| 256 | C2×Dic106 | — | 2 | 2 | no | — |
| 257 | C2×Dic106 | — | 2 | 4 | no | — |
| 258 | C2×Dic106 | — | 2 | 4 | no | — |
| 259 | C2×Dic106 | — | 4 | 4 | no | — |
| 260 | C2×Dic106 | — | 8 | 4 | no | — |
| 261 | C2×Dic106 | C2×D4 | 1 | 2 | yes | — |
| 262 | C2×Dic106 | C2×D4 | 1 | 1 | yes | characteristic |
| 263 | C2×Dic106 | C2×D4 | 1 | 1 | yes | characteristic |
| 264 | C2×Dic106 | C2×Q8 | 1 | 4 | yes | complemented |
| 265 | C2×Dic106 | C24 | 1 | 2 | yes | — |
| 266 | M16×C53 | — | 2 | 4 | no | — |
| 267 | C2×C8×C53 | C24 | 1 | 4 | yes | — |
| 268 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 269 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 270 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 271 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 272 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 273 | C4⋊C4×C53 | C24 | 1 | 4 | yes | — |
| 274 | C4⋊C4×C53 | C24 | 1 | 1 | yes | characteristic |
| 275 | C4⋊C4×C53 | C24 | 1 | 1 | yes | characteristic |
| 276 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 277 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 278 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 279 | C42×C53 | — | 2 | 1 | no | — |
| 280 | C42×C53 | — | 2 | 1 | no | — |
| 281 | C42×C53 | — | 2 | 1 | no | — |
| 282 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 283 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 284 | C42×C53 | C24 | 1 | 1 | yes | characteristic |
| 285 | C42×C53 | C24 | 1 | 1 | yes | characteristic |
| 286 | C22⋊Dic53 | — | 2 | 2 | no | — |
| 287 | C22⋊Dic53 | — | 2 | 2 | no | — |
| 288 | C22⋊Dic53 | — | 2 | 2 | no | — |
| 289 | #11719925 | C2×Q8 | 1 | 8 | yes | complemented |
| 290 | #11719923 | C2×Q8 | 1 | 8 | yes | complemented |
| 291 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 292 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 293 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 294 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 295 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 296 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 297 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 298 | C4⋊Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 299 | C4⋊Dic53 | C2×D4 | 1 | 2 | yes | — |
| 300 | C4⋊Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 301 | C4⋊Dic53 | C24 | 1 | 2 | yes | — |
| 302 | C4⋊Dic53 | C24 | 1 | 2 | yes | — |
| 303 | C4⋊Dic53 | C24 | 1 | 2 | yes | — |
| 304 | #11719919 | — | 2 | 2 | no | — |
| 305 | #11719919 | — | 2 | 2 | no | — |
| 306 | #11719919 | — | 2 | 2 | no | — |
| 307 | #11719919 | — | 2 | 2 | no | — |
| 308 | #11719919 | — | 2 | 4 | no | — |
| 309 | #11719919 | — | 2 | 4 | no | — |
| 310 | #11719919 | — | 2 | 4 | no | — |
| 311 | #11719919 | — | 2 | 4 | no | — |
| 312 | #11719919 | — | 2 | 2 | no | — |
| 313 | #11719919 | — | 2 | 2 | no | — |
| 314 | #11719919 | — | 2 | 2 | no | — |
| 315 | #11719919 | — | 2 | 2 | no | — |
| 316 | #11719919 | C2×D4 | 1 | 2 | yes | — |
| 317 | #11719919 | C2×D4 | 1 | 2 | yes | — |
| 318 | #11719919 | C2×D4 | 1 | 2 | yes | — |
| 319 | #11719919 | C2×D4 | 1 | 2 | yes | — |
| 320 | C4×Dic53 | — | 2 | 2 | no | — |
| 321 | C4×Dic53 | — | 2 | 2 | no | — |
| 322 | C4×Dic53 | — | 2 | 2 | no | — |
| 323 | C4×Dic53 | — | 2 | 2 | no | — |
| 324 | C4×Dic53 | — | 2 | 2 | no | — |
| 325 | C4×Dic53 | — | 2 | 4 | no | — |
| 326 | C4×Dic53 | — | 2 | 4 | no | — |
| 327 | C4×Dic53 | C2×D4 | 1 | 2 | yes | — |
| 328 | C4×Dic53 | C2×D4 | 1 | 2 | yes | — |
| 329 | C4×Dic53 | C24 | 1 | 2 | yes | — |
| 330 | C4×Dic53 | C24 | 1 | 2 | yes | — |
| 331 | #11719917 | — | 2 | 2 | no | — |
| 332 | #11719917 | C2×Q8 | 1 | 4 | yes | complemented |
| 333 | C2×#88322 | C24 | 1 | 2 | yes | — |
| 334 | C2×#88322 | C24 | 1 | 2 | yes | — |
| 335 | C23×C53 | — | 2 | 1 | no | — |
| 336 | C23×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 337 | Q8×C53 | — | 2 | 1 | no | — |
| 338 | Q8×C53 | — | 8 | 2 | no | — |
| 339 | Q8×C53 | — | 8 | 2 | no | — |
| 340 | Q8×C53 | C22×Q8 | 1 | 2 | yes | — |
| 341 | D4×C53 | — | 2 | 4 | no | — |
| 342 | D4×C53 | — | 2 | 1 | no | — |
| 343 | D4×C53 | C22×Q8 | 1 | 2 | yes | — |
| 344 | C2×C4×C53 | — | 2 | 1 | no | — |
| 345 | C2×C4×C53 | — | 2 | 4 | no | — |
| 346 | C2×C4×C53 | — | 2 | 2 | no | — |
| 347 | C2×C4×C53 | — | 2 | 4 | no | — |
| 348 | C2×C4×C53 | — | 2 | 1 | no | — |
| 349 | C2×C4×C53 | — | 2 | 1 | no | — |
| 350 | C2×C4×C53 | — | 4 | 1 | no | — |
| 351 | C2×C4×C53 | — | 4 | 4 | no | — |
| 352 | C2×C4×C53 | — | 4 | 2 | no | — |
| 353 | C2×C4×C53 | — | 8 | 1 | no | — |
| 354 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 355 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 356 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 357 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 358 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 359 | C2×C4×C53 | C22×Q8 | 1 | 2 | yes | — |
| 360 | C2×C4×C53 | 2−1+4 | 1 | 2 | yes | — |
| 361 | C2×C4×C53 | C25 | 1 | 1 | yes | characteristic |
| 362 | C2×Dic53 | — | 2 | 4 | no | — |
| 363 | C2×Dic53 | — | 2 | 2 | no | — |
| 364 | C2×Dic53 | — | 2 | 4 | no | — |
| 365 | C2×Dic53 | — | 2 | 2 | no | — |
| 366 | C2×Dic53 | — | 2 | 2 | no | — |
| 367 | C2×Dic53 | — | 2 | 2 | no | — |
| 368 | C2×Dic53 | — | 4 | 2 | no | — |
| 369 | C2×Dic53 | — | 4 | 2 | no | — |
| 370 | C2×Dic53 | — | 4 | 4 | no | — |
| 371 | C2×Dic53 | — | 8 | 2 | no | — |
| 372 | C2×Dic53 | C22×D4 | 1 | 2 | yes | — |
| 373 | C2×Dic53 | C22×D4 | 1 | 2 | yes | — |
| 374 | C2×Dic53 | C22×D4 | 1 | 2 | yes | — |
| 375 | C2×Dic53 | C22×D4 | 1 | 2 | yes | — |
| 376 | Dic106 | — | 2 | 4 | no | — |
| 377 | Dic106 | — | 2 | 2 | no | — |
| 378 | Dic106 | — | 2 | 2 | no | — |
| 379 | Dic106 | — | 2 | 4 | no | — |
| 380 | Dic106 | — | 4 | 2 | no | — |
| 381 | Dic106 | — | 4 | 4 | no | — |
| 382 | Dic106 | — | 8 | 2 | no | — |
| 383 | Dic106 | — | 8 | 4 | no | — |
| 384 | Dic106 | — | 8 | 4 | no | — |
| 385 | Dic106 | — | 8 | 1 | no | — |
| 386 | Dic106 | #137 | 1 | 4 | yes | complemented |
| 387 | Dic106 | C22×Q8 | 1 | 4 | yes | — |
| 388 | C8×C53 | — | 2 | 4 | no | — |
| 389 | #88322 | — | 2 | 2 | no | — |
| 390 | #88322 | C22×Q8 | 1 | 4 | yes | — |
| 391 | Q8×#137 | — | 53 | 1 | no | maximal, Sylow |
| 392 | C22×C53 | — | 2 | 1 | no | — |
| 393 | C22×C53 | — | 2 | 1 | no | — |
| 394 | C22×C53 | — | 2 | 2 | no | — |
| 395 | C22×C53 | — | 4 | 1 | no | — |
| 396 | C22×C53 | — | 4 | 1 | no | — |
| 397 | C22×C53 | D4×Q8 | 1 | 2 | yes | — |
| 398 | C22×C53 | C23×D4 | 1 | 1 | yes | characteristic |
| 399 | C4×C53 | — | 2 | 1 | no | — |
| 400 | C4×C53 | — | 2 | 1 | no | — |
| 401 | C4×C53 | — | 2 | 2 | no | — |
| 402 | C4×C53 | — | 2 | 1 | no | — |
| 403 | C4×C53 | — | 4 | 4 | no | — |
| 404 | C4×C53 | — | 4 | 1 | no | — |
| 405 | C4×C53 | — | 4 | 1 | no | — |
| 406 | C4×C53 | D4×Q8 | 1 | 2 | yes | — |
| 407 | C4×C53 | C2×#137 | 1 | 2 | yes | — |
| 408 | C4×C53 | C23×Q8 | 1 | 1 | yes | characteristic |
| 409 | C4×C53 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 410 | Dic53 | — | 2 | 2 | no | — |
| 411 | Dic53 | — | 2 | 2 | no | — |
| 412 | Dic53 | — | 2 | 4 | no | — |
| 413 | Dic53 | — | 2 | 2 | no | — |
| 414 | Dic53 | — | 4 | 2 | no | — |
| 415 | Dic53 | — | 4 | 2 | no | — |
| 416 | Dic53 | — | 4 | 2 | no | — |
| 417 | Dic53 | C2×#137 | 1 | 4 | yes | — |
| 418 | Q8×#41 | — | 53 | 1 | no | — |
| 419 | C2×Q82 | — | 53 | 1 | no | — |
| 420 | #3387 | — | 53 | 2 | no | — |
| 421 | #3387 | — | 53 | 4 | no | — |
| 422 | #3385 | — | 53 | 2 | no | — |
| 423 | #3385 | — | 53 | 4 | no | — |
| 424 | Q8×Q16 | — | 53 | 2 | no | — |
| 425 | Q8×SD16 | — | 53 | 2 | no | — |
| 426 | #3165 | — | 53 | 2 | no | — |
| 427 | #3165 | — | 53 | 1 | no | — |
| 428 | #3079 | — | 53 | 2 | no | — |
| 429 | #3079 | D53 | 1 | 1 | yes | characteristic |
| 430 | #3078 | — | 53 | 2 | no | — |
| 431 | #3078 | — | 53 | 1 | no | — |
| 432 | Q8×M16 | — | 53 | 1 | no | — |
| 433 | C4×#137 | — | 53 | 2 | no | — |
| 434 | C4×#137 | — | 53 | 1 | no | — |
| 435 | C2×C53 | — | 2 | 2 | no | — |
| 436 | C2×C53 | — | 4 | 2 | no | — |
| 437 | C2×C53 | C2×D4×Q8 | 1 | 1 | yes | characteristic |
| 438 | C2×C53 | C22×#137 | 1 | 1 | yes | characteristic |
| 439 | C2×C53 | #3585 | 1 | 1 | yes | characteristic |
| 440 | C2×#137 | — | 53 | 1 | no | — |
| 441 | Q82 | — | 53 | 2 | no | — |
| 442 | Q82 | — | 53 | 4 | no | — |
| 443 | Q82 | — | 53 | 2 | no | — |
| 444 | Q82 | — | 53 | 1 | no | — |
| 445 | Q82 | — | 106 | 1 | no | — |
| 446 | Q82 | — | 106 | 2 | no | — |
| 447 | Q82 | — | 106 | 1 | no | — |
| 448 | #557 | — | 53 | 2 | no | — |
| 449 | #557 | — | 53 | 1 | no | — |
| 450 | #554 | — | 53 | 1 | no | — |
| 451 | #554 | — | 53 | 2 | no | — |
| 452 | #554 | — | 106 | 1 | no | — |
| 453 | #554 | — | 106 | 2 | no | — |
| 454 | D4×Q8 | — | 53 | 1 | no | — |
| 455 | D4×Q8 | — | 106 | 1 | no | — |
| 456 | #533 | — | 53 | 2 | no | — |
| 457 | #533 | — | 53 | 1 | no | — |
| 458 | #533 | — | 106 | 1 | no | — |
| 459 | #533 | — | 106 | 2 | no | — |
| 460 | C2×C4⋊Q8 | — | 53 | 2 | no | — |
| 461 | C2×C4⋊Q8 | — | 106 | 1 | no | — |
| 462 | C2×C4⋊Q8 | — | 106 | 2 | no | — |
| 463 | C2×C4⋊Q8 | C2×D53 | 1 | 1 | yes | characteristic |
| 464 | C4×#41 | — | 53 | 2 | no | — |
| 465 | C4×#41 | C2×D53 | 1 | 1 | yes | characteristic |
| 466 | C2×C4×Q8 | — | 53 | 1 | no | — |
| 467 | C2×C4×Q8 | — | 53 | 2 | no | — |
| 468 | C2×C4×Q8 | — | 53 | 1 | no | — |
| 469 | C2×C4×Q8 | — | 106 | 1 | no | — |
| 470 | C2×C4×Q8 | — | 106 | 1 | no | — |
| 471 | #501 | — | 53 | 4 | no | — |
| 472 | #501 | — | 53 | 4 | no | — |
| 473 | #501 | — | 53 | 4 | no | — |
| 474 | #500 | — | 53 | 2 | no | — |
| 475 | #500 | — | 53 | 4 | no | — |
| 476 | #498 | — | 53 | 2 | no | — |
| 477 | #498 | — | 53 | 4 | no | — |
| 478 | #479 | — | 53 | 4 | no | — |
| 479 | #479 | — | 53 | 4 | no | — |
| 480 | #479 | — | 53 | 4 | no | — |
| 481 | #477 | — | 53 | 4 | no | — |
| 482 | #477 | — | 53 | 2 | no | — |
| 483 | #477 | — | 53 | 4 | no | — |
| 484 | #477 | C2×D53 | 1 | 2 | yes | — |
| 485 | #476 | — | 53 | 4 | no | — |
| 486 | #476 | C2×D53 | 1 | 2 | yes | — |
| 487 | #475 | — | 53 | 4 | no | — |
| 488 | #475 | — | 53 | 2 | no | — |
| 489 | #475 | — | 53 | 4 | no | — |
| 490 | #475 | C2×D53 | 1 | 2 | yes | — |
| 491 | #474 | — | 53 | 4 | no | — |
| 492 | #474 | C2×D53 | 1 | 2 | yes | — |
| 493 | #446 | — | 53 | 4 | no | — |
| 494 | #446 | — | 53 | 2 | no | — |
| 495 | C8×Q8 | — | 53 | 2 | no | — |
| 496 | #441 | — | 53 | 2 | no | — |
| 497 | #441 | — | 53 | 4 | no | — |
| 498 | #440 | — | 53 | 2 | no | — |
| 499 | #440 | — | 53 | 4 | no | — |
| 500 | C4×Q16 | — | 53 | 2 | no | — |
| 501 | C4×Q16 | — | 53 | 4 | no | — |
| 502 | C4×SD16 | — | 53 | 2 | no | — |
| 503 | C4×SD16 | — | 53 | 4 | no | — |
| 504 | #428 | — | 53 | 2 | no | — |
| 505 | #428 | — | 53 | 1 | no | — |
| 506 | #428 | — | 53 | 2 | no | — |
| 507 | #428 | — | 53 | 2 | no | — |
| 508 | #428 | C2×D53 | 1 | 2 | yes | — |
| 509 | #423 | — | 53 | 2 | no | — |
| 510 | #423 | C2×D53 | 1 | 1 | yes | characteristic |
| 511 | #419 | — | 53 | 2 | no | — |
| 512 | #419 | — | 53 | 1 | no | — |
| 513 | #417 | — | 53 | 1 | no | — |
| 514 | #417 | C2×D53 | 1 | 2 | yes | — |
| 515 | C4×M16 | — | 53 | 2 | no | — |
| 516 | C4×M16 | — | 53 | 1 | no | — |
| 517 | C53 | Q8×#137 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 518 | C2×#41 | C22×D53 | 1 | 1 | yes | characteristic |
| 519 | C22×Q8 | — | 2 | 1 | no | — |
| 520 | C22×Q8 | — | 53 | 1 | no | — |
| 521 | C22×Q8 | — | 53 | 1 | no | — |
| 522 | C22×Q8 | — | 106 | 2 | no | — |
| 523 | C22×Q8 | — | 106 | 1 | no | — |
| 524 | #137 | — | 53 | 8 | no | — |
| 525 | C2×Q16 | — | 53 | 2 | no | — |
| 526 | C2×SD16 | — | 53 | 2 | no | — |
| 527 | C2×M16 | — | 53 | 1 | no | — |
| 528 | C2×M16 | — | 53 | 1 | no | — |
| 529 | C2×M16 | C22×D53 | 1 | 2 | yes | — |
| 530 | C4⋊Q8 | — | 2 | 1 | no | — |
| 531 | C4⋊Q8 | — | 2 | 1 | no | — |
| 532 | C4⋊Q8 | — | 53 | 4 | no | — |
| 533 | C4⋊Q8 | — | 53 | 4 | no | — |
| 534 | C4⋊Q8 | — | 53 | 2 | no | — |
| 535 | C4⋊Q8 | — | 53 | 2 | no | — |
| 536 | C4⋊Q8 | — | 53 | 1 | no | — |
| 537 | C4⋊Q8 | — | 53 | 1 | no | — |
| 538 | C4⋊Q8 | — | 106 | 1 | no | — |
| 539 | C4⋊Q8 | — | 106 | 1 | no | — |
| 540 | C4⋊Q8 | — | 106 | 2 | no | — |
| 541 | C4⋊Q8 | — | 106 | 2 | no | — |
| 542 | C4⋊Q8 | — | 106 | 2 | no | — |
| 543 | C4⋊Q8 | — | 106 | 4 | no | — |
| 544 | C4⋊Q8 | — | 106 | 2 | no | — |
| 545 | C4⋊Q8 | — | 106 | 2 | no | — |
| 546 | C4⋊Q8 | — | 106 | 2 | no | — |
| 547 | C4⋊Q8 | — | 106 | 4 | no | — |
| 548 | C4⋊Q8 | — | 106 | 4 | no | — |
| 549 | C4⋊Q8 | — | 106 | 4 | no | — |
| 550 | C4⋊Q8 | — | 106 | 4 | no | — |
| 551 | C4⋊Q8 | C22×D53 | 1 | 2 | yes | — |
| 552 | C4⋊Q8 | C22×D53 | 1 | 2 | yes | — |
| 553 | #125 | — | 53 | 2 | no | — |
| 554 | #125 | — | 53 | 2 | no | — |
| 555 | #125 | — | 53 | 2 | no | — |
| 556 | #125 | — | 106 | 2 | no | — |
| 557 | #125 | — | 106 | 2 | no | — |
| 558 | #125 | — | 106 | 2 | no | — |
| 559 | C22⋊Q8 | — | 106 | 2 | no | — |
| 560 | C22⋊Q8 | — | 106 | 2 | no | — |
| 561 | C22⋊Q8 | — | 106 | 2 | no | — |
| 562 | C22⋊Q8 | — | 106 | 2 | no | — |
| 563 | C22⋊Q8 | — | 106 | 2 | no | — |
| 564 | C22⋊Q8 | — | 106 | 2 | no | — |
| 565 | C22⋊Q8 | — | 106 | 1 | no | — |
| 566 | C22⋊Q8 | — | 106 | 2 | no | — |
| 567 | C22⋊Q8 | — | 106 | 1 | no | — |
| 568 | C22⋊Q8 | — | 106 | 1 | no | — |
| 569 | C22⋊Q8 | — | 106 | 1 | no | — |
| 570 | C4×Q8 | — | 53 | 1 | no | — |
| 571 | C4×Q8 | — | 53 | 2 | no | — |
| 572 | C4×Q8 | — | 53 | 1 | no | — |
| 573 | C4×Q8 | — | 53 | 1 | no | — |
| 574 | C4×Q8 | — | 53 | 2 | no | — |
| 575 | C4×Q8 | — | 53 | 1 | no | — |
| 576 | C4×Q8 | — | 53 | 2 | no | — |
| 577 | C4×Q8 | — | 53 | 2 | no | — |
| 578 | C4×Q8 | — | 53 | 4 | no | — |
| 579 | C4×Q8 | — | 53 | 4 | no | — |
| 580 | C4×Q8 | — | 53 | 2 | no | — |
| 581 | C4×Q8 | — | 53 | 2 | no | — |
| 582 | C4×Q8 | — | 106 | 2 | no | — |
| 583 | C4×Q8 | — | 106 | 2 | no | — |
| 584 | C4×Q8 | — | 106 | 2 | no | — |
| 585 | C4×Q8 | — | 106 | 1 | no | — |
| 586 | C4×Q8 | — | 106 | 1 | no | — |
| 587 | C4×Q8 | — | 106 | 2 | no | — |
| 588 | C4×Q8 | — | 106 | 2 | no | — |
| 589 | C4×Q8 | — | 106 | 2 | no | — |
| 590 | C4×Q8 | — | 106 | 4 | no | — |
| 591 | C4×Q8 | — | 106 | 2 | no | — |
| 592 | C4×Q8 | — | 106 | 1 | no | — |
| 593 | C4×Q8 | — | 106 | 1 | no | — |
| 594 | C4×Q8 | — | 106 | 1 | no | — |
| 595 | C4×Q8 | — | 106 | 1 | no | — |
| 596 | C4×Q8 | C22×D53 | 1 | 1 | yes | characteristic |
| 597 | C4×Q8 | C22×D53 | 1 | 1 | yes | characteristic |
| 598 | C4×D4 | — | 2 | 1 | no | — |
| 599 | C4×D4 | — | 2 | 1 | no | — |
| 600 | C4×D4 | — | 53 | 2 | no | — |
| 601 | C4×D4 | — | 53 | 2 | no | — |
| 602 | C4×D4 | — | 106 | 2 | no | — |
| 603 | C4×D4 | — | 106 | 2 | no | — |
| 604 | C4×D4 | C22×D53 | 1 | 1 | yes | characteristic |
| 605 | C4×D4 | C22×D53 | 1 | 1 | yes | characteristic |
| 606 | #117 | — | 2 | 1 | no | — |
| 607 | #117 | — | 53 | 2 | no | — |
| 608 | #117 | — | 106 | 2 | no | — |
| 609 | #117 | C22×D53 | 1 | 1 | yes | characteristic |
| 610 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 611 | C2×C4⋊C4 | — | 53 | 2 | no | — |
| 612 | C2×C4⋊C4 | — | 53 | 1 | no | — |
| 613 | C2×C4⋊C4 | — | 53 | 1 | no | — |
| 614 | C2×C4⋊C4 | — | 106 | 2 | no | — |
| 615 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 616 | C2×C4⋊C4 | — | 106 | 2 | no | — |
| 617 | C2×C4⋊C4 | — | 106 | 2 | no | — |
| 618 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 619 | C2×C4⋊C4 | C22×D53 | 1 | 2 | yes | — |
| 620 | C2×C42 | — | 2 | 1 | no | — |
| 621 | C2×C42 | — | 53 | 2 | no | — |
| 622 | C2×C42 | — | 106 | 2 | no | — |
| 623 | C2×C42 | — | 106 | 2 | no | — |
| 624 | C2×C42 | — | 106 | 1 | no | — |
| 625 | C2×C42 | C22×D53 | 1 | 1 | yes | characteristic |
| 626 | #107 | — | 53 | 4 | no | — |
| 627 | #107 | — | 53 | 2 | no | — |
| 628 | #107 | — | 53 | 4 | no | — |
| 629 | #107 | — | 53 | 4 | no | — |
| 630 | #107 | C22×D53 | 1 | 4 | yes | — |
| 631 | #106 | — | 53 | 4 | no | — |
| 632 | #106 | — | 53 | 2 | no | — |
| 633 | #106 | — | 53 | 4 | no | — |
| 634 | #106 | — | 53 | 4 | no | — |
| 635 | #106 | C22×D53 | 1 | 4 | yes | — |
| 636 | C4⋊C8 | — | 53 | 4 | no | — |
| 637 | C4⋊C8 | — | 53 | 4 | no | — |
| 638 | C4⋊C8 | C22×D53 | 1 | 2 | yes | — |
| 639 | C4⋊C8 | C22×D53 | 1 | 2 | yes | — |
| 640 | #103 | — | 53 | 2 | no | — |
| 641 | #103 | — | 53 | 4 | no | — |
| 642 | #103 | — | 53 | 4 | no | — |
| 643 | #103 | — | 53 | 2 | no | — |
| 644 | #103 | — | 53 | 2 | no | — |
| 645 | #103 | C22×D53 | 1 | 4 | yes | — |
| 646 | #102 | — | 53 | 2 | no | — |
| 647 | #102 | C22×D53 | 1 | 4 | yes | — |
| 648 | #97 | — | 53 | 4 | no | — |
| 649 | #97 | — | 53 | 2 | no | — |
| 650 | C4×C8 | — | 53 | 4 | no | — |
| 651 | C4×C8 | — | 53 | 2 | no | — |
| 652 | #41 | — | 2 | 2 | no | — |
| 653 | #41 | Q8×D53 | 1 | 4 | yes | — |
| 654 | C2×Q8 | — | 2 | 2 | no | — |
| 655 | C2×Q8 | — | 2 | 2 | no | — |
| 656 | C2×Q8 | — | 8 | 2 | no | — |
| 657 | C2×Q8 | — | 53 | 1 | no | — |
| 658 | C2×Q8 | — | 53 | 2 | no | — |
| 659 | C2×Q8 | — | 53 | 1 | no | — |
| 660 | C2×Q8 | — | 53 | 4 | no | — |
| 661 | C2×Q8 | — | 53 | 2 | no | — |
| 662 | C2×Q8 | — | 106 | 2 | no | — |
| 663 | C2×Q8 | — | 106 | 4 | no | — |
| 664 | C2×Q8 | — | 106 | 4 | no | — |
| 665 | C2×Q8 | — | 106 | 2 | no | — |
| 666 | C2×Q8 | — | 106 | 4 | no | — |
| 667 | C2×Q8 | — | 106 | 1 | no | — |
| 668 | C2×Q8 | — | 106 | 1 | no | — |
| 669 | C2×Q8 | — | 106 | 1 | no | — |
| 670 | C2×Q8 | — | 106 | 2 | no | — |
| 671 | C2×Q8 | — | 424 | 4 | no | — |
| 672 | C2×Q8 | — | 212 | 4 | no | — |
| 673 | C2×Q8 | C23×D53 | 1 | 1 | yes | characteristic |
| 674 | C2×D4 | — | 2 | 1 | no | — |
| 675 | C2×D4 | C23×D53 | 1 | 1 | yes | characteristic |
| 676 | C22×C4 | — | 2 | 1 | no | — |
| 677 | C22×C4 | — | 2 | 2 | no | — |
| 678 | C22×C4 | — | 2 | 1 | no | — |
| 679 | C22×C4 | — | 2 | 1 | no | — |
| 680 | C22×C4 | — | 53 | 2 | no | — |
| 681 | C22×C4 | — | 53 | 2 | no | — |
| 682 | C22×C4 | — | 106 | 2 | no | — |
| 683 | C22×C4 | — | 106 | 2 | no | — |
| 684 | C22×C4 | — | 106 | 1 | no | — |
| 685 | C22×C4 | — | 106 | 1 | no | — |
| 686 | C22×C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 687 | C22×C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 688 | C22×C4 | C23×D53 | 1 | 1 | yes | characteristic |
| 689 | Q16 | — | 53 | 8 | no | — |
| 690 | SD16 | — | 53 | 8 | no | — |
| 691 | M16 | — | 2 | 4 | no | — |
| 692 | M16 | — | 53 | 4 | no | — |
| 693 | M16 | — | 106 | 2 | no | — |
| 694 | C2×C8 | — | 53 | 2 | no | — |
| 695 | C2×C8 | — | 53 | 2 | no | — |
| 696 | C2×C8 | C23×D53 | 1 | 4 | yes | — |
| 697 | C4⋊C4 | — | 2 | 2 | no | — |
| 698 | C4⋊C4 | — | 2 | 2 | no | — |
| 699 | C4⋊C4 | — | 2 | 2 | no | — |
| 700 | C4⋊C4 | — | 2 | 1 | no | — |
| 701 | C4⋊C4 | — | 2 | 1 | no | — |
| 702 | C4⋊C4 | — | 53 | 2 | no | — |
| 703 | C4⋊C4 | — | 53 | 1 | no | — |
| 704 | C4⋊C4 | — | 53 | 2 | no | — |
| 705 | C4⋊C4 | — | 53 | 2 | no | — |
| 706 | C4⋊C4 | — | 53 | 2 | no | — |
| 707 | C4⋊C4 | — | 53 | 2 | no | — |
| 708 | C4⋊C4 | — | 53 | 1 | no | — |
| 709 | C4⋊C4 | — | 53 | 2 | no | — |
| 710 | C4⋊C4 | — | 53 | 2 | no | — |
| 711 | C4⋊C4 | — | 53 | 2 | no | — |
| 712 | C4⋊C4 | — | 106 | 4 | no | — |
| 713 | C4⋊C4 | — | 106 | 4 | no | — |
| 714 | C4⋊C4 | — | 106 | 2 | no | — |
| 715 | C4⋊C4 | — | 106 | 2 | no | — |
| 716 | C4⋊C4 | — | 106 | 2 | no | — |
| 717 | C4⋊C4 | — | 106 | 4 | no | — |
| 718 | C4⋊C4 | — | 106 | 4 | no | — |
| 719 | C4⋊C4 | — | 106 | 2 | no | — |
| 720 | C4⋊C4 | — | 106 | 2 | no | — |
| 721 | C4⋊C4 | — | 106 | 2 | no | — |
| 722 | C4⋊C4 | — | 106 | 2 | no | — |
| 723 | C4⋊C4 | — | 106 | 2 | no | — |
| 724 | C4⋊C4 | — | 106 | 1 | no | — |
| 725 | C4⋊C4 | — | 106 | 2 | no | — |
| 726 | C4⋊C4 | — | 106 | 2 | no | — |
| 727 | C4⋊C4 | — | 106 | 2 | no | — |
| 728 | C4⋊C4 | — | 106 | 1 | no | — |
| 729 | C4⋊C4 | — | 106 | 2 | no | — |
| 730 | C4⋊C4 | — | 106 | 1 | no | — |
| 731 | C4⋊C4 | C23×D53 | 1 | 4 | yes | — |
| 732 | C4⋊C4 | C23×D53 | 1 | 1 | yes | characteristic |
| 733 | C4⋊C4 | C23×D53 | 1 | 1 | yes | characteristic |
| 734 | C22⋊C4 | — | 2 | 1 | no | — |
| 735 | C22⋊C4 | — | 2 | 1 | no | — |
| 736 | C22⋊C4 | — | 2 | 1 | no | — |
| 737 | C22⋊C4 | — | 106 | 2 | no | — |
| 738 | C22⋊C4 | — | 106 | 2 | no | — |
| 739 | C22⋊C4 | — | 106 | 2 | no | — |
| 740 | C42 | — | 2 | 1 | no | — |
| 741 | C42 | — | 2 | 1 | no | — |
| 742 | C42 | — | 2 | 1 | no | — |
| 743 | C42 | — | 53 | 2 | no | — |
| 744 | C42 | — | 53 | 2 | no | — |
| 745 | C42 | — | 53 | 2 | no | — |
| 746 | C42 | — | 53 | 2 | no | — |
| 747 | C42 | — | 106 | 2 | no | — |
| 748 | C42 | — | 106 | 2 | no | — |
| 749 | C42 | — | 106 | 4 | no | — |
| 750 | C42 | — | 106 | 4 | no | — |
| 751 | C42 | — | 106 | 2 | no | — |
| 752 | C42 | — | 106 | 2 | no | — |
| 753 | C42 | — | 106 | 2 | no | — |
| 754 | C42 | D4×D53 | 1 | 1 | yes | characteristic |
| 755 | C42 | D4×D53 | 1 | 1 | yes | characteristic |
| 756 | C42 | C23×D53 | 1 | 1 | yes | characteristic |
| 757 | C42 | C23×D53 | 1 | 1 | yes | characteristic |
| 758 | C23 | — | 2 | 1 | no | — |
| 759 | C23 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 760 | Q8 | — | 2 | 1 | no | — |
| 761 | Q8 | — | 8 | 2 | no | — |
| 762 | Q8 | — | 8 | 2 | no | — |
| 763 | Q8 | — | 53 | 4 | no | — |
| 764 | Q8 | — | 53 | 4 | no | — |
| 765 | Q8 | — | 106 | 4 | no | — |
| 766 | Q8 | — | 106 | 4 | no | — |
| 767 | Q8 | — | 106 | 2 | no | — |
| 768 | Q8 | — | 106 | 2 | no | — |
| 769 | Q8 | — | 424 | 1 | no | — |
| 770 | Q8 | — | 424 | 2 | no | — |
| 771 | Q8 | — | 424 | 4 | no | — |
| 772 | Q8 | — | 424 | 4 | no | — |
| 773 | Q8 | — | 212 | 4 | no | — |
| 774 | Q8 | — | 212 | 2 | no | — |
| 775 | Q8 | C2×Q8×D53 | 1 | 2 | yes | — |
| 776 | D4 | — | 2 | 4 | no | — |
| 777 | D4 | — | 2 | 1 | no | — |
| 778 | D4 | C2×Q8×D53 | 1 | 2 | yes | — |
| 779 | C2×C4 | — | 2 | 1 | no | — |
| 780 | C2×C4 | — | 2 | 4 | no | — |
| 781 | C2×C4 | — | 2 | 2 | no | — |
| 782 | C2×C4 | — | 2 | 1 | no | — |
| 783 | C2×C4 | — | 2 | 1 | no | — |
| 784 | C2×C4 | — | 2 | 4 | no | — |
| 785 | C2×C4 | — | 4 | 1 | no | — |
| 786 | C2×C4 | — | 4 | 4 | no | — |
| 787 | C2×C4 | — | 4 | 2 | no | — |
| 788 | C2×C4 | — | 8 | 1 | no | — |
| 789 | C2×C4 | — | 53 | 2 | no | — |
| 790 | C2×C4 | — | 53 | 2 | no | — |
| 791 | C2×C4 | — | 53 | 2 | no | — |
| 792 | C2×C4 | — | 53 | 2 | no | — |
| 793 | C2×C4 | — | 106 | 4 | no | — |
| 794 | C2×C4 | — | 106 | 4 | no | — |
| 795 | C2×C4 | — | 106 | 2 | no | — |
| 796 | C2×C4 | — | 106 | 2 | no | — |
| 797 | C2×C4 | — | 106 | 2 | no | — |
| 798 | C2×C4 | — | 106 | 2 | no | — |
| 799 | C2×C4 | — | 424 | 2 | no | — |
| 800 | C2×C4 | — | 212 | 4 | no | — |
| 801 | C2×C4 | — | 212 | 2 | no | — |
| 802 | C2×C4 | — | 212 | 2 | no | — |
| 803 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 804 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 805 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 806 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 807 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 808 | C2×C4 | C2×Q8×D53 | 1 | 2 | yes | — |
| 809 | C2×C4 | #13133264 | 1 | 2 | yes | — |
| 810 | C2×C4 | C24×D53 | 1 | 1 | yes | characteristic |
| 811 | C8 | — | 2 | 4 | no | — |
| 812 | C8 | — | 53 | 4 | no | — |
| 813 | C8 | — | 106 | 2 | no | — |
| 814 | C22 | — | 2 | 1 | no | — |
| 815 | C22 | — | 2 | 1 | no | — |
| 816 | C22 | — | 2 | 2 | no | — |
| 817 | C22 | — | 4 | 1 | no | — |
| 818 | C22 | — | 4 | 1 | no | — |
| 819 | C22 | #16811286 | 1 | 2 | yes | — |
| 820 | C22 | C22×D4×D53 | 1 | 1 | yes | characteristic |
| 821 | C4 | — | 2 | 1 | no | — |
| 822 | C4 | — | 2 | 2 | no | — |
| 823 | C4 | — | 2 | 1 | no | — |
| 824 | C4 | — | 2 | 1 | no | — |
| 825 | C4 | — | 4 | 1 | no | — |
| 826 | C4 | — | 4 | 4 | no | — |
| 827 | C4 | — | 4 | 1 | no | — |
| 828 | C4 | — | 53 | 4 | no | — |
| 829 | C4 | — | 106 | 2 | no | — |
| 830 | C4 | — | 106 | 4 | no | — |
| 831 | C4 | — | 106 | 2 | no | — |
| 832 | C4 | — | 106 | 2 | no | — |
| 833 | C4 | — | 212 | 2 | no | — |
| 834 | C4 | — | 212 | 2 | no | — |
| 835 | C4 | — | 212 | 2 | no | — |
| 836 | C4 | #16811286 | 1 | 2 | yes | — |
| 837 | C4 | #137×D53 | 1 | 2 | yes | — |
| 838 | C4 | C22×Q8×D53 | 1 | 1 | yes | characteristic |
| 839 | C4 | C2×#13133264 | 1 | 1 | yes | characteristic |
| 840 | C2 | — | 2 | 2 | no | — |
| 841 | C2 | — | 4 | 2 | no | — |
| 842 | C2 | C2×#16811286 | 1 | 1 | yes | characteristic |
| 843 | C2 | C2×#137×D53 | 1 | 1 | yes | characteristic |
| 844 | C2 | #20289491 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta