Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
6608 conjugacy classes of subgroups.
The subgroup lattice has 1216 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #20289405 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20289403 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #20289402 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #20289209 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #20289111 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #20288973 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #20288967 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #20288717 | C2 | 1 | 6 | yes | maximal, complemented |
| 9 | #20288714 | C2 | 1 | 6 | yes | maximal, complemented |
| 10 | #20288685 | C2 | 1 | 6 | yes | maximal, complemented |
| 11 | #20288682 | C2 | 1 | 6 | yes | maximal, complemented |
| 12 | #20288631 | C2 | 1 | 6 | yes | maximal, complemented |
| 13 | #20288629 | C2 | 1 | 6 | yes | maximal, complemented |
| 14 | #20288009 | C2 | 1 | 3 | yes | maximal, complemented |
| 15 | C53×#3567 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C53⋊#564 | C22 | 1 | 3 | yes | complemented |
| 17 | #16811371 | C22 | 1 | 3 | yes | complemented |
| 18 | #16811367 | C22 | 1 | 3 | yes | complemented |
| 19 | #16811367 | C22 | 1 | 3 | yes | complemented |
| 20 | #16811364 | C22 | 1 | 2 | yes | — |
| 21 | #16811363 | C22 | 1 | 6 | yes | — |
| 22 | #16811361 | C22 | 1 | 6 | yes | — |
| 23 | #16811360 | C22 | 1 | 2 | yes | — |
| 24 | #16811350 | C22 | 1 | 6 | yes | complemented |
| 25 | #16811350 | C22 | 1 | 6 | yes | complemented |
| 26 | #16811327 | C22 | 1 | 6 | yes | complemented |
| 27 | #16811327 | C22 | 1 | 6 | yes | complemented |
| 28 | #16811326 | C22 | 1 | 6 | yes | — |
| 29 | #16811326 | C22 | 1 | 6 | yes | complemented |
| 30 | #16811325 | C22 | 1 | 6 | yes | complemented |
| 31 | #16811324 | C22 | 1 | 6 | yes | — |
| 32 | #16811324 | C22 | 1 | 6 | yes | — |
| 33 | #16811324 | C22 | 1 | 6 | yes | complemented |
| 34 | #16811322 | C22 | 1 | 6 | yes | — |
| 35 | #16811322 | C22 | 1 | 6 | yes | — |
| 36 | #16811322 | C22 | 1 | 6 | yes | complemented |
| 37 | #16811321 | C22 | 1 | 6 | yes | — |
| 38 | #16811319 | C22 | 1 | 6 | yes | — |
| 39 | #16811318 | C22 | 1 | 6 | yes | — |
| 40 | #16811318 | C22 | 1 | 6 | yes | — |
| 41 | #16811318 | C22 | 1 | 6 | yes | complemented |
| 42 | #16811317 | C22 | 1 | 6 | yes | — |
| 43 | #16811317 | C22 | 1 | 6 | yes | complemented |
| 44 | #16811316 | C22 | 1 | 6 | yes | — |
| 45 | #16811316 | C22 | 1 | 6 | yes | — |
| 46 | #16811316 | C22 | 1 | 6 | yes | complemented |
| 47 | #16811315 | C22 | 1 | 6 | yes | complemented |
| 48 | #16811314 | C22 | 1 | 6 | yes | complemented |
| 49 | #16811310 | C22 | 1 | 6 | yes | — |
| 50 | #16811310 | C22 | 1 | 6 | yes | complemented |
| 51 | #16811309 | C22 | 1 | 6 | yes | — |
| 52 | #16811309 | C22 | 1 | 6 | yes | complemented |
| 53 | #16811307 | C22 | 1 | 6 | yes | complemented |
| 54 | #16811306 | C22 | 1 | 6 | yes | — |
| 55 | #16811306 | C22 | 1 | 6 | yes | complemented |
| 56 | #16811305 | C22 | 1 | 6 | yes | — |
| 57 | #16811305 | C22 | 1 | 6 | yes | complemented |
| 58 | #16811294 | C22 | 1 | 6 | yes | — |
| 59 | #16811293 | C22 | 1 | 6 | yes | — |
| 60 | #16811291 | C22 | 1 | 6 | yes | — |
| 61 | #16811291 | C22 | 1 | 6 | yes | — |
| 62 | #16811291 | C22 | 1 | 6 | yes | complemented |
| 63 | #16811291 | C22 | 1 | 6 | yes | complemented |
| 64 | #16811274 | C22 | 1 | 6 | yes | — |
| 65 | #16811273 | C22 | 1 | 6 | yes | — |
| 66 | #16811271 | C22 | 1 | 6 | yes | — |
| 67 | #16811271 | C22 | 1 | 6 | yes | — |
| 68 | #16811271 | C22 | 1 | 6 | yes | complemented |
| 69 | #16811271 | C22 | 1 | 6 | yes | complemented |
| 70 | #16811232 | C22 | 1 | 6 | yes | — |
| 71 | #16811232 | C22 | 1 | 6 | yes | — |
| 72 | #16811232 | C22 | 1 | 6 | yes | complemented |
| 73 | #16811230 | C22 | 1 | 6 | yes | complemented |
| 74 | #16811229 | C22 | 1 | 6 | yes | — |
| 75 | #16811226 | C22 | 1 | 6 | yes | — |
| 76 | #16811225 | C22 | 1 | 6 | yes | — |
| 77 | #16811225 | C22 | 1 | 6 | yes | — |
| 78 | #16811225 | C22 | 1 | 6 | yes | — |
| 79 | #16811225 | C22 | 1 | 6 | yes | — |
| 80 | #16811225 | C22 | 1 | 6 | yes | complemented |
| 81 | #16811224 | C22 | 1 | 6 | yes | — |
| 82 | #16811223 | C22 | 1 | 6 | yes | — |
| 83 | #16811223 | C22 | 1 | 6 | yes | — |
| 84 | #16811223 | C22 | 1 | 6 | yes | complemented |
| 85 | #16811222 | C22 | 1 | 6 | yes | — |
| 86 | #16811221 | C22 | 1 | 6 | yes | — |
| 87 | #16811219 | C22 | 1 | 6 | yes | — |
| 88 | #16811219 | C22 | 1 | 6 | yes | — |
| 89 | #16811217 | C22 | 1 | 6 | yes | — |
| 90 | #16811216 | C22 | 1 | 6 | yes | — |
| 91 | #16811215 | C22 | 1 | 6 | yes | — |
| 92 | #16811203 | C22 | 1 | 6 | yes | — |
| 93 | #16811203 | C22 | 1 | 6 | yes | — |
| 94 | #16811200 | C22 | 1 | 6 | yes | — |
| 95 | #16811200 | C22 | 1 | 6 | yes | — |
| 96 | #16811179 | C22 | 1 | 3 | yes | — |
| 97 | #16811177 | C22 | 1 | 3 | yes | — |
| 98 | #16811175 | C22 | 1 | 3 | yes | — |
| 99 | #16811172 | C22 | 1 | 3 | yes | — |
| 100 | #16811170 | C22 | 1 | 3 | yes | — |
| 101 | #16811170 | C22 | 1 | 6 | yes | complemented |
| 102 | #16811168 | C22 | 1 | 3 | yes | — |
| 103 | #16811168 | C22 | 1 | 6 | yes | complemented |
| 104 | #16811158 | C22 | 1 | 3 | yes | — |
| 105 | #16811157 | C22 | 1 | 3 | yes | — |
| 106 | #16811156 | C22 | 1 | 6 | yes | — |
| 107 | #16811156 | C22 | 1 | 6 | yes | — |
| 108 | #16811156 | C22 | 1 | 6 | yes | complemented |
| 109 | #16811153 | C22 | 1 | 6 | yes | complemented |
| 110 | #16811152 | C22 | 1 | 3 | yes | — |
| 111 | #16811151 | C22 | 1 | 6 | yes | — |
| 112 | #16811151 | C22 | 1 | 6 | yes | complemented |
| 113 | #16811150 | C22 | 1 | 6 | yes | — |
| 114 | #16811150 | C22 | 1 | 6 | yes | complemented |
| 115 | C2×#13133207 | C22 | 1 | 6 | yes | complemented |
| 116 | #125×D53 | C22 | 1 | 6 | yes | complemented |
| 117 | #16811136 | C22 | 1 | 3 | yes | — |
| 118 | #16811133 | C22 | 1 | 3 | yes | — |
| 119 | #16811132 | C22 | 1 | 6 | yes | — |
| 120 | #16811131 | C22 | 1 | 6 | yes | — |
| 121 | #16811104 | C22 | 1 | 6 | yes | complemented |
| 122 | #16811103 | C22 | 1 | 6 | yes | complemented |
| 123 | #16811102 | C22 | 1 | 6 | yes | complemented |
| 124 | #16811102 | C22 | 1 | 6 | yes | complemented |
| 125 | C4×#11719949 | C22 | 1 | 3 | yes | — |
| 126 | #16811091 | C22 | 1 | 6 | yes | — |
| 127 | C4×#11719947 | C22 | 1 | 3 | yes | — |
| 128 | C4×#11719947 | C22 | 1 | 6 | yes | — |
| 129 | C2×C42×D53 | C22 | 1 | 1 | yes | characteristic |
| 130 | C53×#564 | C22 | 1 | 1 | yes | characteristic, complemented |
| 131 | C53×#562 | C22 | 1 | 3 | yes | complemented |
| 132 | C53×#553 | C22 | 1 | 6 | yes | complemented |
| 133 | C53×#552 | C22 | 1 | 6 | yes | complemented |
| 134 | C53×#540 | C22 | 1 | 6 | yes | — |
| 135 | C53×#539 | C22 | 1 | 6 | yes | — |
| 136 | C53×#529 | C22 | 1 | 3 | yes | — |
| 137 | C2×#11719949 | C23 | 1 | 3 | yes | — |
| 138 | C2×#11719945 | C23 | 1 | 6 | yes | — |
| 139 | C2×#11719945 | C23 | 1 | 6 | yes | — |
| 140 | C2×#11719945 | C23 | 1 | 6 | yes | — |
| 141 | C2×#11719947 | C23 | 1 | 6 | yes | — |
| 142 | C2×#11719947 | C23 | 1 | 6 | yes | — |
| 143 | C2×#11719947 | C23 | 1 | 6 | yes | — |
| 144 | C2×#11719947 | C23 | 1 | 3 | yes | — |
| 145 | C22×C4×D53 | C23 | 1 | 3 | yes | — |
| 146 | #13133216 | C23 | 1 | 6 | yes | — |
| 147 | #13133216 | C23 | 1 | 6 | yes | — |
| 148 | #13133216 | C23 | 1 | 3 | yes | — |
| 149 | #13133216 | C23 | 1 | 3 | yes | — |
| 150 | #13133215 | C23 | 1 | 3 | yes | — |
| 151 | #13133214 | C23 | 1 | 2 | yes | — |
| 152 | #13133213 | C23 | 1 | 6 | yes | — |
| 153 | #13133213 | C23 | 1 | 6 | yes | — |
| 154 | #13133213 | C23 | 1 | 6 | yes | — |
| 155 | #13133213 | C23 | 1 | 6 | yes | — |
| 156 | #13133213 | C23 | 1 | 3 | yes | — |
| 157 | #13133212 | C23 | 1 | 6 | yes | — |
| 158 | #13133212 | C23 | 1 | 6 | yes | — |
| 159 | #13133212 | C23 | 1 | 6 | yes | — |
| 160 | #13133212 | C23 | 1 | 6 | yes | — |
| 161 | #13133212 | C23 | 1 | 6 | yes | — |
| 162 | #13133212 | C23 | 1 | 6 | yes | — |
| 163 | #13133212 | C23 | 1 | 6 | yes | — |
| 164 | #13133211 | C23 | 1 | 2 | yes | — |
| 165 | #13133211 | C23 | 1 | 6 | yes | — |
| 166 | #13133211 | C23 | 1 | 6 | yes | — |
| 167 | #13133211 | C23 | 1 | 2 | yes | — |
| 168 | #13133211 | C23 | 1 | 2 | yes | — |
| 169 | #13133210 | C23 | 1 | 6 | yes | — |
| 170 | #13133210 | C23 | 1 | 6 | yes | — |
| 171 | #13133210 | C23 | 1 | 6 | yes | — |
| 172 | #13133210 | C23 | 1 | 6 | yes | — |
| 173 | #13133210 | C23 | 1 | 6 | yes | — |
| 174 | #13133209 | C23 | 1 | 6 | yes | — |
| 175 | #13133209 | C23 | 1 | 3 | yes | — |
| 176 | #13133208 | C23 | 1 | 6 | yes | — |
| 177 | #13133208 | C23 | 1 | 6 | yes | — |
| 178 | #13133208 | C23 | 1 | 6 | yes | — |
| 179 | #13133208 | C23 | 1 | 6 | yes | — |
| 180 | #13133207 | C23 | 1 | 6 | yes | — |
| 181 | #13133207 | C23 | 1 | 6 | yes | — |
| 182 | #13133207 | C23 | 1 | 6 | yes | — |
| 183 | #13133207 | C23 | 1 | 6 | yes | — |
| 184 | #13133207 | C23 | 1 | 6 | yes | — |
| 185 | #13133207 | C23 | 1 | 6 | yes | — |
| 186 | #13133207 | C23 | 1 | 6 | yes | — |
| 187 | #13133207 | C23 | 1 | 6 | yes | — |
| 188 | #13133207 | C23 | 1 | 6 | yes | — |
| 189 | #13133207 | C23 | 1 | 6 | yes | — |
| 190 | #13133207 | C23 | 1 | 6 | yes | — |
| 191 | #13133207 | C23 | 1 | 6 | yes | — |
| 192 | #13133207 | C23 | 1 | 6 | yes | — |
| 193 | #13133207 | C23 | 1 | 6 | yes | — |
| 194 | #13133205 | C23 | 1 | 3 | yes | — |
| 195 | #13133203 | C23 | 1 | 6 | yes | — |
| 196 | #13133203 | C23 | 1 | 6 | yes | — |
| 197 | #13133202 | C23 | 1 | 6 | yes | — |
| 198 | #13133202 | C23 | 1 | 6 | yes | — |
| 199 | #13133202 | C23 | 1 | 6 | yes | — |
| 200 | #13133202 | C23 | 1 | 6 | yes | — |
| 201 | #13133202 | C23 | 1 | 6 | yes | — |
| 202 | #13133202 | C23 | 1 | 6 | yes | — |
| 203 | #13133202 | C23 | 1 | 6 | yes | — |
| 204 | #13133202 | C23 | 1 | 6 | yes | — |
| 205 | #13133201 | C23 | 1 | 6 | yes | — |
| 206 | #13133201 | C23 | 1 | 6 | yes | — |
| 207 | #13133201 | C23 | 1 | 6 | yes | — |
| 208 | #13133201 | C23 | 1 | 6 | yes | — |
| 209 | #13133200 | C23 | 1 | 6 | yes | — |
| 210 | #13133200 | C23 | 1 | 6 | yes | — |
| 211 | #13133200 | C23 | 1 | 6 | yes | — |
| 212 | #13133199 | C23 | 1 | 6 | yes | — |
| 213 | #13133199 | C23 | 1 | 6 | yes | — |
| 214 | #13133199 | C23 | 1 | 6 | yes | — |
| 215 | #13133199 | C23 | 1 | 6 | yes | — |
| 216 | #13133199 | C23 | 1 | 6 | yes | — |
| 217 | #13133199 | C23 | 1 | 6 | yes | — |
| 218 | #13133199 | C23 | 1 | 6 | yes | — |
| 219 | #13133199 | C23 | 1 | 6 | yes | — |
| 220 | #13133198 | C23 | 1 | 6 | yes | — |
| 221 | #13133198 | C23 | 1 | 6 | yes | — |
| 222 | #13133197 | C23 | 1 | 3 | yes | — |
| 223 | #13133196 | C23 | 1 | 3 | yes | — |
| 224 | #13133195 | C23 | 1 | 6 | yes | — |
| 225 | #13133195 | C23 | 1 | 6 | yes | — |
| 226 | #13133195 | C23 | 1 | 6 | yes | — |
| 227 | #13133195 | C23 | 1 | 6 | yes | — |
| 228 | #13133195 | C23 | 1 | 6 | yes | — |
| 229 | #13133195 | C23 | 1 | 6 | yes | — |
| 230 | #13133195 | C23 | 1 | 6 | yes | — |
| 231 | #13133194 | C23 | 1 | 6 | yes | — |
| 232 | #13133194 | C23 | 1 | 6 | yes | — |
| 233 | #13133194 | C23 | 1 | 6 | yes | — |
| 234 | #13133194 | C23 | 1 | 6 | yes | — |
| 235 | #13133194 | C23 | 1 | 6 | yes | — |
| 236 | #13133193 | C23 | 1 | 6 | yes | — |
| 237 | #13133193 | C23 | 1 | 6 | yes | — |
| 238 | #13133193 | C23 | 1 | 3 | yes | — |
| 239 | #13133192 | C23 | 1 | 6 | yes | — |
| 240 | #13133192 | C23 | 1 | 6 | yes | — |
| 241 | #13133192 | C23 | 1 | 6 | yes | — |
| 242 | #13133192 | C23 | 1 | 6 | yes | — |
| 243 | #13133192 | C23 | 1 | 6 | yes | — |
| 244 | #13133192 | C23 | 1 | 6 | yes | — |
| 245 | #13133192 | C23 | 1 | 3 | yes | — |
| 246 | #13133191 | C23 | 1 | 6 | yes | — |
| 247 | #13133191 | C23 | 1 | 6 | yes | — |
| 248 | #13133191 | C23 | 1 | 6 | yes | — |
| 249 | #13133191 | C23 | 1 | 6 | yes | — |
| 250 | #13133191 | C23 | 1 | 3 | yes | — |
| 251 | #13133190 | C23 | 1 | 6 | yes | — |
| 252 | #13133190 | C23 | 1 | 6 | yes | — |
| 253 | #13133190 | C23 | 1 | 6 | yes | — |
| 254 | #13133190 | C23 | 1 | 6 | yes | — |
| 255 | #13133190 | C23 | 1 | 6 | yes | — |
| 256 | #13133190 | C23 | 1 | 6 | yes | — |
| 257 | #13133190 | C23 | 1 | 6 | yes | — |
| 258 | #13133190 | C23 | 1 | 6 | yes | — |
| 259 | #13133190 | C23 | 1 | 6 | yes | — |
| 260 | #13133190 | C23 | 1 | 6 | yes | — |
| 261 | #13133190 | C23 | 1 | 6 | yes | — |
| 262 | #13133190 | C23 | 1 | 6 | yes | — |
| 263 | #13133190 | C23 | 1 | 6 | yes | — |
| 264 | #13133189 | C23 | 1 | 6 | yes | — |
| 265 | #13133189 | C23 | 1 | 6 | yes | — |
| 266 | #13133189 | C23 | 1 | 6 | yes | — |
| 267 | #13133189 | C23 | 1 | 6 | yes | — |
| 268 | #13133189 | C23 | 1 | 6 | yes | — |
| 269 | #13133189 | C23 | 1 | 6 | yes | — |
| 270 | #13133189 | C23 | 1 | 6 | yes | — |
| 271 | #13133189 | C23 | 1 | 6 | yes | — |
| 272 | #13133189 | C23 | 1 | 6 | yes | — |
| 273 | #13133189 | C23 | 1 | 6 | yes | — |
| 274 | #13133189 | C23 | 1 | 6 | yes | — |
| 275 | #13133188 | C23 | 1 | 6 | yes | — |
| 276 | #13133188 | C23 | 1 | 6 | yes | — |
| 277 | #13133188 | C23 | 1 | 3 | yes | — |
| 278 | #13133187 | C23 | 1 | 6 | yes | — |
| 279 | #13133185 | C23 | 1 | 6 | yes | — |
| 280 | Q8×Dic53 | C23 | 1 | 3 | yes | — |
| 281 | C4×Dic106 | C23 | 1 | 6 | yes | — |
| 282 | C4×Dic106 | C23 | 1 | 6 | yes | — |
| 283 | C4×Dic106 | C23 | 1 | 3 | yes | — |
| 284 | C4×Dic106 | C23 | 1 | 6 | yes | — |
| 285 | #13133182 | C23 | 1 | 6 | yes | — |
| 286 | #13133182 | C23 | 1 | 6 | yes | — |
| 287 | #13133182 | C23 | 1 | 6 | yes | — |
| 288 | #13133182 | C23 | 1 | 6 | yes | — |
| 289 | #13133182 | C23 | 1 | 3 | yes | — |
| 290 | #13133182 | C23 | 1 | 6 | yes | — |
| 291 | C4×D212 | C23 | 1 | 6 | yes | — |
| 292 | C4×D212 | C23 | 1 | 6 | yes | — |
| 293 | C4×D212 | C23 | 1 | 6 | yes | — |
| 294 | C4×D212 | C23 | 1 | 3 | yes | — |
| 295 | D4×Dic53 | C23 | 1 | 6 | yes | — |
| 296 | D4×Dic53 | C23 | 1 | 6 | yes | — |
| 297 | D4×Dic53 | C23 | 1 | 6 | yes | — |
| 298 | D4×Dic53 | C23 | 1 | 3 | yes | — |
| 299 | #13133179 | C23 | 1 | 6 | yes | — |
| 300 | #13133179 | C23 | 1 | 6 | yes | — |
| 301 | #13133179 | C23 | 1 | 6 | yes | — |
| 302 | #13133179 | C23 | 1 | 6 | yes | — |
| 303 | #13133179 | C23 | 1 | 3 | yes | — |
| 304 | #13133179 | C23 | 1 | 6 | yes | — |
| 305 | C4×C22⋊D53 | C23 | 1 | 6 | yes | — |
| 306 | C4×C22⋊D53 | C23 | 1 | 6 | yes | — |
| 307 | C4×C22⋊D53 | C23 | 1 | 6 | yes | — |
| 308 | C4×C22⋊D53 | C23 | 1 | 6 | yes | — |
| 309 | C4×C22⋊D53 | C23 | 1 | 6 | yes | — |
| 310 | C4×C22⋊D53 | C23 | 1 | 6 | yes | — |
| 311 | C4×C22⋊D53 | C23 | 1 | 6 | yes | — |
| 312 | C4×C22⋊D53 | C23 | 1 | 6 | yes | — |
| 313 | C4×C22⋊D53 | C23 | 1 | 6 | yes | — |
| 314 | #13133177 | C23 | 1 | 6 | yes | — |
| 315 | #13133177 | C23 | 1 | 6 | yes | — |
| 316 | #13133177 | C23 | 1 | 6 | yes | — |
| 317 | #13133177 | C23 | 1 | 6 | yes | — |
| 318 | #13133177 | C23 | 1 | 6 | yes | — |
| 319 | #13133177 | C23 | 1 | 6 | yes | — |
| 320 | #13133177 | C23 | 1 | 6 | yes | — |
| 321 | #13133177 | C23 | 1 | 6 | yes | — |
| 322 | #13133177 | C23 | 1 | 6 | yes | — |
| 323 | #13133177 | C23 | 1 | 6 | yes | — |
| 324 | #13133177 | C23 | 1 | 6 | yes | — |
| 325 | #13133177 | C23 | 1 | 6 | yes | — |
| 326 | #13133177 | C23 | 1 | 6 | yes | — |
| 327 | #13133176 | C23 | 1 | 6 | yes | — |
| 328 | #13133175 | C23 | 1 | 6 | yes | — |
| 329 | #13133175 | C23 | 1 | 6 | yes | — |
| 330 | #13133175 | C23 | 1 | 6 | yes | — |
| 331 | #13133175 | C23 | 1 | 3 | yes | — |
| 332 | #13133175 | C23 | 1 | 6 | yes | — |
| 333 | #13133175 | C23 | 1 | 3 | yes | — |
| 334 | #13133174 | C23 | 1 | 6 | yes | — |
| 335 | #13133174 | C23 | 1 | 6 | yes | — |
| 336 | #13133174 | C23 | 1 | 6 | yes | — |
| 337 | #13133174 | C23 | 1 | 6 | yes | — |
| 338 | #13133173 | C23 | 1 | 6 | yes | — |
| 339 | #13133173 | C23 | 1 | 6 | yes | — |
| 340 | #13133173 | C23 | 1 | 6 | yes | — |
| 341 | #13133173 | C23 | 1 | 6 | yes | — |
| 342 | #13133173 | C23 | 1 | 6 | yes | — |
| 343 | C2×C4⋊Dic53 | C23 | 1 | 6 | yes | — |
| 344 | C2×#11719919 | C23 | 1 | 6 | yes | — |
| 345 | C2×#11719919 | C23 | 1 | 6 | yes | — |
| 346 | C2×#11719919 | C23 | 1 | 6 | yes | — |
| 347 | C2×#11719919 | C23 | 1 | 6 | yes | — |
| 348 | C4⋊C4×D53 | C23 | 1 | 6 | yes | — |
| 349 | C4⋊C4×D53 | C23 | 1 | 6 | yes | — |
| 350 | C4⋊C4×D53 | C23 | 1 | 6 | yes | — |
| 351 | C4⋊C4×D53 | C23 | 1 | 6 | yes | — |
| 352 | C4⋊C4×D53 | C23 | 1 | 6 | yes | — |
| 353 | C4⋊C4×D53 | C23 | 1 | 6 | yes | — |
| 354 | C2×C4×Dic53 | C23 | 1 | 3 | yes | — |
| 355 | C2×C4×Dic53 | C23 | 1 | 6 | yes | — |
| 356 | C42×D53 | C23 | 1 | 3 | yes | — |
| 357 | C42×D53 | C23 | 1 | 3 | yes | — |
| 358 | C42×D53 | C23 | 1 | 1 | yes | characteristic |
| 359 | C42×D53 | C23 | 1 | 1 | yes | characteristic |
| 360 | C42×D53 | C23 | 1 | 6 | yes | — |
| 361 | #127×C53 | C23 | 1 | 2 | yes | — |
| 362 | #126×C53 | C23 | 1 | 6 | yes | — |
| 363 | #126×C53 | C23 | 1 | 2 | yes | — |
| 364 | #126×C53 | C23 | 1 | 6 | yes | — |
| 365 | #125×C53 | C23 | 1 | 6 | yes | — |
| 366 | #125×C53 | C23 | 1 | 6 | yes | — |
| 367 | #125×C53 | C23 | 1 | 3 | yes | — |
| 368 | #125×C53 | C23 | 1 | 6 | yes | — |
| 369 | #124×C53 | C23 | 1 | 3 | yes | — |
| 370 | #123×C53 | C23 | 1 | 6 | yes | — |
| 371 | #123×C53 | C23 | 1 | 6 | yes | — |
| 372 | #123×C53 | C23 | 1 | 6 | yes | — |
| 373 | #123×C53 | C23 | 1 | 6 | yes | — |
| 374 | #123×C53 | C23 | 1 | 6 | yes | — |
| 375 | C22⋊Q8×C53 | C23 | 1 | 6 | yes | — |
| 376 | C22⋊Q8×C53 | C23 | 1 | 3 | yes | — |
| 377 | C22⋊Q8×C53 | C23 | 1 | 6 | yes | — |
| 378 | #121×C53 | C23 | 1 | 6 | yes | — |
| 379 | #121×C53 | C23 | 1 | 6 | yes | — |
| 380 | #121×C53 | C23 | 1 | 6 | yes | — |
| 381 | #121×C53 | C23 | 1 | 6 | yes | — |
| 382 | #121×C53 | C23 | 1 | 3 | yes | — |
| 383 | C4×Q8×C53 | C23 | 1 | 3 | yes | — |
| 384 | C4×D4×C53 | C23 | 1 | 6 | yes | — |
| 385 | C4×D4×C53 | C23 | 1 | 6 | yes | — |
| 386 | C4×D4×C53 | C23 | 1 | 3 | yes | — |
| 387 | C4×D4×C53 | C23 | 1 | 6 | yes | — |
| 388 | #117×C53 | C23 | 1 | 6 | yes | — |
| 389 | #117×C53 | C23 | 1 | 6 | yes | — |
| 390 | C2×C4⋊C4×C53 | C23 | 1 | 6 | yes | — |
| 391 | C2×C42×C53 | C23 | 1 | 1 | yes | characteristic |
| 392 | C23×D53 | C24 | 1 | 1 | yes | characteristic |
| 393 | C2×Q8×C53 | C24 | 1 | 3 | yes | — |
| 394 | C2×D4×C53 | C24 | 1 | 6 | yes | — |
| 395 | C2×D4×C53 | C24 | 1 | 3 | yes | — |
| 396 | C2×D4×C53 | C24 | 1 | 6 | yes | — |
| 397 | C2×D4×C53 | C24 | 1 | 6 | yes | — |
| 398 | C22×C4×C53 | C24 | 1 | 3 | yes | — |
| 399 | C22×C4×C53 | C24 | 1 | 6 | yes | — |
| 400 | C22×C4×C53 | C24 | 1 | 6 | yes | — |
| 401 | C22×C4×C53 | C24 | 1 | 6 | yes | — |
| 402 | C2×C22⋊D53 | C24 | 1 | 6 | yes | — |
| 403 | C2×C22⋊D53 | C24 | 1 | 6 | yes | — |
| 404 | C2×C22⋊D53 | C24 | 1 | 6 | yes | — |
| 405 | C2×C22⋊D53 | C24 | 1 | 6 | yes | — |
| 406 | C2×C22⋊D53 | C24 | 1 | 6 | yes | — |
| 407 | C2×C22⋊D53 | C24 | 1 | 6 | yes | — |
| 408 | C2×C22⋊D53 | C24 | 1 | 6 | yes | — |
| 409 | C2×C22⋊D53 | C24 | 1 | 6 | yes | — |
| 410 | C2×C22⋊D53 | C24 | 1 | 6 | yes | — |
| 411 | C22×Dic53 | C24 | 1 | 3 | yes | — |
| 412 | C22×Dic53 | C24 | 1 | 6 | yes | — |
| 413 | C22×Dic53 | C24 | 1 | 6 | yes | — |
| 414 | C22×Dic53 | C24 | 1 | 6 | yes | — |
| 415 | C22×Dic53 | C24 | 1 | 6 | yes | — |
| 416 | #11719949 | — | 4 | 6 | no | — |
| 417 | #11719947 | — | 4 | 12 | no | — |
| 418 | #11719947 | — | 4 | 12 | no | — |
| 419 | #11719947 | — | 4 | 12 | no | — |
| 420 | #11719947 | — | 4 | 6 | no | — |
| 421 | #11719945 | — | 4 | 12 | no | — |
| 422 | #11719945 | — | 4 | 12 | no | — |
| 423 | #11719945 | — | 4 | 12 | no | — |
| 424 | C2×D212 | C24 | 1 | 6 | yes | — |
| 425 | C2×D212 | C24 | 1 | 6 | yes | — |
| 426 | C2×D212 | C24 | 1 | 6 | yes | — |
| 427 | C2×D212 | C24 | 1 | 3 | yes | — |
| 428 | C2×D212 | C24 | 1 | 6 | yes | — |
| 429 | C2×C4×D53 | — | 4 | 6 | no | — |
| 430 | C2×C4×D53 | C24 | 1 | 3 | yes | — |
| 431 | C2×C4×D53 | C24 | 1 | 3 | yes | — |
| 432 | C2×C4×D53 | C24 | 1 | 6 | yes | — |
| 433 | C2×C4×D53 | C24 | 1 | 3 | yes | — |
| 434 | C2×C4×D53 | C24 | 1 | 3 | yes | — |
| 435 | C2×C4×D53 | C24 | 1 | 6 | yes | — |
| 436 | C2×C4×D53 | C24 | 1 | 6 | yes | — |
| 437 | C2×C4×D53 | C24 | 1 | 6 | yes | — |
| 438 | C2×C4×D53 | C24 | 1 | 6 | yes | — |
| 439 | C2×C4×D53 | C24 | 1 | 6 | yes | — |
| 440 | C2×C4×D53 | C24 | 1 | 6 | yes | — |
| 441 | C2×Dic106 | C24 | 1 | 6 | yes | — |
| 442 | C2×Dic106 | C24 | 1 | 6 | yes | — |
| 443 | C2×Dic106 | C24 | 1 | 3 | yes | — |
| 444 | C4⋊C4×C53 | C24 | 1 | 6 | yes | — |
| 445 | C4⋊C4×C53 | C24 | 1 | 6 | yes | — |
| 446 | C4⋊C4×C53 | C24 | 1 | 6 | yes | — |
| 447 | C4⋊C4×C53 | C24 | 1 | 6 | yes | — |
| 448 | C4⋊C4×C53 | C24 | 1 | 6 | yes | — |
| 449 | C4⋊C4×C53 | C24 | 1 | 6 | yes | — |
| 450 | C4⋊C4×C53 | C24 | 1 | 6 | yes | — |
| 451 | C4⋊C4×C53 | C24 | 1 | 6 | yes | — |
| 452 | C4⋊C4×C53 | C24 | 1 | 3 | yes | — |
| 453 | C4⋊C4×C53 | C24 | 1 | 3 | yes | — |
| 454 | C22⋊C4×C53 | C24 | 1 | 6 | yes | — |
| 455 | C22⋊C4×C53 | C24 | 1 | 6 | yes | — |
| 456 | C22⋊C4×C53 | C24 | 1 | 6 | yes | — |
| 457 | C22⋊C4×C53 | C24 | 1 | 6 | yes | — |
| 458 | C22⋊C4×C53 | C24 | 1 | 6 | yes | — |
| 459 | C22⋊C4×C53 | C24 | 1 | 6 | yes | — |
| 460 | C22⋊C4×C53 | C24 | 1 | 6 | yes | — |
| 461 | C42×C53 | C24 | 1 | 3 | yes | — |
| 462 | C42×C53 | C24 | 1 | 1 | yes | characteristic |
| 463 | C42×C53 | C24 | 1 | 2 | yes | — |
| 464 | C42×C53 | C24 | 1 | 6 | yes | — |
| 465 | C42×C53 | C24 | 1 | 2 | yes | — |
| 466 | C22⋊Dic53 | C24 | 1 | 6 | yes | — |
| 467 | C22⋊Dic53 | C24 | 1 | 6 | yes | — |
| 468 | C22⋊Dic53 | C24 | 1 | 6 | yes | — |
| 469 | C22⋊Dic53 | C24 | 1 | 6 | yes | — |
| 470 | C22⋊Dic53 | C24 | 1 | 6 | yes | — |
| 471 | #11719921 | C24 | 1 | 6 | yes | — |
| 472 | #11719921 | C24 | 1 | 6 | yes | — |
| 473 | #11719921 | C24 | 1 | 6 | yes | — |
| 474 | #11719921 | C24 | 1 | 6 | yes | — |
| 475 | #11719921 | C24 | 1 | 6 | yes | — |
| 476 | #11719921 | C24 | 1 | 6 | yes | — |
| 477 | #11719921 | C24 | 1 | 6 | yes | — |
| 478 | #11719921 | C24 | 1 | 6 | yes | — |
| 479 | #11719921 | C24 | 1 | 6 | yes | — |
| 480 | #11719921 | C24 | 1 | 6 | yes | — |
| 481 | #11719921 | C24 | 1 | 6 | yes | — |
| 482 | #11719921 | C24 | 1 | 6 | yes | — |
| 483 | #11719921 | C24 | 1 | 6 | yes | — |
| 484 | #11719921 | C24 | 1 | 6 | yes | — |
| 485 | C4⋊Dic53 | C24 | 1 | 6 | yes | — |
| 486 | C4⋊Dic53 | C24 | 1 | 6 | yes | — |
| 487 | C4⋊Dic53 | C24 | 1 | 6 | yes | — |
| 488 | C4⋊Dic53 | C24 | 1 | 6 | yes | — |
| 489 | C4⋊Dic53 | C24 | 1 | 6 | yes | — |
| 490 | C4⋊Dic53 | C24 | 1 | 6 | yes | — |
| 491 | C4⋊Dic53 | C24 | 1 | 3 | yes | — |
| 492 | C4⋊Dic53 | C24 | 1 | 3 | yes | — |
| 493 | #11719919 | C24 | 1 | 6 | yes | — |
| 494 | #11719919 | C24 | 1 | 6 | yes | — |
| 495 | #11719919 | C24 | 1 | 6 | yes | — |
| 496 | #11719919 | C24 | 1 | 6 | yes | — |
| 497 | #11719919 | C24 | 1 | 6 | yes | — |
| 498 | #11719919 | C24 | 1 | 6 | yes | — |
| 499 | #11719919 | C24 | 1 | 6 | yes | — |
| 500 | #11719919 | C24 | 1 | 6 | yes | — |
| 501 | #11719919 | C24 | 1 | 6 | yes | — |
| 502 | #11719919 | C24 | 1 | 6 | yes | — |
| 503 | #11719919 | C24 | 1 | 6 | yes | — |
| 504 | #11719919 | C24 | 1 | 6 | yes | — |
| 505 | #11719919 | C24 | 1 | 6 | yes | — |
| 506 | #11719919 | C24 | 1 | 6 | yes | — |
| 507 | #11719919 | C24 | 1 | 6 | yes | — |
| 508 | #11719919 | C24 | 1 | 6 | yes | — |
| 509 | #11719919 | C24 | 1 | 6 | yes | — |
| 510 | #11719919 | C24 | 1 | 6 | yes | — |
| 511 | C4×Dic53 | C24 | 1 | 3 | yes | — |
| 512 | C4×Dic53 | C24 | 1 | 3 | yes | — |
| 513 | C4×Dic53 | C24 | 1 | 3 | yes | — |
| 514 | C4×Dic53 | C24 | 1 | 3 | yes | — |
| 515 | C4×Dic53 | C24 | 1 | 6 | yes | — |
| 516 | C4×Dic53 | C24 | 1 | 6 | yes | — |
| 517 | C4×Dic53 | C24 | 1 | 6 | yes | — |
| 518 | C4×Dic53 | C24 | 1 | 6 | yes | — |
| 519 | C4×Dic53 | C24 | 1 | 6 | yes | — |
| 520 | C4×Dic53 | C24 | 1 | 6 | yes | — |
| 521 | C4×Dic53 | C24 | 1 | 6 | yes | — |
| 522 | C23×C53 | C25 | 1 | 6 | yes | — |
| 523 | C23×C53 | C25 | 1 | 1 | yes | characteristic |
| 524 | C22×D53 | — | 4 | 3 | no | — |
| 525 | C22×D53 | C25 | 1 | 6 | yes | — |
| 526 | C22×D53 | C25 | 1 | 1 | yes | characteristic |
| 527 | C22×D53 | C25 | 1 | 1 | yes | characteristic |
| 528 | Q8×C53 | — | 4 | 3 | no | — |
| 529 | D4×C53 | — | 4 | 6 | no | — |
| 530 | D4×C53 | — | 4 | 6 | no | — |
| 531 | D4×C53 | — | 4 | 6 | no | — |
| 532 | D4×C53 | — | 4 | 3 | no | — |
| 533 | C2×C4×C53 | — | 4 | 3 | no | — |
| 534 | C2×C4×C53 | — | 4 | 6 | no | — |
| 535 | C2×C4×C53 | — | 4 | 6 | no | — |
| 536 | C2×C4×C53 | — | 4 | 6 | no | — |
| 537 | C2×C4×C53 | C25 | 1 | 6 | yes | — |
| 538 | C2×C4×C53 | C25 | 1 | 3 | yes | — |
| 539 | C2×C4×C53 | C25 | 1 | 6 | yes | — |
| 540 | C2×C4×C53 | C25 | 1 | 3 | yes | — |
| 541 | C2×C4×C53 | C25 | 1 | 6 | yes | — |
| 542 | C22⋊D53 | — | 2 | 12 | no | — |
| 543 | C22⋊D53 | — | 2 | 12 | no | — |
| 544 | C22⋊D53 | — | 4 | 6 | no | — |
| 545 | C22⋊D53 | — | 4 | 6 | no | — |
| 546 | C22⋊D53 | — | 4 | 6 | no | — |
| 547 | C22⋊D53 | — | 4 | 6 | no | — |
| 548 | C22⋊D53 | — | 4 | 6 | no | — |
| 549 | C22⋊D53 | — | 4 | 6 | no | — |
| 550 | C22⋊D53 | — | 4 | 6 | no | — |
| 551 | C2×Dic53 | — | 2 | 6 | no | — |
| 552 | C2×Dic53 | — | 2 | 12 | no | — |
| 553 | C2×Dic53 | — | 4 | 6 | no | — |
| 554 | C2×Dic53 | — | 4 | 6 | no | — |
| 555 | C2×Dic53 | — | 4 | 6 | no | — |
| 556 | C2×Dic53 | C25 | 1 | 6 | yes | — |
| 557 | C2×Dic53 | C25 | 1 | 6 | yes | — |
| 558 | C2×Dic53 | C25 | 1 | 6 | yes | — |
| 559 | C2×Dic53 | C25 | 1 | 3 | yes | — |
| 560 | C2×Dic53 | C25 | 1 | 3 | yes | — |
| 561 | D212 | — | 4 | 6 | no | — |
| 562 | D212 | — | 4 | 6 | no | — |
| 563 | D212 | — | 4 | 6 | no | — |
| 564 | D212 | — | 4 | 3 | no | — |
| 565 | D212 | — | 4 | 6 | no | — |
| 566 | C4×D53 | — | 2 | 6 | no | — |
| 567 | C4×D53 | — | 2 | 6 | no | — |
| 568 | C4×D53 | — | 2 | 12 | no | — |
| 569 | C4×D53 | — | 4 | 3 | no | — |
| 570 | C4×D53 | — | 4 | 3 | no | — |
| 571 | C4×D53 | — | 4 | 6 | no | — |
| 572 | C4×D53 | — | 4 | 6 | no | — |
| 573 | C4×D53 | — | 4 | 6 | no | — |
| 574 | C4×D53 | — | 4 | 6 | no | — |
| 575 | C4×D53 | — | 4 | 6 | no | — |
| 576 | C4×D53 | — | 4 | 6 | no | — |
| 577 | Dic106 | — | 2 | 12 | no | — |
| 578 | Dic106 | — | 2 | 12 | no | — |
| 579 | Dic106 | — | 4 | 3 | no | — |
| 580 | #62840 | — | 53 | 1 | no | maximal, Sylow |
| 581 | C22×C53 | — | 2 | 6 | no | — |
| 582 | C22×C53 | — | 2 | 3 | no | — |
| 583 | C22×C53 | — | 2 | 6 | no | — |
| 584 | C22×C53 | — | 2 | 6 | no | — |
| 585 | C22×C53 | C26 | 1 | 1 | yes | characteristic |
| 586 | C2×D53 | — | 2 | 3 | no | — |
| 587 | C2×D53 | — | 2 | 3 | no | — |
| 588 | C2×D53 | — | 2 | 6 | no | — |
| 589 | C2×D53 | — | 2 | 6 | no | — |
| 590 | C2×D53 | — | 2 | 6 | no | — |
| 591 | C2×D53 | — | 4 | 4 | no | — |
| 592 | C4×C53 | — | 2 | 6 | no | — |
| 593 | C4×C53 | — | 2 | 6 | no | — |
| 594 | C4×C53 | — | 2 | 3 | no | — |
| 595 | C4×C53 | — | 2 | 3 | no | — |
| 596 | C4×C53 | — | 2 | 6 | no | — |
| 597 | Dic53 | — | 2 | 6 | no | — |
| 598 | Dic53 | — | 2 | 6 | no | — |
| 599 | Dic53 | — | 2 | 6 | no | — |
| 600 | Dic53 | — | 2 | 3 | no | — |
| 601 | Dic53 | #585 | 1 | 6 | yes | — |
| 602 | #3567 | — | 53 | 1 | no | — |
| 603 | #3567 | — | 53 | 3 | no | — |
| 604 | #3567 | — | 53 | 3 | no | — |
| 605 | #3567 | D53 | 1 | 1 | yes | characteristic, complemented |
| 606 | #3556 | — | 53 | 1 | no | — |
| 607 | #3548 | — | 53 | 3 | no | — |
| 608 | #3539 | — | 53 | 6 | no | — |
| 609 | #3539 | — | 53 | 6 | no | — |
| 610 | #3517 | — | 53 | 6 | no | — |
| 611 | #3517 | — | 53 | 6 | no | — |
| 612 | #3515 | — | 53 | 6 | no | — |
| 613 | #3515 | — | 53 | 6 | no | — |
| 614 | #3512 | — | 53 | 6 | no | — |
| 615 | #3512 | — | 53 | 6 | no | — |
| 616 | #3444 | — | 53 | 3 | no | — |
| 617 | C2×C53 | — | 4 | 1 | no | — |
| 618 | C2×C53 | — | 4 | 6 | no | — |
| 619 | C2×C53 | C2×#585 | 1 | 3 | yes | — |
| 620 | D53 | — | 4 | 6 | no | — |
| 621 | D53 | — | 4 | 1 | no | — |
| 622 | D53 | — | 4 | 1 | no | — |
| 623 | #564 | — | 53 | 3 | no | — |
| 624 | #564 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 625 | #562 | — | 53 | 3 | no | — |
| 626 | #562 | — | 53 | 3 | no | — |
| 627 | #562 | — | 53 | 3 | no | — |
| 628 | #562 | C2×D53 | 1 | 3 | yes | complemented |
| 629 | #560 | — | 53 | 2 | no | — |
| 630 | #560 | — | 53 | 2 | no | — |
| 631 | #560 | — | 53 | 6 | no | — |
| 632 | #560 | — | 53 | 6 | no | — |
| 633 | #557 | — | 53 | 6 | no | — |
| 634 | #557 | — | 53 | 6 | no | — |
| 635 | #554 | — | 53 | 6 | no | — |
| 636 | #554 | — | 53 | 6 | no | — |
| 637 | #553 | — | 53 | 6 | no | — |
| 638 | #553 | — | 53 | 6 | no | — |
| 639 | #553 | — | 53 | 6 | no | — |
| 640 | #553 | — | 53 | 6 | no | — |
| 641 | #553 | — | 53 | 6 | no | — |
| 642 | #553 | — | 53 | 6 | no | — |
| 643 | #553 | — | 53 | 6 | no | — |
| 644 | #553 | — | 53 | 6 | no | — |
| 645 | #553 | — | 53 | 6 | no | — |
| 646 | #553 | — | 53 | 6 | no | — |
| 647 | #553 | — | 53 | 6 | no | — |
| 648 | #553 | — | 53 | 6 | no | — |
| 649 | #553 | — | 53 | 6 | no | — |
| 650 | #553 | — | 53 | 6 | no | — |
| 651 | #553 | — | 53 | 6 | no | — |
| 652 | #553 | — | 53 | 6 | no | — |
| 653 | #553 | — | 53 | 6 | no | — |
| 654 | #553 | — | 53 | 6 | no | — |
| 655 | #553 | — | 53 | 6 | no | — |
| 656 | #553 | C2×D53 | 1 | 6 | yes | complemented |
| 657 | #552 | — | 53 | 6 | no | — |
| 658 | #552 | — | 53 | 6 | no | — |
| 659 | #552 | — | 53 | 6 | no | — |
| 660 | #552 | — | 53 | 6 | no | — |
| 661 | #552 | — | 53 | 6 | no | — |
| 662 | #552 | — | 53 | 6 | no | — |
| 663 | #552 | — | 53 | 6 | no | — |
| 664 | #552 | — | 53 | 6 | no | — |
| 665 | #552 | — | 53 | 6 | no | — |
| 666 | #552 | — | 53 | 6 | no | — |
| 667 | #552 | — | 53 | 6 | no | — |
| 668 | #552 | C2×D53 | 1 | 6 | yes | complemented |
| 669 | #550 | — | 53 | 6 | no | — |
| 670 | #550 | — | 53 | 6 | no | — |
| 671 | #550 | — | 53 | 6 | no | — |
| 672 | #550 | — | 53 | 6 | no | — |
| 673 | #550 | — | 53 | 6 | no | — |
| 674 | #550 | — | 53 | 6 | no | — |
| 675 | #547 | — | 53 | 6 | no | — |
| 676 | #547 | — | 53 | 6 | no | — |
| 677 | #547 | — | 53 | 6 | no | — |
| 678 | #547 | — | 53 | 6 | no | — |
| 679 | #547 | — | 53 | 6 | no | — |
| 680 | #547 | — | 53 | 6 | no | — |
| 681 | #541 | — | 53 | 6 | no | — |
| 682 | #541 | — | 53 | 6 | no | — |
| 683 | #541 | — | 53 | 6 | no | — |
| 684 | #541 | — | 53 | 6 | no | — |
| 685 | #540 | — | 53 | 6 | no | — |
| 686 | #540 | — | 53 | 6 | no | — |
| 687 | #540 | — | 53 | 6 | no | — |
| 688 | #540 | — | 53 | 6 | no | — |
| 689 | #540 | — | 53 | 6 | no | — |
| 690 | #540 | — | 53 | 6 | no | — |
| 691 | #540 | — | 53 | 6 | no | — |
| 692 | #540 | — | 53 | 6 | no | — |
| 693 | #540 | — | 53 | 6 | no | — |
| 694 | #540 | — | 53 | 6 | no | — |
| 695 | #540 | — | 53 | 6 | no | — |
| 696 | #540 | C2×D53 | 1 | 6 | yes | — |
| 697 | #539 | — | 53 | 6 | no | — |
| 698 | #539 | — | 53 | 6 | no | — |
| 699 | #539 | — | 53 | 6 | no | — |
| 700 | #539 | — | 53 | 6 | no | — |
| 701 | #539 | — | 53 | 6 | no | — |
| 702 | #539 | — | 53 | 6 | no | — |
| 703 | #539 | — | 53 | 6 | no | — |
| 704 | #539 | C2×D53 | 1 | 6 | yes | — |
| 705 | #537 | — | 53 | 6 | no | — |
| 706 | #537 | — | 53 | 6 | no | — |
| 707 | #537 | — | 53 | 6 | no | — |
| 708 | #537 | — | 53 | 6 | no | — |
| 709 | #533 | — | 53 | 3 | no | — |
| 710 | #533 | — | 53 | 3 | no | — |
| 711 | #533 | — | 53 | 3 | no | — |
| 712 | #532 | — | 53 | 3 | no | — |
| 713 | #532 | — | 53 | 3 | no | — |
| 714 | #532 | — | 53 | 6 | no | — |
| 715 | #532 | — | 53 | 3 | no | — |
| 716 | #532 | — | 53 | 6 | no | — |
| 717 | #529 | — | 53 | 6 | no | — |
| 718 | #529 | — | 53 | 6 | no | — |
| 719 | #529 | — | 53 | 6 | no | — |
| 720 | #529 | — | 53 | 3 | no | — |
| 721 | #529 | — | 53 | 3 | no | — |
| 722 | #529 | — | 53 | 6 | no | — |
| 723 | #529 | — | 53 | 6 | no | — |
| 724 | #529 | — | 53 | 6 | no | — |
| 725 | #529 | — | 53 | 6 | no | — |
| 726 | #529 | — | 53 | 6 | no | — |
| 727 | #529 | — | 53 | 3 | no | — |
| 728 | #529 | C2×D53 | 1 | 3 | yes | — |
| 729 | C2×#125 | — | 53 | 6 | no | — |
| 730 | C2×#125 | — | 53 | 6 | no | — |
| 731 | #525 | — | 53 | 6 | no | — |
| 732 | #525 | — | 53 | 3 | no | — |
| 733 | #525 | — | 53 | 3 | no | — |
| 734 | #525 | — | 53 | 6 | no | — |
| 735 | #520 | — | 53 | 6 | no | — |
| 736 | #520 | — | 53 | 6 | no | — |
| 737 | #520 | — | 53 | 6 | no | — |
| 738 | #520 | — | 53 | 6 | no | — |
| 739 | C4×#41 | — | 53 | 3 | no | — |
| 740 | C4×#41 | — | 53 | 3 | no | — |
| 741 | C4×#41 | — | 53 | 6 | no | — |
| 742 | C4×#41 | — | 53 | 6 | no | — |
| 743 | C22×C42 | — | 53 | 1 | no | — |
| 744 | C53 | #62840 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 745 | C2×#41 | — | 53 | 3 | no | — |
| 746 | C2×#41 | — | 53 | 3 | no | — |
| 747 | C2×#41 | — | 53 | 6 | no | — |
| 748 | C2×#41 | — | 53 | 6 | no | — |
| 749 | C2×#41 | — | 53 | 6 | no | — |
| 750 | C2×#41 | — | 53 | 6 | no | — |
| 751 | C2×#41 | — | 53 | 6 | no | — |
| 752 | C2×#41 | — | 53 | 6 | no | — |
| 753 | C23×C4 | — | 53 | 3 | no | — |
| 754 | C4⋊Q8 | — | 53 | 3 | no | — |
| 755 | C4⋊Q8 | — | 53 | 3 | no | — |
| 756 | C4⋊Q8 | — | 53 | 3 | no | — |
| 757 | C4⋊Q8 | — | 53 | 6 | no | — |
| 758 | C4⋊Q8 | — | 53 | 6 | no | — |
| 759 | #127 | — | 53 | 3 | no | — |
| 760 | #127 | — | 53 | 6 | no | — |
| 761 | #127 | — | 53 | 6 | no | — |
| 762 | #127 | — | 53 | 6 | no | — |
| 763 | #127 | — | 53 | 6 | no | — |
| 764 | #127 | — | 53 | 2 | no | — |
| 765 | #127 | C22×D53 | 1 | 2 | yes | — |
| 766 | #126 | — | 53 | 6 | no | — |
| 767 | #126 | — | 53 | 6 | no | — |
| 768 | #126 | — | 53 | 6 | no | — |
| 769 | #126 | — | 53 | 6 | no | — |
| 770 | #126 | — | 53 | 6 | no | — |
| 771 | #126 | — | 53 | 6 | no | — |
| 772 | #126 | — | 53 | 6 | no | — |
| 773 | #126 | — | 53 | 6 | no | — |
| 774 | #126 | — | 53 | 6 | no | — |
| 775 | #126 | — | 53 | 6 | no | — |
| 776 | #126 | — | 53 | 6 | no | — |
| 777 | #126 | — | 53 | 6 | no | — |
| 778 | #126 | — | 53 | 6 | no | — |
| 779 | #126 | — | 53 | 6 | no | — |
| 780 | #126 | — | 53 | 2 | no | — |
| 781 | #126 | — | 53 | 2 | no | — |
| 782 | #126 | — | 53 | 2 | no | — |
| 783 | #126 | C22×D53 | 1 | 6 | yes | — |
| 784 | #126 | C22×D53 | 1 | 6 | yes | — |
| 785 | #126 | C22×D53 | 1 | 2 | yes | — |
| 786 | #125 | — | 53 | 6 | no | — |
| 787 | #125 | — | 53 | 6 | no | — |
| 788 | #125 | — | 53 | 6 | no | — |
| 789 | #125 | — | 53 | 6 | no | — |
| 790 | #125 | — | 53 | 6 | no | — |
| 791 | #125 | — | 53 | 6 | no | — |
| 792 | #125 | — | 53 | 6 | no | — |
| 793 | #125 | — | 53 | 6 | no | — |
| 794 | #125 | — | 53 | 6 | no | — |
| 795 | #125 | — | 53 | 6 | no | — |
| 796 | #125 | — | 53 | 6 | no | — |
| 797 | #125 | — | 53 | 6 | no | — |
| 798 | #125 | — | 53 | 6 | no | — |
| 799 | #125 | — | 53 | 6 | no | — |
| 800 | #125 | — | 53 | 6 | no | — |
| 801 | #125 | — | 53 | 6 | no | — |
| 802 | #125 | — | 53 | 6 | no | — |
| 803 | #125 | — | 53 | 6 | no | — |
| 804 | #125 | — | 53 | 6 | no | — |
| 805 | #125 | — | 53 | 3 | no | — |
| 806 | #125 | C22×D53 | 1 | 6 | yes | — |
| 807 | #125 | C22×D53 | 1 | 3 | yes | — |
| 808 | #125 | C22×D53 | 1 | 6 | yes | — |
| 809 | #125 | C22×D53 | 1 | 6 | yes | — |
| 810 | #124 | — | 53 | 6 | no | — |
| 811 | #124 | — | 53 | 6 | no | — |
| 812 | #124 | — | 53 | 3 | no | — |
| 813 | #124 | C22×D53 | 1 | 3 | yes | — |
| 814 | #123 | — | 53 | 6 | no | — |
| 815 | #123 | — | 53 | 6 | no | — |
| 816 | #123 | — | 53 | 6 | no | — |
| 817 | #123 | — | 53 | 6 | no | — |
| 818 | #123 | — | 53 | 6 | no | — |
| 819 | #123 | — | 53 | 6 | no | — |
| 820 | #123 | — | 53 | 6 | no | — |
| 821 | #123 | — | 53 | 6 | no | — |
| 822 | #123 | — | 53 | 6 | no | — |
| 823 | #123 | — | 53 | 6 | no | — |
| 824 | #123 | — | 53 | 6 | no | — |
| 825 | #123 | — | 53 | 6 | no | — |
| 826 | #123 | — | 53 | 6 | no | — |
| 827 | #123 | — | 53 | 6 | no | — |
| 828 | #123 | — | 53 | 6 | no | — |
| 829 | #123 | — | 53 | 6 | no | — |
| 830 | #123 | — | 53 | 6 | no | — |
| 831 | #123 | — | 53 | 6 | no | — |
| 832 | #123 | — | 53 | 6 | no | — |
| 833 | #123 | — | 53 | 6 | no | — |
| 834 | #123 | — | 53 | 6 | no | — |
| 835 | #123 | — | 53 | 6 | no | — |
| 836 | #123 | — | 53 | 6 | no | — |
| 837 | #123 | — | 53 | 6 | no | — |
| 838 | #123 | — | 53 | 6 | no | — |
| 839 | #123 | C22×D53 | 1 | 6 | yes | — |
| 840 | #123 | C22×D53 | 1 | 6 | yes | — |
| 841 | #123 | C22×D53 | 1 | 6 | yes | — |
| 842 | #123 | C22×D53 | 1 | 6 | yes | — |
| 843 | #123 | C22×D53 | 1 | 6 | yes | — |
| 844 | C22⋊Q8 | — | 53 | 3 | no | — |
| 845 | C22⋊Q8 | — | 53 | 6 | no | — |
| 846 | C22⋊Q8 | — | 53 | 6 | no | — |
| 847 | C22⋊Q8 | — | 53 | 3 | no | — |
| 848 | C22⋊Q8 | — | 53 | 6 | no | — |
| 849 | C22⋊Q8 | — | 53 | 6 | no | — |
| 850 | C22⋊Q8 | — | 53 | 3 | no | — |
| 851 | C22⋊Q8 | — | 53 | 6 | no | — |
| 852 | C22⋊Q8 | — | 53 | 6 | no | — |
| 853 | C22⋊Q8 | — | 53 | 6 | no | — |
| 854 | C22⋊Q8 | — | 53 | 6 | no | — |
| 855 | C22⋊Q8 | — | 53 | 6 | no | — |
| 856 | C22⋊Q8 | — | 53 | 6 | no | — |
| 857 | C22⋊Q8 | — | 53 | 6 | no | — |
| 858 | C22⋊Q8 | — | 53 | 6 | no | — |
| 859 | C22⋊Q8 | — | 53 | 6 | no | — |
| 860 | C22⋊Q8 | — | 53 | 6 | no | — |
| 861 | C22⋊Q8 | C22×D53 | 1 | 3 | yes | — |
| 862 | C22⋊Q8 | C22×D53 | 1 | 6 | yes | — |
| 863 | C22⋊Q8 | C22×D53 | 1 | 6 | yes | — |
| 864 | #121 | — | 53 | 3 | no | — |
| 865 | #121 | — | 53 | 6 | no | — |
| 866 | #121 | — | 53 | 6 | no | — |
| 867 | #121 | — | 53 | 6 | no | — |
| 868 | #121 | — | 53 | 6 | no | — |
| 869 | #121 | — | 53 | 6 | no | — |
| 870 | #121 | — | 53 | 6 | no | — |
| 871 | #121 | — | 53 | 6 | no | — |
| 872 | #121 | — | 53 | 6 | no | — |
| 873 | #121 | — | 53 | 6 | no | — |
| 874 | #121 | — | 53 | 6 | no | — |
| 875 | #121 | — | 53 | 6 | no | — |
| 876 | #121 | — | 53 | 6 | no | — |
| 877 | #121 | — | 53 | 6 | no | — |
| 878 | #121 | — | 53 | 3 | no | — |
| 879 | #121 | — | 53 | 6 | no | — |
| 880 | #121 | — | 53 | 6 | no | — |
| 881 | #121 | — | 53 | 6 | no | — |
| 882 | #121 | — | 53 | 6 | no | — |
| 883 | #121 | — | 53 | 3 | no | — |
| 884 | #121 | — | 53 | 6 | no | — |
| 885 | #121 | — | 53 | 6 | no | — |
| 886 | #121 | — | 53 | 6 | no | — |
| 887 | #121 | — | 53 | 6 | no | — |
| 888 | #121 | — | 53 | 6 | no | — |
| 889 | #121 | — | 53 | 6 | no | — |
| 890 | #121 | — | 53 | 6 | no | — |
| 891 | #121 | — | 53 | 6 | no | — |
| 892 | #121 | — | 53 | 6 | no | — |
| 893 | #121 | — | 53 | 6 | no | — |
| 894 | #121 | — | 53 | 6 | no | — |
| 895 | #121 | — | 53 | 6 | no | — |
| 896 | #121 | — | 53 | 6 | no | — |
| 897 | #121 | — | 53 | 6 | no | — |
| 898 | #121 | — | 53 | 6 | no | — |
| 899 | #121 | — | 53 | 6 | no | — |
| 900 | #121 | — | 53 | 6 | no | — |
| 901 | #121 | — | 53 | 6 | no | — |
| 902 | #121 | — | 53 | 6 | no | — |
| 903 | #121 | C22×D53 | 1 | 3 | yes | — |
| 904 | #121 | C22×D53 | 1 | 6 | yes | — |
| 905 | #121 | C22×D53 | 1 | 6 | yes | — |
| 906 | #121 | C22×D53 | 1 | 6 | yes | — |
| 907 | #121 | C22×D53 | 1 | 6 | yes | — |
| 908 | #120 | — | 53 | 6 | no | — |
| 909 | #120 | — | 53 | 6 | no | — |
| 910 | C4×Q8 | — | 53 | 3 | no | — |
| 911 | C4×Q8 | — | 53 | 6 | no | — |
| 912 | C4×Q8 | — | 53 | 6 | no | — |
| 913 | C4×Q8 | — | 53 | 6 | no | — |
| 914 | C4×Q8 | — | 53 | 3 | no | — |
| 915 | C4×Q8 | — | 53 | 6 | no | — |
| 916 | C4×Q8 | — | 53 | 6 | no | — |
| 917 | C4×Q8 | — | 53 | 6 | no | — |
| 918 | C4×Q8 | — | 53 | 3 | no | — |
| 919 | C4×Q8 | — | 53 | 6 | no | — |
| 920 | C4×Q8 | — | 53 | 6 | no | — |
| 921 | C4×Q8 | C22×D53 | 1 | 3 | yes | — |
| 922 | C4×D4 | — | 53 | 6 | no | — |
| 923 | C4×D4 | — | 53 | 3 | no | — |
| 924 | C4×D4 | — | 53 | 6 | no | — |
| 925 | C4×D4 | — | 53 | 6 | no | — |
| 926 | C4×D4 | — | 53 | 6 | no | — |
| 927 | C4×D4 | — | 53 | 6 | no | — |
| 928 | C4×D4 | — | 53 | 6 | no | — |
| 929 | C4×D4 | — | 53 | 6 | no | — |
| 930 | C4×D4 | — | 53 | 6 | no | — |
| 931 | C4×D4 | — | 53 | 6 | no | — |
| 932 | C4×D4 | — | 53 | 6 | no | — |
| 933 | C4×D4 | — | 53 | 6 | no | — |
| 934 | C4×D4 | — | 53 | 6 | no | — |
| 935 | C4×D4 | — | 53 | 6 | no | — |
| 936 | C4×D4 | — | 53 | 6 | no | — |
| 937 | C4×D4 | — | 53 | 6 | no | — |
| 938 | C4×D4 | — | 53 | 3 | no | — |
| 939 | C4×D4 | — | 53 | 6 | no | — |
| 940 | C4×D4 | — | 53 | 6 | no | — |
| 941 | C4×D4 | — | 53 | 6 | no | — |
| 942 | C4×D4 | — | 53 | 6 | no | — |
| 943 | C4×D4 | — | 53 | 6 | no | — |
| 944 | C4×D4 | — | 53 | 6 | no | — |
| 945 | C4×D4 | — | 53 | 6 | no | — |
| 946 | C4×D4 | — | 53 | 6 | no | — |
| 947 | C4×D4 | — | 53 | 6 | no | — |
| 948 | C4×D4 | — | 53 | 6 | no | — |
| 949 | C4×D4 | — | 53 | 6 | no | — |
| 950 | C4×D4 | — | 53 | 6 | no | — |
| 951 | C4×D4 | — | 53 | 6 | no | — |
| 952 | C4×D4 | — | 53 | 6 | no | — |
| 953 | C4×D4 | — | 53 | 6 | no | — |
| 954 | C4×D4 | — | 53 | 6 | no | — |
| 955 | C4×D4 | — | 53 | 3 | no | — |
| 956 | C4×D4 | — | 53 | 6 | no | — |
| 957 | C4×D4 | — | 53 | 6 | no | — |
| 958 | C4×D4 | C22×D53 | 1 | 6 | yes | — |
| 959 | C4×D4 | C22×D53 | 1 | 3 | yes | — |
| 960 | C4×D4 | C22×D53 | 1 | 6 | yes | — |
| 961 | C4×D4 | C22×D53 | 1 | 6 | yes | — |
| 962 | #117 | — | 53 | 6 | no | — |
| 963 | #117 | — | 53 | 6 | no | — |
| 964 | #117 | — | 53 | 3 | no | — |
| 965 | #117 | — | 53 | 3 | no | — |
| 966 | #117 | — | 53 | 6 | no | — |
| 967 | #117 | — | 53 | 6 | no | — |
| 968 | #117 | — | 53 | 6 | no | — |
| 969 | #117 | — | 53 | 6 | no | — |
| 970 | #117 | — | 53 | 6 | no | — |
| 971 | #117 | — | 53 | 6 | no | — |
| 972 | #117 | — | 53 | 6 | no | — |
| 973 | #117 | — | 53 | 6 | no | — |
| 974 | #117 | — | 53 | 6 | no | — |
| 975 | #117 | — | 53 | 6 | no | — |
| 976 | #117 | — | 53 | 6 | no | — |
| 977 | #117 | — | 53 | 6 | no | — |
| 978 | #117 | C22×D53 | 1 | 6 | yes | — |
| 979 | #117 | C22×D53 | 1 | 6 | yes | — |
| 980 | C2×C4⋊C4 | — | 53 | 6 | no | — |
| 981 | C2×C4⋊C4 | — | 53 | 6 | no | — |
| 982 | C2×C4⋊C4 | — | 53 | 6 | no | — |
| 983 | C2×C4⋊C4 | — | 53 | 6 | no | — |
| 984 | C2×C4⋊C4 | — | 53 | 6 | no | — |
| 985 | C2×C4⋊C4 | — | 53 | 6 | no | — |
| 986 | C2×C4⋊C4 | — | 53 | 6 | no | — |
| 987 | C2×C4⋊C4 | — | 53 | 6 | no | — |
| 988 | C2×C4⋊C4 | — | 53 | 6 | no | — |
| 989 | C2×C4⋊C4 | — | 53 | 6 | no | — |
| 990 | C2×C4⋊C4 | — | 53 | 6 | no | — |
| 991 | C2×C4⋊C4 | C22×D53 | 1 | 6 | yes | — |
| 992 | C2×C42 | — | 53 | 6 | no | — |
| 993 | C2×C42 | — | 53 | 3 | no | — |
| 994 | C2×C42 | — | 53 | 6 | no | — |
| 995 | C2×C42 | — | 53 | 3 | no | — |
| 996 | C2×C42 | — | 53 | 3 | no | — |
| 997 | C2×C42 | — | 53 | 1 | no | — |
| 998 | C2×C42 | — | 53 | 1 | no | — |
| 999 | C2×C42 | C22×D53 | 1 | 1 | yes | characteristic |
| 1000 | C24 | — | 53 | 1 | no | — |
| 1001 | #41 | — | 212 | 12 | no | — |
| 1002 | #41 | — | 212 | 12 | no | — |
| 1003 | #41 | — | 212 | 12 | no | — |
| 1004 | #41 | — | 212 | 6 | no | — |
| 1005 | #41 | — | 212 | 6 | no | — |
| 1006 | #41 | — | 212 | 12 | no | — |
| 1007 | #41 | — | 212 | 12 | no | — |
| 1008 | #41 | — | 212 | 12 | no | — |
| 1009 | C2×Q8 | — | 53 | 6 | no | — |
| 1010 | C2×Q8 | — | 53 | 6 | no | — |
| 1011 | C2×Q8 | — | 53 | 3 | no | — |
| 1012 | C2×Q8 | C23×D53 | 1 | 3 | yes | — |
| 1013 | C2×D4 | — | 53 | 6 | no | — |
| 1014 | C2×D4 | — | 53 | 6 | no | — |
| 1015 | C2×D4 | — | 53 | 6 | no | — |
| 1016 | C2×D4 | — | 53 | 6 | no | — |
| 1017 | C2×D4 | — | 53 | 6 | no | — |
| 1018 | C2×D4 | — | 53 | 6 | no | — |
| 1019 | C2×D4 | — | 53 | 6 | no | — |
| 1020 | C2×D4 | — | 53 | 6 | no | — |
| 1021 | C2×D4 | — | 53 | 6 | no | — |
| 1022 | C2×D4 | — | 53 | 6 | no | — |
| 1023 | C2×D4 | — | 53 | 6 | no | — |
| 1024 | C2×D4 | — | 53 | 3 | no | — |
| 1025 | C2×D4 | — | 53 | 6 | no | — |
| 1026 | C2×D4 | — | 53 | 6 | no | — |
| 1027 | C2×D4 | C23×D53 | 1 | 6 | yes | — |
| 1028 | C2×D4 | C23×D53 | 1 | 3 | yes | — |
| 1029 | C2×D4 | C23×D53 | 1 | 6 | yes | — |
| 1030 | C2×D4 | C23×D53 | 1 | 6 | yes | — |
| 1031 | C22×C4 | — | 53 | 3 | no | — |
| 1032 | C22×C4 | — | 53 | 6 | no | — |
| 1033 | C22×C4 | — | 53 | 6 | no | — |
| 1034 | C22×C4 | — | 53 | 6 | no | — |
| 1035 | C22×C4 | — | 53 | 6 | no | — |
| 1036 | C22×C4 | — | 53 | 3 | no | — |
| 1037 | C22×C4 | — | 53 | 3 | no | — |
| 1038 | C22×C4 | — | 53 | 6 | no | — |
| 1039 | C22×C4 | — | 53 | 3 | no | — |
| 1040 | C22×C4 | — | 53 | 3 | no | — |
| 1041 | C22×C4 | — | 53 | 6 | no | — |
| 1042 | C22×C4 | — | 53 | 6 | no | — |
| 1043 | C22×C4 | — | 53 | 6 | no | — |
| 1044 | C22×C4 | — | 53 | 6 | no | — |
| 1045 | C22×C4 | — | 53 | 6 | no | — |
| 1046 | C22×C4 | — | 53 | 6 | no | — |
| 1047 | C22×C4 | — | 212 | 6 | no | — |
| 1048 | C22×C4 | C23×D53 | 1 | 3 | yes | — |
| 1049 | C22×C4 | C23×D53 | 1 | 6 | yes | — |
| 1050 | C22×C4 | C23×D53 | 1 | 6 | yes | — |
| 1051 | C22×C4 | C23×D53 | 1 | 6 | yes | — |
| 1052 | C4⋊C4 | — | 53 | 6 | no | — |
| 1053 | C4⋊C4 | — | 53 | 6 | no | — |
| 1054 | C4⋊C4 | — | 53 | 6 | no | — |
| 1055 | C4⋊C4 | — | 53 | 6 | no | — |
| 1056 | C4⋊C4 | — | 53 | 6 | no | — |
| 1057 | C4⋊C4 | — | 53 | 6 | no | — |
| 1058 | C4⋊C4 | — | 53 | 6 | no | — |
| 1059 | C4⋊C4 | — | 53 | 6 | no | — |
| 1060 | C4⋊C4 | — | 53 | 6 | no | — |
| 1061 | C4⋊C4 | — | 53 | 6 | no | — |
| 1062 | C4⋊C4 | — | 53 | 6 | no | — |
| 1063 | C4⋊C4 | — | 53 | 6 | no | — |
| 1064 | C4⋊C4 | — | 53 | 6 | no | — |
| 1065 | C4⋊C4 | — | 53 | 6 | no | — |
| 1066 | C4⋊C4 | — | 53 | 6 | no | — |
| 1067 | C4⋊C4 | — | 53 | 6 | no | — |
| 1068 | C4⋊C4 | — | 53 | 6 | no | — |
| 1069 | C4⋊C4 | — | 53 | 6 | no | — |
| 1070 | C4⋊C4 | — | 53 | 6 | no | — |
| 1071 | C4⋊C4 | — | 53 | 6 | no | — |
| 1072 | C4⋊C4 | — | 53 | 6 | no | — |
| 1073 | C4⋊C4 | — | 53 | 6 | no | — |
| 1074 | C4⋊C4 | — | 53 | 6 | no | — |
| 1075 | C4⋊C4 | — | 53 | 6 | no | — |
| 1076 | C4⋊C4 | — | 53 | 3 | no | — |
| 1077 | C4⋊C4 | — | 53 | 3 | no | — |
| 1078 | C4⋊C4 | C23×D53 | 1 | 6 | yes | — |
| 1079 | C4⋊C4 | C23×D53 | 1 | 6 | yes | — |
| 1080 | C4⋊C4 | C23×D53 | 1 | 6 | yes | — |
| 1081 | C4⋊C4 | C23×D53 | 1 | 6 | yes | — |
| 1082 | C4⋊C4 | C23×D53 | 1 | 6 | yes | — |
| 1083 | C4⋊C4 | C23×D53 | 1 | 6 | yes | — |
| 1084 | C4⋊C4 | C23×D53 | 1 | 3 | yes | — |
| 1085 | C4⋊C4 | C23×D53 | 1 | 6 | yes | — |
| 1086 | C4⋊C4 | C23×D53 | 1 | 3 | yes | — |
| 1087 | C4⋊C4 | C23×D53 | 1 | 6 | yes | — |
| 1088 | C22⋊C4 | — | 53 | 6 | no | — |
| 1089 | C22⋊C4 | — | 53 | 6 | no | — |
| 1090 | C22⋊C4 | — | 53 | 6 | no | — |
| 1091 | C22⋊C4 | — | 53 | 6 | no | — |
| 1092 | C22⋊C4 | — | 53 | 6 | no | — |
| 1093 | C22⋊C4 | — | 53 | 6 | no | — |
| 1094 | C22⋊C4 | — | 53 | 6 | no | — |
| 1095 | C22⋊C4 | — | 53 | 6 | no | — |
| 1096 | C22⋊C4 | — | 53 | 6 | no | — |
| 1097 | C22⋊C4 | — | 53 | 6 | no | — |
| 1098 | C22⋊C4 | — | 53 | 6 | no | — |
| 1099 | C22⋊C4 | — | 53 | 6 | no | — |
| 1100 | C22⋊C4 | — | 53 | 6 | no | — |
| 1101 | C22⋊C4 | — | 53 | 6 | no | — |
| 1102 | C22⋊C4 | — | 53 | 6 | no | — |
| 1103 | C22⋊C4 | — | 53 | 6 | no | — |
| 1104 | C22⋊C4 | — | 53 | 6 | no | — |
| 1105 | C22⋊C4 | — | 53 | 6 | no | — |
| 1106 | C22⋊C4 | — | 53 | 6 | no | — |
| 1107 | C22⋊C4 | C23×D53 | 1 | 6 | yes | — |
| 1108 | C22⋊C4 | C23×D53 | 1 | 6 | yes | — |
| 1109 | C22⋊C4 | C23×D53 | 1 | 6 | yes | — |
| 1110 | C22⋊C4 | C23×D53 | 1 | 6 | yes | — |
| 1111 | C22⋊C4 | C23×D53 | 1 | 6 | yes | — |
| 1112 | C22⋊C4 | C23×D53 | 1 | 6 | yes | — |
| 1113 | C22⋊C4 | C23×D53 | 1 | 6 | yes | — |
| 1114 | C42 | — | 53 | 3 | no | — |
| 1115 | C42 | — | 53 | 3 | no | — |
| 1116 | C42 | — | 53 | 3 | no | — |
| 1117 | C42 | — | 53 | 3 | no | — |
| 1118 | C42 | — | 53 | 6 | no | — |
| 1119 | C42 | — | 53 | 6 | no | — |
| 1120 | C42 | — | 53 | 6 | no | — |
| 1121 | C42 | — | 53 | 6 | no | — |
| 1122 | C42 | — | 53 | 6 | no | — |
| 1123 | C42 | — | 53 | 6 | no | — |
| 1124 | C42 | — | 53 | 6 | no | — |
| 1125 | C42 | C23×D53 | 1 | 3 | yes | — |
| 1126 | C42 | C23×D53 | 1 | 1 | yes | characteristic |
| 1127 | C42 | C23×D53 | 1 | 6 | yes | — |
| 1128 | C42 | C23×D53 | 1 | 2 | yes | — |
| 1129 | C42 | C23×D53 | 1 | 2 | yes | — |
| 1130 | C23 | — | 53 | 1 | no | — |
| 1131 | C23 | — | 53 | 1 | no | — |
| 1132 | C23 | — | 53 | 6 | no | — |
| 1133 | C23 | — | 212 | 3 | no | — |
| 1134 | C23 | C24×D53 | 1 | 1 | yes | characteristic |
| 1135 | C23 | C24×D53 | 1 | 6 | yes | — |
| 1136 | Q8 | — | 4 | 3 | no | — |
| 1137 | Q8 | — | 106 | 12 | no | — |
| 1138 | Q8 | — | 106 | 12 | no | — |
| 1139 | Q8 | — | 212 | 3 | no | — |
| 1140 | D4 | — | 4 | 6 | no | — |
| 1141 | D4 | — | 4 | 3 | no | — |
| 1142 | D4 | — | 4 | 6 | no | — |
| 1143 | D4 | — | 4 | 6 | no | — |
| 1144 | D4 | — | 106 | 12 | no | — |
| 1145 | D4 | — | 106 | 12 | no | — |
| 1146 | D4 | — | 212 | 6 | no | — |
| 1147 | D4 | — | 212 | 6 | no | — |
| 1148 | D4 | — | 212 | 6 | no | — |
| 1149 | D4 | — | 212 | 3 | no | — |
| 1150 | D4 | — | 212 | 6 | no | — |
| 1151 | D4 | — | 212 | 6 | no | — |
| 1152 | D4 | — | 212 | 6 | no | — |
| 1153 | D4 | — | 212 | 6 | no | — |
| 1154 | D4 | — | 212 | 6 | no | — |
| 1155 | D4 | — | 212 | 6 | no | — |
| 1156 | D4 | — | 212 | 6 | no | — |
| 1157 | D4 | — | 212 | 6 | no | — |
| 1158 | C2×C4 | — | 4 | 3 | no | — |
| 1159 | C2×C4 | — | 4 | 6 | no | — |
| 1160 | C2×C4 | — | 4 | 6 | no | — |
| 1161 | C2×C4 | — | 4 | 6 | no | — |
| 1162 | C2×C4 | — | 53 | 3 | no | — |
| 1163 | C2×C4 | — | 53 | 3 | no | — |
| 1164 | C2×C4 | — | 53 | 6 | no | — |
| 1165 | C2×C4 | — | 53 | 6 | no | — |
| 1166 | C2×C4 | — | 53 | 6 | no | — |
| 1167 | C2×C4 | — | 106 | 6 | no | — |
| 1168 | C2×C4 | — | 106 | 6 | no | — |
| 1169 | C2×C4 | — | 106 | 12 | no | — |
| 1170 | C2×C4 | — | 106 | 6 | no | — |
| 1171 | C2×C4 | — | 106 | 12 | no | — |
| 1172 | C2×C4 | — | 212 | 3 | no | — |
| 1173 | C2×C4 | — | 212 | 3 | no | — |
| 1174 | C2×C4 | — | 212 | 6 | no | — |
| 1175 | C2×C4 | — | 212 | 6 | no | — |
| 1176 | C2×C4 | — | 212 | 6 | no | — |
| 1177 | C2×C4 | — | 212 | 6 | no | — |
| 1178 | C2×C4 | — | 212 | 6 | no | — |
| 1179 | C2×C4 | — | 212 | 6 | no | — |
| 1180 | C2×C4 | — | 212 | 6 | no | — |
| 1181 | C2×C4 | — | 212 | 6 | no | — |
| 1182 | C2×C4 | — | 212 | 6 | no | — |
| 1183 | C2×C4 | C24×D53 | 1 | 3 | yes | — |
| 1184 | C2×C4 | C24×D53 | 1 | 6 | yes | — |
| 1185 | C2×C4 | C24×D53 | 1 | 3 | yes | — |
| 1186 | C2×C4 | C24×D53 | 1 | 6 | yes | — |
| 1187 | C2×C4 | C24×D53 | 1 | 6 | yes | — |
| 1188 | C22 | — | 2 | 6 | no | — |
| 1189 | C22 | — | 2 | 3 | no | — |
| 1190 | C22 | — | 2 | 6 | no | — |
| 1191 | C22 | — | 2 | 6 | no | — |
| 1192 | C22 | — | 106 | 3 | no | — |
| 1193 | C22 | — | 106 | 3 | no | — |
| 1194 | C22 | — | 106 | 6 | no | — |
| 1195 | C22 | — | 106 | 6 | no | — |
| 1196 | C22 | — | 106 | 6 | no | — |
| 1197 | C22 | — | 212 | 4 | no | — |
| 1198 | C22 | C25×D53 | 1 | 1 | yes | characteristic |
| 1199 | C4 | — | 2 | 3 | no | — |
| 1200 | C4 | — | 2 | 6 | no | — |
| 1201 | C4 | — | 2 | 6 | no | — |
| 1202 | C4 | — | 2 | 3 | no | — |
| 1203 | C4 | — | 2 | 6 | no | — |
| 1204 | C4 | — | 53 | 6 | no | — |
| 1205 | C4 | — | 106 | 3 | no | — |
| 1206 | C4 | — | 106 | 6 | no | — |
| 1207 | C4 | — | 106 | 6 | no | — |
| 1208 | C4 | — | 106 | 6 | no | — |
| 1209 | C2 | — | 4 | 1 | no | — |
| 1210 | C2 | — | 4 | 6 | no | — |
| 1211 | C2 | — | 212 | 1 | no | — |
| 1212 | C2 | — | 212 | 1 | no | — |
| 1213 | C2 | — | 212 | 6 | no | — |
| 1214 | C2 | #585×D53 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C25×D53 |
| commutator, socle, cosocle | C22×C53 | C26 |
| Fitting | C53×#3567 | C2 |
| hypercenter | #3567 | D53 |
| hypocenter | C53 | #62840 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ #3567 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20289405 | C2 | semidirect |
| 2. #20289403 | C2 | semidirect |
| 3. #20289402 | C2 | semidirect |
| 4. #20289209 | C2 | semidirect |
| 5. #20289111 | C2 | semidirect |
| 6. #20288973 | C2 | semidirect |
| 7. #20288967 | C2 | semidirect |
| 8. #20288717 | C2 | semidirect |
| 9. #20288714 | C2 | semidirect |
| 10. #20288685 | C2 | semidirect |
| 11. #20288682 | C2 | semidirect |
| 12. #20288631 | C2 | semidirect |
| 13. #20288629 | C2 | semidirect |
| 14. #20288009 | C2 | semidirect |
| 15. C53×#3567 | C2 | semidirect |
| 16. C53⋊#564 | C22 | semidirect |
| 17. #16811371 | C22 | semidirect |
| 18. #16811367 | C22 | semidirect |
| 19. #16811367 | C22 | semidirect |
| 24. #16811350 | C22 | semidirect |
| 25. #16811350 | C22 | semidirect |
| 26. #16811327 | C22 | semidirect |
| 27. #16811327 | C22 | semidirect |
| 29. #16811326 | C22 | semidirect |
| 30. #16811325 | C22 | semidirect |
| 33. #16811324 | C22 | semidirect |
| 36. #16811322 | C22 | semidirect |
| 41. #16811318 | C22 | semidirect |
| 43. #16811317 | C22 | semidirect |
| 46. #16811316 | C22 | semidirect |
| 47. #16811315 | C22 | semidirect |
| 48. #16811314 | C22 | semidirect |
| 50. #16811310 | C22 | semidirect |
| 52. #16811309 | C22 | semidirect |
| 53. #16811307 | C22 | semidirect |
| 55. #16811306 | C22 | semidirect |
| 57. #16811305 | C22 | semidirect |
| 62. #16811291 | C22 | semidirect |
| 63. #16811291 | C22 | semidirect |
| 68. #16811271 | C22 | semidirect |
| 69. #16811271 | C22 | semidirect |
| 72. #16811232 | C22 | semidirect |
| 73. #16811230 | C22 | semidirect |
| 80. #16811225 | C22 | semidirect |
| 84. #16811223 | C22 | semidirect |
| 101. #16811170 | C22 | semidirect |
| 103. #16811168 | C22 | semidirect |
| 108. #16811156 | C22 | semidirect |
| 109. #16811153 | C22 | semidirect |
| 112. #16811151 | C22 | semidirect |
| 114. #16811150 | C22 | semidirect |
| 115. C2×#13133207 | C22 | semidirect |
| 116. #125×D53 | C22 | semidirect |
| 121. #16811104 | C22 | semidirect |
| 122. #16811103 | C22 | semidirect |
| 123. #16811102 | C22 | semidirect |
| 124. #16811102 | C22 | semidirect |
| 130. C53×#564 | C22 | semidirect |
| 131. C53×#562 | C22 | semidirect |
| 132. C53×#553 | C22 | semidirect |
| 133. C53×#552 | C22 | semidirect |
| 605. #3567 | D53 | semidirect |
| 624. #564 | C2×D53 | semidirect |
| 628. #562 | C2×D53 | semidirect |
| 656. #553 | C2×D53 | semidirect |
| 668. #552 | C2×D53 | semidirect |
| 744. C53 | #62840 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289405 | 2 |
| #20289403 | 2 |
| #20289402 | 2 |
| #20289209 | 2 |
| #20289111 | 2 |
| #20288973 | 2 |
| #20288967 | 2 |
| #20288717 | 2 |
| #20288714 | 2 |
| #20288685 | 2 |
| #20288682 | 2 |
| #20288631 | 2 |
| #20288629 | 2 |
| #20288009 | 2 |
| C53×#3567 | 2 |
| #62840 | 53 |