Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2600 conjugacy classes of subgroups.
The subgroup lattice has 728 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #20289503 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #20289499 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #20286520 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #20286509 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #20286491 | C2 | 1 | 8 | yes | maximal, complemented |
| 6 | #20285174 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #20284453 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #20284452 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #20284066 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | C2×#16810807 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #20283626 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C53×#2956 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #16811459 | C22 | 1 | 2 | yes | complemented |
| 14 | C2×#13133264 | C22 | 1 | 2 | yes | — |
| 15 | #16811440 | — | 2 | 4 | no | — |
| 16 | #16811440 | C22 | 1 | 8 | yes | complemented |
| 17 | #16811439 | — | 2 | 4 | no | — |
| 18 | #16811437 | C22 | 1 | 8 | yes | complemented |
| 19 | #16811435 | — | 2 | 4 | no | — |
| 20 | #16811435 | C22 | 1 | 8 | yes | complemented |
| 21 | #16811433 | — | 2 | 4 | no | — |
| 22 | #16811430 | C22 | 1 | 8 | yes | complemented |
| 23 | #16811423 | — | 2 | 4 | no | — |
| 24 | #16811423 | C22 | 1 | 2 | yes | — |
| 25 | #16811423 | C22 | 1 | 1 | yes | characteristic |
| 26 | #16811421 | C22 | 1 | 2 | yes | — |
| 27 | #16811419 | — | 2 | 4 | no | — |
| 28 | C2×#13133250 | — | 2 | 4 | no | — |
| 29 | C2×#13133250 | C22 | 1 | 2 | yes | complemented |
| 30 | C2×#13133250 | C22 | 1 | 2 | yes | complemented |
| 31 | C2×#13133250 | C22 | 1 | 2 | yes | complemented |
| 32 | C2×#13133247 | C22 | 1 | 2 | yes | complemented |
| 33 | #137×D53 | — | 2 | 4 | no | — |
| 34 | #16811389 | C22 | 1 | 2 | yes | complemented |
| 35 | #16811173 | C22 | 1 | 1 | yes | characteristic |
| 36 | C2×#13133217 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | #16811017 | C22 | 1 | 4 | yes | complemented |
| 38 | #16811003 | C22 | 1 | 2 | yes | complemented |
| 39 | #16810996 | C22 | 1 | 2 | yes | complemented |
| 40 | #16810899 | C22 | 1 | 8 | yes | complemented |
| 41 | #16810898 | C22 | 1 | 8 | yes | complemented |
| 42 | #16810887 | C22 | 1 | 8 | yes | complemented |
| 43 | #16810886 | C22 | 1 | 8 | yes | complemented |
| 44 | #16810807 | C22 | 1 | 8 | yes | complemented |
| 45 | #16810807 | C22 | 1 | 8 | yes | complemented |
| 46 | #16810807 | C22 | 1 | 4 | yes | complemented |
| 47 | #16810802 | C22 | 1 | 4 | yes | complemented |
| 48 | #16810797 | C22 | 1 | 4 | yes | complemented |
| 49 | #16810792 | C22 | 1 | 4 | yes | complemented |
| 50 | #16810746 | C22 | 1 | 4 | yes | complemented |
| 51 | #16810741 | C22 | 1 | 4 | yes | complemented |
| 52 | #16810672 | C22 | 1 | 1 | yes | characteristic, complemented |
| 53 | C2×#13133145 | C22 | 1 | 2 | yes | complemented |
| 54 | #16810605 | C22 | 1 | 2 | yes | complemented |
| 55 | C2×#13133135 | C22 | 1 | 2 | yes | complemented |
| 56 | C53×#575 | C22 | 1 | 1 | yes | characteristic |
| 57 | C53×#568 | C22 | 1 | 2 | yes | complemented |
| 58 | C53×#444 | C22 | 1 | 4 | yes | complemented |
| 59 | C53×#443 | C22 | 1 | 4 | yes | complemented |
| 60 | C53×#430 | C22 | 1 | 1 | yes | characteristic, complemented |
| 61 | C2×#104×C53 | C22 | 1 | 2 | yes | complemented |
| 62 | C4×M16×C53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 63 | #13133265 | — | 2 | 2 | no | — |
| 64 | #13133264 | — | 2 | 4 | no | — |
| 65 | #13133264 | — | 2 | 2 | no | — |
| 66 | #13133264 | — | 2 | 4 | no | — |
| 67 | #13133264 | — | 4 | 2 | no | — |
| 68 | #13133264 | C23 | 1 | 4 | yes | — |
| 69 | #13133264 | C23 | 1 | 8 | yes | — |
| 70 | #13133263 | — | 2 | 2 | no | — |
| 71 | #13133263 | C23 | 1 | 4 | yes | — |
| 72 | #13133262 | — | 2 | 2 | no | — |
| 73 | #13133262 | — | 4 | 2 | no | — |
| 74 | C2×#11719945 | — | 2 | 4 | no | — |
| 75 | C2×#11719945 | — | 2 | 2 | no | — |
| 76 | C2×#11719945 | C23 | 1 | 2 | yes | — |
| 77 | C2×#11719945 | C23 | 1 | 2 | yes | — |
| 78 | C2×#11719947 | — | 2 | 2 | no | — |
| 79 | C2×#11719947 | — | 4 | 2 | no | — |
| 80 | #41×D53 | — | 2 | 4 | no | — |
| 81 | #41×D53 | — | 4 | 2 | no | — |
| 82 | C22×Dic106 | — | 2 | 2 | no | — |
| 83 | C22×Dic106 | C23 | 1 | 2 | yes | — |
| 84 | C2×Q8×D53 | — | 2 | 2 | no | — |
| 85 | #13133250 | — | 2 | 4 | no | — |
| 86 | #13133250 | — | 2 | 4 | no | — |
| 87 | #13133250 | — | 2 | 4 | no | — |
| 88 | #13133250 | — | 2 | 4 | no | — |
| 89 | #13133250 | — | 2 | 8 | no | — |
| 90 | #13133250 | — | 2 | 8 | no | — |
| 91 | #13133250 | — | 2 | 8 | no | — |
| 92 | #13133250 | — | 2 | 4 | no | — |
| 93 | #13133250 | — | 2 | 2 | no | — |
| 94 | #13133250 | D4 | 1 | 4 | yes | complemented |
| 95 | #13133250 | C23 | 1 | 4 | yes | — |
| 96 | #13133250 | C23 | 1 | 8 | yes | — |
| 97 | #13133249 | — | 2 | 8 | no | — |
| 98 | #13133248 | — | 2 | 2 | no | — |
| 99 | #13133247 | — | 2 | 4 | no | — |
| 100 | #13133247 | C23 | 1 | 4 | yes | — |
| 101 | #13133247 | C23 | 1 | 8 | yes | — |
| 102 | #13133246 | — | 2 | 8 | no | — |
| 103 | #13133246 | — | 2 | 8 | no | — |
| 104 | #13133245 | — | 2 | 8 | no | — |
| 105 | #13133245 | — | 2 | 2 | no | — |
| 106 | #13133245 | D4 | 1 | 4 | yes | complemented |
| 107 | #13133245 | C23 | 1 | 4 | yes | — |
| 108 | #13133243 | — | 2 | 2 | no | — |
| 109 | #13133242 | C23 | 1 | 4 | yes | — |
| 110 | #13133241 | — | 2 | 8 | no | — |
| 111 | #13133239 | — | 2 | 8 | no | — |
| 112 | #13133239 | — | 2 | 8 | no | — |
| 113 | #13133239 | — | 2 | 4 | no | — |
| 114 | #13133239 | C23 | 1 | 4 | yes | — |
| 115 | #13133238 | — | 2 | 8 | no | — |
| 116 | #13133237 | — | 2 | 4 | no | — |
| 117 | #13133236 | — | 2 | 8 | no | — |
| 118 | C2×Dic212 | — | 2 | 8 | no | — |
| 119 | C2×Dic212 | — | 2 | 2 | no | — |
| 120 | C2×Dic212 | C23 | 1 | 4 | yes | — |
| 121 | C2×Dic212 | C23 | 1 | 4 | yes | — |
| 122 | C2×#11719925 | — | 2 | 2 | no | — |
| 123 | Q16×D53 | — | 2 | 8 | no | — |
| 124 | C2×#11719913 | — | 2 | 8 | no | — |
| 125 | C2×#11719913 | — | 2 | 2 | no | — |
| 126 | C2×#11719913 | C23 | 1 | 4 | yes | — |
| 127 | C2×#11719913 | C23 | 1 | 4 | yes | — |
| 128 | C2×#11719923 | — | 2 | 2 | no | — |
| 129 | SD16×D53 | — | 2 | 8 | no | — |
| 130 | #13133225 | — | 2 | 4 | no | — |
| 131 | #13133223 | C23 | 1 | 8 | yes | — |
| 132 | C2×#11719917 | C23 | 1 | 2 | yes | — |
| 133 | M16×D53 | — | 2 | 4 | no | — |
| 134 | #13133217 | — | 4 | 1 | no | — |
| 135 | #13133217 | C23 | 1 | 2 | yes | — |
| 136 | #13133217 | C23 | 1 | 2 | yes | — |
| 137 | #13133217 | C23 | 1 | 1 | yes | characteristic |
| 138 | #13133214 | C23 | 1 | 1 | yes | characteristic |
| 139 | #13133205 | C23 | 1 | 2 | yes | — |
| 140 | #13133191 | — | 4 | 1 | no | — |
| 141 | C4×D212 | — | 4 | 1 | no | — |
| 142 | C2×C4⋊Dic53 | — | 4 | 1 | no | — |
| 143 | #13133153 | C23 | 1 | 4 | yes | — |
| 144 | #13133145 | C23 | 1 | 4 | yes | — |
| 145 | #13133145 | C23 | 1 | 4 | yes | — |
| 146 | #13133135 | C23 | 1 | 4 | yes | — |
| 147 | #13133135 | C23 | 1 | 8 | yes | — |
| 148 | #13133133 | C23 | 1 | 4 | yes | — |
| 149 | C2×#41×C53 | C23 | 1 | 2 | yes | — |
| 150 | #137×C53 | D4 | 1 | 4 | yes | complemented |
| 151 | AGL(1,ℤ/8)×C53 | D4 | 1 | 4 | yes | complemented |
| 152 | #135×C53 | C23 | 1 | 4 | yes | — |
| 153 | #131×C53 | — | 2 | 4 | no | — |
| 154 | #131×C53 | C23 | 1 | 8 | yes | — |
| 155 | C2×M16×C53 | — | 2 | 4 | no | — |
| 156 | C2×M16×C53 | C23 | 1 | 2 | yes | — |
| 157 | C2×M16×C53 | C23 | 1 | 1 | yes | characteristic |
| 158 | C2×M16×C53 | C23 | 1 | 1 | yes | characteristic |
| 159 | C2×C42×C53 | C23 | 1 | 1 | yes | characteristic |
| 160 | #108×C53 | C23 | 1 | 4 | yes | — |
| 161 | #104×C53 | C23 | 1 | 4 | yes | — |
| 162 | #104×C53 | C23 | 1 | 4 | yes | — |
| 163 | #97×C53 | C23 | 1 | 2 | yes | — |
| 164 | C4×C8×C53 | C23 | 1 | 2 | yes | — |
| 165 | #41×C53 | — | 2 | 2 | no | — |
| 166 | #41×C53 | — | 2 | 2 | no | — |
| 167 | #41×C53 | C2×D4 | 1 | 4 | yes | — |
| 168 | #41×C53 | C24 | 1 | 4 | yes | — |
| 169 | C2×Q8×C53 | C2×D4 | 1 | 2 | yes | — |
| 170 | C2×D4×C53 | — | 2 | 2 | no | — |
| 171 | C2×D4×C53 | C2×D4 | 1 | 2 | yes | — |
| 172 | C22×C4×C53 | — | 2 | 2 | no | — |
| 173 | C22×C4×C53 | — | 2 | 1 | no | — |
| 174 | C22×C4×C53 | C24 | 1 | 1 | yes | characteristic |
| 175 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 176 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 177 | C2×C22⋊D53 | — | 4 | 4 | no | — |
| 178 | C2×C22⋊D53 | — | 4 | 2 | no | — |
| 179 | C22×Dic53 | — | 2 | 2 | no | — |
| 180 | C22×Dic53 | — | 4 | 2 | no | — |
| 181 | #11719949 | — | 2 | 4 | no | — |
| 182 | #11719949 | — | 4 | 2 | no | — |
| 183 | Q8×D53 | — | 2 | 8 | no | — |
| 184 | Q8×D53 | — | 2 | 4 | no | — |
| 185 | Q8×D53 | — | 4 | 2 | no | — |
| 186 | Q8×D53 | — | 4 | 4 | no | — |
| 187 | #11719947 | — | 2 | 4 | no | — |
| 188 | #11719947 | — | 2 | 8 | no | — |
| 189 | #11719947 | — | 4 | 2 | no | — |
| 190 | #11719947 | — | 4 | 4 | no | — |
| 191 | #11719947 | — | 4 | 4 | no | — |
| 192 | #11719947 | — | 4 | 8 | no | — |
| 193 | #11719947 | — | 4 | 4 | no | — |
| 194 | #11719947 | — | 4 | 8 | no | — |
| 195 | D4×D53 | — | 2 | 4 | no | — |
| 196 | D4×D53 | — | 4 | 2 | no | — |
| 197 | D4×D53 | — | 4 | 4 | no | — |
| 198 | D4×D53 | — | 4 | 4 | no | — |
| 199 | #11719945 | — | 2 | 2 | no | — |
| 200 | #11719945 | — | 2 | 2 | no | — |
| 201 | #11719945 | — | 2 | 2 | no | — |
| 202 | #11719945 | — | 2 | 2 | no | — |
| 203 | #11719945 | — | 2 | 2 | no | — |
| 204 | #11719945 | — | 2 | 2 | no | — |
| 205 | #11719945 | — | 2 | 8 | no | — |
| 206 | #11719945 | — | 2 | 4 | no | — |
| 207 | #11719945 | — | 2 | 4 | no | — |
| 208 | #11719945 | — | 4 | 4 | no | — |
| 209 | #11719945 | — | 4 | 4 | no | — |
| 210 | #11719945 | — | 4 | 4 | no | — |
| 211 | #11719945 | C2×D4 | 1 | 4 | yes | — |
| 212 | #11719945 | C24 | 1 | 4 | yes | — |
| 213 | C2×D212 | — | 2 | 4 | no | — |
| 214 | C2×D212 | — | 4 | 1 | no | — |
| 215 | C2×D212 | C2×D4 | 1 | 2 | yes | — |
| 216 | C2×D212 | C24 | 1 | 2 | yes | — |
| 217 | C2×C4×D53 | — | 2 | 2 | no | — |
| 218 | C2×C4×D53 | — | 2 | 2 | no | — |
| 219 | C2×C4×D53 | — | 4 | 4 | no | — |
| 220 | C2×C4×D53 | — | 4 | 2 | no | — |
| 221 | C2×Dic106 | — | 2 | 2 | no | — |
| 222 | C2×Dic106 | — | 2 | 2 | no | — |
| 223 | C2×Dic106 | — | 2 | 2 | no | — |
| 224 | C2×Dic106 | — | 2 | 2 | no | — |
| 225 | C2×Dic106 | — | 2 | 8 | no | — |
| 226 | C2×Dic106 | — | 2 | 4 | no | — |
| 227 | C2×Dic106 | — | 2 | 2 | no | — |
| 228 | C2×Dic106 | — | 4 | 4 | no | — |
| 229 | C2×Dic106 | — | 4 | 2 | no | — |
| 230 | C2×Dic106 | C2×D4 | 1 | 2 | yes | — |
| 231 | C2×Dic106 | C24 | 1 | 2 | yes | — |
| 232 | C2×Dic106 | C24 | 1 | 4 | yes | — |
| 233 | Q16×C53 | C2×D4 | 1 | 4 | yes | — |
| 234 | SD16×C53 | C2×D4 | 1 | 8 | yes | — |
| 235 | D8×C53 | C2×D4 | 1 | 4 | yes | — |
| 236 | M16×C53 | — | 2 | 2 | no | — |
| 237 | M16×C53 | — | 2 | 8 | no | — |
| 238 | M16×C53 | C2×D4 | 1 | 4 | yes | — |
| 239 | M16×C53 | C2×D4 | 1 | 4 | yes | — |
| 240 | M16×C53 | C24 | 1 | 4 | yes | — |
| 241 | C2×C8×C53 | — | 2 | 2 | no | — |
| 242 | C2×C8×C53 | — | 2 | 8 | no | — |
| 243 | C2×C8×C53 | C24 | 1 | 2 | yes | — |
| 244 | C2×C8×C53 | C24 | 1 | 2 | yes | — |
| 245 | C42×C53 | — | 2 | 1 | no | — |
| 246 | C42×C53 | C24 | 1 | 1 | yes | characteristic |
| 247 | C42×C53 | C24 | 1 | 1 | yes | characteristic |
| 248 | #11719925 | — | 2 | 4 | no | — |
| 249 | #11719925 | — | 2 | 8 | no | — |
| 250 | #11719924 | — | 2 | 4 | no | — |
| 251 | #11719923 | — | 2 | 8 | no | — |
| 252 | #11719923 | — | 2 | 4 | no | — |
| 253 | #11719922 | — | 2 | 4 | no | — |
| 254 | #11719921 | — | 4 | 2 | no | — |
| 255 | C4⋊Dic53 | — | 4 | 2 | no | — |
| 256 | C4⋊Dic53 | — | 4 | 2 | no | — |
| 257 | C4⋊Dic53 | — | 4 | 1 | no | — |
| 258 | #11719917 | — | 2 | 2 | no | — |
| 259 | #11719917 | C24 | 1 | 4 | yes | — |
| 260 | C2×#88322 | — | 2 | 2 | no | — |
| 261 | Dic212 | — | 2 | 8 | no | — |
| 262 | Dic212 | — | 2 | 4 | no | — |
| 263 | Dic212 | — | 2 | 8 | no | — |
| 264 | Dic212 | — | 2 | 8 | no | — |
| 265 | Dic212 | C2×D4 | 1 | 4 | yes | — |
| 266 | D424 | — | 2 | 4 | no | — |
| 267 | D424 | C2×D4 | 1 | 4 | yes | — |
| 268 | #11719913 | — | 2 | 8 | no | — |
| 269 | #11719913 | — | 2 | 4 | no | — |
| 270 | #11719913 | — | 2 | 4 | no | — |
| 271 | #11719913 | — | 2 | 8 | no | — |
| 272 | #11719913 | — | 2 | 8 | no | — |
| 273 | #11719913 | C2×D4 | 1 | 8 | yes | — |
| 274 | #11719912 | — | 2 | 8 | no | — |
| 275 | C8×D53 | — | 2 | 8 | no | — |
| 276 | C23×C53 | — | 2 | 2 | no | — |
| 277 | C23×C53 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 278 | C22×D53 | — | 2 | 2 | no | — |
| 279 | C22×D53 | — | 2 | 2 | no | — |
| 280 | C22×D53 | — | 4 | 4 | no | — |
| 281 | Q8×C53 | — | 2 | 2 | no | — |
| 282 | Q8×C53 | C22×D4 | 1 | 4 | yes | — |
| 283 | D4×C53 | — | 2 | 4 | no | — |
| 284 | D4×C53 | — | 2 | 4 | no | — |
| 285 | D4×C53 | — | 2 | 2 | no | — |
| 286 | D4×C53 | C22×D4 | 1 | 4 | yes | — |
| 287 | C2×C4×C53 | — | 2 | 2 | no | — |
| 288 | C2×C4×C53 | — | 2 | 1 | no | — |
| 289 | C2×C4×C53 | — | 2 | 4 | no | — |
| 290 | C2×C4×C53 | — | 2 | 4 | no | — |
| 291 | C2×C4×C53 | — | 2 | 1 | no | — |
| 292 | C2×C4×C53 | — | 4 | 2 | no | — |
| 293 | C2×C4×C53 | C22×D4 | 1 | 2 | yes | — |
| 294 | C2×C4×C53 | C22×D4 | 1 | 2 | yes | — |
| 295 | C2×C4×C53 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 296 | C2×C4×C53 | C25 | 1 | 1 | yes | characteristic |
| 297 | C22⋊D53 | — | 2 | 4 | no | — |
| 298 | C22⋊D53 | — | 2 | 4 | no | — |
| 299 | C22⋊D53 | — | 4 | 4 | no | — |
| 300 | C22⋊D53 | — | 4 | 4 | no | — |
| 301 | C22⋊D53 | — | 4 | 8 | no | — |
| 302 | C22⋊D53 | — | 4 | 2 | no | — |
| 303 | C22⋊D53 | — | 4 | 2 | no | — |
| 304 | C2×Dic53 | — | 2 | 2 | no | — |
| 305 | C2×Dic53 | — | 2 | 4 | no | — |
| 306 | C2×Dic53 | — | 2 | 2 | no | — |
| 307 | C2×Dic53 | — | 4 | 8 | no | — |
| 308 | C2×Dic53 | — | 4 | 4 | no | — |
| 309 | C2×Dic53 | — | 4 | 2 | no | — |
| 310 | C2×Dic53 | — | 4 | 2 | no | — |
| 311 | D212 | — | 2 | 2 | no | — |
| 312 | D212 | — | 2 | 2 | no | — |
| 313 | D212 | — | 2 | 2 | no | — |
| 314 | D212 | — | 4 | 4 | no | — |
| 315 | D212 | — | 8 | 2 | no | — |
| 316 | D212 | C22×D4 | 1 | 4 | yes | — |
| 317 | C4×D53 | — | 2 | 4 | no | — |
| 318 | C4×D53 | — | 2 | 4 | no | — |
| 319 | C4×D53 | — | 4 | 4 | no | — |
| 320 | C4×D53 | — | 4 | 4 | no | — |
| 321 | C4×D53 | — | 4 | 8 | no | — |
| 322 | C4×D53 | — | 4 | 2 | no | — |
| 323 | C4×D53 | — | 4 | 2 | no | — |
| 324 | Dic106 | — | 2 | 2 | no | — |
| 325 | Dic106 | — | 2 | 4 | no | — |
| 326 | Dic106 | — | 2 | 2 | no | — |
| 327 | Dic106 | — | 2 | 4 | no | — |
| 328 | Dic106 | — | 2 | 2 | no | — |
| 329 | Dic106 | — | 4 | 8 | no | — |
| 330 | Dic106 | — | 4 | 4 | no | — |
| 331 | Dic106 | — | 4 | 2 | no | — |
| 332 | Dic106 | — | 4 | 2 | no | — |
| 333 | Dic106 | C22×D4 | 1 | 4 | yes | — |
| 334 | C8×C53 | — | 2 | 4 | no | — |
| 335 | C8×C53 | C22×D4 | 1 | 4 | yes | — |
| 336 | C8×C53 | C22×D4 | 1 | 4 | yes | — |
| 337 | #88322 | — | 2 | 4 | no | — |
| 338 | #61111 | — | 53 | 1 | no | maximal, Sylow |
| 339 | C22×C53 | — | 2 | 4 | no | — |
| 340 | C22×C53 | — | 4 | 1 | no | — |
| 341 | C22×C53 | — | 8 | 2 | no | — |
| 342 | C22×C53 | D42 | 1 | 2 | yes | — |
| 343 | C22×C53 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 344 | C2×D53 | — | 2 | 4 | no | — |
| 345 | C2×D53 | — | 4 | 2 | no | — |
| 346 | C2×D53 | — | 8 | 2 | no | — |
| 347 | C2×D53 | — | 8 | 2 | no | — |
| 348 | C2×D53 | — | 16 | 4 | no | — |
| 349 | C4×C53 | — | 2 | 2 | no | — |
| 350 | C4×C53 | — | 2 | 4 | no | — |
| 351 | C4×C53 | — | 4 | 1 | no | — |
| 352 | C4×C53 | D42 | 1 | 2 | yes | — |
| 353 | C4×C53 | C23×D4 | 1 | 1 | yes | characteristic |
| 354 | C4×C53 | C23×D4 | 1 | 1 | yes | characteristic |
| 355 | Dic53 | — | 2 | 4 | no | — |
| 356 | Dic53 | — | 4 | 4 | no | — |
| 357 | Dic53 | — | 4 | 2 | no | — |
| 358 | #3586 | — | 53 | 2 | no | — |
| 359 | #3586 | — | 53 | 2 | no | — |
| 360 | #3293 | — | 53 | 4 | no | — |
| 361 | #3291 | — | 53 | 4 | no | — |
| 362 | #3289 | — | 53 | 8 | no | — |
| 363 | #3152 | — | 53 | 1 | no | — |
| 364 | #3069 | — | 53 | 2 | no | — |
| 365 | #3069 | — | 53 | 2 | no | — |
| 366 | #3018 | — | 53 | 2 | no | — |
| 367 | C2×#456 | — | 53 | 2 | no | — |
| 368 | #2956 | — | 53 | 1 | no | — |
| 369 | #2956 | D53 | 1 | 1 | yes | characteristic, complemented |
| 370 | C2×C53 | — | 2 | 1 | no | — |
| 371 | C2×C53 | — | 2 | 2 | no | — |
| 372 | C2×C53 | — | 4 | 4 | no | — |
| 373 | C2×C53 | C2×D42 | 1 | 1 | yes | characteristic |
| 374 | D53 | — | 4 | 4 | no | — |
| 375 | D53 | — | 8 | 2 | no | — |
| 376 | #585 | — | 53 | 2 | no | — |
| 377 | C2×2−1+4 | — | 53 | 2 | no | — |
| 378 | #578 | — | 53 | 8 | no | — |
| 379 | #578 | — | 53 | 8 | no | — |
| 380 | #578 | — | 106 | 4 | no | — |
| 381 | #578 | — | 106 | 4 | no | — |
| 382 | #577 | — | 53 | 8 | no | — |
| 383 | #577 | — | 53 | 8 | no | — |
| 384 | #577 | — | 106 | 4 | no | — |
| 385 | #577 | — | 106 | 4 | no | — |
| 386 | #575 | — | 53 | 2 | no | — |
| 387 | #575 | — | 53 | 1 | no | — |
| 388 | #575 | — | 53 | 2 | no | — |
| 389 | #575 | — | 106 | 4 | no | — |
| 390 | #575 | — | 106 | 4 | no | — |
| 391 | #575 | C2×D53 | 1 | 1 | yes | characteristic |
| 392 | C2×#137 | — | 53 | 2 | no | — |
| 393 | C2×#137 | — | 53 | 2 | no | — |
| 394 | C2×#137 | — | 53 | 2 | no | — |
| 395 | C2×#137 | — | 53 | 2 | no | — |
| 396 | C2×#137 | — | 106 | 4 | no | — |
| 397 | C2×#137 | — | 106 | 4 | no | — |
| 398 | #568 | — | 53 | 2 | no | — |
| 399 | #568 | C2×D53 | 1 | 2 | yes | complemented |
| 400 | #532 | — | 53 | 1 | no | — |
| 401 | C2×C4⋊Q8 | — | 53 | 1 | no | — |
| 402 | #497 | — | 53 | 4 | no | — |
| 403 | #494 | — | 53 | 2 | no | — |
| 404 | #492 | — | 53 | 2 | no | — |
| 405 | #473 | — | 53 | 8 | no | — |
| 406 | #473 | — | 53 | 8 | no | — |
| 407 | #471 | — | 53 | 8 | no | — |
| 408 | #471 | — | 53 | 8 | no | — |
| 409 | #456 | — | 53 | 8 | no | — |
| 410 | #456 | — | 53 | 8 | no | — |
| 411 | #456 | — | 53 | 4 | no | — |
| 412 | #455 | — | 53 | 4 | no | — |
| 413 | #454 | — | 53 | 4 | no | — |
| 414 | #453 | — | 53 | 4 | no | — |
| 415 | #444 | — | 53 | 4 | no | — |
| 416 | #444 | C2×D53 | 1 | 4 | yes | complemented |
| 417 | #443 | — | 53 | 4 | no | — |
| 418 | #443 | C2×D53 | 1 | 4 | yes | complemented |
| 419 | #430 | — | 53 | 1 | no | — |
| 420 | #430 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 421 | C2×#104 | — | 53 | 2 | no | — |
| 422 | C2×#104 | C2×D53 | 1 | 2 | yes | complemented |
| 423 | #413 | — | 53 | 2 | no | — |
| 424 | C2×#101 | — | 53 | 2 | no | — |
| 425 | C4×M16 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 426 | C53 | #61111 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 427 | 2−1+4 | — | 53 | 8 | no | — |
| 428 | 2−1+4 | — | 53 | 4 | no | — |
| 429 | 2−1+4 | — | 106 | 2 | no | — |
| 430 | 2−1+4 | — | 106 | 4 | no | — |
| 431 | 2−1+4 | — | 106 | 4 | no | — |
| 432 | 2−1+4 | — | 106 | 2 | no | — |
| 433 | 2−1+4 | — | 212 | 2 | no | — |
| 434 | H(5,𝔽2) | — | 53 | 4 | no | — |
| 435 | H(5,𝔽2) | — | 106 | 2 | no | — |
| 436 | H(5,𝔽2) | — | 106 | 2 | no | — |
| 437 | H(5,𝔽2) | — | 212 | 2 | no | — |
| 438 | C2×#41 | — | 53 | 2 | no | — |
| 439 | C2×#41 | — | 53 | 2 | no | — |
| 440 | C2×#41 | — | 106 | 2 | no | — |
| 441 | C2×#41 | — | 106 | 4 | no | — |
| 442 | C2×#41 | — | 106 | 4 | no | — |
| 443 | C2×#41 | — | 106 | 2 | no | — |
| 444 | C2×#41 | — | 212 | 2 | no | — |
| 445 | C2×#41 | — | 212 | 2 | no | — |
| 446 | C2×#41 | C22×D53 | 1 | 2 | yes | — |
| 447 | C22×Q8 | — | 53 | 2 | no | — |
| 448 | C22×Q8 | — | 106 | 2 | no | — |
| 449 | C22×Q8 | — | 106 | 2 | no | — |
| 450 | #137 | — | 53 | 8 | no | — |
| 451 | #137 | — | 53 | 4 | no | — |
| 452 | #137 | — | 53 | 4 | no | — |
| 453 | #137 | — | 53 | 8 | no | — |
| 454 | #137 | — | 53 | 4 | no | — |
| 455 | #137 | — | 106 | 8 | no | — |
| 456 | #137 | — | 106 | 8 | no | — |
| 457 | #137 | — | 106 | 8 | no | — |
| 458 | #137 | — | 106 | 2 | no | — |
| 459 | #137 | — | 106 | 4 | no | — |
| 460 | #137 | — | 106 | 4 | no | — |
| 461 | #137 | — | 106 | 2 | no | — |
| 462 | #137 | — | 106 | 8 | no | — |
| 463 | #137 | — | 106 | 8 | no | — |
| 464 | #137 | — | 106 | 8 | no | — |
| 465 | #137 | — | 106 | 4 | no | — |
| 466 | #137 | — | 106 | 4 | no | — |
| 467 | #137 | — | 106 | 4 | no | — |
| 468 | #137 | — | 106 | 4 | no | — |
| 469 | #137 | D212 | 1 | 4 | yes | complemented |
| 470 | AGL(1,ℤ/8) | — | 53 | 4 | no | — |
| 471 | AGL(1,ℤ/8) | — | 53 | 4 | no | — |
| 472 | AGL(1,ℤ/8) | — | 53 | 4 | no | — |
| 473 | AGL(1,ℤ/8) | — | 106 | 8 | no | — |
| 474 | AGL(1,ℤ/8) | — | 106 | 2 | no | — |
| 475 | AGL(1,ℤ/8) | — | 106 | 2 | no | — |
| 476 | AGL(1,ℤ/8) | — | 106 | 8 | no | — |
| 477 | AGL(1,ℤ/8) | D212 | 1 | 4 | yes | complemented |
| 478 | #135 | — | 53 | 4 | no | — |
| 479 | #135 | — | 106 | 8 | no | — |
| 480 | #135 | — | 106 | 8 | no | — |
| 481 | #135 | — | 106 | 4 | no | — |
| 482 | #135 | — | 106 | 4 | no | — |
| 483 | #135 | — | 106 | 8 | no | — |
| 484 | #135 | — | 106 | 8 | no | — |
| 485 | #135 | C22×D53 | 1 | 4 | yes | — |
| 486 | C2×Q16 | — | 53 | 4 | no | — |
| 487 | C2×Q16 | — | 53 | 4 | no | — |
| 488 | C2×Q16 | — | 106 | 8 | no | — |
| 489 | C2×Q16 | — | 106 | 2 | no | — |
| 490 | C2×Q16 | — | 106 | 2 | no | — |
| 491 | C2×Q16 | — | 106 | 8 | no | — |
| 492 | C2×SD16 | — | 53 | 4 | no | — |
| 493 | C2×SD16 | — | 53 | 4 | no | — |
| 494 | C2×SD16 | — | 106 | 8 | no | — |
| 495 | C2×SD16 | — | 106 | 2 | no | — |
| 496 | C2×SD16 | — | 106 | 2 | no | — |
| 497 | C2×SD16 | — | 106 | 8 | no | — |
| 498 | #131 | — | 2 | 4 | no | — |
| 499 | #131 | — | 53 | 8 | no | — |
| 500 | #131 | — | 106 | 4 | no | — |
| 501 | #131 | C22×D53 | 1 | 8 | yes | — |
| 502 | C2×M16 | — | 2 | 4 | no | — |
| 503 | C2×M16 | — | 53 | 2 | no | — |
| 504 | C2×M16 | — | 106 | 4 | no | — |
| 505 | C2×M16 | C22×D53 | 1 | 2 | yes | — |
| 506 | C2×M16 | C22×D53 | 1 | 1 | yes | characteristic |
| 507 | C2×M16 | C22×D53 | 1 | 1 | yes | characteristic |
| 508 | C4⋊Q8 | — | 53 | 2 | no | — |
| 509 | C4⋊Q8 | — | 53 | 2 | no | — |
| 510 | C4⋊Q8 | — | 53 | 1 | no | — |
| 511 | C4⋊Q8 | — | 212 | 1 | no | — |
| 512 | #127 | — | 53 | 1 | no | — |
| 513 | #124 | — | 53 | 2 | no | — |
| 514 | #121 | — | 212 | 1 | no | — |
| 515 | C4×D4 | — | 212 | 1 | no | — |
| 516 | C2×C4⋊C4 | — | 212 | 1 | no | — |
| 517 | C2×C42 | C22×D53 | 1 | 1 | yes | characteristic |
| 518 | #108 | — | 53 | 4 | no | — |
| 519 | #108 | C22×D53 | 1 | 4 | yes | — |
| 520 | #104 | — | 53 | 4 | no | — |
| 521 | #104 | — | 53 | 4 | no | — |
| 522 | #104 | C22×D53 | 1 | 4 | yes | — |
| 523 | #104 | C22×D53 | 1 | 4 | yes | — |
| 524 | #101 | — | 53 | 8 | no | — |
| 525 | #101 | — | 53 | 4 | no | — |
| 526 | #100 | — | 53 | 4 | no | — |
| 527 | #97 | C22×D53 | 1 | 2 | yes | — |
| 528 | C4×C8 | C22×D53 | 1 | 2 | yes | — |
| 529 | #41 | — | 2 | 2 | no | — |
| 530 | #41 | — | 2 | 2 | no | — |
| 531 | #41 | — | 53 | 4 | no | — |
| 532 | #41 | — | 53 | 4 | no | — |
| 533 | #41 | — | 106 | 8 | no | — |
| 534 | #41 | — | 106 | 4 | no | — |
| 535 | #41 | — | 106 | 4 | no | — |
| 536 | #41 | — | 106 | 2 | no | — |
| 537 | #41 | — | 106 | 2 | no | — |
| 538 | #41 | — | 106 | 4 | no | — |
| 539 | #41 | — | 106 | 8 | no | — |
| 540 | #41 | — | 106 | 4 | no | — |
| 541 | #41 | — | 106 | 2 | no | — |
| 542 | #41 | — | 106 | 2 | no | — |
| 543 | #41 | — | 106 | 2 | no | — |
| 544 | #41 | — | 106 | 2 | no | — |
| 545 | #41 | — | 212 | 4 | no | — |
| 546 | #41 | — | 212 | 4 | no | — |
| 547 | #41 | — | 212 | 4 | no | — |
| 548 | #41 | — | 212 | 4 | no | — |
| 549 | #41 | — | 212 | 8 | no | — |
| 550 | #41 | — | 212 | 4 | no | — |
| 551 | #41 | — | 212 | 4 | no | — |
| 552 | #41 | — | 212 | 8 | no | — |
| 553 | #41 | — | 212 | 2 | no | — |
| 554 | #41 | — | 212 | 2 | no | — |
| 555 | #41 | C2×D212 | 1 | 4 | yes | — |
| 556 | #41 | C23×D53 | 1 | 4 | yes | — |
| 557 | C2×Q8 | — | 53 | 2 | no | — |
| 558 | C2×Q8 | — | 53 | 2 | no | — |
| 559 | C2×Q8 | — | 53 | 4 | no | — |
| 560 | C2×Q8 | — | 106 | 8 | no | — |
| 561 | C2×Q8 | — | 106 | 4 | no | — |
| 562 | C2×Q8 | — | 106 | 2 | no | — |
| 563 | C2×Q8 | — | 106 | 8 | no | — |
| 564 | C2×Q8 | — | 106 | 4 | no | — |
| 565 | C2×Q8 | — | 106 | 2 | no | — |
| 566 | C2×Q8 | — | 106 | 2 | no | — |
| 567 | C2×Q8 | — | 106 | 2 | no | — |
| 568 | C2×Q8 | — | 106 | 2 | no | — |
| 569 | C2×Q8 | — | 212 | 2 | no | — |
| 570 | C2×Q8 | — | 212 | 4 | no | — |
| 571 | C2×Q8 | — | 212 | 4 | no | — |
| 572 | C2×Q8 | — | 212 | 2 | no | — |
| 573 | C2×Q8 | C2×D212 | 1 | 2 | yes | — |
| 574 | C2×D4 | — | 2 | 2 | no | — |
| 575 | C2×D4 | — | 53 | 2 | no | — |
| 576 | C2×D4 | — | 53 | 2 | no | — |
| 577 | C2×D4 | — | 106 | 4 | no | — |
| 578 | C2×D4 | — | 106 | 2 | no | — |
| 579 | C2×D4 | — | 106 | 4 | no | — |
| 580 | C2×D4 | — | 106 | 2 | no | — |
| 581 | C2×D4 | — | 212 | 1 | no | — |
| 582 | C2×D4 | — | 212 | 4 | no | — |
| 583 | C2×D4 | — | 212 | 2 | no | — |
| 584 | C2×D4 | — | 212 | 4 | no | — |
| 585 | C2×D4 | — | 212 | 4 | no | — |
| 586 | C2×D4 | — | 212 | 2 | no | — |
| 587 | C2×D4 | C2×D212 | 1 | 2 | yes | — |
| 588 | C22×C4 | — | 2 | 2 | no | — |
| 589 | C22×C4 | — | 2 | 1 | no | — |
| 590 | C22×C4 | — | 106 | 2 | no | — |
| 591 | C22×C4 | — | 106 | 2 | no | — |
| 592 | C22×C4 | — | 106 | 2 | no | — |
| 593 | C22×C4 | — | 212 | 4 | no | — |
| 594 | C22×C4 | — | 212 | 2 | no | — |
| 595 | C22×C4 | — | 212 | 2 | no | — |
| 596 | C22×C4 | C23×D53 | 1 | 1 | yes | characteristic |
| 597 | Q16 | — | 53 | 4 | no | — |
| 598 | Q16 | — | 106 | 8 | no | — |
| 599 | Q16 | — | 106 | 4 | no | — |
| 600 | Q16 | — | 106 | 8 | no | — |
| 601 | Q16 | — | 106 | 4 | no | — |
| 602 | Q16 | — | 106 | 8 | no | — |
| 603 | Q16 | — | 106 | 8 | no | — |
| 604 | Q16 | C2×D212 | 1 | 4 | yes | — |
| 605 | SD16 | — | 53 | 8 | no | — |
| 606 | SD16 | — | 106 | 8 | no | — |
| 607 | SD16 | — | 106 | 4 | no | — |
| 608 | SD16 | — | 106 | 4 | no | — |
| 609 | SD16 | — | 106 | 4 | no | — |
| 610 | SD16 | — | 106 | 8 | no | — |
| 611 | SD16 | — | 106 | 4 | no | — |
| 612 | SD16 | — | 106 | 8 | no | — |
| 613 | SD16 | — | 106 | 8 | no | — |
| 614 | SD16 | C2×D212 | 1 | 8 | yes | — |
| 615 | D8 | — | 53 | 4 | no | — |
| 616 | D8 | — | 106 | 4 | no | — |
| 617 | D8 | — | 106 | 4 | no | — |
| 618 | D8 | C2×D212 | 1 | 4 | yes | — |
| 619 | M16 | — | 2 | 2 | no | — |
| 620 | M16 | — | 2 | 8 | no | — |
| 621 | M16 | — | 53 | 4 | no | — |
| 622 | M16 | — | 106 | 2 | no | — |
| 623 | M16 | — | 106 | 8 | no | — |
| 624 | M16 | C2×D212 | 1 | 4 | yes | — |
| 625 | M16 | D4×D53 | 1 | 4 | yes | — |
| 626 | M16 | C23×D53 | 1 | 4 | yes | — |
| 627 | C2×C8 | — | 2 | 2 | no | — |
| 628 | C2×C8 | — | 2 | 8 | no | — |
| 629 | C2×C8 | — | 106 | 2 | no | — |
| 630 | C2×C8 | — | 106 | 8 | no | — |
| 631 | C2×C8 | C23×D53 | 1 | 2 | yes | — |
| 632 | C2×C8 | C23×D53 | 1 | 2 | yes | — |
| 633 | C4⋊C4 | — | 212 | 2 | no | — |
| 634 | C4⋊C4 | — | 212 | 2 | no | — |
| 635 | C4⋊C4 | — | 212 | 1 | no | — |
| 636 | C22⋊C4 | — | 212 | 2 | no | — |
| 637 | C42 | — | 2 | 1 | no | — |
| 638 | C42 | C23×D53 | 1 | 1 | yes | characteristic |
| 639 | C42 | C23×D53 | 1 | 1 | yes | characteristic |
| 640 | C23 | — | 2 | 2 | no | — |
| 641 | C23 | — | 106 | 2 | no | — |
| 642 | C23 | — | 106 | 2 | no | — |
| 643 | C23 | — | 212 | 4 | no | — |
| 644 | C23 | #13133263 | 1 | 1 | yes | characteristic |
| 645 | Q8 | — | 2 | 2 | no | — |
| 646 | Q8 | — | 53 | 4 | no | — |
| 647 | Q8 | — | 106 | 2 | no | — |
| 648 | Q8 | — | 106 | 4 | no | — |
| 649 | Q8 | — | 106 | 2 | no | — |
| 650 | Q8 | — | 106 | 4 | no | — |
| 651 | Q8 | — | 106 | 2 | no | — |
| 652 | Q8 | — | 212 | 8 | no | — |
| 653 | Q8 | — | 212 | 4 | no | — |
| 654 | Q8 | — | 212 | 2 | no | — |
| 655 | Q8 | — | 212 | 2 | no | — |
| 656 | Q8 | C22×D212 | 1 | 4 | yes | — |
| 657 | D4 | — | 2 | 4 | no | — |
| 658 | D4 | — | 2 | 4 | no | — |
| 659 | D4 | — | 2 | 2 | no | — |
| 660 | D4 | — | 53 | 4 | no | — |
| 661 | D4 | — | 106 | 4 | no | — |
| 662 | D4 | — | 106 | 4 | no | — |
| 663 | D4 | — | 106 | 2 | no | — |
| 664 | D4 | — | 106 | 2 | no | — |
| 665 | D4 | — | 106 | 2 | no | — |
| 666 | D4 | — | 424 | 2 | no | — |
| 667 | D4 | — | 212 | 4 | no | — |
| 668 | D4 | — | 212 | 4 | no | — |
| 669 | D4 | — | 212 | 4 | no | — |
| 670 | D4 | — | 212 | 8 | no | — |
| 671 | D4 | — | 212 | 2 | no | — |
| 672 | D4 | — | 212 | 2 | no | — |
| 673 | D4 | C22×D212 | 1 | 4 | yes | — |
| 674 | C2×C4 | — | 2 | 1 | no | — |
| 675 | C2×C4 | — | 2 | 2 | no | — |
| 676 | C2×C4 | — | 2 | 4 | no | — |
| 677 | C2×C4 | — | 2 | 4 | no | — |
| 678 | C2×C4 | — | 2 | 1 | no | — |
| 679 | C2×C4 | — | 4 | 2 | no | — |
| 680 | C2×C4 | — | 106 | 2 | no | — |
| 681 | C2×C4 | — | 106 | 4 | no | — |
| 682 | C2×C4 | — | 106 | 4 | no | — |
| 683 | C2×C4 | — | 106 | 2 | no | — |
| 684 | C2×C4 | — | 106 | 4 | no | — |
| 685 | C2×C4 | — | 212 | 4 | no | — |
| 686 | C2×C4 | — | 212 | 4 | no | — |
| 687 | C2×C4 | — | 212 | 8 | no | — |
| 688 | C2×C4 | — | 212 | 4 | no | — |
| 689 | C2×C4 | — | 212 | 8 | no | — |
| 690 | C2×C4 | — | 212 | 2 | no | — |
| 691 | C2×C4 | — | 212 | 2 | no | — |
| 692 | C2×C4 | — | 212 | 2 | no | — |
| 693 | C2×C4 | — | 212 | 2 | no | — |
| 694 | C2×C4 | C2×D4×D53 | 1 | 2 | yes | — |
| 695 | C2×C4 | C22×D212 | 1 | 2 | yes | — |
| 696 | C2×C4 | #13133263 | 1 | 1 | yes | characteristic |
| 697 | C2×C4 | C24×D53 | 1 | 1 | yes | characteristic |
| 698 | C8 | — | 2 | 4 | no | — |
| 699 | C8 | — | 106 | 4 | no | — |
| 700 | C8 | C2×D4×D53 | 1 | 4 | yes | — |
| 701 | C8 | C22×D212 | 1 | 4 | yes | — |
| 702 | C22 | — | 2 | 4 | no | — |
| 703 | C22 | — | 4 | 1 | no | — |
| 704 | C22 | — | 8 | 2 | no | — |
| 705 | C22 | — | 848 | 4 | no | — |
| 706 | C22 | — | 106 | 4 | no | — |
| 707 | C22 | — | 424 | 2 | no | — |
| 708 | C22 | — | 424 | 2 | no | — |
| 709 | C22 | — | 212 | 2 | no | — |
| 710 | C22 | D4×D212 | 1 | 2 | yes | — |
| 711 | C22 | C2×#13133263 | 1 | 1 | yes | characteristic |
| 712 | C4 | — | 2 | 2 | no | — |
| 713 | C4 | — | 2 | 4 | no | — |
| 714 | C4 | — | 4 | 1 | no | — |
| 715 | C4 | — | 106 | 4 | no | — |
| 716 | C4 | — | 212 | 2 | no | — |
| 717 | C4 | — | 212 | 4 | no | — |
| 718 | C4 | D4×D212 | 1 | 2 | yes | — |
| 719 | C4 | C22×D4×D53 | 1 | 1 | yes | characteristic |
| 720 | C4 | C23×D212 | 1 | 1 | yes | characteristic |
| 721 | C2 | — | 2 | 1 | no | — |
| 722 | C2 | — | 2 | 2 | no | — |
| 723 | C2 | — | 4 | 4 | no | — |
| 724 | C2 | — | 424 | 2 | no | — |
| 725 | C2 | — | 212 | 4 | no | — |
| 726 | C2 | C2×D4×D212 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20289503 | C2 | semidirect |
| 2. #20289499 | C2 | semidirect |
| 3. #20286520 | C2 | semidirect |
| 4. #20286509 | C2 | semidirect |
| 5. #20286491 | C2 | semidirect |
| 6. #20285174 | C2 | semidirect |
| 7. #20284453 | C2 | semidirect |
| 8. #20284452 | C2 | semidirect |
| 9. #20284066 | C2 | semidirect |
| 10. C2×#16810807 | C2 | semidirect |
| 11. #20283626 | C2 | semidirect |
| 12. C53×#2956 | C2 | semidirect |
| 13. #16811459 | C22 | semidirect |
| 16. #16811440 | C22 | semidirect |
| 18. #16811437 | C22 | semidirect |
| 20. #16811435 | C22 | semidirect |
| 22. #16811430 | C22 | semidirect |
| 29. C2×#13133250 | C22 | semidirect |
| 30. C2×#13133250 | C22 | semidirect |
| 31. C2×#13133250 | C22 | semidirect |
| 32. C2×#13133247 | C22 | semidirect |
| 34. #16811389 | C22 | semidirect |
| 36. C2×#13133217 | C22 | semidirect |
| 37. #16811017 | C22 | semidirect |
| 38. #16811003 | C22 | semidirect |
| 39. #16810996 | C22 | semidirect |
| 40. #16810899 | C22 | semidirect |
| 41. #16810898 | C22 | semidirect |
| 42. #16810887 | C22 | semidirect |
| 43. #16810886 | C22 | semidirect |
| 44. #16810807 | C22 | semidirect |
| 45. #16810807 | C22 | semidirect |
| 46. #16810807 | C22 | semidirect |
| 47. #16810802 | C22 | semidirect |
| 48. #16810797 | C22 | semidirect |
| 49. #16810792 | C22 | semidirect |
| 50. #16810746 | C22 | semidirect |
| 51. #16810741 | C22 | semidirect |
| 52. #16810672 | C22 | semidirect |
| 53. C2×#13133145 | C22 | semidirect |
| 54. #16810605 | C22 | semidirect |
| 55. C2×#13133135 | C22 | semidirect |
| 57. C53×#568 | C22 | semidirect |
| 58. C53×#444 | C22 | semidirect |
| 59. C53×#443 | C22 | semidirect |
| 60. C53×#430 | C22 | semidirect |
| 61. C2×#104×C53 | C22 | semidirect |
| 62. C4×M16×C53 | C22 | semidirect |
| 94. #13133250 | D4 | semidirect |
| 106. #13133245 | D4 | semidirect |
| 150. #137×C53 | D4 | semidirect |
| 151. AGL(1,ℤ/8)×C53 | D4 | semidirect |
| 369. #2956 | D53 | semidirect |
| 399. #568 | C2×D53 | semidirect |
| 416. #444 | C2×D53 | semidirect |
| 418. #443 | C2×D53 | semidirect |
| 420. #430 | C2×D53 | semidirect |
| 422. C2×#104 | C2×D53 | semidirect |
| 425. C4×M16 | C2×D53 | semidirect |
| 426. C53 | #61111 | semidirect |
| 469. #137 | D212 | semidirect |
| 477. AGL(1,ℤ/8) | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289503 | 2 |
| #20289499 | 2 |
| #20286520 | 2 |
| #20286509 | 2 |
| #20286491 | 2 |
| #20285174 | 2 |
| #20284453 | 2 |
| #20284452 | 2 |
| #20284066 | 2 |
| C2×#16810807 | 2 |
| #20283626 | 2 |
| C53×#2956 | 2 |
| #61111 | 53 |