Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
720 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #13125697 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13124239 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #13124207 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13116527 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #13114785 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13112964 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C13×#2122 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11719648 | C22 | 1 | 1 | yes | characteristic |
| 9 | C13×#535 | C22 | 1 | 1 | yes | characteristic |
| 10 | #11719535 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×#88186 | — | 2 | 1 | no | — |
| 12 | #11719230 | — | 2 | 1 | no | — |
| 13 | C13×#413 | C22 | 1 | 1 | yes | characteristic |
| 14 | C13×#410 | C22 | 1 | 1 | yes | characteristic |
| 15 | #11718898 | C22 | 1 | 1 | yes | characteristic |
| 16 | #11718895 | C22 | 1 | 1 | yes | characteristic |
| 17 | #11718878 | — | 2 | 1 | no | — |
| 18 | #11718793 | — | 2 | 1 | no | — |
| 19 | #11718790 | — | 2 | 1 | no | — |
| 20 | #11718738 | — | 2 | 2 | no | — |
| 21 | #11718723 | — | 2 | 2 | no | — |
| 22 | #11718700 | — | 2 | 1 | no | — |
| 23 | #11718699 | — | 2 | 1 | no | — |
| 24 | #11718697 | — | 2 | 1 | no | — |
| 25 | #11718696 | — | 2 | 1 | no | — |
| 26 | #11718667 | — | 2 | 1 | no | — |
| 27 | #11718666 | — | 2 | 1 | no | — |
| 28 | #11718664 | — | 2 | 1 | no | — |
| 29 | #11718402 | — | 2 | 2 | no | — |
| 30 | #11718402 | — | 2 | 2 | no | — |
| 31 | C13×AΣL(1,𝔽16) | — | 2 | 2 | no | — |
| 32 | #11718069 | — | 2 | 2 | no | — |
| 33 | C2×C13×#41 | C23 | 1 | 1 | yes | characteristic |
| 34 | C22×D4×C13 | D4 | 1 | 1 | yes | characteristic, complemented |
| 35 | #88257 | — | 4 | 1 | no | — |
| 36 | #88256 | — | 4 | 1 | no | — |
| 37 | #41×D13 | — | 4 | 2 | no | — |
| 38 | #88254 | — | 2 | 1 | no | — |
| 39 | #88251 | — | 2 | 1 | no | — |
| 40 | #88251 | — | 2 | 1 | no | — |
| 41 | #88251 | D4 | 1 | 2 | yes | — |
| 42 | C2×#6127 | — | 2 | 1 | no | — |
| 43 | C2×#6127 | — | 2 | 1 | no | — |
| 44 | C2×#6127 | — | 2 | 1 | no | — |
| 45 | C22×D52 | D4 | 1 | 1 | yes | characteristic |
| 46 | C2×C13×M16 | — | 2 | 1 | no | — |
| 47 | C13×#127 | — | 2 | 1 | no | — |
| 48 | C13×#124 | — | 2 | 1 | no | — |
| 49 | C13×#121 | — | 2 | 1 | no | — |
| 50 | C13×#121 | — | 2 | 1 | no | — |
| 51 | C13×#120 | — | 2 | 1 | no | — |
| 52 | C13×#120 | — | 2 | 1 | no | — |
| 53 | C13×#117 | — | 2 | 1 | no | — |
| 54 | C13×#117 | D4 | 1 | 1 | yes | characteristic, complemented |
| 55 | #88201 | — | 2 | 1 | no | — |
| 56 | #88194 | — | 2 | 1 | no | — |
| 57 | #88191 | — | 2 | 1 | no | — |
| 58 | #88191 | — | 2 | 1 | no | — |
| 59 | C2×#6105 | — | 4 | 1 | no | — |
| 60 | #88186 | — | 2 | 4 | no | — |
| 61 | #88186 | — | 4 | 2 | no | — |
| 62 | C2×#6104 | — | 2 | 1 | no | — |
| 63 | C2×#6104 | — | 2 | 1 | no | — |
| 64 | C2×#6104 | — | 4 | 1 | no | — |
| 65 | #88184 | — | 2 | 1 | no | — |
| 66 | #88184 | — | 2 | 1 | no | — |
| 67 | #88180 | D4 | 1 | 1 | yes | characteristic |
| 68 | C2×#6099 | — | 2 | 1 | no | — |
| 69 | C2×#6099 | D4 | 1 | 1 | yes | characteristic, complemented |
| 70 | C22×#1055 | D4 | 1 | 1 | yes | characteristic, complemented |
| 71 | #88149 | — | 4 | 2 | no | — |
| 72 | #88136 | — | 2 | 4 | no | — |
| 73 | #88129 | — | 4 | 1 | no | — |
| 74 | #88128 | — | 4 | 1 | no | — |
| 75 | C13×#101 | — | 2 | 1 | no | — |
| 76 | C13×#100 | — | 2 | 1 | no | — |
| 77 | C13×#99 | — | 2 | 1 | no | — |
| 78 | C13×#99 | D4 | 1 | 2 | yes | — |
| 79 | #88076 | D4 | 1 | 2 | yes | complemented |
| 80 | #88073 | — | 2 | 1 | no | — |
| 81 | #88072 | — | 2 | 1 | no | — |
| 82 | #88072 | — | 2 | 1 | no | — |
| 83 | C22⋊#1055 | — | 2 | 1 | no | — |
| 84 | C22⋊#1055 | — | 2 | 1 | no | — |
| 85 | #88064 | — | 4 | 1 | no | — |
| 86 | #88063 | — | 4 | 1 | no | — |
| 87 | #88060 | — | 4 | 2 | no | — |
| 88 | #88049 | — | 2 | 1 | no | — |
| 89 | #88049 | — | 2 | 1 | no | — |
| 90 | #88048 | — | 2 | 1 | no | — |
| 91 | #88047 | — | 2 | 1 | no | — |
| 92 | #88046 | — | 2 | 4 | no | — |
| 93 | #88045 | — | 2 | 4 | no | — |
| 94 | #13353 | — | 13 | 1 | no | maximal, Sylow |
| 95 | C24×C13 | — | 2 | 1 | no | — |
| 96 | C23×D13 | — | 2 | 1 | no | — |
| 97 | C13×#41 | — | 4 | 1 | no | — |
| 98 | C13×#41 | — | 4 | 1 | no | — |
| 99 | C2×Q8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 100 | C2×D4×C13 | — | 2 | 1 | no | — |
| 101 | C2×D4×C13 | — | 2 | 1 | no | — |
| 102 | C2×D4×C13 | — | 4 | 1 | no | — |
| 103 | C2×D4×C13 | — | 4 | 1 | no | — |
| 104 | C2×D4×C13 | — | 4 | 1 | no | — |
| 105 | C2×D4×C13 | — | 4 | 1 | no | — |
| 106 | C2×D4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 107 | C2×D4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 108 | C2×D4×C13 | #41 | 1 | 1 | yes | characteristic |
| 109 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 110 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 111 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 112 | C2×C22⋊D13 | — | 2 | 2 | no | — |
| 113 | C2×C22⋊D13 | — | 2 | 2 | no | — |
| 114 | C2×C22⋊D13 | — | 4 | 1 | no | — |
| 115 | C2×C22⋊D13 | — | 4 | 1 | no | — |
| 116 | C2×C22⋊D13 | — | 4 | 1 | no | — |
| 117 | #6131 | — | 4 | 2 | no | — |
| 118 | Q8×D13 | — | 4 | 2 | no | — |
| 119 | #6129 | — | 4 | 2 | no | — |
| 120 | #6129 | — | 4 | 2 | no | — |
| 121 | #6129 | — | 4 | 2 | no | — |
| 122 | D4×D13 | — | 4 | 2 | no | — |
| 123 | D4×D13 | — | 4 | 2 | no | — |
| 124 | D4×D13 | — | 4 | 2 | no | — |
| 125 | #6127 | — | 2 | 2 | no | — |
| 126 | #6127 | — | 2 | 2 | no | — |
| 127 | #6127 | — | 4 | 1 | no | — |
| 128 | #6127 | — | 4 | 1 | no | — |
| 129 | #6127 | — | 4 | 1 | no | — |
| 130 | #6127 | — | 4 | 1 | no | — |
| 131 | #6127 | — | 4 | 1 | no | — |
| 132 | #6127 | — | 4 | 1 | no | — |
| 133 | #6127 | — | 4 | 1 | no | — |
| 134 | #6127 | — | 4 | 1 | no | — |
| 135 | C2×D52 | — | 2 | 1 | no | — |
| 136 | C2×D52 | — | 2 | 1 | no | — |
| 137 | C2×D52 | — | 2 | 1 | no | — |
| 138 | C2×D52 | — | 2 | 1 | no | — |
| 139 | C2×D52 | — | 2 | 1 | no | — |
| 140 | C2×D52 | — | 4 | 1 | no | — |
| 141 | C2×D52 | — | 4 | 1 | no | — |
| 142 | C2×D52 | — | 4 | 4 | no | — |
| 143 | C2×C4×D13 | — | 2 | 2 | no | — |
| 144 | C2×C4×D13 | — | 2 | 2 | no | — |
| 145 | C2×C4×D13 | — | 4 | 1 | no | — |
| 146 | C2×Dic26 | — | 2 | 1 | no | — |
| 147 | C2×Dic26 | — | 2 | 1 | no | — |
| 148 | C2×Dic26 | — | 2 | 1 | no | — |
| 149 | C13×M16 | — | 4 | 1 | no | — |
| 150 | C13×M16 | — | 4 | 1 | no | — |
| 151 | C2×C8×C13 | — | 4 | 1 | no | — |
| 152 | C13×C4⋊C4 | — | 2 | 1 | no | — |
| 153 | C13×C4⋊C4 | — | 4 | 1 | no | — |
| 154 | C13×C22⋊C4 | — | 2 | 2 | no | — |
| 155 | C13×C22⋊C4 | — | 2 | 1 | no | — |
| 156 | C13×C22⋊C4 | — | 4 | 1 | no | — |
| 157 | C13×C22⋊C4 | — | 4 | 1 | no | — |
| 158 | C42×C13 | — | 2 | 1 | no | — |
| 159 | C42×C13 | — | 4 | 1 | no | — |
| 160 | C22⋊Dic13 | — | 2 | 1 | no | — |
| 161 | #6105 | — | 4 | 4 | no | — |
| 162 | #6104 | — | 4 | 4 | no | — |
| 163 | #6104 | — | 8 | 1 | no | — |
| 164 | #6104 | — | 8 | 1 | no | — |
| 165 | #6103 | — | 4 | 4 | no | — |
| 166 | #6103 | — | 4 | 1 | no | — |
| 167 | #6103 | — | 4 | 1 | no | — |
| 168 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 169 | C4×Dic13 | — | 2 | 1 | no | — |
| 170 | #6099 | — | 2 | 2 | no | — |
| 171 | #6099 | — | 4 | 1 | no | — |
| 172 | #6099 | — | 4 | 1 | no | — |
| 173 | C2×#1055 | — | 2 | 1 | no | — |
| 174 | C2×#1055 | — | 2 | 1 | no | — |
| 175 | C2×#1055 | — | 4 | 1 | no | — |
| 176 | C2×#1055 | — | 4 | 1 | no | — |
| 177 | #3199 | — | 13 | 1 | no | — |
| 178 | #3027 | — | 13 | 1 | no | — |
| 179 | #3021 | — | 13 | 1 | no | — |
| 180 | #2134 | — | 13 | 1 | no | — |
| 181 | #2122 | D13 | 1 | 1 | yes | characteristic, complemented |
| 182 | #1791 | — | 13 | 1 | no | — |
| 183 | #1395 | — | 13 | 1 | no | — |
| 184 | C23×C13 | — | 4 | 1 | no | — |
| 185 | C23×C13 | — | 8 | 1 | no | — |
| 186 | C23×C13 | — | 16 | 1 | no | — |
| 187 | C23×C13 | #120 | 1 | 1 | yes | characteristic |
| 188 | C23×C13 | #121 | 1 | 1 | yes | characteristic |
| 189 | C23×C13 | #121 | 1 | 1 | yes | characteristic |
| 190 | C22×D13 | — | 2 | 2 | no | — |
| 191 | C22×D13 | — | 2 | 2 | no | — |
| 192 | C22×D13 | — | 4 | 1 | no | — |
| 193 | C22×D13 | — | 4 | 2 | no | — |
| 194 | C22×D13 | — | 4 | 1 | no | — |
| 195 | C22×D13 | — | 16 | 1 | no | — |
| 196 | Q8×C13 | — | 4 | 1 | no | — |
| 197 | D4×C13 | — | 4 | 1 | no | — |
| 198 | D4×C13 | — | 4 | 1 | no | — |
| 199 | D4×C13 | — | 4 | 1 | no | — |
| 200 | D4×C13 | — | 4 | 2 | no | — |
| 201 | D4×C13 | — | 4 | 1 | no | — |
| 202 | D4×C13 | — | 4 | 1 | no | — |
| 203 | D4×C13 | — | 16 | 1 | no | — |
| 204 | D4×C13 | — | 16 | 1 | no | — |
| 205 | C2×C4×C13 | — | 2 | 1 | no | — |
| 206 | C2×C4×C13 | — | 2 | 1 | no | — |
| 207 | C2×C4×C13 | — | 2 | 1 | no | — |
| 208 | C2×C4×C13 | — | 2 | 1 | no | — |
| 209 | C2×C4×C13 | — | 2 | 1 | no | — |
| 210 | C2×C4×C13 | — | 2 | 1 | no | — |
| 211 | C2×C4×C13 | — | 4 | 2 | no | — |
| 212 | C2×C4×C13 | — | 4 | 1 | no | — |
| 213 | C2×C4×C13 | #120 | 1 | 1 | yes | characteristic |
| 214 | C2×C4×C13 | #120 | 1 | 1 | yes | characteristic |
| 215 | C2×C4×C13 | #121 | 1 | 1 | yes | characteristic |
| 216 | C2×C4×C13 | #127 | 1 | 1 | yes | characteristic |
| 217 | C22⋊D13 | — | 4 | 2 | no | — |
| 218 | C22⋊D13 | — | 4 | 2 | no | — |
| 219 | C22⋊D13 | — | 4 | 2 | no | — |
| 220 | C22⋊D13 | — | 4 | 2 | no | — |
| 221 | C22⋊D13 | — | 16 | 1 | no | — |
| 222 | C22⋊D13 | — | 16 | 1 | no | — |
| 223 | C2×Dic13 | — | 2 | 2 | no | — |
| 224 | C2×Dic13 | — | 2 | 2 | no | — |
| 225 | C2×Dic13 | — | 4 | 1 | no | — |
| 226 | C2×Dic13 | — | 4 | 1 | no | — |
| 227 | D52 | — | 2 | 2 | no | — |
| 228 | D52 | — | 4 | 1 | no | — |
| 229 | D52 | — | 4 | 1 | no | — |
| 230 | D52 | — | 4 | 1 | no | — |
| 231 | D52 | — | 4 | 1 | no | — |
| 232 | D52 | — | 4 | 1 | no | — |
| 233 | D52 | — | 8 | 1 | no | — |
| 234 | D52 | — | 16 | 4 | no | — |
| 235 | C4×D13 | — | 4 | 2 | no | — |
| 236 | C4×D13 | — | 4 | 2 | no | — |
| 237 | C4×D13 | — | 4 | 2 | no | — |
| 238 | C4×D13 | — | 4 | 2 | no | — |
| 239 | Dic26 | — | 2 | 2 | no | — |
| 240 | Dic26 | — | 4 | 1 | no | — |
| 241 | Dic26 | — | 4 | 1 | no | — |
| 242 | Dic26 | — | 4 | 1 | no | — |
| 243 | C8×C13 | — | 8 | 1 | no | — |
| 244 | #1055 | — | 4 | 2 | no | — |
| 245 | #1055 | — | 4 | 1 | no | — |
| 246 | #1055 | — | 4 | 1 | no | — |
| 247 | #585 | — | 13 | 1 | no | — |
| 248 | C2×AGL(1,ℤ/8) | — | 26 | 1 | no | — |
| 249 | #535 | — | 13 | 1 | no | — |
| 250 | #535 | — | 26 | 1 | no | — |
| 251 | #535 | C2×D13 | 1 | 1 | yes | characteristic |
| 252 | #482 | — | 26 | 1 | no | — |
| 253 | #482 | — | 26 | 1 | no | — |
| 254 | #469 | — | 26 | 1 | no | — |
| 255 | #466 | — | 26 | 1 | no | — |
| 256 | B(4,𝔽2) | — | 26 | 2 | no | — |
| 257 | B(4,𝔽2) | — | 26 | 2 | no | — |
| 258 | #454 | — | 26 | 2 | no | — |
| 259 | #453 | — | 26 | 2 | no | — |
| 260 | #447 | — | 26 | 1 | no | — |
| 261 | #447 | — | 26 | 1 | no | — |
| 262 | #421 | — | 26 | 1 | no | — |
| 263 | #413 | — | 13 | 1 | no | — |
| 264 | #413 | — | 26 | 1 | no | — |
| 265 | #413 | C2×D13 | 1 | 1 | yes | characteristic |
| 266 | #410 | — | 26 | 1 | no | — |
| 267 | #410 | C2×D13 | 1 | 1 | yes | characteristic |
| 268 | #408 | — | 13 | 1 | no | — |
| 269 | #408 | — | 26 | 1 | no | — |
| 270 | #355 | — | 26 | 2 | no | — |
| 271 | AΣL(1,𝔽16) | — | 2 | 2 | no | — |
| 272 | C22×C13 | — | 2 | 1 | no | — |
| 273 | C22×C13 | — | 2 | 1 | no | — |
| 274 | C22×C13 | — | 2 | 1 | no | — |
| 275 | C22×C13 | — | 4 | 1 | no | — |
| 276 | C22×C13 | — | 4 | 1 | no | — |
| 277 | C22×C13 | — | 4 | 1 | no | — |
| 278 | C22×C13 | — | 8 | 1 | no | — |
| 279 | C22×C13 | — | 8 | 1 | no | — |
| 280 | C22×C13 | — | 8 | 1 | no | — |
| 281 | C22×C13 | — | 16 | 2 | no | — |
| 282 | C22×C13 | #392 | 1 | 1 | yes | characteristic |
| 283 | C2×D13 | — | 4 | 2 | no | — |
| 284 | C2×D13 | — | 8 | 2 | no | — |
| 285 | C2×D13 | — | 8 | 2 | no | — |
| 286 | C2×D13 | — | 8 | 1 | no | — |
| 287 | C2×D13 | — | 8 | 1 | no | — |
| 288 | C2×D13 | — | 8 | 4 | no | — |
| 289 | C2×D13 | — | 8 | 1 | no | — |
| 290 | C2×D13 | — | 16 | 1 | no | — |
| 291 | C4×C13 | — | 2 | 1 | no | — |
| 292 | C4×C13 | — | 2 | 1 | no | — |
| 293 | C4×C13 | — | 2 | 1 | no | — |
| 294 | C4×C13 | — | 8 | 1 | no | — |
| 295 | C4×C13 | — | 8 | 2 | no | — |
| 296 | C4×C13 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 297 | C4×C13 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 298 | Dic13 | — | 4 | 2 | no | — |
| 299 | Dic13 | — | 8 | 1 | no | — |
| 300 | 2−1+4 | — | 26 | 1 | no | — |
| 301 | 2−1+4 | — | 52 | 1 | no | — |
| 302 | H(5,𝔽2) | — | 13 | 2 | no | — |
| 303 | H(5,𝔽2) | — | 26 | 1 | no | — |
| 304 | H(5,𝔽2) | — | 26 | 1 | no | — |
| 305 | H(5,𝔽2) | — | 52 | 1 | no | — |
| 306 | C2×#41 | — | 26 | 1 | no | — |
| 307 | C2×#41 | — | 26 | 1 | no | — |
| 308 | C2×#41 | — | 26 | 1 | no | — |
| 309 | C2×#41 | — | 52 | 2 | no | — |
| 310 | C2×#41 | C22×D13 | 1 | 1 | yes | characteristic |
| 311 | C22×D4 | — | 13 | 1 | no | — |
| 312 | C22×D4 | D52 | 1 | 1 | yes | characteristic, complemented |
| 313 | AGL(1,ℤ/8) | — | 26 | 4 | no | — |
| 314 | AGL(1,ℤ/8) | — | 52 | 2 | no | — |
| 315 | C2×SD16 | — | 52 | 1 | no | — |
| 316 | C2×D8 | — | 26 | 1 | no | — |
| 317 | C2×D8 | — | 26 | 1 | no | — |
| 318 | C2×D8 | — | 52 | 1 | no | — |
| 319 | C2×M16 | — | 2 | 1 | no | — |
| 320 | C2×M16 | — | 13 | 1 | no | — |
| 321 | C2×M16 | — | 26 | 1 | no | — |
| 322 | C22×C8 | — | 13 | 1 | no | — |
| 323 | #127 | — | 2 | 1 | no | — |
| 324 | #127 | — | 26 | 1 | no | — |
| 325 | #127 | — | 52 | 1 | no | — |
| 326 | #124 | — | 2 | 1 | no | — |
| 327 | #124 | — | 26 | 1 | no | — |
| 328 | #124 | — | 52 | 1 | no | — |
| 329 | #121 | — | 2 | 1 | no | — |
| 330 | #121 | — | 2 | 1 | no | — |
| 331 | #121 | — | 26 | 1 | no | — |
| 332 | #121 | — | 26 | 1 | no | — |
| 333 | #121 | — | 52 | 2 | no | — |
| 334 | #120 | — | 2 | 1 | no | — |
| 335 | #120 | — | 2 | 1 | no | — |
| 336 | #120 | — | 26 | 4 | no | — |
| 337 | #120 | — | 26 | 1 | no | — |
| 338 | #120 | — | 26 | 1 | no | — |
| 339 | #117 | — | 2 | 1 | no | — |
| 340 | #117 | — | 13 | 1 | no | — |
| 341 | #117 | D52 | 1 | 1 | yes | characteristic, complemented |
| 342 | #107 | — | 26 | 1 | no | — |
| 343 | #106 | — | 26 | 1 | no | — |
| 344 | #104 | — | 26 | 4 | no | — |
| 345 | #102 | — | 26 | 1 | no | — |
| 346 | #102 | — | 26 | 1 | no | — |
| 347 | #102 | — | 26 | 1 | no | — |
| 348 | #102 | — | 26 | 1 | no | — |
| 349 | #101 | — | 2 | 1 | no | — |
| 350 | #101 | — | 13 | 2 | no | — |
| 351 | #101 | — | 52 | 1 | no | — |
| 352 | #100 | — | 2 | 1 | no | — |
| 353 | #100 | — | 26 | 1 | no | — |
| 354 | #100 | — | 52 | 1 | no | — |
| 355 | #99 | — | 2 | 1 | no | — |
| 356 | #99 | — | 26 | 4 | no | — |
| 357 | #99 | C22⋊D13 | 1 | 2 | yes | — |
| 358 | C22⋊C8 | — | 26 | 1 | no | — |
| 359 | C22⋊C8 | — | 26 | 1 | no | — |
| 360 | C22⋊C8 | — | 52 | 2 | no | — |
| 361 | C2×C13 | — | 2 | 1 | no | — |
| 362 | C2×C13 | — | 4 | 1 | no | — |
| 363 | C2×C13 | — | 4 | 1 | no | — |
| 364 | C2×C13 | — | 4 | 1 | no | — |
| 365 | C2×C13 | — | 16 | 1 | no | — |
| 366 | C2×C13 | #2021 | 1 | 1 | yes | characteristic |
| 367 | D13 | — | 8 | 2 | no | — |
| 368 | D13 | — | 16 | 1 | no | — |
| 369 | C24 | — | 2 | 1 | no | — |
| 370 | C24 | — | 26 | 1 | no | — |
| 371 | #41 | — | 4 | 1 | no | — |
| 372 | #41 | — | 4 | 1 | no | — |
| 373 | #41 | — | 26 | 2 | no | — |
| 374 | #41 | — | 26 | 2 | no | — |
| 375 | #41 | — | 52 | 1 | no | — |
| 376 | #41 | — | 52 | 1 | no | — |
| 377 | #41 | — | 52 | 1 | no | — |
| 378 | #41 | — | 52 | 1 | no | — |
| 379 | #41 | — | 52 | 1 | no | — |
| 380 | #41 | — | 52 | 2 | no | — |
| 381 | #41 | — | 52 | 2 | no | — |
| 382 | #41 | — | 52 | 2 | no | — |
| 383 | #41 | — | 52 | 2 | no | — |
| 384 | #41 | — | 52 | 1 | no | — |
| 385 | #41 | — | 52 | 1 | no | — |
| 386 | #41 | — | 52 | 1 | no | — |
| 387 | C2×Q8 | — | 26 | 1 | no | — |
| 388 | C2×Q8 | — | 26 | 1 | no | — |
| 389 | C2×Q8 | — | 26 | 1 | no | — |
| 390 | C2×Q8 | — | 52 | 2 | no | — |
| 391 | C2×Q8 | D4×D13 | 1 | 1 | yes | characteristic |
| 392 | C2×D4 | — | 2 | 1 | no | — |
| 393 | C2×D4 | — | 2 | 1 | no | — |
| 394 | C2×D4 | — | 4 | 1 | no | — |
| 395 | C2×D4 | — | 4 | 1 | no | — |
| 396 | C2×D4 | — | 4 | 1 | no | — |
| 397 | C2×D4 | — | 4 | 1 | no | — |
| 398 | C2×D4 | — | 26 | 1 | no | — |
| 399 | C2×D4 | — | 26 | 1 | no | — |
| 400 | C2×D4 | — | 26 | 1 | no | — |
| 401 | C2×D4 | — | 26 | 2 | no | — |
| 402 | C2×D4 | — | 26 | 2 | no | — |
| 403 | C2×D4 | — | 26 | 1 | no | — |
| 404 | C2×D4 | — | 26 | 1 | no | — |
| 405 | C2×D4 | — | 52 | 1 | no | — |
| 406 | C2×D4 | — | 52 | 1 | no | — |
| 407 | C2×D4 | — | 52 | 4 | no | — |
| 408 | C2×D4 | — | 52 | 2 | no | — |
| 409 | C2×D4 | — | 52 | 2 | no | — |
| 410 | C2×D4 | — | 52 | 2 | no | — |
| 411 | C2×D4 | — | 52 | 1 | no | — |
| 412 | C2×D4 | — | 52 | 1 | no | — |
| 413 | C2×D4 | — | 52 | 1 | no | — |
| 414 | C2×D4 | #6127 | 1 | 1 | yes | characteristic |
| 415 | C2×D4 | D4×D13 | 1 | 1 | yes | characteristic |
| 416 | C2×D4 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 417 | C22×C4 | — | 26 | 2 | no | — |
| 418 | C22×C4 | — | 26 | 2 | no | — |
| 419 | C22×C4 | — | 52 | 1 | no | — |
| 420 | C22×C4 | C2×D52 | 1 | 1 | yes | characteristic |
| 421 | C22×C4 | D4×D13 | 1 | 1 | yes | characteristic |
| 422 | C22×C4 | D4×D13 | 1 | 1 | yes | characteristic |
| 423 | SD16 | — | 52 | 4 | no | — |
| 424 | D8 | — | 52 | 4 | no | — |
| 425 | D8 | — | 104 | 1 | no | — |
| 426 | D8 | — | 104 | 1 | no | — |
| 427 | M16 | — | 4 | 1 | no | — |
| 428 | M16 | — | 4 | 1 | no | — |
| 429 | M16 | — | 26 | 2 | no | — |
| 430 | M16 | — | 52 | 1 | no | — |
| 431 | M16 | — | 52 | 1 | no | — |
| 432 | C2×C8 | — | 4 | 1 | no | — |
| 433 | C2×C8 | — | 26 | 1 | no | — |
| 434 | C2×C8 | — | 26 | 1 | no | — |
| 435 | C2×C8 | — | 52 | 1 | no | — |
| 436 | C2×C8 | — | 52 | 1 | no | — |
| 437 | C4⋊C4 | — | 2 | 1 | no | — |
| 438 | C4⋊C4 | — | 4 | 1 | no | — |
| 439 | C4⋊C4 | — | 26 | 1 | no | — |
| 440 | C22⋊C4 | — | 2 | 1 | no | — |
| 441 | C22⋊C4 | — | 2 | 2 | no | — |
| 442 | C22⋊C4 | — | 4 | 1 | no | — |
| 443 | C22⋊C4 | — | 4 | 1 | no | — |
| 444 | C22⋊C4 | — | 26 | 1 | no | — |
| 445 | C22⋊C4 | — | 52 | 4 | no | — |
| 446 | C22⋊C4 | — | 52 | 1 | no | — |
| 447 | C22⋊C4 | — | 52 | 1 | no | — |
| 448 | C42 | — | 2 | 1 | no | — |
| 449 | C42 | — | 4 | 1 | no | — |
| 450 | C42 | — | 26 | 1 | no | — |
| 451 | C13 | #13353 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 452 | C23 | — | 4 | 1 | no | — |
| 453 | C23 | — | 8 | 1 | no | — |
| 454 | C23 | — | 16 | 1 | no | — |
| 455 | C23 | — | 26 | 2 | no | — |
| 456 | C23 | — | 26 | 2 | no | — |
| 457 | C23 | — | 52 | 1 | no | — |
| 458 | C23 | — | 52 | 2 | no | — |
| 459 | C23 | — | 52 | 1 | no | — |
| 460 | C23 | — | 208 | 1 | no | — |
| 461 | C23 | #88138 | 1 | 1 | yes | characteristic |
| 462 | C23 | #88184 | 1 | 1 | yes | characteristic |
| 463 | C23 | #88191 | 1 | 1 | yes | characteristic |
| 464 | Q8 | — | 4 | 1 | no | — |
| 465 | Q8 | — | 26 | 2 | no | — |
| 466 | Q8 | — | 52 | 1 | no | — |
| 467 | Q8 | — | 52 | 1 | no | — |
| 468 | Q8 | — | 52 | 1 | no | — |
| 469 | D4 | — | 4 | 1 | no | — |
| 470 | D4 | — | 4 | 1 | no | — |
| 471 | D4 | — | 4 | 1 | no | — |
| 472 | D4 | — | 4 | 2 | no | — |
| 473 | D4 | — | 4 | 1 | no | — |
| 474 | D4 | — | 4 | 1 | no | — |
| 475 | D4 | — | 16 | 1 | no | — |
| 476 | D4 | — | 16 | 1 | no | — |
| 477 | D4 | — | 26 | 2 | no | — |
| 478 | D4 | — | 52 | 1 | no | — |
| 479 | D4 | — | 52 | 1 | no | — |
| 480 | D4 | — | 52 | 2 | no | — |
| 481 | D4 | — | 52 | 2 | no | — |
| 482 | D4 | — | 52 | 2 | no | — |
| 483 | D4 | — | 52 | 2 | no | — |
| 484 | D4 | — | 52 | 1 | no | — |
| 485 | D4 | — | 52 | 1 | no | — |
| 486 | D4 | — | 52 | 1 | no | — |
| 487 | D4 | — | 104 | 1 | no | — |
| 488 | D4 | — | 208 | 4 | no | — |
| 489 | D4 | — | 208 | 1 | no | — |
| 490 | D4 | — | 208 | 1 | no | — |
| 491 | C2×C4 | — | 2 | 1 | no | — |
| 492 | C2×C4 | — | 2 | 1 | no | — |
| 493 | C2×C4 | — | 2 | 1 | no | — |
| 494 | C2×C4 | — | 2 | 1 | no | — |
| 495 | C2×C4 | — | 2 | 1 | no | — |
| 496 | C2×C4 | — | 2 | 1 | no | — |
| 497 | C2×C4 | — | 4 | 2 | no | — |
| 498 | C2×C4 | — | 4 | 1 | no | — |
| 499 | C2×C4 | — | 26 | 2 | no | — |
| 500 | C2×C4 | — | 26 | 2 | no | — |
| 501 | C2×C4 | — | 52 | 2 | no | — |
| 502 | C2×C4 | — | 52 | 2 | no | — |
| 503 | C2×C4 | — | 52 | 2 | no | — |
| 504 | C2×C4 | — | 52 | 1 | no | — |
| 505 | C2×C4 | — | 52 | 2 | no | — |
| 506 | C2×C4 | — | 52 | 1 | no | — |
| 507 | C2×C4 | #88136 | 1 | 1 | yes | characteristic |
| 508 | C2×C4 | #88136 | 1 | 1 | yes | characteristic |
| 509 | C2×C4 | #88138 | 1 | 1 | yes | characteristic |
| 510 | C2×C4 | #88194 | 1 | 1 | yes | characteristic |
| 511 | C8 | — | 8 | 1 | no | — |
| 512 | C8 | — | 52 | 2 | no | — |
| 513 | C8 | — | 52 | 1 | no | — |
| 514 | C8 | — | 52 | 1 | no | — |
| 515 | C22 | — | 2 | 1 | no | — |
| 516 | C22 | — | 2 | 1 | no | — |
| 517 | C22 | — | 2 | 1 | no | — |
| 518 | C22 | — | 4 | 1 | no | — |
| 519 | C22 | — | 4 | 1 | no | — |
| 520 | C22 | — | 4 | 1 | no | — |
| 521 | C22 | — | 8 | 1 | no | — |
| 522 | C22 | — | 8 | 1 | no | — |
| 523 | C22 | — | 8 | 1 | no | — |
| 524 | C22 | — | 16 | 2 | no | — |
| 525 | C22 | — | 52 | 2 | no | — |
| 526 | C22 | — | 104 | 1 | no | — |
| 527 | C22 | — | 104 | 1 | no | — |
| 528 | C22 | — | 104 | 2 | no | — |
| 529 | C22 | — | 104 | 2 | no | — |
| 530 | C22 | — | 104 | 4 | no | — |
| 531 | C22 | — | 104 | 1 | no | — |
| 532 | C22 | — | 208 | 1 | no | — |
| 533 | C22 | #11718621 | 1 | 1 | yes | characteristic |
| 534 | C4 | — | 2 | 1 | no | — |
| 535 | C4 | — | 2 | 1 | no | — |
| 536 | C4 | — | 2 | 1 | no | — |
| 537 | C4 | — | 8 | 1 | no | — |
| 538 | C4 | — | 8 | 2 | no | — |
| 539 | C4 | — | 52 | 2 | no | — |
| 540 | C4 | — | 104 | 1 | no | — |
| 541 | C4 | #11718402 | 1 | 1 | yes | characteristic |
| 542 | C4 | #11718402 | 1 | 1 | yes | characteristic |
| 543 | C2 | — | 2 | 1 | no | — |
| 544 | C2 | — | 4 | 1 | no | — |
| 545 | C2 | — | 4 | 1 | no | — |
| 546 | C2 | — | 4 | 1 | no | — |
| 547 | C2 | — | 16 | 1 | no | — |
| 548 | C2 | — | 104 | 2 | no | — |
| 549 | C2 | — | 208 | 1 | no | — |
| 550 | C2 | #13115961 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13125697 | C2 | semidirect |
| 2. #13124239 | C2 | semidirect |
| 3. #13124207 | C2 | semidirect |
| 4. #13116527 | C2 | semidirect |
| 5. #13114785 | C2 | semidirect |
| 6. #13112964 | C2 | semidirect |
| 7. C13×#2122 | C2 | semidirect |
| 34. C22×D4×C13 | D4 | semidirect |
| 54. C13×#117 | D4 | semidirect |
| 69. C2×#6099 | D4 | semidirect |
| 70. C22×#1055 | D4 | semidirect |
| 79. #88076 | D4 | semidirect |
| 181. #2122 | D13 | semidirect |
| 312. C22×D4 | D52 | semidirect |
| 341. #117 | D52 | semidirect |
| 451. C13 | #13353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13125697 | 2 |
| #13124239 | 2 |
| #13124207 | 2 |
| #13116527 | 2 |
| #13114785 | 2 |
| #13112964 | 2 |
| C13×#2122 | 2 |
| #13353 | 13 |