Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
6554 conjugacy classes of subgroups.
The subgroup lattice has 550 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #13128984 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13128983 | C2 | 1 | 5 | yes | maximal, complemented |
| 3 | #13128982 | C2 | 1 | 10 | yes | maximal, complemented |
| 4 | #13128981 | C2 | 1 | 10 | yes | maximal, complemented |
| 5 | #13128980 | C2 | 1 | 5 | yes | maximal, complemented |
| 6 | D13×#564 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | D13×#563 | C2 | 1 | 10 | yes | maximal, complemented |
| 8 | D13×#562 | C2 | 1 | 5 | yes | maximal, complemented |
| 9 | D13×#533 | C2 | 1 | 5 | yes | maximal, complemented |
| 10 | D13×#529 | C2 | 1 | 10 | yes | maximal, complemented |
| 11 | C13×#3531 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C13×#564 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | C13×#563 | C22 | 1 | 10 | yes | complemented |
| 14 | C13×#562 | C22 | 1 | 5 | yes | complemented |
| 15 | C13×#533 | C22 | 1 | 5 | yes | complemented |
| 16 | C13×#529 | C22 | 1 | 10 | yes | complemented |
| 17 | #11719440 | C22 | 1 | 20 | yes | complemented |
| 18 | #11719433 | C22 | 1 | 10 | yes | complemented |
| 19 | D13×C4⋊Q8 | C22 | 1 | 10 | yes | — |
| 20 | #11719417 | C22 | 1 | 20 | yes | complemented |
| 21 | #11719417 | C22 | 1 | 20 | yes | complemented |
| 22 | #11719411 | C22 | 1 | 20 | yes | complemented |
| 23 | D13×#126 | C22 | 1 | 20 | yes | — |
| 24 | #11719405 | C22 | 1 | 5 | yes | complemented |
| 25 | #11719404 | C22 | 1 | 10 | yes | complemented |
| 26 | #11719404 | C22 | 1 | 10 | yes | complemented |
| 27 | #11719396 | C22 | 1 | 10 | yes | complemented |
| 28 | #11719393 | C22 | 1 | 5 | yes | complemented |
| 29 | #11719393 | C22 | 1 | 5 | yes | complemented |
| 30 | D13×#125 | C22 | 1 | 5 | yes | — |
| 31 | D13×#125 | C22 | 1 | 10 | yes | — |
| 32 | D13×#125 | C22 | 1 | 5 | yes | — |
| 33 | C13⋊#564 | C22 | 1 | 5 | yes | complemented |
| 34 | C13⋊#564 | C22 | 1 | 10 | yes | complemented |
| 35 | #11719389 | C22 | 1 | 10 | yes | complemented |
| 36 | #11719385 | C22 | 1 | 10 | yes | complemented |
| 37 | D13×#124 | C22 | 1 | 10 | yes | — |
| 38 | #11719377 | C22 | 1 | 10 | yes | complemented |
| 39 | #11719372 | C22 | 1 | 20 | yes | complemented |
| 40 | D13×#123 | C22 | 1 | 20 | yes | — |
| 41 | #11719356 | C22 | 1 | 20 | yes | complemented |
| 42 | #11719354 | C22 | 1 | 20 | yes | complemented |
| 43 | #11719352 | C22 | 1 | 20 | yes | complemented |
| 44 | #11719351 | C22 | 1 | 20 | yes | complemented |
| 45 | #11719351 | C22 | 1 | 20 | yes | complemented |
| 46 | D13×C22⋊Q8 | C22 | 1 | 10 | yes | — |
| 47 | D13×C22⋊Q8 | C22 | 1 | 20 | yes | — |
| 48 | #11719329 | C22 | 1 | 10 | yes | complemented |
| 49 | #11719327 | C22 | 1 | 20 | yes | complemented |
| 50 | #11719326 | C22 | 1 | 20 | yes | complemented |
| 51 | D13×#121 | C22 | 1 | 10 | yes | — |
| 52 | #11719305 | C22 | 1 | 10 | yes | complemented |
| 53 | #11719285 | C22 | 1 | 10 | yes | complemented |
| 54 | #11719283 | C22 | 1 | 20 | yes | complemented |
| 55 | C4×Q8×D13 | C22 | 1 | 10 | yes | — |
| 56 | #11719262 | C22 | 1 | 10 | yes | complemented |
| 57 | C4×D4×D13 | C22 | 1 | 10 | yes | — |
| 58 | #11719243 | C22 | 1 | 20 | yes | complemented |
| 59 | #11719233 | C22 | 1 | 20 | yes | complemented |
| 60 | D13×#117 | C22 | 1 | 10 | yes | — |
| 61 | #11719222 | C22 | 1 | 10 | yes | complemented |
| 62 | #11719184 | C22 | 1 | 10 | yes | complemented |
| 63 | C2×C42×D13 | C22 | 1 | 5 | yes | — |
| 64 | #11719175 | C22 | 1 | 5 | yes | complemented |
| 65 | C2×Q8×D13 | C23 | 1 | 10 | yes | — |
| 66 | C2×D4×D13 | C23 | 1 | 10 | yes | — |
| 67 | C22×C4×D13 | C23 | 1 | 5 | yes | — |
| 68 | C22×C4×D13 | C23 | 1 | 10 | yes | — |
| 69 | C13×C4⋊Q8 | C23 | 1 | 10 | yes | — |
| 70 | C13×#126 | C23 | 1 | 20 | yes | — |
| 71 | C13×#125 | C23 | 1 | 10 | yes | — |
| 72 | C13×#125 | C23 | 1 | 5 | yes | — |
| 73 | C13×#125 | C23 | 1 | 5 | yes | — |
| 74 | C13×#124 | C23 | 1 | 10 | yes | — |
| 75 | C13×#123 | C23 | 1 | 20 | yes | — |
| 76 | C13×C22⋊Q8 | C23 | 1 | 10 | yes | — |
| 77 | C13×C22⋊Q8 | C23 | 1 | 20 | yes | — |
| 78 | C13×#121 | C23 | 1 | 10 | yes | — |
| 79 | C4×Q8×C13 | C23 | 1 | 10 | yes | — |
| 80 | C4×D4×C13 | C23 | 1 | 10 | yes | — |
| 81 | C13×#117 | C23 | 1 | 10 | yes | — |
| 82 | C2×C42×C13 | C23 | 1 | 5 | yes | — |
| 83 | #88201 | C23 | 1 | 10 | yes | — |
| 84 | #88200 | C23 | 1 | 20 | yes | — |
| 85 | #88200 | C23 | 1 | 10 | yes | — |
| 86 | Q8×Dic13 | C23 | 1 | 10 | yes | — |
| 87 | #88198 | C23 | 1 | 20 | yes | — |
| 88 | #88193 | C23 | 1 | 20 | yes | — |
| 89 | #88192 | C23 | 1 | 10 | yes | — |
| 90 | #88190 | C23 | 1 | 10 | yes | — |
| 91 | #88189 | C23 | 1 | 20 | yes | — |
| 92 | D4×Dic13 | C23 | 1 | 10 | yes | — |
| 93 | #88184 | C23 | 1 | 10 | yes | — |
| 94 | #88183 | C23 | 1 | 20 | yes | — |
| 95 | C4×C22⋊D13 | C23 | 1 | 20 | yes | — |
| 96 | #88180 | C23 | 1 | 10 | yes | — |
| 97 | #88178 | C23 | 1 | 20 | yes | — |
| 98 | #88178 | C23 | 1 | 10 | yes | — |
| 99 | C2×C4×Dic13 | C23 | 1 | 5 | yes | — |
| 100 | C2×C4×Dic13 | C23 | 1 | 10 | yes | — |
| 101 | #88152 | C23 | 1 | 20 | yes | — |
| 102 | #88152 | C23 | 1 | 20 | yes | — |
| 103 | #88152 | C23 | 1 | 20 | yes | — |
| 104 | #88151 | C23 | 1 | 20 | yes | — |
| 105 | #88151 | C23 | 1 | 10 | yes | — |
| 106 | #88150 | C23 | 1 | 20 | yes | — |
| 107 | #88150 | C23 | 1 | 20 | yes | — |
| 108 | #88150 | C23 | 1 | 20 | yes | — |
| 109 | #88149 | C23 | 1 | 10 | yes | — |
| 110 | #88148 | C23 | 1 | 20 | yes | — |
| 111 | #88148 | C23 | 1 | 20 | yes | — |
| 112 | #88147 | C23 | 1 | 10 | yes | — |
| 113 | #88146 | C23 | 1 | 10 | yes | — |
| 114 | #88146 | C23 | 1 | 10 | yes | — |
| 115 | C4⋊C4×D13 | C23 | 1 | 10 | yes | — |
| 116 | C4⋊C4×D13 | C23 | 1 | 10 | yes | — |
| 117 | C4⋊C4×D13 | C23 | 1 | 20 | yes | — |
| 118 | C4⋊C4×D13 | C23 | 1 | 10 | yes | — |
| 119 | C4⋊C4×D13 | C23 | 1 | 10 | yes | — |
| 120 | #88144 | C23 | 1 | 10 | yes | — |
| 121 | #88144 | C23 | 1 | 10 | yes | — |
| 122 | #88144 | C23 | 1 | 10 | yes | — |
| 123 | #88144 | C23 | 1 | 10 | yes | — |
| 124 | #88143 | C23 | 1 | 20 | yes | — |
| 125 | #88143 | C23 | 1 | 20 | yes | — |
| 126 | #88143 | C23 | 1 | 20 | yes | — |
| 127 | #88143 | C23 | 1 | 20 | yes | — |
| 128 | #88142 | C23 | 1 | 10 | yes | — |
| 129 | #88142 | C23 | 1 | 10 | yes | — |
| 130 | #88142 | C23 | 1 | 20 | yes | — |
| 131 | #88141 | C23 | 1 | 20 | yes | — |
| 132 | #88141 | C23 | 1 | 10 | yes | — |
| 133 | #88140 | C23 | 1 | 20 | yes | — |
| 134 | #88139 | C23 | 1 | 20 | yes | — |
| 135 | #88139 | C23 | 1 | 20 | yes | — |
| 136 | #88138 | C23 | 1 | 20 | yes | — |
| 137 | #88137 | C23 | 1 | 20 | yes | — |
| 138 | #88137 | C23 | 1 | 20 | yes | — |
| 139 | #88135 | C23 | 1 | 20 | yes | — |
| 140 | C22⋊C4×D13 | C23 | 1 | 20 | yes | — |
| 141 | C22⋊C4×D13 | C23 | 1 | 20 | yes | — |
| 142 | #88133 | C23 | 1 | 20 | yes | — |
| 143 | #88133 | C23 | 1 | 20 | yes | — |
| 144 | #88133 | C23 | 1 | 20 | yes | — |
| 145 | #88132 | C23 | 1 | 20 | yes | — |
| 146 | #88132 | C23 | 1 | 20 | yes | — |
| 147 | #88132 | C23 | 1 | 20 | yes | — |
| 148 | #88131 | C23 | 1 | 20 | yes | — |
| 149 | #88130 | C23 | 1 | 20 | yes | — |
| 150 | #88129 | C23 | 1 | 10 | yes | — |
| 151 | C4×D52 | C23 | 1 | 10 | yes | — |
| 152 | #88126 | C23 | 1 | 20 | yes | — |
| 153 | C42×D13 | C23 | 1 | 5 | yes | — |
| 154 | C42×D13 | C23 | 1 | 5 | yes | — |
| 155 | C42×D13 | C23 | 1 | 10 | yes | — |
| 156 | C42×D13 | C23 | 1 | 10 | yes | — |
| 157 | C42×D13 | C23 | 1 | 5 | yes | — |
| 158 | C42×D13 | C23 | 1 | 5 | yes | — |
| 159 | #88124 | C23 | 1 | 5 | yes | — |
| 160 | #88124 | C23 | 1 | 5 | yes | — |
| 161 | #88124 | C23 | 1 | 10 | yes | — |
| 162 | #88123 | C23 | 1 | 10 | yes | — |
| 163 | C4×Dic26 | C23 | 1 | 20 | yes | — |
| 164 | C4×Dic26 | C23 | 1 | 10 | yes | — |
| 165 | C2×#3531 | — | 13 | 1 | no | maximal, Sylow |
| 166 | C23×D13 | C24 | 1 | 5 | yes | — |
| 167 | C2×Q8×C13 | C24 | 1 | 10 | yes | — |
| 168 | C2×D4×C13 | C24 | 1 | 10 | yes | — |
| 169 | C22×C4×C13 | C24 | 1 | 5 | yes | — |
| 170 | C22×C4×C13 | C24 | 1 | 10 | yes | — |
| 171 | C2×C22⋊D13 | C24 | 1 | 20 | yes | — |
| 172 | C22×Dic13 | C24 | 1 | 5 | yes | — |
| 173 | C22×Dic13 | C24 | 1 | 10 | yes | — |
| 174 | Q8×D13 | — | 4 | 20 | no | — |
| 175 | D4×D13 | — | 4 | 20 | no | — |
| 176 | C2×D52 | C24 | 1 | 10 | yes | — |
| 177 | C2×C4×D13 | — | 2 | 20 | no | — |
| 178 | C2×C4×D13 | — | 4 | 20 | no | — |
| 179 | C2×C4×D13 | C24 | 1 | 5 | yes | — |
| 180 | C2×C4×D13 | C24 | 1 | 5 | yes | — |
| 181 | C2×C4×D13 | C24 | 1 | 10 | yes | — |
| 182 | C2×C4×D13 | C24 | 1 | 10 | yes | — |
| 183 | C2×C4×D13 | C24 | 1 | 5 | yes | — |
| 184 | C2×C4×D13 | C24 | 1 | 10 | yes | — |
| 185 | C2×C4×D13 | C24 | 1 | 10 | yes | — |
| 186 | C2×C4×D13 | C24 | 1 | 1 | yes | characteristic |
| 187 | C2×Dic26 | C24 | 1 | 20 | yes | — |
| 188 | C2×Dic26 | C24 | 1 | 10 | yes | — |
| 189 | C13×C4⋊C4 | C24 | 1 | 20 | yes | — |
| 190 | C13×C4⋊C4 | C24 | 1 | 10 | yes | — |
| 191 | C13×C4⋊C4 | C24 | 1 | 10 | yes | — |
| 192 | C13×C4⋊C4 | C24 | 1 | 10 | yes | — |
| 193 | C13×C4⋊C4 | C24 | 1 | 10 | yes | — |
| 194 | C13×C22⋊C4 | C24 | 1 | 20 | yes | — |
| 195 | C13×C22⋊C4 | C24 | 1 | 20 | yes | — |
| 196 | C42×C13 | C24 | 1 | 10 | yes | — |
| 197 | C42×C13 | C24 | 1 | 5 | yes | — |
| 198 | C42×C13 | C24 | 1 | 5 | yes | — |
| 199 | C22⋊Dic13 | C24 | 1 | 20 | yes | — |
| 200 | C22⋊Dic13 | C24 | 1 | 20 | yes | — |
| 201 | #6103 | C24 | 1 | 20 | yes | — |
| 202 | #6103 | C24 | 1 | 20 | yes | — |
| 203 | #6103 | C24 | 1 | 20 | yes | — |
| 204 | #6103 | C24 | 1 | 20 | yes | — |
| 205 | C4⋊Dic13 | C24 | 1 | 20 | yes | — |
| 206 | C4⋊Dic13 | C24 | 1 | 10 | yes | — |
| 207 | C4⋊Dic13 | C24 | 1 | 10 | yes | — |
| 208 | C4⋊Dic13 | C24 | 1 | 10 | yes | — |
| 209 | C4⋊Dic13 | C24 | 1 | 10 | yes | — |
| 210 | #6101 | C24 | 1 | 20 | yes | — |
| 211 | #6101 | C24 | 1 | 20 | yes | — |
| 212 | #6101 | C24 | 1 | 20 | yes | — |
| 213 | #6101 | C24 | 1 | 20 | yes | — |
| 214 | #6101 | C24 | 1 | 20 | yes | — |
| 215 | #6101 | C24 | 1 | 20 | yes | — |
| 216 | C4×Dic13 | C24 | 1 | 10 | yes | — |
| 217 | C4×Dic13 | C24 | 1 | 10 | yes | — |
| 218 | C4×Dic13 | C24 | 1 | 10 | yes | — |
| 219 | C4×Dic13 | C24 | 1 | 5 | yes | — |
| 220 | C4×Dic13 | C24 | 1 | 10 | yes | — |
| 221 | C4×Dic13 | C24 | 1 | 5 | yes | — |
| 222 | C4×Dic13 | C24 | 1 | 10 | yes | — |
| 223 | #3531 | — | 13 | 1 | no | — |
| 224 | #3531 | — | 13 | 10 | no | — |
| 225 | #3531 | — | 13 | 5 | no | — |
| 226 | #3531 | — | 13 | 5 | no | — |
| 227 | #3531 | — | 13 | 10 | no | — |
| 228 | #3531 | D13 | 1 | 1 | yes | characteristic, direct product factor |
| 229 | C2×#564 | — | 13 | 1 | no | — |
| 230 | C2×#563 | — | 13 | 10 | no | — |
| 231 | C2×#562 | — | 13 | 5 | no | — |
| 232 | C2×#533 | — | 13 | 5 | no | — |
| 233 | C2×#529 | — | 13 | 10 | no | — |
| 234 | C23×C13 | C25 | 1 | 5 | yes | — |
| 235 | C22×D13 | — | 2 | 10 | no | — |
| 236 | C22×D13 | — | 2 | 20 | no | — |
| 237 | C22×D13 | C25 | 1 | 5 | yes | — |
| 238 | C22×D13 | C25 | 1 | 1 | yes | characteristic |
| 239 | Q8×C13 | — | 4 | 10 | no | — |
| 240 | D4×C13 | — | 4 | 10 | no | — |
| 241 | C2×C4×C13 | — | 2 | 10 | no | — |
| 242 | C2×C4×C13 | — | 4 | 10 | no | — |
| 243 | C2×C4×C13 | C25 | 1 | 10 | yes | — |
| 244 | C2×C4×C13 | C25 | 1 | 5 | yes | — |
| 245 | C2×C4×C13 | C25 | 1 | 10 | yes | — |
| 246 | C2×C4×C13 | C25 | 1 | 1 | yes | characteristic |
| 247 | C22⋊D13 | — | 4 | 20 | no | — |
| 248 | C2×Dic13 | — | 2 | 10 | no | — |
| 249 | C2×Dic13 | — | 4 | 10 | no | — |
| 250 | C2×Dic13 | C25 | 1 | 5 | yes | — |
| 251 | C2×Dic13 | C25 | 1 | 10 | yes | — |
| 252 | C2×Dic13 | C25 | 1 | 10 | yes | — |
| 253 | C2×Dic13 | C25 | 1 | 1 | yes | characteristic |
| 254 | D52 | — | 4 | 10 | no | — |
| 255 | C4×D13 | — | 2 | 10 | no | — |
| 256 | C4×D13 | — | 2 | 20 | no | — |
| 257 | C4×D13 | — | 2 | 20 | no | — |
| 258 | C4×D13 | — | 2 | 10 | no | — |
| 259 | C4×D13 | — | 2 | 10 | no | — |
| 260 | C4×D13 | — | 4 | 10 | no | — |
| 261 | C4×D13 | — | 4 | 10 | no | — |
| 262 | C4×D13 | 2−1+4 | 1 | 4 | yes | — |
| 263 | Dic26 | — | 4 | 10 | no | — |
| 264 | Dic26 | — | 4 | 20 | no | — |
| 265 | #564 | — | 13 | 10 | no | — |
| 266 | #564 | — | 13 | 5 | no | — |
| 267 | #564 | C2×D13 | 1 | 1 | yes | characteristic, complemented |
| 268 | #563 | — | 13 | 20 | no | — |
| 269 | #563 | — | 13 | 20 | no | — |
| 270 | #563 | — | 13 | 20 | no | — |
| 271 | #563 | — | 13 | 10 | no | — |
| 272 | #563 | — | 13 | 10 | no | — |
| 273 | #563 | — | 13 | 10 | no | — |
| 274 | #563 | — | 13 | 20 | no | — |
| 275 | #563 | — | 13 | 20 | no | — |
| 276 | #563 | — | 13 | 20 | no | — |
| 277 | #563 | C2×D13 | 1 | 10 | yes | complemented |
| 278 | #562 | — | 13 | 5 | no | — |
| 279 | #562 | — | 13 | 10 | no | — |
| 280 | #562 | — | 13 | 20 | no | — |
| 281 | #562 | — | 13 | 20 | no | — |
| 282 | #562 | — | 13 | 20 | no | — |
| 283 | #562 | C2×D13 | 1 | 5 | yes | complemented |
| 284 | #533 | — | 13 | 10 | no | — |
| 285 | #533 | — | 13 | 5 | no | — |
| 286 | #533 | — | 13 | 5 | no | — |
| 287 | #533 | — | 13 | 20 | no | — |
| 288 | #533 | — | 13 | 20 | no | — |
| 289 | #533 | — | 13 | 10 | no | — |
| 290 | #533 | — | 13 | 5 | no | — |
| 291 | #533 | C2×D13 | 1 | 5 | yes | complemented |
| 292 | C2×C4⋊Q8 | — | 13 | 10 | no | — |
| 293 | #529 | — | 13 | 20 | no | — |
| 294 | #529 | — | 13 | 10 | no | — |
| 295 | #529 | — | 13 | 10 | no | — |
| 296 | #529 | — | 13 | 20 | no | — |
| 297 | #529 | — | 13 | 10 | no | — |
| 298 | #529 | — | 13 | 10 | no | — |
| 299 | #529 | — | 13 | 10 | no | — |
| 300 | #529 | — | 13 | 20 | no | — |
| 301 | #529 | — | 13 | 10 | no | — |
| 302 | #529 | — | 13 | 20 | no | — |
| 303 | #529 | — | 13 | 10 | no | — |
| 304 | #529 | C2×D13 | 1 | 10 | yes | complemented |
| 305 | C2×#126 | — | 13 | 20 | no | — |
| 306 | C2×#125 | — | 13 | 10 | no | — |
| 307 | C2×#125 | — | 13 | 5 | no | — |
| 308 | C2×#125 | — | 13 | 5 | no | — |
| 309 | C2×#124 | — | 13 | 10 | no | — |
| 310 | C2×#123 | — | 13 | 20 | no | — |
| 311 | C2×C22⋊Q8 | — | 13 | 10 | no | — |
| 312 | C2×C22⋊Q8 | — | 13 | 20 | no | — |
| 313 | C2×#121 | — | 13 | 10 | no | — |
| 314 | C2×C4×Q8 | — | 13 | 10 | no | — |
| 315 | C2×C4×D4 | — | 13 | 10 | no | — |
| 316 | C2×#117 | — | 13 | 10 | no | — |
| 317 | C22×C42 | — | 13 | 5 | no | — |
| 318 | C22×C13 | — | 2 | 5 | no | — |
| 319 | C22×C13 | — | 2 | 10 | no | — |
| 320 | C22×C13 | C26 | 1 | 1 | yes | characteristic |
| 321 | C2×D13 | — | 2 | 5 | no | — |
| 322 | C2×D13 | — | 2 | 10 | no | — |
| 323 | C2×D13 | — | 4 | 20 | no | — |
| 324 | C2×D13 | C2×2−1+4 | 1 | 2 | yes | — |
| 325 | C2×D13 | #585 | 1 | 4 | yes | — |
| 326 | C4×C13 | — | 2 | 5 | no | — |
| 327 | C4×C13 | — | 2 | 10 | no | — |
| 328 | C4×C13 | — | 2 | 10 | no | — |
| 329 | C4×C13 | C2×2−1+4 | 1 | 2 | yes | — |
| 330 | Dic13 | — | 2 | 5 | no | — |
| 331 | Dic13 | — | 2 | 10 | no | — |
| 332 | Dic13 | — | 2 | 10 | no | — |
| 333 | Dic13 | C2×2−1+4 | 1 | 2 | yes | — |
| 334 | C22×Q8 | — | 13 | 10 | no | — |
| 335 | C22×D4 | — | 13 | 10 | no | — |
| 336 | C23×C4 | — | 13 | 5 | no | — |
| 337 | C23×C4 | — | 13 | 10 | no | — |
| 338 | C4⋊Q8 | — | 13 | 20 | no | — |
| 339 | C4⋊Q8 | — | 13 | 20 | no | — |
| 340 | C4⋊Q8 | — | 13 | 10 | no | — |
| 341 | C4⋊Q8 | — | 13 | 10 | no | — |
| 342 | C4⋊Q8 | — | 13 | 10 | no | — |
| 343 | C4⋊Q8 | C22×D13 | 1 | 10 | yes | — |
| 344 | #126 | — | 13 | 20 | no | — |
| 345 | #126 | — | 13 | 20 | no | — |
| 346 | #126 | — | 13 | 20 | no | — |
| 347 | #126 | — | 13 | 20 | no | — |
| 348 | #126 | — | 13 | 20 | no | — |
| 349 | #126 | — | 13 | 20 | no | — |
| 350 | #126 | — | 13 | 20 | no | — |
| 351 | #126 | C22×D13 | 1 | 20 | yes | — |
| 352 | #125 | — | 13 | 20 | no | — |
| 353 | #125 | — | 13 | 20 | no | — |
| 354 | #125 | — | 13 | 10 | no | — |
| 355 | #125 | — | 13 | 10 | no | — |
| 356 | #125 | — | 13 | 20 | no | — |
| 357 | #125 | — | 13 | 10 | no | — |
| 358 | #125 | — | 13 | 20 | no | — |
| 359 | #125 | — | 13 | 10 | no | — |
| 360 | #125 | — | 13 | 10 | no | — |
| 361 | #125 | — | 13 | 5 | no | — |
| 362 | #125 | — | 13 | 5 | no | — |
| 363 | #125 | C22×D13 | 1 | 10 | yes | — |
| 364 | #125 | C22×D13 | 1 | 5 | yes | — |
| 365 | #125 | C22×D13 | 1 | 5 | yes | — |
| 366 | #124 | — | 13 | 10 | no | — |
| 367 | #124 | — | 13 | 10 | no | — |
| 368 | #124 | — | 13 | 20 | no | — |
| 369 | #124 | — | 13 | 20 | no | — |
| 370 | #124 | — | 13 | 10 | no | — |
| 371 | #124 | C22×D13 | 1 | 10 | yes | — |
| 372 | #123 | — | 13 | 20 | no | — |
| 373 | #123 | — | 13 | 20 | no | — |
| 374 | #123 | — | 13 | 20 | no | — |
| 375 | #123 | — | 13 | 20 | no | — |
| 376 | #123 | — | 13 | 20 | no | — |
| 377 | #123 | — | 13 | 20 | no | — |
| 378 | #123 | — | 13 | 20 | no | — |
| 379 | #123 | C22×D13 | 1 | 20 | yes | — |
| 380 | C22⋊Q8 | — | 13 | 10 | no | — |
| 381 | C22⋊Q8 | — | 13 | 20 | no | — |
| 382 | C22⋊Q8 | — | 13 | 10 | no | — |
| 383 | C22⋊Q8 | — | 13 | 20 | no | — |
| 384 | C22⋊Q8 | — | 13 | 20 | no | — |
| 385 | C22⋊Q8 | — | 13 | 10 | no | — |
| 386 | C22⋊Q8 | — | 13 | 20 | no | — |
| 387 | C22⋊Q8 | — | 13 | 20 | no | — |
| 388 | C22⋊Q8 | — | 13 | 20 | no | — |
| 389 | C22⋊Q8 | — | 13 | 20 | no | — |
| 390 | C22⋊Q8 | — | 13 | 20 | no | — |
| 391 | C22⋊Q8 | — | 13 | 20 | no | — |
| 392 | C22⋊Q8 | C22×D13 | 1 | 10 | yes | — |
| 393 | C22⋊Q8 | C22×D13 | 1 | 20 | yes | — |
| 394 | #121 | — | 13 | 10 | no | — |
| 395 | #121 | — | 13 | 20 | no | — |
| 396 | #121 | — | 13 | 10 | no | — |
| 397 | #121 | — | 13 | 10 | no | — |
| 398 | #121 | — | 13 | 20 | no | — |
| 399 | #121 | C22×D13 | 1 | 10 | yes | — |
| 400 | C4×Q8 | — | 13 | 10 | no | — |
| 401 | C4×Q8 | — | 13 | 20 | no | — |
| 402 | C4×Q8 | — | 13 | 10 | no | — |
| 403 | C4×Q8 | — | 13 | 20 | no | — |
| 404 | C4×Q8 | — | 13 | 10 | no | — |
| 405 | C4×Q8 | C22×D13 | 1 | 10 | yes | — |
| 406 | C4×D4 | — | 13 | 10 | no | — |
| 407 | C4×D4 | — | 13 | 20 | no | — |
| 408 | C4×D4 | — | 13 | 10 | no | — |
| 409 | C4×D4 | — | 13 | 20 | no | — |
| 410 | C4×D4 | — | 13 | 10 | no | — |
| 411 | C4×D4 | C22×D13 | 1 | 10 | yes | — |
| 412 | #117 | — | 13 | 10 | no | — |
| 413 | #117 | — | 13 | 10 | no | — |
| 414 | #117 | — | 13 | 10 | no | — |
| 415 | #117 | — | 13 | 20 | no | — |
| 416 | #117 | — | 13 | 20 | no | — |
| 417 | #117 | C22×D13 | 1 | 10 | yes | — |
| 418 | C2×C4⋊C4 | — | 13 | 10 | no | — |
| 419 | C2×C4⋊C4 | — | 13 | 10 | no | — |
| 420 | C2×C4⋊C4 | — | 13 | 10 | no | — |
| 421 | C2×C4⋊C4 | — | 13 | 10 | no | — |
| 422 | C2×C4⋊C4 | — | 13 | 20 | no | — |
| 423 | C2×C22⋊C4 | — | 13 | 20 | no | — |
| 424 | C2×C22⋊C4 | — | 13 | 20 | no | — |
| 425 | C2×C42 | — | 13 | 10 | no | — |
| 426 | C2×C42 | — | 13 | 5 | no | — |
| 427 | C2×C42 | — | 13 | 10 | no | — |
| 428 | C2×C42 | — | 13 | 5 | no | — |
| 429 | C2×C42 | — | 13 | 5 | no | — |
| 430 | C2×C42 | — | 13 | 5 | no | — |
| 431 | C2×C42 | — | 13 | 5 | no | — |
| 432 | C2×C42 | — | 13 | 10 | no | — |
| 433 | C2×C42 | C22×D13 | 1 | 5 | yes | — |
| 434 | C2×C13 | — | 4 | 5 | no | — |
| 435 | C2×C13 | C22×2−1+4 | 1 | 1 | yes | characteristic |
| 436 | C2×C13 | C2×#585 | 1 | 2 | yes | — |
| 437 | D13 | — | 4 | 5 | no | — |
| 438 | D13 | #3531 | 1 | 4 | yes | direct product factor |
| 439 | C24 | — | 13 | 5 | no | — |
| 440 | C2×Q8 | — | 13 | 10 | no | — |
| 441 | C2×Q8 | — | 13 | 20 | no | — |
| 442 | C2×Q8 | — | 52 | 20 | no | — |
| 443 | C2×Q8 | C23×D13 | 1 | 10 | yes | — |
| 444 | C2×D4 | — | 13 | 20 | no | — |
| 445 | C2×D4 | — | 13 | 10 | no | — |
| 446 | C2×D4 | — | 52 | 20 | no | — |
| 447 | C2×D4 | C23×D13 | 1 | 10 | yes | — |
| 448 | C22×C4 | — | 13 | 1 | no | — |
| 449 | C22×C4 | — | 13 | 5 | no | — |
| 450 | C22×C4 | — | 13 | 10 | no | — |
| 451 | C22×C4 | — | 13 | 5 | no | — |
| 452 | C22×C4 | — | 13 | 10 | no | — |
| 453 | C22×C4 | — | 13 | 10 | no | — |
| 454 | C22×C4 | — | 13 | 5 | no | — |
| 455 | C22×C4 | — | 13 | 5 | no | — |
| 456 | C22×C4 | — | 13 | 10 | no | — |
| 457 | C22×C4 | — | 13 | 10 | no | — |
| 458 | C22×C4 | — | 26 | 20 | no | — |
| 459 | C22×C4 | — | 52 | 20 | no | — |
| 460 | C22×C4 | C23×D13 | 1 | 5 | yes | — |
| 461 | C22×C4 | C23×D13 | 1 | 10 | yes | — |
| 462 | C4⋊C4 | — | 13 | 20 | no | — |
| 463 | C4⋊C4 | — | 13 | 10 | no | — |
| 464 | C4⋊C4 | — | 13 | 20 | no | — |
| 465 | C4⋊C4 | — | 13 | 10 | no | — |
| 466 | C4⋊C4 | — | 13 | 20 | no | — |
| 467 | C4⋊C4 | — | 13 | 10 | no | — |
| 468 | C4⋊C4 | — | 13 | 20 | no | — |
| 469 | C4⋊C4 | — | 13 | 10 | no | — |
| 470 | C4⋊C4 | — | 13 | 20 | no | — |
| 471 | C4⋊C4 | — | 13 | 20 | no | — |
| 472 | C4⋊C4 | — | 13 | 20 | no | — |
| 473 | C4⋊C4 | C23×D13 | 1 | 10 | yes | — |
| 474 | C4⋊C4 | C23×D13 | 1 | 10 | yes | — |
| 475 | C4⋊C4 | C23×D13 | 1 | 10 | yes | — |
| 476 | C4⋊C4 | C23×D13 | 1 | 10 | yes | — |
| 477 | C4⋊C4 | C23×D13 | 1 | 20 | yes | — |
| 478 | C22⋊C4 | — | 13 | 20 | no | — |
| 479 | C22⋊C4 | — | 13 | 20 | no | — |
| 480 | C22⋊C4 | — | 13 | 20 | no | — |
| 481 | C22⋊C4 | — | 13 | 20 | no | — |
| 482 | C22⋊C4 | — | 13 | 20 | no | — |
| 483 | C22⋊C4 | — | 13 | 20 | no | — |
| 484 | C22⋊C4 | C23×D13 | 1 | 20 | yes | — |
| 485 | C22⋊C4 | C23×D13 | 1 | 20 | yes | — |
| 486 | C42 | — | 13 | 10 | no | — |
| 487 | C42 | — | 13 | 10 | no | — |
| 488 | C42 | — | 13 | 10 | no | — |
| 489 | C42 | — | 13 | 5 | no | — |
| 490 | C42 | — | 13 | 10 | no | — |
| 491 | C42 | — | 13 | 5 | no | — |
| 492 | C42 | — | 13 | 10 | no | — |
| 493 | C42 | C23×D13 | 1 | 5 | yes | — |
| 494 | C42 | C23×D13 | 1 | 5 | yes | — |
| 495 | C42 | C23×D13 | 1 | 10 | yes | — |
| 496 | C13 | C2×#3531 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 497 | C23 | — | 13 | 1 | no | — |
| 498 | C23 | — | 13 | 5 | no | — |
| 499 | C23 | — | 26 | 10 | no | — |
| 500 | C23 | — | 26 | 20 | no | — |
| 501 | C23 | C24×D13 | 1 | 5 | yes | — |
| 502 | Q8 | — | 4 | 10 | no | — |
| 503 | Q8 | — | 52 | 10 | no | — |
| 504 | Q8 | — | 52 | 20 | no | — |
| 505 | D4 | — | 4 | 10 | no | — |
| 506 | D4 | — | 52 | 10 | no | — |
| 507 | D4 | — | 52 | 20 | no | — |
| 508 | C2×C4 | — | 2 | 10 | no | — |
| 509 | C2×C4 | — | 4 | 10 | no | — |
| 510 | C2×C4 | — | 13 | 1 | no | — |
| 511 | C2×C4 | — | 13 | 4 | no | — |
| 512 | C2×C4 | — | 13 | 5 | no | — |
| 513 | C2×C4 | — | 13 | 10 | no | — |
| 514 | C2×C4 | — | 13 | 10 | no | — |
| 515 | C2×C4 | — | 26 | 10 | no | — |
| 516 | C2×C4 | — | 26 | 10 | no | — |
| 517 | C2×C4 | — | 26 | 20 | no | — |
| 518 | C2×C4 | — | 26 | 20 | no | — |
| 519 | C2×C4 | — | 26 | 10 | no | — |
| 520 | C2×C4 | — | 26 | 10 | no | — |
| 521 | C2×C4 | — | 52 | 10 | no | — |
| 522 | C2×C4 | — | 52 | 10 | no | — |
| 523 | C2×C4 | — | 52 | 10 | no | — |
| 524 | C2×C4 | C24×D13 | 1 | 5 | yes | — |
| 525 | C2×C4 | C24×D13 | 1 | 10 | yes | — |
| 526 | C2×C4 | C24×D13 | 1 | 10 | yes | — |
| 527 | C2×C4 | C24×D13 | 1 | 1 | yes | characteristic |
| 528 | C22 | — | 2 | 5 | no | — |
| 529 | C22 | — | 2 | 10 | no | — |
| 530 | C22 | — | 13 | 2 | no | — |
| 531 | C22 | — | 13 | 4 | no | — |
| 532 | C22 | — | 26 | 5 | no | — |
| 533 | C22 | — | 26 | 10 | no | — |
| 534 | C22 | — | 52 | 20 | no | — |
| 535 | C22 | C25×D13 | 1 | 1 | yes | characteristic |
| 536 | C4 | — | 2 | 5 | no | — |
| 537 | C4 | — | 2 | 10 | no | — |
| 538 | C4 | — | 2 | 10 | no | — |
| 539 | C4 | — | 13 | 2 | no | — |
| 540 | C4 | — | 26 | 5 | no | — |
| 541 | C4 | — | 26 | 10 | no | — |
| 542 | C4 | — | 26 | 10 | no | — |
| 543 | C4 | D13×2−1+4 | 1 | 2 | yes | — |
| 544 | C2 | — | 4 | 5 | no | — |
| 545 | C2 | — | 13 | 4 | no | — |
| 546 | C2 | — | 52 | 5 | no | — |
| 547 | C2 | C2×D13×2−1+4 | 1 | 1 | yes | characteristic |
| 548 | C2 | D13×#585 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C24×D13 |
| commutator, socle, cosocle | C22×C13 | C26 |
| Frattini | C22 | C25×D13 |
| Fitting | C13×#3531 | C2 |
| hypercenter | #3531 | D13 |
| hypocenter | C13 | C2×#3531 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C2×C4 ◁ #3531 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13128984 | C2 | semidirect |
| 2. #13128983 | C2 | semidirect |
| 3. #13128982 | C2 | semidirect |
| 4. #13128981 | C2 | semidirect |
| 5. #13128980 | C2 | semidirect |
| 6. D13×#564 | C2 | semidirect |
| 7. D13×#563 | C2 | semidirect |
| 8. D13×#562 | C2 | semidirect |
| 9. D13×#533 | C2 | semidirect |
| 10. D13×#529 | C2 | semidirect |
| 11. C13×#3531 | C2 | semidirect |
| 12. C13×#564 | C22 | semidirect |
| 13. C13×#563 | C22 | semidirect |
| 14. C13×#562 | C22 | semidirect |
| 15. C13×#533 | C22 | semidirect |
| 16. C13×#529 | C22 | semidirect |
| 17. #11719440 | C22 | semidirect |
| 18. #11719433 | C22 | semidirect |
| 20. #11719417 | C22 | semidirect |
| 21. #11719417 | C22 | semidirect |
| 22. #11719411 | C22 | semidirect |
| 24. #11719405 | C22 | semidirect |
| 25. #11719404 | C22 | semidirect |
| 26. #11719404 | C22 | semidirect |
| 27. #11719396 | C22 | semidirect |
| 28. #11719393 | C22 | semidirect |
| 29. #11719393 | C22 | semidirect |
| 33. C13⋊#564 | C22 | semidirect |
| 34. C13⋊#564 | C22 | semidirect |
| 35. #11719389 | C22 | semidirect |
| 36. #11719385 | C22 | semidirect |
| 38. #11719377 | C22 | semidirect |
| 39. #11719372 | C22 | semidirect |
| 41. #11719356 | C22 | semidirect |
| 42. #11719354 | C22 | semidirect |
| 43. #11719352 | C22 | semidirect |
| 44. #11719351 | C22 | semidirect |
| 45. #11719351 | C22 | semidirect |
| 48. #11719329 | C22 | semidirect |
| 49. #11719327 | C22 | semidirect |
| 50. #11719326 | C22 | semidirect |
| 52. #11719305 | C22 | semidirect |
| 53. #11719285 | C22 | semidirect |
| 54. #11719283 | C22 | semidirect |
| 56. #11719262 | C22 | semidirect |
| 58. #11719243 | C22 | semidirect |
| 59. #11719233 | C22 | semidirect |
| 61. #11719222 | C22 | semidirect |
| 62. #11719184 | C22 | semidirect |
| 64. #11719175 | C22 | semidirect |
| 228. #3531 | D13 | direct (N × H) |
| 267. #564 | C2×D13 | semidirect |
| 277. #563 | C2×D13 | semidirect |
| 283. #562 | C2×D13 | semidirect |
| 291. #533 | C2×D13 | semidirect |
| 304. #529 | C2×D13 | semidirect |
| 438. D13 | #3531 | direct (N × H) |
| 496. C13 | C2×#3531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13128984 | 2 |
| #13128983 | 2 |
| #13128982 | 2 |
| #13128981 | 2 |
| #13128980 | 2 |
| D13×#564 | 2 |
| D13×#563 | 2 |
| D13×#562 | 2 |
| D13×#533 | 2 |
| D13×#529 | 2 |
| C13×#3531 | 2 |
| C2×#3531 | 13 |