Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1282 conjugacy classes of subgroups.
The subgroup lattice has 588 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #13128612 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13125959 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#11718731 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13124324 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #13114030 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #13114016 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #13113286 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #13113216 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C13×#1545 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×#88251 | — | 2 | 1 | no | — |
| 11 | C2×C13×#127 | C22 | 1 | 1 | yes | characteristic |
| 12 | #11719510 | — | 2 | 1 | no | — |
| 13 | D4×C22⋊D13 | — | 2 | 2 | no | — |
| 14 | D4×C22⋊D13 | — | 2 | 2 | no | — |
| 15 | C2×#88163 | — | 2 | 1 | no | — |
| 16 | #11719423 | — | 2 | 1 | no | — |
| 17 | #11719423 | C22 | 1 | 2 | yes | — |
| 18 | #11719422 | — | 2 | 1 | no | — |
| 19 | #11719422 | C22 | 1 | 2 | yes | — |
| 20 | #11719421 | — | 2 | 1 | no | — |
| 21 | #11719420 | — | 2 | 2 | no | — |
| 22 | D13×#127 | — | 2 | 1 | no | — |
| 23 | #11719182 | C22 | 1 | 1 | yes | characteristic |
| 24 | C4×#6127 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#88123 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | C13×#431 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | C13×#423 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | C2×#88072 | — | 2 | 2 | no | — |
| 29 | #11718781 | — | 2 | 1 | no | — |
| 30 | #11718731 | — | 2 | 2 | no | — |
| 31 | #11718731 | C22 | 1 | 4 | yes | complemented |
| 32 | C2×C4×#1055 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #11718510 | — | 2 | 1 | no | — |
| 34 | #11718510 | C22 | 1 | 2 | yes | complemented |
| 35 | #11718507 | C22 | 1 | 4 | yes | complemented |
| 36 | #11718502 | — | 2 | 1 | no | — |
| 37 | #11718502 | C22 | 1 | 2 | yes | complemented |
| 38 | #11718397 | — | 2 | 2 | no | — |
| 39 | #11718355 | — | 2 | 1 | no | — |
| 40 | #11718343 | — | 2 | 1 | no | — |
| 41 | C13×#331 | C22 | 1 | 4 | yes | complemented |
| 42 | #11718076 | C22 | 1 | 2 | yes | complemented |
| 43 | #11718075 | C22 | 1 | 2 | yes | complemented |
| 44 | #11718075 | C22 | 1 | 4 | yes | complemented |
| 45 | C22×D4×C13 | — | 2 | 1 | no | — |
| 46 | C22×D4×C13 | — | 2 | 1 | no | — |
| 47 | C22×D4×C13 | D4 | 1 | 2 | yes | — |
| 48 | C22×C22⋊D13 | — | 2 | 4 | no | — |
| 49 | #88251 | — | 4 | 4 | no | — |
| 50 | #88251 | — | 4 | 4 | no | — |
| 51 | C2×#6129 | — | 2 | 2 | no | — |
| 52 | C2×#6129 | — | 2 | 2 | no | — |
| 53 | C2×D4×D13 | — | 2 | 2 | no | — |
| 54 | C2×D4×D13 | — | 2 | 2 | no | — |
| 55 | C2×D4×D13 | — | 2 | 2 | no | — |
| 56 | C2×D4×D13 | — | 2 | 2 | no | — |
| 57 | C2×#6127 | — | 2 | 1 | no | — |
| 58 | C2×#6127 | D4 | 1 | 1 | yes | characteristic |
| 59 | C22×Dic26 | — | 2 | 1 | no | — |
| 60 | C2×C13×M16 | — | 2 | 1 | no | — |
| 61 | C13×#127 | — | 2 | 1 | no | — |
| 62 | C13×#127 | — | 2 | 1 | no | — |
| 63 | C13×#127 | D4 | 1 | 2 | yes | — |
| 64 | C13×#127 | C23 | 1 | 2 | yes | — |
| 65 | C2×C42×C13 | C23 | 1 | 1 | yes | characteristic |
| 66 | #88207 | — | 2 | 4 | no | — |
| 67 | #88194 | — | 2 | 2 | no | — |
| 68 | #88194 | — | 2 | 2 | no | — |
| 69 | #88194 | — | 2 | 2 | no | — |
| 70 | #88193 | — | 2 | 4 | no | — |
| 71 | #88193 | — | 2 | 4 | no | — |
| 72 | #88192 | — | 2 | 2 | no | — |
| 73 | #88192 | — | 2 | 2 | no | — |
| 74 | #88192 | — | 2 | 2 | no | — |
| 75 | #88192 | — | 2 | 2 | no | — |
| 76 | #88191 | — | 2 | 4 | no | — |
| 77 | #88191 | — | 2 | 4 | no | — |
| 78 | #88190 | — | 2 | 2 | no | — |
| 79 | D4×Dic13 | — | 2 | 2 | no | — |
| 80 | D4×Dic13 | — | 2 | 2 | no | — |
| 81 | #88184 | — | 2 | 1 | no | — |
| 82 | #88184 | D4 | 1 | 2 | yes | — |
| 83 | C4×C22⋊D13 | — | 2 | 1 | no | — |
| 84 | C4×C22⋊D13 | — | 2 | 1 | no | — |
| 85 | #88180 | D4 | 1 | 1 | yes | characteristic |
| 86 | C2×C4⋊Dic13 | — | 2 | 1 | no | — |
| 87 | C2×C4⋊Dic13 | — | 2 | 1 | no | — |
| 88 | C22×#1055 | — | 2 | 1 | no | — |
| 89 | #88163 | — | 4 | 4 | no | — |
| 90 | C2×Dic52 | — | 2 | 2 | no | — |
| 91 | C2×#6095 | — | 2 | 2 | no | — |
| 92 | #88129 | — | 2 | 1 | no | — |
| 93 | #88128 | D4 | 1 | 1 | yes | characteristic |
| 94 | C4×D52 | — | 2 | 1 | no | — |
| 95 | C4×D52 | D4 | 1 | 1 | yes | characteristic |
| 96 | C4×D52 | C23 | 1 | 1 | yes | characteristic |
| 97 | C4×D52 | C23 | 1 | 2 | yes | — |
| 98 | #88126 | — | 2 | 1 | no | — |
| 99 | C42×D13 | — | 2 | 1 | no | — |
| 100 | #88123 | — | 2 | 1 | no | — |
| 101 | #88123 | — | 2 | 1 | no | — |
| 102 | #88123 | — | 2 | 1 | no | — |
| 103 | #88123 | D4 | 1 | 1 | yes | characteristic |
| 104 | #88123 | C23 | 1 | 2 | yes | — |
| 105 | C4×Dic26 | D4 | 1 | 1 | yes | characteristic |
| 106 | C4×Dic26 | C23 | 1 | 1 | yes | characteristic |
| 107 | C13×C4⋊C8 | — | 2 | 1 | no | — |
| 108 | C13×C4⋊C8 | C23 | 1 | 2 | yes | — |
| 109 | C13×C4⋊C8 | C23 | 1 | 2 | yes | — |
| 110 | C13×C22⋊C8 | — | 2 | 1 | no | — |
| 111 | C4×C8×C13 | — | 2 | 1 | no | — |
| 112 | #88072 | — | 2 | 8 | no | — |
| 113 | #88061 | — | 2 | 4 | no | — |
| 114 | #88058 | — | 2 | 4 | no | — |
| 115 | #88056 | — | 2 | 2 | no | — |
| 116 | #88056 | — | 2 | 2 | no | — |
| 117 | C4×#1055 | — | 2 | 1 | no | — |
| 118 | C4×#1055 | C23 | 1 | 2 | yes | — |
| 119 | #18630 | — | 13 | 1 | no | maximal, Sylow |
| 120 | C24×C13 | — | 2 | 2 | no | — |
| 121 | C23×D13 | — | 2 | 4 | no | — |
| 122 | C2×D4×C13 | — | 2 | 2 | no | — |
| 123 | C2×D4×C13 | — | 2 | 2 | no | — |
| 124 | C2×D4×C13 | — | 2 | 2 | no | — |
| 125 | C2×D4×C13 | — | 2 | 2 | no | — |
| 126 | C2×D4×C13 | — | 2 | 2 | no | — |
| 127 | C2×D4×C13 | — | 4 | 4 | no | — |
| 128 | C2×D4×C13 | — | 4 | 2 | no | — |
| 129 | C2×D4×C13 | — | 4 | 2 | no | — |
| 130 | C2×D4×C13 | — | 8 | 2 | no | — |
| 131 | C2×D4×C13 | C2×D4 | 1 | 4 | yes | — |
| 132 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 133 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 134 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 135 | C2×C22⋊D13 | — | 2 | 1 | no | — |
| 136 | C2×C22⋊D13 | — | 2 | 4 | no | — |
| 137 | C2×C22⋊D13 | — | 2 | 4 | no | — |
| 138 | C2×C22⋊D13 | — | 2 | 2 | no | — |
| 139 | C2×C22⋊D13 | — | 2 | 4 | no | — |
| 140 | C2×C22⋊D13 | — | 2 | 4 | no | — |
| 141 | C2×C22⋊D13 | — | 4 | 16 | no | — |
| 142 | C22×Dic13 | — | 2 | 4 | no | — |
| 143 | C22×Dic13 | — | 4 | 1 | no | — |
| 144 | #6129 | — | 4 | 4 | no | — |
| 145 | #6129 | — | 4 | 8 | no | — |
| 146 | #6129 | — | 4 | 4 | no | — |
| 147 | D4×D13 | — | 4 | 8 | no | — |
| 148 | D4×D13 | — | 4 | 4 | no | — |
| 149 | D4×D13 | — | 4 | 4 | no | — |
| 150 | D4×D13 | — | 8 | 4 | no | — |
| 151 | D4×D13 | — | 8 | 4 | no | — |
| 152 | #6127 | — | 2 | 2 | no | — |
| 153 | #6127 | — | 4 | 2 | no | — |
| 154 | #6127 | — | 4 | 2 | no | — |
| 155 | #6127 | D8 | 1 | 4 | yes | — |
| 156 | C2×D52 | — | 2 | 1 | no | — |
| 157 | C2×D52 | — | 2 | 1 | no | — |
| 158 | C2×D52 | C2×D4 | 1 | 2 | yes | — |
| 159 | C2×D52 | C2×D4 | 1 | 1 | yes | characteristic |
| 160 | C2×C4×D13 | — | 2 | 1 | no | — |
| 161 | C2×C4×D13 | — | 2 | 1 | no | — |
| 162 | C2×C4×D13 | — | 2 | 1 | no | — |
| 163 | C2×C4×D13 | — | 2 | 2 | no | — |
| 164 | C2×Dic26 | — | 2 | 1 | no | — |
| 165 | C2×Dic26 | — | 2 | 2 | no | — |
| 166 | C2×Dic26 | — | 4 | 2 | no | — |
| 167 | C2×Dic26 | — | 4 | 2 | no | — |
| 168 | C2×Dic26 | — | 4 | 1 | no | — |
| 169 | C2×Dic26 | C2×D4 | 1 | 1 | yes | characteristic |
| 170 | C13×M16 | — | 4 | 2 | no | — |
| 171 | C2×C8×C13 | — | 2 | 2 | no | — |
| 172 | C2×C8×C13 | — | 2 | 2 | no | — |
| 173 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 174 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 175 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 176 | C42×C13 | C24 | 1 | 1 | yes | characteristic |
| 177 | C22⋊Dic13 | — | 2 | 4 | no | — |
| 178 | C22⋊Dic13 | — | 2 | 4 | no | — |
| 179 | C22⋊Dic13 | — | 2 | 1 | no | — |
| 180 | #6103 | — | 2 | 1 | no | — |
| 181 | #6103 | — | 2 | 2 | no | — |
| 182 | #6103 | — | 2 | 1 | no | — |
| 183 | #6103 | — | 2 | 2 | no | — |
| 184 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 185 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 186 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 187 | C4⋊Dic13 | — | 4 | 1 | no | — |
| 188 | C4⋊Dic13 | — | 4 | 1 | no | — |
| 189 | C4⋊Dic13 | C2×D4 | 1 | 1 | yes | characteristic |
| 190 | C4⋊Dic13 | C2×D4 | 1 | 1 | yes | characteristic |
| 191 | C4⋊Dic13 | C2×D4 | 1 | 2 | yes | — |
| 192 | #6101 | — | 2 | 1 | no | — |
| 193 | #6101 | — | 2 | 1 | no | — |
| 194 | C4×Dic13 | — | 2 | 1 | no | — |
| 195 | C4×Dic13 | — | 2 | 1 | no | — |
| 196 | C4×Dic13 | — | 2 | 1 | no | — |
| 197 | C2×#1055 | — | 2 | 2 | no | — |
| 198 | C2×#1055 | — | 4 | 2 | no | — |
| 199 | Dic52 | — | 4 | 4 | no | — |
| 200 | #6095 | — | 4 | 4 | no | — |
| 201 | #3498 | — | 13 | 1 | no | — |
| 202 | #3226 | — | 13 | 1 | no | — |
| 203 | C2×#486 | — | 13 | 1 | no | — |
| 204 | #3039 | — | 13 | 1 | no | — |
| 205 | #1641 | — | 13 | 4 | no | — |
| 206 | #1639 | — | 13 | 4 | no | — |
| 207 | #1545 | D13 | 1 | 1 | yes | characteristic, complemented |
| 208 | #1492 | — | 13 | 1 | no | — |
| 209 | #1476 | — | 13 | 1 | no | — |
| 210 | C23×C13 | — | 2 | 4 | no | — |
| 211 | C23×C13 | — | 4 | 4 | no | — |
| 212 | C23×C13 | — | 8 | 2 | no | — |
| 213 | C23×C13 | — | 8 | 2 | no | — |
| 214 | C23×C13 | #120 | 1 | 1 | yes | characteristic |
| 215 | C22×D13 | — | 2 | 1 | no | — |
| 216 | C22×D13 | — | 2 | 2 | no | — |
| 217 | C22×D13 | — | 4 | 8 | no | — |
| 218 | C22×D13 | — | 8 | 4 | no | — |
| 219 | C22×D13 | — | 8 | 4 | no | — |
| 220 | D4×C13 | — | 4 | 4 | no | — |
| 221 | D4×C13 | — | 4 | 2 | no | — |
| 222 | D4×C13 | — | 4 | 2 | no | — |
| 223 | D4×C13 | — | 4 | 4 | no | — |
| 224 | D4×C13 | — | 4 | 4 | no | — |
| 225 | D4×C13 | — | 4 | 4 | no | — |
| 226 | D4×C13 | — | 8 | 2 | no | — |
| 227 | C2×C4×C13 | — | 2 | 2 | no | — |
| 228 | C2×C4×C13 | — | 2 | 2 | no | — |
| 229 | C2×C4×C13 | #120 | 1 | 1 | yes | characteristic |
| 230 | C2×C4×C13 | #120 | 1 | 1 | yes | characteristic |
| 231 | C2×C4×C13 | #120 | 1 | 1 | yes | characteristic |
| 232 | C2×C4×C13 | C2×D8 | 1 | 2 | yes | — |
| 233 | C2×C4×C13 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 234 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 235 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 236 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 237 | C22⋊D13 | — | 2 | 4 | no | — |
| 238 | C22⋊D13 | — | 4 | 8 | no | — |
| 239 | C22⋊D13 | — | 4 | 8 | no | — |
| 240 | C22⋊D13 | — | 4 | 4 | no | — |
| 241 | C22⋊D13 | — | 8 | 4 | no | — |
| 242 | C22⋊D13 | — | 8 | 4 | no | — |
| 243 | C2×Dic13 | — | 2 | 1 | no | — |
| 244 | C2×Dic13 | — | 2 | 1 | no | — |
| 245 | C2×Dic13 | — | 2 | 1 | no | — |
| 246 | C2×Dic13 | — | 2 | 2 | no | — |
| 247 | C2×Dic13 | — | 4 | 8 | no | — |
| 248 | C2×Dic13 | — | 4 | 2 | no | — |
| 249 | C2×Dic13 | — | 8 | 2 | no | — |
| 250 | D52 | — | 2 | 1 | no | — |
| 251 | D52 | — | 2 | 4 | no | — |
| 252 | D52 | — | 4 | 2 | no | — |
| 253 | D52 | — | 4 | 2 | no | — |
| 254 | D52 | C2×D8 | 1 | 2 | yes | — |
| 255 | C4×D13 | — | 2 | 4 | no | — |
| 256 | C4×D13 | — | 4 | 2 | no | — |
| 257 | C4×D13 | — | 4 | 2 | no | — |
| 258 | C4×D13 | — | 4 | 2 | no | — |
| 259 | C4×D13 | — | 4 | 2 | no | — |
| 260 | Dic26 | — | 2 | 1 | no | — |
| 261 | Dic26 | — | 4 | 2 | no | — |
| 262 | Dic26 | — | 4 | 2 | no | — |
| 263 | Dic26 | — | 4 | 2 | no | — |
| 264 | Dic26 | — | 8 | 2 | no | — |
| 265 | Dic26 | C2×D8 | 1 | 2 | yes | — |
| 266 | C8×C13 | — | 4 | 2 | no | — |
| 267 | C8×C13 | — | 4 | 2 | no | — |
| 268 | #1055 | — | 4 | 2 | no | — |
| 269 | C2×H(5,𝔽2) | — | 26 | 1 | no | — |
| 270 | C2×#137 | — | 26 | 1 | no | — |
| 271 | #550 | — | 13 | 2 | no | — |
| 272 | #550 | — | 26 | 1 | no | — |
| 273 | D42 | — | 13 | 2 | no | — |
| 274 | D42 | — | 26 | 1 | no | — |
| 275 | D42 | — | 26 | 2 | no | — |
| 276 | D42 | — | 26 | 2 | no | — |
| 277 | #535 | — | 26 | 1 | no | — |
| 278 | #535 | — | 26 | 2 | no | — |
| 279 | #532 | — | 13 | 1 | no | — |
| 280 | #532 | — | 26 | 1 | no | — |
| 281 | C2×C4⋊Q8 | — | 13 | 1 | no | — |
| 282 | C2×#127 | — | 26 | 1 | no | — |
| 283 | C2×#127 | C2×D13 | 1 | 1 | yes | characteristic |
| 284 | C4×#41 | — | 13 | 1 | no | — |
| 285 | #500 | — | 26 | 1 | no | — |
| 286 | #486 | — | 13 | 4 | no | — |
| 287 | #486 | — | 26 | 1 | no | — |
| 288 | #486 | — | 26 | 2 | no | — |
| 289 | #480 | — | 26 | 2 | no | — |
| 290 | #474 | — | 13 | 4 | no | — |
| 291 | #462 | — | 13 | 2 | no | — |
| 292 | #462 | — | 26 | 1 | no | — |
| 293 | #461 | — | 13 | 2 | no | — |
| 294 | #461 | — | 26 | 1 | no | — |
| 295 | #431 | C2×D13 | 1 | 1 | yes | characteristic, complemented |
| 296 | #423 | C2×D13 | 1 | 1 | yes | characteristic, complemented |
| 297 | #419 | — | 26 | 1 | no | — |
| 298 | C2×#102 | — | 26 | 2 | no | — |
| 299 | C2×C4×C8 | — | 13 | 1 | no | — |
| 300 | #331 | C2×D13 | 1 | 4 | yes | complemented |
| 301 | Q8⋊C8 | — | 13 | 2 | no | — |
| 302 | D4⋊C8 | — | 13 | 2 | no | — |
| 303 | D4⋊C8 | — | 13 | 4 | no | — |
| 304 | C22×C13 | — | 2 | 1 | no | — |
| 305 | C22×C13 | — | 2 | 1 | no | — |
| 306 | C22×C13 | — | 4 | 4 | no | — |
| 307 | C22×C13 | — | 4 | 4 | no | — |
| 308 | C22×C13 | — | 4 | 4 | no | — |
| 309 | C22×C13 | — | 16 | 4 | no | — |
| 310 | C22×C13 | #447 | 1 | 2 | yes | — |
| 311 | C22×C13 | C2×#120 | 1 | 1 | yes | characteristic |
| 312 | C2×D13 | — | 2 | 2 | no | — |
| 313 | C2×D13 | — | 4 | 1 | no | — |
| 314 | C2×D13 | — | 4 | 1 | no | — |
| 315 | C2×D13 | — | 4 | 2 | no | — |
| 316 | C2×D13 | — | 4 | 2 | no | — |
| 317 | C2×D13 | — | 4 | 2 | no | — |
| 318 | C2×D13 | — | 16 | 8 | no | — |
| 319 | C4×C13 | — | 2 | 1 | no | — |
| 320 | C4×C13 | — | 2 | 1 | no | — |
| 321 | C4×C13 | #447 | 1 | 2 | yes | — |
| 322 | C4×C13 | #455 | 1 | 2 | yes | — |
| 323 | C4×C13 | C22×D8 | 1 | 1 | yes | characteristic |
| 324 | C4×C13 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 325 | C4×C13 | #577 | 1 | 2 | yes | — |
| 326 | Dic13 | — | 2 | 2 | no | — |
| 327 | Dic13 | — | 4 | 2 | no | — |
| 328 | Dic13 | — | 4 | 1 | no | — |
| 329 | Dic13 | — | 4 | 1 | no | — |
| 330 | Dic13 | — | 8 | 2 | no | — |
| 331 | H(5,𝔽2) | — | 52 | 4 | no | — |
| 332 | H(5,𝔽2) | — | 52 | 4 | no | — |
| 333 | C2×#41 | — | 13 | 1 | no | — |
| 334 | C2×#41 | — | 26 | 2 | no | — |
| 335 | C2×#41 | — | 26 | 2 | no | — |
| 336 | C2×#41 | — | 26 | 1 | no | — |
| 337 | C22×Q8 | — | 26 | 1 | no | — |
| 338 | C22×D4 | — | 2 | 1 | no | — |
| 339 | C22×D4 | — | 2 | 1 | no | — |
| 340 | C22×D4 | — | 26 | 2 | no | — |
| 341 | C22×D4 | — | 26 | 2 | no | — |
| 342 | C22×D4 | — | 26 | 2 | no | — |
| 343 | C22×D4 | — | 26 | 2 | no | — |
| 344 | C22×D4 | — | 26 | 4 | no | — |
| 345 | C22×D4 | D52 | 1 | 2 | yes | — |
| 346 | #137 | — | 52 | 4 | no | — |
| 347 | C2×Q16 | — | 26 | 2 | no | — |
| 348 | C2×SD16 | — | 26 | 2 | no | — |
| 349 | C2×M16 | — | 2 | 1 | no | — |
| 350 | C22×C8 | — | 26 | 1 | no | — |
| 351 | C4⋊Q8 | — | 13 | 1 | no | — |
| 352 | C4⋊Q8 | — | 13 | 2 | no | — |
| 353 | C4⋊Q8 | — | 26 | 1 | no | — |
| 354 | C4⋊Q8 | — | 26 | 1 | no | — |
| 355 | C4⋊Q8 | — | 26 | 1 | no | — |
| 356 | #127 | — | 2 | 1 | no | — |
| 357 | #127 | — | 2 | 1 | no | — |
| 358 | #127 | — | 13 | 1 | no | — |
| 359 | #127 | — | 26 | 2 | no | — |
| 360 | #127 | — | 26 | 2 | no | — |
| 361 | #127 | — | 26 | 2 | no | — |
| 362 | #127 | D52 | 1 | 2 | yes | — |
| 363 | #127 | C22×D13 | 1 | 2 | yes | — |
| 364 | #124 | — | 26 | 2 | no | — |
| 365 | #124 | — | 26 | 1 | no | — |
| 366 | #121 | — | 13 | 2 | no | — |
| 367 | #121 | — | 26 | 2 | no | — |
| 368 | #121 | — | 26 | 2 | no | — |
| 369 | #121 | — | 26 | 2 | no | — |
| 370 | #121 | — | 26 | 2 | no | — |
| 371 | #121 | — | 26 | 4 | no | — |
| 372 | #121 | — | 26 | 4 | no | — |
| 373 | #121 | — | 26 | 1 | no | — |
| 374 | #120 | — | 26 | 4 | no | — |
| 375 | #120 | — | 26 | 4 | no | — |
| 376 | #120 | — | 26 | 4 | no | — |
| 377 | C4×Q8 | — | 13 | 1 | no | — |
| 378 | C4×Q8 | — | 13 | 1 | no | — |
| 379 | C4×D4 | — | 13 | 1 | no | — |
| 380 | C4×D4 | — | 13 | 1 | no | — |
| 381 | C4×D4 | — | 13 | 2 | no | — |
| 382 | C4×D4 | — | 26 | 2 | no | — |
| 383 | C4×D4 | — | 26 | 2 | no | — |
| 384 | C4×D4 | — | 26 | 1 | no | — |
| 385 | C4×D4 | — | 26 | 1 | no | — |
| 386 | C4×D4 | — | 26 | 1 | no | — |
| 387 | #117 | — | 13 | 1 | no | — |
| 388 | #117 | — | 26 | 1 | no | — |
| 389 | C2×C4⋊C4 | — | 26 | 1 | no | — |
| 390 | C2×C4⋊C4 | — | 26 | 1 | no | — |
| 391 | C2×C42 | — | 26 | 1 | no | — |
| 392 | C2×C42 | C22×D13 | 1 | 1 | yes | characteristic |
| 393 | #107 | — | 26 | 4 | no | — |
| 394 | C4⋊C8 | — | 2 | 1 | no | — |
| 395 | C4⋊C8 | C22×D13 | 1 | 2 | yes | — |
| 396 | C4⋊C8 | C22×D13 | 1 | 2 | yes | — |
| 397 | #103 | — | 26 | 2 | no | — |
| 398 | #103 | — | 26 | 2 | no | — |
| 399 | #102 | — | 26 | 4 | no | — |
| 400 | #102 | — | 26 | 8 | no | — |
| 401 | C22⋊C8 | — | 2 | 1 | no | — |
| 402 | C4×C8 | — | 2 | 1 | no | — |
| 403 | C4×C8 | — | 13 | 2 | no | — |
| 404 | C4×C8 | — | 26 | 1 | no | — |
| 405 | C2×C13 | — | 2 | 2 | no | — |
| 406 | C2×C13 | — | 8 | 4 | no | — |
| 407 | C2×C13 | C2×#447 | 1 | 1 | yes | characteristic |
| 408 | C2×C13 | #3009 | 1 | 1 | yes | characteristic |
| 409 | C2×C13 | C2×#455 | 1 | 1 | yes | characteristic |
| 410 | D13 | — | 4 | 2 | no | — |
| 411 | D13 | — | 8 | 2 | no | — |
| 412 | C24 | — | 2 | 2 | no | — |
| 413 | C24 | — | 26 | 4 | no | — |
| 414 | #41 | — | 13 | 4 | no | — |
| 415 | #41 | — | 26 | 2 | no | — |
| 416 | #41 | — | 52 | 8 | no | — |
| 417 | #41 | — | 52 | 4 | no | — |
| 418 | #41 | — | 52 | 4 | no | — |
| 419 | #41 | — | 52 | 2 | no | — |
| 420 | #41 | — | 52 | 2 | no | — |
| 421 | C2×Q8 | — | 13 | 1 | no | — |
| 422 | C2×Q8 | — | 26 | 1 | no | — |
| 423 | C2×Q8 | — | 26 | 2 | no | — |
| 424 | C2×Q8 | — | 52 | 1 | no | — |
| 425 | C2×Q8 | — | 52 | 2 | no | — |
| 426 | C2×Q8 | — | 52 | 2 | no | — |
| 427 | C2×D4 | — | 2 | 2 | no | — |
| 428 | C2×D4 | — | 2 | 2 | no | — |
| 429 | C2×D4 | — | 2 | 2 | no | — |
| 430 | C2×D4 | — | 2 | 2 | no | — |
| 431 | C2×D4 | — | 2 | 2 | no | — |
| 432 | C2×D4 | — | 4 | 4 | no | — |
| 433 | C2×D4 | — | 4 | 2 | no | — |
| 434 | C2×D4 | — | 4 | 2 | no | — |
| 435 | C2×D4 | — | 8 | 2 | no | — |
| 436 | C2×D4 | — | 13 | 1 | no | — |
| 437 | C2×D4 | — | 13 | 2 | no | — |
| 438 | C2×D4 | — | 26 | 1 | no | — |
| 439 | C2×D4 | — | 26 | 4 | no | — |
| 440 | C2×D4 | — | 26 | 4 | no | — |
| 441 | C2×D4 | — | 26 | 2 | no | — |
| 442 | C2×D4 | — | 26 | 4 | no | — |
| 443 | C2×D4 | — | 26 | 4 | no | — |
| 444 | C2×D4 | — | 26 | 1 | no | — |
| 445 | C2×D4 | — | 26 | 1 | no | — |
| 446 | C2×D4 | — | 52 | 8 | no | — |
| 447 | C2×D4 | — | 52 | 4 | no | — |
| 448 | C2×D4 | — | 52 | 4 | no | — |
| 449 | C2×D4 | — | 52 | 16 | no | — |
| 450 | C2×D4 | — | 104 | 4 | no | — |
| 451 | C2×D4 | — | 104 | 4 | no | — |
| 452 | C2×D4 | C2×D52 | 1 | 4 | yes | — |
| 453 | C22×C4 | — | 26 | 1 | no | — |
| 454 | C22×C4 | — | 26 | 4 | no | — |
| 455 | C22×C4 | — | 26 | 1 | no | — |
| 456 | C22×C4 | — | 26 | 1 | no | — |
| 457 | C22×C4 | — | 26 | 2 | no | — |
| 458 | C22×C4 | — | 52 | 1 | no | — |
| 459 | C22×C4 | C2×D52 | 1 | 1 | yes | characteristic |
| 460 | C22×C4 | D4×D13 | 1 | 1 | yes | characteristic |
| 461 | C22×C4 | D4×D13 | 1 | 1 | yes | characteristic |
| 462 | Q16 | — | 52 | 4 | no | — |
| 463 | SD16 | — | 52 | 4 | no | — |
| 464 | M16 | — | 4 | 2 | no | — |
| 465 | C2×C8 | — | 2 | 2 | no | — |
| 466 | C2×C8 | — | 2 | 2 | no | — |
| 467 | C2×C8 | — | 26 | 2 | no | — |
| 468 | C2×C8 | — | 52 | 2 | no | — |
| 469 | C4⋊C4 | — | 13 | 1 | no | — |
| 470 | C4⋊C4 | — | 13 | 1 | no | — |
| 471 | C4⋊C4 | — | 13 | 2 | no | — |
| 472 | C4⋊C4 | — | 26 | 1 | no | — |
| 473 | C4⋊C4 | — | 26 | 1 | no | — |
| 474 | C4⋊C4 | — | 26 | 1 | no | — |
| 475 | C4⋊C4 | — | 26 | 2 | no | — |
| 476 | C4⋊C4 | — | 26 | 2 | no | — |
| 477 | C4⋊C4 | — | 52 | 1 | no | — |
| 478 | C4⋊C4 | — | 52 | 1 | no | — |
| 479 | C22⋊C4 | — | 26 | 4 | no | — |
| 480 | C22⋊C4 | — | 26 | 4 | no | — |
| 481 | C22⋊C4 | — | 26 | 1 | no | — |
| 482 | C22⋊C4 | — | 26 | 1 | no | — |
| 483 | C22⋊C4 | — | 26 | 2 | no | — |
| 484 | C22⋊C4 | — | 26 | 1 | no | — |
| 485 | C22⋊C4 | — | 26 | 2 | no | — |
| 486 | C42 | — | 26 | 1 | no | — |
| 487 | C42 | — | 26 | 1 | no | — |
| 488 | C42 | — | 26 | 1 | no | — |
| 489 | C42 | C2×D52 | 1 | 1 | yes | characteristic |
| 490 | C42 | D4×D13 | 1 | 1 | yes | characteristic |
| 491 | C42 | D4×D13 | 1 | 1 | yes | characteristic |
| 492 | C42 | C23×D13 | 1 | 1 | yes | characteristic |
| 493 | C13 | #18630 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 494 | C23 | — | 2 | 4 | no | — |
| 495 | C23 | — | 4 | 4 | no | — |
| 496 | C23 | — | 8 | 2 | no | — |
| 497 | C23 | — | 8 | 2 | no | — |
| 498 | C23 | — | 26 | 1 | no | — |
| 499 | C23 | — | 26 | 2 | no | — |
| 500 | C23 | — | 52 | 8 | no | — |
| 501 | C23 | — | 104 | 4 | no | — |
| 502 | C23 | — | 104 | 4 | no | — |
| 503 | C23 | #88136 | 1 | 1 | yes | characteristic |
| 504 | Q8 | — | 13 | 2 | no | — |
| 505 | Q8 | — | 26 | 1 | no | — |
| 506 | Q8 | — | 52 | 2 | no | — |
| 507 | Q8 | — | 52 | 2 | no | — |
| 508 | Q8 | — | 52 | 2 | no | — |
| 509 | Q8 | — | 104 | 2 | no | — |
| 510 | D4 | — | 4 | 4 | no | — |
| 511 | D4 | — | 4 | 4 | no | — |
| 512 | D4 | — | 4 | 4 | no | — |
| 513 | D4 | — | 4 | 2 | no | — |
| 514 | D4 | — | 4 | 2 | no | — |
| 515 | D4 | — | 4 | 4 | no | — |
| 516 | D4 | — | 8 | 2 | no | — |
| 517 | D4 | — | 13 | 2 | no | — |
| 518 | D4 | — | 26 | 4 | no | — |
| 519 | D4 | — | 26 | 1 | no | — |
| 520 | D4 | — | 26 | 4 | no | — |
| 521 | D4 | — | 52 | 8 | no | — |
| 522 | D4 | — | 52 | 8 | no | — |
| 523 | D4 | — | 52 | 4 | no | — |
| 524 | D4 | — | 52 | 2 | no | — |
| 525 | D4 | — | 52 | 2 | no | — |
| 526 | D4 | — | 104 | 4 | no | — |
| 527 | D4 | — | 104 | 4 | no | — |
| 528 | C2×C4 | — | 2 | 2 | no | — |
| 529 | C2×C4 | — | 2 | 2 | no | — |
| 530 | C2×C4 | — | 26 | 1 | no | — |
| 531 | C2×C4 | — | 26 | 4 | no | — |
| 532 | C2×C4 | — | 26 | 1 | no | — |
| 533 | C2×C4 | — | 26 | 1 | no | — |
| 534 | C2×C4 | — | 26 | 2 | no | — |
| 535 | C2×C4 | — | 52 | 8 | no | — |
| 536 | C2×C4 | — | 52 | 2 | no | — |
| 537 | C2×C4 | — | 52 | 2 | no | — |
| 538 | C2×C4 | — | 52 | 2 | no | — |
| 539 | C2×C4 | — | 52 | 2 | no | — |
| 540 | C2×C4 | — | 52 | 2 | no | — |
| 541 | C2×C4 | — | 104 | 2 | no | — |
| 542 | C2×C4 | #88136 | 1 | 1 | yes | characteristic |
| 543 | C2×C4 | #88136 | 1 | 1 | yes | characteristic |
| 544 | C2×C4 | #88136 | 1 | 1 | yes | characteristic |
| 545 | C2×C4 | D8×D13 | 1 | 2 | yes | — |
| 546 | C2×C4 | #88168 | 1 | 2 | yes | — |
| 547 | C2×C4 | C22×D52 | 1 | 1 | yes | characteristic |
| 548 | C2×C4 | C2×D4×D13 | 1 | 1 | yes | characteristic |
| 549 | C2×C4 | C2×D4×D13 | 1 | 1 | yes | characteristic |
| 550 | C8 | — | 4 | 2 | no | — |
| 551 | C8 | — | 4 | 2 | no | — |
| 552 | C8 | — | 52 | 2 | no | — |
| 553 | C22 | — | 2 | 1 | no | — |
| 554 | C22 | — | 2 | 1 | no | — |
| 555 | C22 | — | 4 | 4 | no | — |
| 556 | C22 | — | 4 | 4 | no | — |
| 557 | C22 | — | 4 | 4 | no | — |
| 558 | C22 | — | 16 | 4 | no | — |
| 559 | C22 | — | 26 | 2 | no | — |
| 560 | C22 | — | 52 | 1 | no | — |
| 561 | C22 | — | 52 | 1 | no | — |
| 562 | C22 | — | 52 | 2 | no | — |
| 563 | C22 | — | 52 | 2 | no | — |
| 564 | C22 | — | 52 | 2 | no | — |
| 565 | C22 | — | 208 | 8 | no | — |
| 566 | C22 | #11718434 | 1 | 2 | yes | — |
| 567 | C22 | C2×#88136 | 1 | 1 | yes | characteristic |
| 568 | C4 | — | 2 | 1 | no | — |
| 569 | C4 | — | 2 | 1 | no | — |
| 570 | C4 | — | 26 | 2 | no | — |
| 571 | C4 | — | 52 | 1 | no | — |
| 572 | C4 | — | 52 | 1 | no | — |
| 573 | C4 | — | 52 | 2 | no | — |
| 574 | C4 | — | 104 | 2 | no | — |
| 575 | C4 | #11718407 | 1 | 2 | yes | — |
| 576 | C4 | #11718434 | 1 | 2 | yes | — |
| 577 | C4 | C2×D8×D13 | 1 | 1 | yes | characteristic |
| 578 | C4 | C2×#88168 | 1 | 1 | yes | characteristic |
| 579 | C4 | #11719480 | 1 | 2 | yes | — |
| 580 | C2 | — | 2 | 2 | no | — |
| 581 | C2 | — | 8 | 4 | no | — |
| 582 | C2 | — | 52 | 2 | no | — |
| 583 | C2 | — | 104 | 2 | no | — |
| 584 | C2 | C2×#11718434 | 1 | 1 | yes | characteristic |
| 585 | C2 | #13124114 | 1 | 1 | yes | characteristic |
| 586 | C2 | C2×#11718407 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #13125959 | C2 | semidirect |
| 3. C2×#11718731 | C2 | semidirect |
| 4. #13124324 | C2 | semidirect |
| 5. #13114030 | C2 | semidirect |
| 6. #13114016 | C2 | semidirect |
| 7. #13113286 | C2 | semidirect |
| 8. #13113216 | C2 | semidirect |
| 9. C13×#1545 | C2 | semidirect |
| 25. C2×#88123 | C22 | semidirect |
| 26. C13×#431 | C22 | semidirect |
| 27. C13×#423 | C22 | semidirect |
| 31. #11718731 | C22 | semidirect |
| 32. C2×C4×#1055 | C22 | semidirect |
| 34. #11718510 | C22 | semidirect |
| 35. #11718507 | C22 | semidirect |
| 37. #11718502 | C22 | semidirect |
| 41. C13×#331 | C22 | semidirect |
| 42. #11718076 | C22 | semidirect |
| 43. #11718075 | C22 | semidirect |
| 44. #11718075 | C22 | semidirect |
| 207. #1545 | D13 | semidirect |
| 295. #431 | C2×D13 | semidirect |
| 296. #423 | C2×D13 | semidirect |
| 300. #331 | C2×D13 | semidirect |
| 493. C13 | #18630 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13128612 | 2 |
| #13125959 | 2 |
| C2×#11718731 | 2 |
| #13124324 | 2 |
| #13114030 | 2 |
| #13114016 | 2 |
| #13113286 | 2 |
| #13113216 | 2 |
| C13×#1545 | 2 |
| #18630 | 13 |