Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1270 conjugacy classes of subgroups.
The subgroup lattice has 646 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#11719471 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13124557 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #13124487 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13124203 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #13123740 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13116115 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #13115898 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #13115734 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #13114891 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #13114808 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | C13×#1979 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#88254 | C22 | 1 | 2 | yes | — |
| 13 | C22×C13×Q16 | C22 | 1 | 1 | yes | characteristic |
| 14 | #11719521 | C22 | 1 | 2 | yes | — |
| 15 | C2×#88196 | C22 | 1 | 2 | yes | — |
| 16 | #11719471 | — | 2 | 2 | no | — |
| 17 | #11719471 | — | 2 | 2 | no | — |
| 18 | #11719471 | — | 2 | 2 | no | — |
| 19 | #11719471 | — | 2 | 2 | no | — |
| 20 | C2×#88173 | — | 2 | 1 | no | — |
| 21 | C2×#88172 | — | 2 | 2 | no | — |
| 22 | C2×Q16×D13 | — | 2 | 1 | no | — |
| 23 | #11719453 | C22 | 1 | 1 | yes | characteristic |
| 24 | #11719453 | C22 | 1 | 2 | yes | — |
| 25 | C2×#88158 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×#88155 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×#88155 | C22 | 1 | 1 | yes | characteristic |
| 28 | C2×C13×#108 | C22 | 1 | 1 | yes | characteristic |
| 29 | C13×#419 | C22 | 1 | 2 | yes | — |
| 30 | C2×C13×#101 | C22 | 1 | 2 | yes | — |
| 31 | C13×#405 | C22 | 1 | 1 | yes | characteristic |
| 32 | #11718886 | C22 | 1 | 2 | yes | — |
| 33 | #11718850 | — | 2 | 2 | no | — |
| 34 | #11718849 | — | 2 | 2 | no | — |
| 35 | #11718800 | C22 | 1 | 2 | yes | — |
| 36 | #11718800 | C22 | 1 | 2 | yes | — |
| 37 | #11718793 | C22 | 1 | 2 | yes | — |
| 38 | #11718786 | C22 | 1 | 1 | yes | characteristic |
| 39 | #11718767 | C22 | 1 | 1 | yes | characteristic |
| 40 | #11718667 | C22 | 1 | 2 | yes | — |
| 41 | #11718666 | C22 | 1 | 1 | yes | characteristic |
| 42 | #11718666 | C22 | 1 | 1 | yes | characteristic |
| 43 | #11718559 | — | 2 | 2 | no | — |
| 44 | #11718558 | — | 2 | 1 | no | — |
| 45 | #11718557 | — | 2 | 1 | no | — |
| 46 | #11718414 | — | 2 | 4 | no | — |
| 47 | #11718413 | — | 2 | 4 | no | — |
| 48 | #11718378 | — | 2 | 2 | no | — |
| 49 | #11718361 | — | 2 | 2 | no | — |
| 50 | #11718148 | C22 | 1 | 2 | yes | — |
| 51 | C22×Q8×C13 | C23 | 1 | 2 | yes | — |
| 52 | #88254 | — | 2 | 4 | no | — |
| 53 | #88254 | — | 2 | 4 | no | — |
| 54 | #88254 | — | 2 | 4 | no | — |
| 55 | #88254 | — | 4 | 2 | no | — |
| 56 | C2×#6131 | — | 2 | 2 | no | — |
| 57 | C2×#6131 | — | 2 | 2 | no | — |
| 58 | C2×Q8×D13 | — | 2 | 2 | no | — |
| 59 | C2×Q8×D13 | — | 2 | 2 | no | — |
| 60 | C2×#6127 | — | 4 | 2 | no | — |
| 61 | C2×#6127 | C23 | 1 | 1 | yes | characteristic |
| 62 | C2×#6127 | C23 | 1 | 2 | yes | — |
| 63 | C2×#6127 | C23 | 1 | 1 | yes | characteristic |
| 64 | C2×C13×Q16 | — | 2 | 1 | no | — |
| 65 | C2×C13×Q16 | — | 2 | 1 | no | — |
| 66 | C2×C13×Q16 | — | 2 | 1 | no | — |
| 67 | C2×C13×Q16 | — | 2 | 1 | no | — |
| 68 | C2×C13×Q16 | D4 | 1 | 2 | yes | — |
| 69 | C2×C13×Q16 | D4 | 1 | 2 | yes | — |
| 70 | C2×C13×M16 | C23 | 1 | 2 | yes | — |
| 71 | C2×C13×M16 | C23 | 1 | 1 | yes | characteristic |
| 72 | C22×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 73 | C13×#117 | C23 | 1 | 1 | yes | characteristic |
| 74 | #88201 | — | 2 | 2 | no | — |
| 75 | #88200 | — | 2 | 4 | no | — |
| 76 | #88198 | — | 2 | 2 | no | — |
| 77 | C2×#6107 | — | 2 | 2 | no | — |
| 78 | #88196 | — | 2 | 4 | no | — |
| 79 | #88196 | — | 2 | 4 | no | — |
| 80 | C2×#6106 | — | 2 | 2 | no | — |
| 81 | #88183 | — | 4 | 2 | no | — |
| 82 | #88180 | C23 | 1 | 2 | yes | — |
| 83 | C2×#6099 | C23 | 1 | 1 | yes | characteristic |
| 84 | C2×#6099 | C23 | 1 | 1 | yes | characteristic |
| 85 | #88173 | — | 2 | 4 | no | — |
| 86 | #88173 | — | 2 | 4 | no | — |
| 87 | #88172 | — | 2 | 8 | no | — |
| 88 | #88172 | — | 2 | 8 | no | — |
| 89 | Q16×D13 | — | 2 | 4 | no | — |
| 90 | Q16×D13 | — | 2 | 4 | no | — |
| 91 | #88163 | — | 2 | 1 | no | — |
| 92 | #88163 | — | 2 | 2 | no | — |
| 93 | #88163 | — | 2 | 2 | no | — |
| 94 | #88163 | D4 | 1 | 2 | yes | — |
| 95 | #88162 | — | 2 | 1 | no | — |
| 96 | #88162 | — | 2 | 2 | no | — |
| 97 | #88162 | — | 2 | 2 | no | — |
| 98 | #88162 | D4 | 1 | 2 | yes | — |
| 99 | C2×Dic52 | D4 | 1 | 1 | yes | characteristic |
| 100 | #88158 | — | 2 | 2 | no | — |
| 101 | #88158 | — | 2 | 1 | no | — |
| 102 | #88158 | — | 2 | 1 | no | — |
| 103 | #88158 | — | 2 | 1 | no | — |
| 104 | #88158 | — | 2 | 1 | no | — |
| 105 | #88158 | — | 4 | 2 | no | — |
| 106 | C2×D104 | D4 | 1 | 1 | yes | characteristic |
| 107 | C2×#6095 | D4 | 1 | 2 | yes | — |
| 108 | #88155 | — | 2 | 1 | no | — |
| 109 | #88155 | — | 2 | 1 | no | — |
| 110 | #88155 | — | 2 | 1 | no | — |
| 111 | #88155 | — | 2 | 1 | no | — |
| 112 | #88155 | — | 2 | 1 | no | — |
| 113 | #88155 | — | 2 | 1 | no | — |
| 114 | #88155 | D4 | 1 | 2 | yes | — |
| 115 | #88155 | D4 | 1 | 2 | yes | — |
| 116 | C2×#6094 | — | 2 | 1 | no | — |
| 117 | C2×#6094 | — | 2 | 1 | no | — |
| 118 | C2×C8×D13 | — | 2 | 1 | no | — |
| 119 | C2×C8×D13 | — | 2 | 1 | no | — |
| 120 | C13×#108 | — | 2 | 1 | no | — |
| 121 | C13×#108 | — | 2 | 1 | no | — |
| 122 | C13×#103 | — | 4 | 2 | no | — |
| 123 | C13×#101 | — | 2 | 4 | no | — |
| 124 | C13×#97 | — | 2 | 1 | no | — |
| 125 | C4×C8×C13 | — | 2 | 1 | no | — |
| 126 | #88075 | — | 2 | 4 | no | — |
| 127 | #88065 | — | 2 | 4 | no | — |
| 128 | #88065 | — | 2 | 4 | no | — |
| 129 | #88064 | — | 2 | 2 | no | — |
| 130 | #88063 | — | 2 | 2 | no | — |
| 131 | #88059 | — | 2 | 2 | no | — |
| 132 | #88058 | — | 2 | 1 | no | — |
| 133 | #88057 | — | 2 | 1 | no | — |
| 134 | #88046 | — | 4 | 2 | no | — |
| 135 | #88045 | — | 2 | 2 | no | — |
| 136 | #88045 | — | 2 | 2 | no | — |
| 137 | #24296 | — | 13 | 1 | no | maximal, Sylow |
| 138 | C2×Q8×C13 | — | 2 | 2 | no | — |
| 139 | C2×Q8×C13 | — | 2 | 2 | no | — |
| 140 | C2×Q8×C13 | — | 2 | 2 | no | — |
| 141 | C2×Q8×C13 | — | 2 | 2 | no | — |
| 142 | C2×Q8×C13 | — | 2 | 2 | no | — |
| 143 | C2×Q8×C13 | C2×D4 | 1 | 4 | yes | — |
| 144 | C22×C4×C13 | — | 2 | 2 | no | — |
| 145 | C22×C4×C13 | C24 | 1 | 1 | yes | characteristic |
| 146 | C2×C22⋊D13 | — | 2 | 1 | no | — |
| 147 | C2×C22⋊D13 | — | 2 | 1 | no | — |
| 148 | C2×C22⋊D13 | — | 2 | 2 | no | — |
| 149 | #6131 | — | 2 | 8 | no | — |
| 150 | #6131 | — | 4 | 4 | no | — |
| 151 | #6131 | — | 4 | 4 | no | — |
| 152 | #6131 | — | 4 | 4 | no | — |
| 153 | Q8×D13 | — | 2 | 8 | no | — |
| 154 | Q8×D13 | — | 4 | 4 | no | — |
| 155 | Q8×D13 | — | 4 | 4 | no | — |
| 156 | Q8×D13 | — | 4 | 4 | no | — |
| 157 | #6127 | — | 2 | 1 | no | — |
| 158 | #6127 | — | 2 | 1 | no | — |
| 159 | #6127 | — | 2 | 2 | no | — |
| 160 | #6127 | — | 2 | 1 | no | — |
| 161 | #6127 | — | 2 | 1 | no | — |
| 162 | #6127 | — | 2 | 2 | no | — |
| 163 | #6127 | — | 2 | 2 | no | — |
| 164 | #6127 | — | 2 | 1 | no | — |
| 165 | #6127 | — | 2 | 1 | no | — |
| 166 | #6127 | — | 2 | 2 | no | — |
| 167 | #6127 | — | 4 | 8 | no | — |
| 168 | #6127 | — | 4 | 8 | no | — |
| 169 | #6127 | C2×D4 | 1 | 2 | yes | — |
| 170 | #6127 | C2×D4 | 1 | 2 | yes | — |
| 171 | C2×D52 | — | 4 | 2 | no | — |
| 172 | C2×D52 | C2×D4 | 1 | 2 | yes | — |
| 173 | C2×D52 | C2×D4 | 1 | 1 | yes | characteristic |
| 174 | C2×D52 | #41 | 1 | 1 | yes | characteristic |
| 175 | C2×C4×D13 | — | 2 | 1 | no | — |
| 176 | C2×C4×D13 | — | 2 | 1 | no | — |
| 177 | C2×C4×D13 | — | 2 | 2 | no | — |
| 178 | C2×C4×D13 | — | 4 | 2 | no | — |
| 179 | C2×C4×D13 | — | 4 | 2 | no | — |
| 180 | C2×Dic26 | — | 4 | 2 | no | — |
| 181 | C2×Dic26 | C2×D4 | 1 | 2 | yes | — |
| 182 | C2×Dic26 | C2×D4 | 1 | 1 | yes | characteristic |
| 183 | C2×Dic26 | #41 | 1 | 1 | yes | characteristic |
| 184 | C13×Q16 | — | 2 | 2 | no | — |
| 185 | C13×Q16 | — | 2 | 2 | no | — |
| 186 | C13×Q16 | — | 2 | 2 | no | — |
| 187 | C13×Q16 | — | 2 | 2 | no | — |
| 188 | C13×M16 | — | 2 | 1 | no | — |
| 189 | C13×M16 | — | 2 | 2 | no | — |
| 190 | C13×M16 | — | 2 | 2 | no | — |
| 191 | C13×M16 | C2×D4 | 1 | 2 | yes | — |
| 192 | C2×C8×C13 | — | 2 | 1 | no | — |
| 193 | C2×C8×C13 | — | 2 | 2 | no | — |
| 194 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 195 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 196 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 197 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 198 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 199 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 200 | C13×C4⋊C4 | — | 2 | 1 | no | — |
| 201 | C13×C22⋊C4 | — | 2 | 1 | no | — |
| 202 | C42×C13 | — | 2 | 1 | no | — |
| 203 | C22⋊Dic13 | — | 2 | 2 | no | — |
| 204 | #6107 | — | 2 | 8 | no | — |
| 205 | #6106 | — | 2 | 8 | no | — |
| 206 | #6103 | — | 4 | 4 | no | — |
| 207 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 208 | #6101 | — | 4 | 4 | no | — |
| 209 | C4×Dic13 | — | 2 | 2 | no | — |
| 210 | #6099 | — | 2 | 1 | no | — |
| 211 | #6099 | — | 2 | 1 | no | — |
| 212 | #6099 | — | 2 | 1 | no | — |
| 213 | #6099 | C2×D4 | 1 | 2 | yes | — |
| 214 | C2×#1055 | — | 2 | 1 | no | — |
| 215 | C2×#1055 | — | 2 | 1 | no | — |
| 216 | Dic52 | — | 2 | 2 | no | — |
| 217 | Dic52 | — | 2 | 1 | no | — |
| 218 | Dic52 | — | 2 | 1 | no | — |
| 219 | Dic52 | — | 4 | 2 | no | — |
| 220 | D104 | — | 2 | 2 | no | — |
| 221 | D104 | — | 2 | 1 | no | — |
| 222 | D104 | — | 2 | 1 | no | — |
| 223 | D104 | — | 4 | 2 | no | — |
| 224 | #6095 | — | 2 | 2 | no | — |
| 225 | #6095 | — | 2 | 2 | no | — |
| 226 | #6095 | — | 2 | 2 | no | — |
| 227 | #6095 | — | 2 | 2 | no | — |
| 228 | #6095 | — | 4 | 2 | no | — |
| 229 | #6095 | — | 4 | 2 | no | — |
| 230 | #6094 | — | 2 | 2 | no | — |
| 231 | #6094 | — | 2 | 2 | no | — |
| 232 | #6094 | — | 4 | 1 | no | — |
| 233 | #6094 | — | 4 | 1 | no | — |
| 234 | C8×D13 | — | 2 | 2 | no | — |
| 235 | C8×D13 | — | 2 | 2 | no | — |
| 236 | C8×D13 | — | 4 | 1 | no | — |
| 237 | C8×D13 | — | 4 | 1 | no | — |
| 238 | C2×#578 | — | 13 | 1 | no | — |
| 239 | #3067 | — | 13 | 1 | no | — |
| 240 | #3059 | — | 13 | 1 | no | — |
| 241 | #3020 | — | 13 | 2 | no | — |
| 242 | #2955 | — | 13 | 1 | no | — |
| 243 | #2049 | — | 13 | 2 | no | — |
| 244 | #2009 | — | 13 | 2 | no | — |
| 245 | #1979 | D13 | 1 | 1 | yes | characteristic, complemented |
| 246 | #1976 | — | 13 | 1 | no | — |
| 247 | #1814 | — | 13 | 1 | no | — |
| 248 | #1796 | — | 13 | 2 | no | — |
| 249 | C23×C13 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 250 | C22×D13 | — | 2 | 1 | no | — |
| 251 | C22×D13 | — | 2 | 1 | no | — |
| 252 | C22×D13 | — | 2 | 2 | no | — |
| 253 | Q8×C13 | — | 2 | 4 | no | — |
| 254 | Q8×C13 | — | 2 | 4 | no | — |
| 255 | Q8×C13 | — | 4 | 2 | no | — |
| 256 | Q8×C13 | — | 4 | 2 | no | — |
| 257 | C2×C4×C13 | — | 2 | 4 | no | — |
| 258 | C2×C4×C13 | — | 4 | 2 | no | — |
| 259 | C2×C4×C13 | — | 4 | 2 | no | — |
| 260 | C2×C4×C13 | — | 4 | 1 | no | — |
| 261 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 262 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 263 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 264 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 265 | C2×C4×C13 | C2×#41 | 1 | 1 | yes | characteristic |
| 266 | C2×C4×C13 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 267 | C22⋊D13 | — | 2 | 2 | no | — |
| 268 | C22⋊D13 | — | 2 | 2 | no | — |
| 269 | C22⋊D13 | — | 4 | 2 | no | — |
| 270 | C22⋊D13 | — | 4 | 1 | no | — |
| 271 | C22⋊D13 | — | 4 | 2 | no | — |
| 272 | C22⋊D13 | — | 4 | 1 | no | — |
| 273 | C2×Dic13 | — | 2 | 1 | no | — |
| 274 | C2×Dic13 | — | 2 | 1 | no | — |
| 275 | C2×Dic13 | — | 2 | 2 | no | — |
| 276 | C2×Dic13 | — | 4 | 2 | no | — |
| 277 | D52 | — | 2 | 2 | no | — |
| 278 | D52 | — | 2 | 1 | no | — |
| 279 | D52 | — | 2 | 1 | no | — |
| 280 | D52 | — | 2 | 2 | no | — |
| 281 | D52 | — | 2 | 1 | no | — |
| 282 | D52 | — | 4 | 8 | no | — |
| 283 | D52 | #121 | 1 | 2 | yes | — |
| 284 | C4×D13 | — | 2 | 2 | no | — |
| 285 | C4×D13 | — | 2 | 2 | no | — |
| 286 | C4×D13 | — | 4 | 8 | no | — |
| 287 | C4×D13 | — | 4 | 8 | no | — |
| 288 | C4×D13 | — | 4 | 1 | no | — |
| 289 | C4×D13 | — | 4 | 2 | no | — |
| 290 | C4×D13 | — | 4 | 1 | no | — |
| 291 | C4×D13 | — | 4 | 2 | no | — |
| 292 | Dic26 | — | 2 | 1 | no | — |
| 293 | Dic26 | — | 2 | 2 | no | — |
| 294 | Dic26 | — | 2 | 1 | no | — |
| 295 | Dic26 | — | 2 | 1 | no | — |
| 296 | Dic26 | — | 2 | 2 | no | — |
| 297 | Dic26 | — | 4 | 8 | no | — |
| 298 | Dic26 | #121 | 1 | 2 | yes | — |
| 299 | C8×C13 | — | 2 | 2 | no | — |
| 300 | C8×C13 | — | 4 | 2 | no | — |
| 301 | C8×C13 | #120 | 1 | 1 | yes | characteristic |
| 302 | C8×C13 | #120 | 1 | 1 | yes | characteristic |
| 303 | C8×C13 | #120 | 1 | 1 | yes | characteristic |
| 304 | C8×C13 | #120 | 1 | 1 | yes | characteristic |
| 305 | #1055 | — | 2 | 2 | no | — |
| 306 | #1055 | — | 4 | 1 | no | — |
| 307 | C2×2−1+4 | — | 13 | 2 | no | — |
| 308 | #578 | — | 26 | 2 | no | — |
| 309 | #578 | — | 26 | 2 | no | — |
| 310 | #578 | — | 26 | 2 | no | — |
| 311 | #578 | — | 26 | 2 | no | — |
| 312 | #575 | — | 13 | 1 | no | — |
| 313 | #575 | — | 13 | 2 | no | — |
| 314 | C2×#137 | — | 13 | 2 | no | — |
| 315 | C2×#137 | — | 26 | 2 | no | — |
| 316 | C2×#135 | — | 13 | 1 | no | — |
| 317 | C2×#135 | — | 26 | 1 | no | — |
| 318 | C22×Q16 | — | 26 | 1 | no | — |
| 319 | C22×Q16 | C2×D13 | 1 | 1 | yes | characteristic |
| 320 | C2×#131 | — | 13 | 1 | no | — |
| 321 | C2×#131 | — | 13 | 1 | no | — |
| 322 | #536 | — | 13 | 2 | no | — |
| 323 | #473 | — | 26 | 1 | no | — |
| 324 | #472 | — | 26 | 1 | no | — |
| 325 | #471 | — | 26 | 2 | no | — |
| 326 | #470 | — | 26 | 2 | no | — |
| 327 | #467 | — | 26 | 2 | no | — |
| 328 | #456 | — | 26 | 4 | no | — |
| 329 | #454 | — | 26 | 4 | no | — |
| 330 | #444 | — | 26 | 2 | no | — |
| 331 | #443 | — | 26 | 2 | no | — |
| 332 | #430 | — | 13 | 1 | no | — |
| 333 | C2×#108 | C2×D13 | 1 | 1 | yes | characteristic |
| 334 | #427 | — | 13 | 1 | no | — |
| 335 | #421 | — | 13 | 2 | no | — |
| 336 | #421 | — | 13 | 2 | no | — |
| 337 | #421 | — | 13 | 1 | no | — |
| 338 | #421 | — | 13 | 1 | no | — |
| 339 | #419 | — | 13 | 2 | no | — |
| 340 | #419 | C2×D13 | 1 | 2 | yes | — |
| 341 | #413 | — | 13 | 2 | no | — |
| 342 | C2×#101 | C2×D13 | 1 | 2 | yes | — |
| 343 | #410 | — | 13 | 2 | no | — |
| 344 | #405 | C2×D13 | 1 | 1 | yes | characteristic |
| 345 | #344 | — | 13 | 2 | no | — |
| 346 | C22×C13 | — | 4 | 1 | no | — |
| 347 | C22×C13 | #535 | 1 | 1 | yes | characteristic |
| 348 | C22×C13 | D42 | 1 | 1 | yes | characteristic |
| 349 | C22×C13 | #546 | 1 | 1 | yes | characteristic |
| 350 | C2×D13 | — | 2 | 2 | no | — |
| 351 | C2×D13 | — | 4 | 2 | no | — |
| 352 | C2×D13 | — | 4 | 2 | no | — |
| 353 | C2×D13 | — | 4 | 2 | no | — |
| 354 | C2×D13 | — | 4 | 1 | no | — |
| 355 | C2×D13 | — | 8 | 2 | no | — |
| 356 | C4×C13 | — | 4 | 4 | no | — |
| 357 | C4×C13 | — | 8 | 1 | no | — |
| 358 | C4×C13 | C2×#120 | 1 | 1 | yes | characteristic |
| 359 | C4×C13 | C2×#121 | 1 | 1 | yes | characteristic |
| 360 | C4×C13 | D42 | 1 | 1 | yes | characteristic |
| 361 | C4×C13 | #546 | 1 | 1 | yes | characteristic |
| 362 | Dic13 | — | 2 | 2 | no | — |
| 363 | Dic13 | — | 4 | 2 | no | — |
| 364 | Dic13 | — | 4 | 1 | no | — |
| 365 | Dic13 | — | 8 | 2 | no | — |
| 366 | 2−1+4 | — | 26 | 4 | no | — |
| 367 | 2−1+4 | — | 26 | 4 | no | — |
| 368 | 2−1+4 | — | 26 | 4 | no | — |
| 369 | 2−1+4 | — | 52 | 2 | no | — |
| 370 | C2×#41 | — | 13 | 1 | no | — |
| 371 | C2×#41 | — | 13 | 1 | no | — |
| 372 | C2×#41 | — | 13 | 2 | no | — |
| 373 | C2×#41 | — | 26 | 2 | no | — |
| 374 | C2×#41 | — | 26 | 2 | no | — |
| 375 | C2×#41 | — | 52 | 2 | no | — |
| 376 | C22×Q8 | — | 26 | 2 | no | — |
| 377 | C22×Q8 | — | 26 | 2 | no | — |
| 378 | C22×Q8 | C22×D13 | 1 | 2 | yes | — |
| 379 | #137 | — | 13 | 2 | no | — |
| 380 | #137 | — | 26 | 1 | no | — |
| 381 | #137 | — | 26 | 2 | no | — |
| 382 | #137 | — | 26 | 2 | no | — |
| 383 | #137 | — | 26 | 4 | no | — |
| 384 | #137 | — | 26 | 8 | no | — |
| 385 | #137 | — | 26 | 8 | no | — |
| 386 | #137 | — | 26 | 4 | no | — |
| 387 | AGL(1,ℤ/8) | — | 13 | 2 | no | — |
| 388 | AGL(1,ℤ/8) | — | 26 | 1 | no | — |
| 389 | AGL(1,ℤ/8) | — | 26 | 2 | no | — |
| 390 | AGL(1,ℤ/8) | — | 26 | 2 | no | — |
| 391 | #135 | — | 26 | 2 | no | — |
| 392 | #135 | — | 26 | 4 | no | — |
| 393 | #135 | — | 26 | 4 | no | — |
| 394 | #135 | — | 26 | 1 | no | — |
| 395 | #135 | — | 26 | 1 | no | — |
| 396 | #135 | — | 26 | 1 | no | — |
| 397 | #135 | — | 26 | 1 | no | — |
| 398 | #135 | — | 52 | 2 | no | — |
| 399 | C2×Q16 | — | 2 | 1 | no | — |
| 400 | C2×Q16 | — | 2 | 1 | no | — |
| 401 | C2×Q16 | — | 2 | 1 | no | — |
| 402 | C2×Q16 | — | 2 | 1 | no | — |
| 403 | C2×Q16 | — | 13 | 1 | no | — |
| 404 | C2×Q16 | — | 26 | 4 | no | — |
| 405 | C2×Q16 | — | 26 | 4 | no | — |
| 406 | C2×Q16 | — | 26 | 2 | no | — |
| 407 | C2×Q16 | D52 | 1 | 2 | yes | — |
| 408 | C2×Q16 | D52 | 1 | 2 | yes | — |
| 409 | C2×SD16 | — | 13 | 2 | no | — |
| 410 | C2×SD16 | — | 26 | 2 | no | — |
| 411 | C2×D8 | — | 13 | 1 | no | — |
| 412 | #131 | — | 13 | 2 | no | — |
| 413 | #131 | — | 13 | 2 | no | — |
| 414 | #131 | — | 26 | 1 | no | — |
| 415 | #131 | — | 26 | 1 | no | — |
| 416 | #131 | — | 26 | 1 | no | — |
| 417 | #131 | — | 26 | 1 | no | — |
| 418 | #131 | — | 26 | 1 | no | — |
| 419 | #131 | — | 26 | 1 | no | — |
| 420 | C2×M16 | — | 13 | 1 | no | — |
| 421 | C2×M16 | — | 13 | 1 | no | — |
| 422 | C2×M16 | — | 26 | 1 | no | — |
| 423 | C2×M16 | — | 26 | 1 | no | — |
| 424 | C2×M16 | C22×D13 | 1 | 2 | yes | — |
| 425 | C2×M16 | C22×D13 | 1 | 1 | yes | characteristic |
| 426 | C22×C8 | — | 26 | 1 | no | — |
| 427 | C22×C8 | — | 26 | 1 | no | — |
| 428 | C22×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 429 | C4⋊Q8 | — | 26 | 2 | no | — |
| 430 | #124 | — | 26 | 2 | no | — |
| 431 | #123 | — | 52 | 2 | no | — |
| 432 | C22⋊Q8 | — | 26 | 4 | no | — |
| 433 | #117 | — | 13 | 2 | no | — |
| 434 | #117 | C22×D13 | 1 | 1 | yes | characteristic |
| 435 | #108 | — | 2 | 1 | no | — |
| 436 | #108 | — | 2 | 1 | no | — |
| 437 | #108 | — | 26 | 2 | no | — |
| 438 | #107 | — | 26 | 1 | no | — |
| 439 | #106 | — | 26 | 1 | no | — |
| 440 | #104 | — | 26 | 2 | no | — |
| 441 | #104 | — | 26 | 2 | no | — |
| 442 | #104 | — | 26 | 4 | no | — |
| 443 | #104 | — | 26 | 4 | no | — |
| 444 | #103 | — | 4 | 2 | no | — |
| 445 | #103 | — | 26 | 4 | no | — |
| 446 | #101 | — | 2 | 4 | no | — |
| 447 | #101 | — | 26 | 2 | no | — |
| 448 | #100 | — | 26 | 2 | no | — |
| 449 | #99 | — | 52 | 2 | no | — |
| 450 | #97 | — | 2 | 1 | no | — |
| 451 | C4×C8 | — | 2 | 1 | no | — |
| 452 | C2×C13 | — | 2 | 1 | no | — |
| 453 | C2×C13 | — | 2 | 1 | no | — |
| 454 | C2×C13 | — | 2 | 1 | no | — |
| 455 | C2×C13 | #2408 | 1 | 1 | yes | characteristic |
| 456 | D13 | — | 4 | 2 | no | — |
| 457 | D13 | — | 8 | 1 | no | — |
| 458 | D13 | — | 8 | 2 | no | — |
| 459 | #41 | — | 13 | 2 | no | — |
| 460 | #41 | — | 13 | 2 | no | — |
| 461 | #41 | — | 26 | 1 | no | — |
| 462 | #41 | — | 26 | 1 | no | — |
| 463 | #41 | — | 26 | 8 | no | — |
| 464 | #41 | — | 26 | 2 | no | — |
| 465 | #41 | — | 26 | 1 | no | — |
| 466 | #41 | — | 26 | 2 | no | — |
| 467 | #41 | — | 26 | 1 | no | — |
| 468 | #41 | — | 26 | 2 | no | — |
| 469 | #41 | — | 26 | 1 | no | — |
| 470 | #41 | — | 26 | 2 | no | — |
| 471 | #41 | — | 26 | 1 | no | — |
| 472 | #41 | — | 52 | 8 | no | — |
| 473 | #41 | — | 52 | 8 | no | — |
| 474 | #41 | — | 52 | 4 | no | — |
| 475 | #41 | — | 52 | 4 | no | — |
| 476 | #41 | — | 52 | 4 | no | — |
| 477 | C2×Q8 | — | 2 | 2 | no | — |
| 478 | C2×Q8 | — | 2 | 2 | no | — |
| 479 | C2×Q8 | — | 2 | 2 | no | — |
| 480 | C2×Q8 | — | 2 | 2 | no | — |
| 481 | C2×Q8 | — | 2 | 2 | no | — |
| 482 | C2×Q8 | — | 13 | 2 | no | — |
| 483 | C2×Q8 | — | 13 | 1 | no | — |
| 484 | C2×Q8 | — | 13 | 1 | no | — |
| 485 | C2×Q8 | — | 26 | 8 | no | — |
| 486 | C2×Q8 | — | 52 | 2 | no | — |
| 487 | C2×Q8 | — | 52 | 4 | no | — |
| 488 | C2×Q8 | — | 52 | 4 | no | — |
| 489 | C2×Q8 | — | 52 | 4 | no | — |
| 490 | C2×Q8 | C2×D52 | 1 | 4 | yes | — |
| 491 | C2×D4 | — | 13 | 2 | no | — |
| 492 | C2×D4 | — | 13 | 1 | no | — |
| 493 | C2×D4 | — | 13 | 1 | no | — |
| 494 | C2×D4 | — | 26 | 1 | no | — |
| 495 | C2×D4 | — | 26 | 2 | no | — |
| 496 | C2×D4 | — | 26 | 1 | no | — |
| 497 | C2×D4 | — | 52 | 2 | no | — |
| 498 | C22×C4 | — | 2 | 2 | no | — |
| 499 | C22×C4 | — | 26 | 1 | no | — |
| 500 | C22×C4 | — | 26 | 1 | no | — |
| 501 | C22×C4 | — | 26 | 2 | no | — |
| 502 | C22×C4 | — | 52 | 2 | no | — |
| 503 | C22×C4 | — | 52 | 2 | no | — |
| 504 | C22×C4 | C23×D13 | 1 | 1 | yes | characteristic |
| 505 | Q16 | — | 2 | 2 | no | — |
| 506 | Q16 | — | 2 | 2 | no | — |
| 507 | Q16 | — | 2 | 2 | no | — |
| 508 | Q16 | — | 2 | 2 | no | — |
| 509 | Q16 | — | 26 | 2 | no | — |
| 510 | Q16 | — | 26 | 8 | no | — |
| 511 | Q16 | — | 26 | 1 | no | — |
| 512 | Q16 | — | 26 | 1 | no | — |
| 513 | Q16 | — | 52 | 2 | no | — |
| 514 | SD16 | — | 26 | 2 | no | — |
| 515 | SD16 | — | 26 | 2 | no | — |
| 516 | SD16 | — | 26 | 8 | no | — |
| 517 | SD16 | — | 26 | 2 | no | — |
| 518 | SD16 | — | 26 | 2 | no | — |
| 519 | SD16 | — | 52 | 2 | no | — |
| 520 | SD16 | — | 52 | 2 | no | — |
| 521 | D8 | — | 26 | 2 | no | — |
| 522 | D8 | — | 26 | 1 | no | — |
| 523 | D8 | — | 26 | 1 | no | — |
| 524 | D8 | — | 52 | 2 | no | — |
| 525 | M16 | — | 2 | 1 | no | — |
| 526 | M16 | — | 2 | 2 | no | — |
| 527 | M16 | — | 2 | 2 | no | — |
| 528 | M16 | — | 13 | 2 | no | — |
| 529 | M16 | — | 26 | 1 | no | — |
| 530 | M16 | — | 26 | 2 | no | — |
| 531 | M16 | — | 26 | 2 | no | — |
| 532 | M16 | — | 26 | 1 | no | — |
| 533 | M16 | — | 26 | 1 | no | — |
| 534 | M16 | — | 52 | 1 | no | — |
| 535 | M16 | — | 52 | 1 | no | — |
| 536 | M16 | D4×D13 | 1 | 2 | yes | — |
| 537 | C2×C8 | — | 2 | 1 | no | — |
| 538 | C2×C8 | — | 2 | 2 | no | — |
| 539 | C2×C8 | — | 26 | 1 | no | — |
| 540 | C2×C8 | — | 26 | 2 | no | — |
| 541 | C2×C8 | — | 26 | 2 | no | — |
| 542 | C2×C8 | — | 26 | 1 | no | — |
| 543 | C2×C8 | — | 52 | 1 | no | — |
| 544 | C2×C8 | — | 52 | 1 | no | — |
| 545 | C2×C8 | C2×D52 | 1 | 1 | yes | characteristic |
| 546 | C2×C8 | C2×D52 | 1 | 1 | yes | characteristic |
| 547 | C2×C8 | D4×D13 | 1 | 1 | yes | characteristic |
| 548 | C2×C8 | D4×D13 | 1 | 1 | yes | characteristic |
| 549 | C2×C8 | D4×D13 | 1 | 1 | yes | characteristic |
| 550 | C2×C8 | D4×D13 | 1 | 1 | yes | characteristic |
| 551 | C4⋊C4 | — | 2 | 1 | no | — |
| 552 | C4⋊C4 | — | 26 | 2 | no | — |
| 553 | C4⋊C4 | — | 52 | 4 | no | — |
| 554 | C22⋊C4 | — | 2 | 1 | no | — |
| 555 | C22⋊C4 | — | 26 | 2 | no | — |
| 556 | C22⋊C4 | — | 52 | 4 | no | — |
| 557 | C42 | — | 2 | 1 | no | — |
| 558 | C42 | — | 26 | 2 | no | — |
| 559 | C13 | #24296 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 560 | C23 | — | 26 | 1 | no | — |
| 561 | C23 | — | 26 | 1 | no | — |
| 562 | C23 | — | 26 | 2 | no | — |
| 563 | C23 | #88256 | 1 | 1 | yes | characteristic |
| 564 | Q8 | — | 2 | 4 | no | — |
| 565 | Q8 | — | 2 | 4 | no | — |
| 566 | Q8 | — | 4 | 2 | no | — |
| 567 | Q8 | — | 4 | 2 | no | — |
| 568 | Q8 | — | 13 | 2 | no | — |
| 569 | Q8 | — | 26 | 1 | no | — |
| 570 | Q8 | — | 26 | 2 | no | — |
| 571 | Q8 | — | 26 | 1 | no | — |
| 572 | Q8 | — | 26 | 1 | no | — |
| 573 | Q8 | — | 26 | 2 | no | — |
| 574 | Q8 | — | 52 | 8 | no | — |
| 575 | D4 | — | 13 | 2 | no | — |
| 576 | D4 | — | 26 | 2 | no | — |
| 577 | D4 | — | 26 | 2 | no | — |
| 578 | D4 | — | 26 | 2 | no | — |
| 579 | D4 | — | 26 | 1 | no | — |
| 580 | D4 | — | 26 | 1 | no | — |
| 581 | D4 | — | 26 | 1 | no | — |
| 582 | D4 | — | 26 | 2 | no | — |
| 583 | D4 | — | 52 | 8 | no | — |
| 584 | D4 | — | 52 | 2 | no | — |
| 585 | D4 | — | 52 | 1 | no | — |
| 586 | D4 | — | 52 | 2 | no | — |
| 587 | D4 | — | 52 | 1 | no | — |
| 588 | C2×C4 | — | 2 | 4 | no | — |
| 589 | C2×C4 | — | 4 | 2 | no | — |
| 590 | C2×C4 | — | 4 | 2 | no | — |
| 591 | C2×C4 | — | 4 | 1 | no | — |
| 592 | C2×C4 | — | 26 | 1 | no | — |
| 593 | C2×C4 | — | 26 | 2 | no | — |
| 594 | C2×C4 | — | 26 | 2 | no | — |
| 595 | C2×C4 | — | 26 | 1 | no | — |
| 596 | C2×C4 | — | 26 | 2 | no | — |
| 597 | C2×C4 | — | 52 | 8 | no | — |
| 598 | C2×C4 | — | 52 | 8 | no | — |
| 599 | C2×C4 | — | 52 | 1 | no | — |
| 600 | C2×C4 | — | 52 | 2 | no | — |
| 601 | C2×C4 | — | 52 | 1 | no | — |
| 602 | C2×C4 | — | 52 | 2 | no | — |
| 603 | C2×C4 | — | 52 | 2 | no | — |
| 604 | C2×C4 | C22×D52 | 1 | 1 | yes | characteristic |
| 605 | C2×C4 | C2×D4×D13 | 1 | 1 | yes | characteristic |
| 606 | C2×C4 | C2×D4×D13 | 1 | 1 | yes | characteristic |
| 607 | C2×C4 | C2×D4×D13 | 1 | 1 | yes | characteristic |
| 608 | C2×C4 | #88251 | 1 | 1 | yes | characteristic |
| 609 | C2×C4 | #41×D13 | 1 | 1 | yes | characteristic |
| 610 | C8 | — | 2 | 2 | no | — |
| 611 | C8 | — | 4 | 2 | no | — |
| 612 | C8 | — | 26 | 2 | no | — |
| 613 | C8 | — | 52 | 1 | no | — |
| 614 | C8 | #88136 | 1 | 1 | yes | characteristic |
| 615 | C8 | #88136 | 1 | 1 | yes | characteristic |
| 616 | C8 | #88136 | 1 | 1 | yes | characteristic |
| 617 | C8 | #88136 | 1 | 1 | yes | characteristic |
| 618 | C22 | — | 4 | 1 | no | — |
| 619 | C22 | — | 26 | 2 | no | — |
| 620 | C22 | — | 52 | 2 | no | — |
| 621 | C22 | — | 52 | 2 | no | — |
| 622 | C22 | — | 52 | 2 | no | — |
| 623 | C22 | — | 52 | 1 | no | — |
| 624 | C22 | — | 104 | 2 | no | — |
| 625 | C22 | D4×D52 | 1 | 1 | yes | characteristic |
| 626 | C22 | #11719312 | 1 | 1 | yes | characteristic |
| 627 | C22 | #11719381 | 1 | 1 | yes | characteristic |
| 628 | C4 | — | 4 | 4 | no | — |
| 629 | C4 | — | 8 | 1 | no | — |
| 630 | C4 | — | 26 | 2 | no | — |
| 631 | C4 | — | 52 | 2 | no | — |
| 632 | C4 | — | 52 | 1 | no | — |
| 633 | C4 | — | 104 | 2 | no | — |
| 634 | C4 | C2×#88136 | 1 | 1 | yes | characteristic |
| 635 | C4 | #11719259 | 1 | 1 | yes | characteristic |
| 636 | C4 | D13×#121 | 1 | 1 | yes | characteristic |
| 637 | C4 | #11719422 | 1 | 1 | yes | characteristic |
| 638 | C2 | — | 2 | 1 | no | — |
| 639 | C2 | — | 2 | 1 | no | — |
| 640 | C2 | — | 2 | 1 | no | — |
| 641 | C2 | — | 52 | 2 | no | — |
| 642 | C2 | — | 104 | 1 | no | — |
| 643 | C2 | — | 104 | 2 | no | — |
| 644 | C2 | #13118190 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11719471 | C2 | semidirect |
| 2. #13124557 | C2 | semidirect |
| 3. #13124487 | C2 | semidirect |
| 4. #13124203 | C2 | semidirect |
| 5. #13123740 | C2 | semidirect |
| 6. #13116115 | C2 | semidirect |
| 7. #13115898 | C2 | semidirect |
| 8. #13115734 | C2 | semidirect |
| 9. #13114891 | C2 | semidirect |
| 10. #13114808 | C2 | semidirect |
| 11. C13×#1979 | C2 | semidirect |
| 245. #1979 | D13 | semidirect |
| 559. C13 | #24296 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11719471 | 2 |
| #13124557 | 2 |
| #13124487 | 2 |
| #13124203 | 2 |
| #13123740 | 2 |
| #13116115 | 2 |
| #13115898 | 2 |
| #13115734 | 2 |
| #13114891 | 2 |
| #13114808 | 2 |
| C13×#1979 | 2 |
| #24296 | 13 |