Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1284 conjugacy classes of subgroups.
The subgroup lattice has 580 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #13129623 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13124573 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #13124217 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13124131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #13116115 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #13115956 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #13115386 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #13115198 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #13115058 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #13114785 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C13×#2889 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×C13×2−1+4 | C22 | 1 | 1 | yes | characteristic |
| 13 | #11719648 | C22 | 1 | 1 | yes | characteristic |
| 14 | C13×#568 | C22 | 1 | 2 | yes | complemented |
| 15 | #11719543 | — | 2 | 4 | no | — |
| 16 | #11719542 | — | 2 | 4 | no | — |
| 17 | #11719530 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#88205 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | #11719527 | — | 2 | 2 | no | — |
| 20 | #11719527 | C22 | 1 | 2 | yes | — |
| 21 | #11719524 | C22 | 1 | 1 | yes | characteristic |
| 22 | C22×#6107 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | C2×#88196 | — | 2 | 2 | no | — |
| 24 | C2×#88196 | C22 | 1 | 2 | yes | — |
| 25 | C2×#88163 | C22 | 1 | 2 | yes | — |
| 26 | C13×#413 | — | 2 | 2 | no | — |
| 27 | C13×#413 | C22 | 1 | 1 | yes | characteristic |
| 28 | C13×#413 | C22 | 1 | 1 | yes | characteristic |
| 29 | C2×C13×#101 | — | 2 | 2 | no | — |
| 30 | C2×C13×#101 | C22 | 1 | 2 | yes | complemented |
| 31 | #11718900 | — | 2 | 2 | no | — |
| 32 | #11718895 | C22 | 1 | 1 | yes | characteristic |
| 33 | #11718894 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | #11718889 | — | 2 | 2 | no | — |
| 35 | #11718886 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | #11718804 | — | 2 | 4 | no | — |
| 37 | #11718802 | — | 2 | 4 | no | — |
| 38 | #11718800 | C22 | 1 | 2 | yes | — |
| 39 | C2×#88064 | C22 | 1 | 2 | yes | complemented |
| 40 | #11718793 | C22 | 1 | 2 | yes | — |
| 41 | #11718790 | C22 | 1 | 2 | yes | — |
| 42 | #11718786 | C22 | 1 | 2 | yes | complemented |
| 43 | #11718413 | — | 2 | 2 | no | — |
| 44 | #11718407 | — | 2 | 2 | no | — |
| 45 | #11718150 | C22 | 1 | 2 | yes | complemented |
| 46 | #11718148 | C22 | 1 | 2 | yes | complemented |
| 47 | C13×2−1+4 | — | 2 | 4 | no | — |
| 48 | C13×2−1+4 | — | 4 | 2 | no | — |
| 49 | C2×C13×#41 | — | 2 | 1 | no | — |
| 50 | C2×C13×#41 | — | 2 | 2 | no | — |
| 51 | C2×C13×#41 | D4 | 1 | 2 | yes | — |
| 52 | C2×C13×#41 | C23 | 1 | 1 | yes | characteristic |
| 53 | C2×C13×#41 | C23 | 1 | 1 | yes | characteristic |
| 54 | C22×Q8×C13 | — | 2 | 1 | no | — |
| 55 | C22×Q8×C13 | D4 | 1 | 2 | yes | — |
| 56 | C22×Q8×C13 | C23 | 1 | 1 | yes | characteristic |
| 57 | #88257 | — | 2 | 2 | no | — |
| 58 | #88256 | — | 2 | 2 | no | — |
| 59 | #41×D13 | — | 4 | 2 | no | — |
| 60 | #88254 | — | 2 | 1 | no | — |
| 61 | #88251 | — | 2 | 1 | no | — |
| 62 | #88251 | — | 2 | 2 | no | — |
| 63 | C2×#6127 | — | 2 | 2 | no | — |
| 64 | C2×#6127 | C23 | 1 | 2 | yes | — |
| 65 | C22×Dic26 | C23 | 1 | 1 | yes | characteristic |
| 66 | C13×#131 | — | 2 | 4 | no | — |
| 67 | C13×#131 | — | 4 | 2 | no | — |
| 68 | C2×C13×M16 | — | 2 | 4 | no | — |
| 69 | C2×C13×M16 | C23 | 1 | 2 | yes | — |
| 70 | C2×C13×M16 | C23 | 1 | 2 | yes | — |
| 71 | #88205 | — | 2 | 4 | no | — |
| 72 | #88205 | — | 2 | 4 | no | — |
| 73 | #88205 | D4 | 1 | 4 | yes | — |
| 74 | #88204 | — | 2 | 8 | no | — |
| 75 | #88204 | — | 2 | 4 | no | — |
| 76 | #88203 | — | 2 | 4 | no | — |
| 77 | #88203 | D4 | 1 | 4 | yes | — |
| 78 | #88202 | — | 2 | 4 | no | — |
| 79 | #88198 | — | 2 | 1 | no | — |
| 80 | C2×#6107 | — | 2 | 4 | no | — |
| 81 | C2×#6107 | — | 2 | 2 | no | — |
| 82 | C2×#6107 | — | 2 | 2 | no | — |
| 83 | C2×#6107 | — | 2 | 1 | no | — |
| 84 | C2×#6107 | — | 4 | 2 | no | — |
| 85 | #88196 | — | 2 | 8 | no | — |
| 86 | #88196 | — | 2 | 2 | no | — |
| 87 | #88196 | — | 2 | 4 | no | — |
| 88 | #88196 | — | 2 | 4 | no | — |
| 89 | C2×#6106 | — | 2 | 4 | no | — |
| 90 | C2×#6106 | — | 2 | 2 | no | — |
| 91 | #88190 | — | 2 | 1 | no | — |
| 92 | #88189 | — | 2 | 2 | no | — |
| 93 | C2×#6105 | — | 2 | 1 | no | — |
| 94 | #88186 | — | 2 | 2 | no | — |
| 95 | #88180 | C23 | 1 | 1 | yes | characteristic |
| 96 | #88178 | — | 2 | 2 | no | — |
| 97 | C2×#6099 | — | 2 | 2 | no | — |
| 98 | C2×#6099 | C23 | 1 | 1 | yes | characteristic |
| 99 | C2×#6099 | C23 | 1 | 2 | yes | — |
| 100 | C22×#1055 | C23 | 1 | 1 | yes | characteristic |
| 101 | #88163 | — | 2 | 4 | no | — |
| 102 | #88163 | — | 4 | 2 | no | — |
| 103 | C2×Dic52 | — | 2 | 2 | no | — |
| 104 | C2×#6095 | — | 2 | 2 | no | — |
| 105 | C13×#101 | — | 2 | 1 | no | — |
| 106 | C13×#101 | — | 2 | 4 | no | — |
| 107 | C13×#101 | D4 | 1 | 2 | yes | — |
| 108 | C13×#100 | — | 2 | 1 | no | — |
| 109 | C13×#100 | D4 | 1 | 2 | yes | — |
| 110 | #88075 | — | 2 | 2 | no | — |
| 111 | #88075 | — | 2 | 1 | no | — |
| 112 | #88072 | — | 2 | 1 | no | — |
| 113 | C22⋊#1055 | — | 2 | 2 | no | — |
| 114 | #88065 | — | 2 | 4 | no | — |
| 115 | #88064 | — | 2 | 2 | no | — |
| 116 | #88064 | — | 2 | 4 | no | — |
| 117 | #88063 | — | 2 | 2 | no | — |
| 118 | #88060 | — | 4 | 2 | no | — |
| 119 | #88059 | — | 2 | 4 | no | — |
| 120 | #24423 | — | 13 | 1 | no | maximal, Sylow |
| 121 | C13×#41 | — | 2 | 2 | no | — |
| 122 | C13×#41 | — | 2 | 2 | no | — |
| 123 | C13×#41 | — | 2 | 2 | no | — |
| 124 | C13×#41 | — | 2 | 4 | no | — |
| 125 | C13×#41 | — | 4 | 2 | no | — |
| 126 | C13×#41 | — | 4 | 4 | no | — |
| 127 | C13×#41 | — | 4 | 8 | no | — |
| 128 | C13×#41 | C2×D4 | 1 | 4 | yes | — |
| 129 | C2×Q8×C13 | — | 2 | 2 | no | — |
| 130 | C2×Q8×C13 | — | 2 | 1 | no | — |
| 131 | C2×Q8×C13 | — | 2 | 4 | no | — |
| 132 | C2×Q8×C13 | — | 2 | 2 | no | — |
| 133 | C2×Q8×C13 | — | 2 | 2 | no | — |
| 134 | C2×Q8×C13 | — | 4 | 2 | no | — |
| 135 | C2×Q8×C13 | — | 4 | 4 | no | — |
| 136 | C2×Q8×C13 | C2×D4 | 1 | 2 | yes | — |
| 137 | C2×Q8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 138 | C2×Q8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 139 | C2×D4×C13 | — | 2 | 1 | no | — |
| 140 | C2×D4×C13 | — | 2 | 2 | no | — |
| 141 | C2×D4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 142 | C2×D4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 143 | C2×D4×C13 | #41 | 1 | 2 | yes | — |
| 144 | C22×C4×C13 | — | 2 | 1 | no | — |
| 145 | C22×C4×C13 | — | 2 | 2 | no | — |
| 146 | C22×C4×C13 | — | 2 | 1 | no | — |
| 147 | C22×C4×C13 | — | 2 | 2 | no | — |
| 148 | C22×C4×C13 | C2×D4 | 1 | 2 | yes | — |
| 149 | C22×C4×C13 | C24 | 1 | 1 | yes | characteristic |
| 150 | C2×C22⋊D13 | — | 2 | 2 | no | — |
| 151 | C2×C22⋊D13 | — | 4 | 2 | no | — |
| 152 | C22×Dic13 | — | 2 | 1 | no | — |
| 153 | #6131 | — | 4 | 2 | no | — |
| 154 | Q8×D13 | — | 4 | 2 | no | — |
| 155 | #6129 | — | 4 | 2 | no | — |
| 156 | #6129 | — | 4 | 4 | no | — |
| 157 | D4×D13 | — | 4 | 2 | no | — |
| 158 | D4×D13 | — | 4 | 4 | no | — |
| 159 | #6127 | — | 2 | 4 | no | — |
| 160 | #6127 | — | 2 | 2 | no | — |
| 161 | #6127 | — | 2 | 2 | no | — |
| 162 | #6127 | — | 2 | 2 | no | — |
| 163 | #6127 | — | 2 | 2 | no | — |
| 164 | #6127 | — | 4 | 2 | no | — |
| 165 | #6127 | — | 4 | 2 | no | — |
| 166 | C2×D52 | — | 2 | 2 | no | — |
| 167 | C2×D52 | C2×D4 | 1 | 2 | yes | — |
| 168 | C2×C4×D13 | — | 2 | 2 | no | — |
| 169 | C2×C4×D13 | — | 4 | 2 | no | — |
| 170 | C2×Dic26 | — | 2 | 2 | no | — |
| 171 | C2×Dic26 | — | 2 | 2 | no | — |
| 172 | C2×Dic26 | — | 2 | 1 | no | — |
| 173 | C2×Dic26 | — | 2 | 1 | no | — |
| 174 | C2×Dic26 | — | 2 | 2 | no | — |
| 175 | C2×Dic26 | C2×D4 | 1 | 2 | yes | — |
| 176 | C13×M16 | — | 2 | 2 | no | — |
| 177 | C13×M16 | — | 2 | 2 | no | — |
| 178 | C13×M16 | — | 2 | 2 | no | — |
| 179 | C13×M16 | — | 4 | 4 | no | — |
| 180 | C13×M16 | C2×D4 | 1 | 4 | yes | — |
| 181 | C2×C8×C13 | — | 2 | 2 | no | — |
| 182 | C2×C8×C13 | — | 2 | 2 | no | — |
| 183 | C2×C8×C13 | — | 4 | 4 | no | — |
| 184 | C22⋊Dic13 | — | 2 | 1 | no | — |
| 185 | C22⋊Dic13 | — | 4 | 2 | no | — |
| 186 | #6107 | — | 2 | 8 | no | — |
| 187 | #6107 | — | 2 | 4 | no | — |
| 188 | #6107 | — | 4 | 4 | no | — |
| 189 | #6107 | — | 4 | 2 | no | — |
| 190 | #6106 | — | 2 | 8 | no | — |
| 191 | #6106 | — | 2 | 4 | no | — |
| 192 | #6105 | — | 2 | 4 | no | — |
| 193 | #6105 | — | 4 | 2 | no | — |
| 194 | #6104 | — | 2 | 4 | no | — |
| 195 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 196 | #6101 | — | 4 | 2 | no | — |
| 197 | C4×Dic13 | — | 2 | 1 | no | — |
| 198 | #6099 | — | 2 | 4 | no | — |
| 199 | #6099 | — | 2 | 2 | no | — |
| 200 | #6099 | — | 2 | 2 | no | — |
| 201 | #6099 | C2×D4 | 1 | 4 | yes | — |
| 202 | C2×#1055 | — | 2 | 4 | no | — |
| 203 | C2×#1055 | — | 2 | 2 | no | — |
| 204 | C2×#1055 | — | 2 | 1 | no | — |
| 205 | C2×#1055 | — | 2 | 1 | no | — |
| 206 | C2×#1055 | — | 2 | 2 | no | — |
| 207 | Dic52 | — | 4 | 4 | no | — |
| 208 | #6095 | — | 4 | 4 | no | — |
| 209 | #3586 | — | 13 | 1 | no | — |
| 210 | #3069 | — | 13 | 2 | no | — |
| 211 | #3022 | — | 13 | 1 | no | — |
| 212 | #3011 | — | 13 | 1 | no | — |
| 213 | #2889 | D13 | 1 | 1 | yes | characteristic, complemented |
| 214 | #2049 | — | 13 | 2 | no | — |
| 215 | #2020 | — | 13 | 2 | no | — |
| 216 | #1915 | — | 13 | 1 | no | — |
| 217 | #1881 | — | 13 | 2 | no | — |
| 218 | #1858 | — | 13 | 1 | no | — |
| 219 | #1791 | — | 13 | 1 | no | — |
| 220 | C23×C13 | — | 2 | 1 | no | — |
| 221 | C23×C13 | #121 | 1 | 2 | yes | — |
| 222 | C23×C13 | C2×#41 | 1 | 1 | yes | characteristic |
| 223 | C22×D13 | — | 2 | 2 | no | — |
| 224 | C22×D13 | — | 4 | 2 | no | — |
| 225 | Q8×C13 | — | 2 | 1 | no | — |
| 226 | Q8×C13 | — | 2 | 2 | no | — |
| 227 | Q8×C13 | — | 2 | 2 | no | — |
| 228 | Q8×C13 | — | 2 | 2 | no | — |
| 229 | Q8×C13 | — | 4 | 4 | no | — |
| 230 | Q8×C13 | — | 4 | 2 | no | — |
| 231 | Q8×C13 | #120 | 1 | 2 | yes | — |
| 232 | D4×C13 | — | 2 | 4 | no | — |
| 233 | D4×C13 | — | 2 | 4 | no | — |
| 234 | D4×C13 | — | 2 | 1 | no | — |
| 235 | D4×C13 | — | 2 | 2 | no | — |
| 236 | D4×C13 | — | 4 | 4 | no | — |
| 237 | D4×C13 | #120 | 1 | 2 | yes | — |
| 238 | C2×C4×C13 | — | 2 | 1 | no | — |
| 239 | C2×C4×C13 | — | 2 | 2 | no | — |
| 240 | C2×C4×C13 | — | 2 | 2 | no | — |
| 241 | C2×C4×C13 | — | 2 | 4 | no | — |
| 242 | C2×C4×C13 | — | 2 | 2 | no | — |
| 243 | C2×C4×C13 | — | 4 | 4 | no | — |
| 244 | C2×C4×C13 | — | 4 | 4 | no | — |
| 245 | C2×C4×C13 | — | 4 | 2 | no | — |
| 246 | C2×C4×C13 | #121 | 1 | 2 | yes | — |
| 247 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 248 | C2×C4×C13 | C22×D4 | 1 | 2 | yes | — |
| 249 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 250 | C2×C4×C13 | H(5,𝔽2) | 1 | 2 | yes | — |
| 251 | C22⋊D13 | — | 4 | 4 | no | — |
| 252 | C22⋊D13 | — | 4 | 2 | no | — |
| 253 | C22⋊D13 | — | 4 | 2 | no | — |
| 254 | C2×Dic13 | — | 2 | 2 | no | — |
| 255 | C2×Dic13 | — | 4 | 2 | no | — |
| 256 | C2×Dic13 | — | 4 | 1 | no | — |
| 257 | C2×Dic13 | — | 4 | 1 | no | — |
| 258 | C2×Dic13 | — | 4 | 2 | no | — |
| 259 | D52 | — | 2 | 2 | no | — |
| 260 | D52 | — | 2 | 2 | no | — |
| 261 | D52 | — | 4 | 2 | no | — |
| 262 | C4×D13 | — | 4 | 4 | no | — |
| 263 | C4×D13 | — | 4 | 2 | no | — |
| 264 | C4×D13 | — | 4 | 2 | no | — |
| 265 | Dic26 | — | 2 | 2 | no | — |
| 266 | Dic26 | — | 2 | 2 | no | — |
| 267 | Dic26 | — | 4 | 2 | no | — |
| 268 | Dic26 | — | 4 | 1 | no | — |
| 269 | Dic26 | — | 4 | 1 | no | — |
| 270 | Dic26 | — | 4 | 2 | no | — |
| 271 | C8×C13 | — | 2 | 4 | no | — |
| 272 | C8×C13 | — | 4 | 2 | no | — |
| 273 | #1055 | — | 2 | 4 | no | — |
| 274 | #1055 | — | 4 | 1 | no | — |
| 275 | #1055 | — | 4 | 1 | no | — |
| 276 | #585 | — | 13 | 1 | no | — |
| 277 | C2×2−1+4 | C2×D13 | 1 | 1 | yes | characteristic |
| 278 | #578 | — | 26 | 4 | no | — |
| 279 | #577 | — | 26 | 4 | no | — |
| 280 | #575 | — | 13 | 2 | no | — |
| 281 | #575 | — | 26 | 2 | no | — |
| 282 | C2×#137 | — | 13 | 1 | no | — |
| 283 | C2×#137 | — | 13 | 2 | no | — |
| 284 | C2×#137 | — | 13 | 2 | no | — |
| 285 | C2×#137 | — | 26 | 2 | no | — |
| 286 | C22×Q16 | — | 13 | 1 | no | — |
| 287 | #568 | — | 13 | 1 | no | — |
| 288 | #568 | C2×D13 | 1 | 2 | yes | complemented |
| 289 | #536 | — | 13 | 1 | no | — |
| 290 | #473 | — | 26 | 4 | no | — |
| 291 | #471 | — | 26 | 4 | no | — |
| 292 | #456 | — | 26 | 2 | no | — |
| 293 | #455 | — | 26 | 2 | no | — |
| 294 | #452 | — | 26 | 2 | no | — |
| 295 | #451 | — | 26 | 2 | no | — |
| 296 | #430 | — | 13 | 2 | no | — |
| 297 | #421 | — | 13 | 2 | no | — |
| 298 | #419 | — | 13 | 1 | no | — |
| 299 | #416 | — | 13 | 1 | no | — |
| 300 | #413 | — | 2 | 2 | no | — |
| 301 | #413 | — | 13 | 2 | no | — |
| 302 | #413 | C2×D13 | 1 | 1 | yes | characteristic |
| 303 | #413 | C2×D13 | 1 | 1 | yes | characteristic |
| 304 | C2×#101 | — | 2 | 2 | no | — |
| 305 | C2×#101 | — | 13 | 2 | no | — |
| 306 | C2×#101 | C2×D13 | 1 | 2 | yes | complemented |
| 307 | #408 | — | 13 | 1 | no | — |
| 308 | #408 | — | 13 | 2 | no | — |
| 309 | #344 | — | 13 | 2 | no | — |
| 310 | #341 | — | 13 | 2 | no | — |
| 311 | C22×C13 | — | 2 | 2 | no | — |
| 312 | C22×C13 | — | 2 | 2 | no | — |
| 313 | C22×C13 | — | 4 | 1 | no | — |
| 314 | C22×C13 | — | 4 | 2 | no | — |
| 315 | C22×C13 | — | 8 | 1 | no | — |
| 316 | C22×C13 | C2×#121 | 1 | 1 | yes | characteristic |
| 317 | C22×C13 | #546 | 1 | 2 | yes | — |
| 318 | C2×D13 | — | 4 | 2 | no | — |
| 319 | C2×D13 | — | 8 | 2 | no | — |
| 320 | C2×D13 | — | 16 | 2 | no | — |
| 321 | C4×C13 | — | 2 | 2 | no | — |
| 322 | C4×C13 | — | 2 | 2 | no | — |
| 323 | C4×C13 | — | 4 | 2 | no | — |
| 324 | C4×C13 | C2×#120 | 1 | 1 | yes | characteristic |
| 325 | C4×C13 | #534 | 1 | 1 | yes | characteristic |
| 326 | C4×C13 | D42 | 1 | 2 | yes | — |
| 327 | Dic13 | — | 4 | 2 | no | — |
| 328 | Dic13 | — | 8 | 1 | no | — |
| 329 | Dic13 | — | 8 | 1 | no | — |
| 330 | 2−1+4 | — | 2 | 4 | no | — |
| 331 | 2−1+4 | — | 4 | 2 | no | — |
| 332 | 2−1+4 | — | 26 | 2 | no | — |
| 333 | 2−1+4 | — | 26 | 1 | no | — |
| 334 | H(5,𝔽2) | — | 26 | 2 | no | — |
| 335 | H(5,𝔽2) | — | 26 | 2 | no | — |
| 336 | H(5,𝔽2) | — | 26 | 1 | no | — |
| 337 | C2×#41 | — | 2 | 2 | no | — |
| 338 | C2×#41 | — | 2 | 1 | no | — |
| 339 | C2×#41 | — | 13 | 2 | no | — |
| 340 | C2×#41 | — | 26 | 2 | no | — |
| 341 | C2×#41 | — | 52 | 2 | no | — |
| 342 | C2×#41 | D52 | 1 | 2 | yes | — |
| 343 | C2×#41 | C22×D13 | 1 | 1 | yes | characteristic |
| 344 | C2×#41 | C22×D13 | 1 | 1 | yes | characteristic |
| 345 | C22×Q8 | — | 2 | 1 | no | — |
| 346 | C22×Q8 | — | 13 | 1 | no | — |
| 347 | C22×Q8 | D52 | 1 | 2 | yes | — |
| 348 | C22×Q8 | C22×D13 | 1 | 1 | yes | characteristic |
| 349 | #137 | — | 13 | 4 | no | — |
| 350 | #137 | — | 26 | 4 | no | — |
| 351 | #137 | — | 26 | 8 | no | — |
| 352 | #137 | — | 26 | 4 | no | — |
| 353 | #137 | — | 26 | 4 | no | — |
| 354 | #137 | — | 26 | 2 | no | — |
| 355 | #137 | — | 26 | 4 | no | — |
| 356 | #137 | — | 26 | 4 | no | — |
| 357 | #137 | — | 52 | 2 | no | — |
| 358 | AGL(1,ℤ/8) | — | 13 | 4 | no | — |
| 359 | AGL(1,ℤ/8) | — | 26 | 4 | no | — |
| 360 | AGL(1,ℤ/8) | — | 26 | 2 | no | — |
| 361 | #135 | — | 26 | 8 | no | — |
| 362 | #135 | — | 26 | 4 | no | — |
| 363 | C2×Q16 | — | 26 | 2 | no | — |
| 364 | C2×Q16 | — | 26 | 2 | no | — |
| 365 | C2×Q16 | — | 26 | 4 | no | — |
| 366 | C2×Q16 | — | 26 | 2 | no | — |
| 367 | C2×Q16 | — | 26 | 1 | no | — |
| 368 | C2×Q16 | — | 52 | 2 | no | — |
| 369 | C2×SD16 | — | 26 | 2 | no | — |
| 370 | C2×SD16 | — | 26 | 2 | no | — |
| 371 | C2×SD16 | — | 26 | 4 | no | — |
| 372 | C2×SD16 | — | 26 | 1 | no | — |
| 373 | #131 | — | 2 | 4 | no | — |
| 374 | #131 | — | 4 | 2 | no | — |
| 375 | #131 | — | 26 | 4 | no | — |
| 376 | C2×M16 | — | 2 | 4 | no | — |
| 377 | C2×M16 | — | 13 | 2 | no | — |
| 378 | C2×M16 | — | 13 | 1 | no | — |
| 379 | C2×M16 | — | 26 | 2 | no | — |
| 380 | C2×M16 | C22×D13 | 1 | 2 | yes | — |
| 381 | C2×M16 | C22×D13 | 1 | 2 | yes | — |
| 382 | C22×C8 | — | 13 | 1 | no | — |
| 383 | C4⋊Q8 | — | 26 | 1 | no | — |
| 384 | #124 | — | 26 | 1 | no | — |
| 385 | #123 | — | 26 | 2 | no | — |
| 386 | C22⋊Q8 | — | 26 | 2 | no | — |
| 387 | #117 | — | 13 | 1 | no | — |
| 388 | #108 | — | 26 | 4 | no | — |
| 389 | #104 | — | 26 | 4 | no | — |
| 390 | #103 | — | 26 | 1 | no | — |
| 391 | #103 | — | 26 | 2 | no | — |
| 392 | #102 | — | 26 | 1 | no | — |
| 393 | #101 | — | 2 | 1 | no | — |
| 394 | #101 | — | 2 | 4 | no | — |
| 395 | #101 | — | 26 | 4 | no | — |
| 396 | #101 | — | 26 | 2 | no | — |
| 397 | #101 | C22⋊D13 | 1 | 2 | yes | — |
| 398 | #100 | — | 2 | 1 | no | — |
| 399 | #100 | — | 26 | 2 | no | — |
| 400 | #100 | C22⋊D13 | 1 | 2 | yes | — |
| 401 | C22⋊C8 | — | 26 | 2 | no | — |
| 402 | C22⋊C8 | — | 52 | 2 | no | — |
| 403 | C2×C13 | — | 2 | 1 | no | — |
| 404 | C2×C13 | — | 2 | 2 | no | — |
| 405 | C2×C13 | — | 4 | 2 | no | — |
| 406 | C2×C13 | — | 4 | 2 | no | — |
| 407 | C2×C13 | #2410 | 1 | 1 | yes | characteristic |
| 408 | D13 | — | 8 | 2 | no | — |
| 409 | #41 | — | 2 | 2 | no | — |
| 410 | #41 | — | 2 | 2 | no | — |
| 411 | #41 | — | 2 | 2 | no | — |
| 412 | #41 | — | 2 | 4 | no | — |
| 413 | #41 | — | 4 | 2 | no | — |
| 414 | #41 | — | 4 | 4 | no | — |
| 415 | #41 | — | 4 | 8 | no | — |
| 416 | #41 | — | 26 | 4 | no | — |
| 417 | #41 | — | 26 | 2 | no | — |
| 418 | #41 | — | 26 | 2 | no | — |
| 419 | #41 | — | 26 | 2 | no | — |
| 420 | #41 | — | 26 | 2 | no | — |
| 421 | #41 | — | 52 | 2 | no | — |
| 422 | #41 | — | 52 | 4 | no | — |
| 423 | #41 | — | 52 | 2 | no | — |
| 424 | #41 | — | 52 | 2 | no | — |
| 425 | #41 | — | 52 | 2 | no | — |
| 426 | #41 | D4×D13 | 1 | 4 | yes | — |
| 427 | C2×Q8 | — | 2 | 2 | no | — |
| 428 | C2×Q8 | — | 2 | 1 | no | — |
| 429 | C2×Q8 | — | 2 | 4 | no | — |
| 430 | C2×Q8 | — | 2 | 2 | no | — |
| 431 | C2×Q8 | — | 2 | 2 | no | — |
| 432 | C2×Q8 | — | 4 | 2 | no | — |
| 433 | C2×Q8 | — | 4 | 4 | no | — |
| 434 | C2×Q8 | — | 13 | 2 | no | — |
| 435 | C2×Q8 | — | 26 | 2 | no | — |
| 436 | C2×Q8 | — | 26 | 1 | no | — |
| 437 | C2×Q8 | — | 26 | 2 | no | — |
| 438 | C2×Q8 | — | 26 | 2 | no | — |
| 439 | C2×Q8 | — | 26 | 1 | no | — |
| 440 | C2×Q8 | — | 52 | 2 | no | — |
| 441 | C2×Q8 | C2×D52 | 1 | 2 | yes | — |
| 442 | C2×Q8 | C2×D52 | 1 | 1 | yes | characteristic |
| 443 | C2×Q8 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 444 | C2×D4 | — | 2 | 1 | no | — |
| 445 | C2×D4 | — | 2 | 2 | no | — |
| 446 | C2×D4 | — | 13 | 2 | no | — |
| 447 | C2×D4 | — | 26 | 2 | no | — |
| 448 | C2×D4 | — | 26 | 2 | no | — |
| 449 | C2×D4 | — | 52 | 2 | no | — |
| 450 | C2×D4 | — | 52 | 4 | no | — |
| 451 | C2×D4 | — | 52 | 2 | no | — |
| 452 | C2×D4 | C2×D52 | 1 | 1 | yes | characteristic |
| 453 | C2×D4 | #6127 | 1 | 2 | yes | — |
| 454 | C2×D4 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 455 | C22×C4 | — | 2 | 1 | no | — |
| 456 | C22×C4 | — | 2 | 2 | no | — |
| 457 | C22×C4 | — | 2 | 1 | no | — |
| 458 | C22×C4 | — | 2 | 2 | no | — |
| 459 | C22×C4 | — | 26 | 2 | no | — |
| 460 | C22×C4 | — | 26 | 1 | no | — |
| 461 | C22×C4 | — | 52 | 2 | no | — |
| 462 | C22×C4 | C2×D52 | 1 | 2 | yes | — |
| 463 | C22×C4 | C23×D13 | 1 | 1 | yes | characteristic |
| 464 | Q16 | — | 26 | 8 | no | — |
| 465 | Q16 | — | 26 | 4 | no | — |
| 466 | Q16 | — | 52 | 4 | no | — |
| 467 | Q16 | — | 52 | 4 | no | — |
| 468 | Q16 | — | 52 | 2 | no | — |
| 469 | SD16 | — | 26 | 8 | no | — |
| 470 | SD16 | — | 26 | 4 | no | — |
| 471 | SD16 | — | 26 | 4 | no | — |
| 472 | SD16 | — | 52 | 4 | no | — |
| 473 | SD16 | — | 52 | 2 | no | — |
| 474 | D8 | — | 26 | 4 | no | — |
| 475 | M16 | — | 2 | 2 | no | — |
| 476 | M16 | — | 2 | 2 | no | — |
| 477 | M16 | — | 2 | 2 | no | — |
| 478 | M16 | — | 4 | 4 | no | — |
| 479 | M16 | — | 13 | 4 | no | — |
| 480 | M16 | — | 26 | 4 | no | — |
| 481 | M16 | — | 26 | 2 | no | — |
| 482 | M16 | — | 26 | 2 | no | — |
| 483 | M16 | C2×C22⋊D13 | 1 | 4 | yes | — |
| 484 | C2×C8 | — | 2 | 2 | no | — |
| 485 | C2×C8 | — | 2 | 2 | no | — |
| 486 | C2×C8 | — | 4 | 4 | no | — |
| 487 | C2×C8 | — | 26 | 4 | no | — |
| 488 | C2×C8 | — | 26 | 2 | no | — |
| 489 | C2×C8 | — | 26 | 1 | no | — |
| 490 | C2×C8 | — | 26 | 1 | no | — |
| 491 | C2×C8 | — | 26 | 2 | no | — |
| 492 | C4⋊C4 | — | 26 | 1 | no | — |
| 493 | C4⋊C4 | — | 52 | 2 | no | — |
| 494 | C22⋊C4 | — | 26 | 1 | no | — |
| 495 | C22⋊C4 | — | 52 | 2 | no | — |
| 496 | C42 | — | 26 | 1 | no | — |
| 497 | C13 | #24423 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 498 | C23 | — | 2 | 1 | no | — |
| 499 | C23 | — | 26 | 2 | no | — |
| 500 | C23 | — | 52 | 2 | no | — |
| 501 | C23 | #88184 | 1 | 2 | yes | — |
| 502 | C23 | C2×#6127 | 1 | 1 | yes | characteristic |
| 503 | Q8 | — | 2 | 1 | no | — |
| 504 | Q8 | — | 2 | 2 | no | — |
| 505 | Q8 | — | 2 | 2 | no | — |
| 506 | Q8 | — | 2 | 2 | no | — |
| 507 | Q8 | — | 4 | 4 | no | — |
| 508 | Q8 | — | 4 | 2 | no | — |
| 509 | Q8 | — | 26 | 2 | no | — |
| 510 | Q8 | — | 26 | 2 | no | — |
| 511 | Q8 | — | 52 | 2 | no | — |
| 512 | Q8 | — | 52 | 1 | no | — |
| 513 | Q8 | — | 52 | 1 | no | — |
| 514 | Q8 | — | 52 | 2 | no | — |
| 515 | Q8 | #88136 | 1 | 2 | yes | — |
| 516 | D4 | — | 2 | 4 | no | — |
| 517 | D4 | — | 2 | 4 | no | — |
| 518 | D4 | — | 2 | 1 | no | — |
| 519 | D4 | — | 2 | 2 | no | — |
| 520 | D4 | — | 4 | 4 | no | — |
| 521 | D4 | — | 26 | 2 | no | — |
| 522 | D4 | — | 26 | 2 | no | — |
| 523 | D4 | — | 52 | 2 | no | — |
| 524 | D4 | — | 52 | 4 | no | — |
| 525 | D4 | — | 52 | 2 | no | — |
| 526 | D4 | — | 52 | 2 | no | — |
| 527 | D4 | #88136 | 1 | 2 | yes | — |
| 528 | C2×C4 | — | 2 | 1 | no | — |
| 529 | C2×C4 | — | 2 | 2 | no | — |
| 530 | C2×C4 | — | 2 | 2 | no | — |
| 531 | C2×C4 | — | 2 | 4 | no | — |
| 532 | C2×C4 | — | 2 | 2 | no | — |
| 533 | C2×C4 | — | 4 | 4 | no | — |
| 534 | C2×C4 | — | 4 | 4 | no | — |
| 535 | C2×C4 | — | 4 | 2 | no | — |
| 536 | C2×C4 | — | 26 | 2 | no | — |
| 537 | C2×C4 | — | 52 | 4 | no | — |
| 538 | C2×C4 | — | 52 | 2 | no | — |
| 539 | C2×C4 | — | 52 | 2 | no | — |
| 540 | C2×C4 | — | 52 | 2 | no | — |
| 541 | C2×C4 | — | 52 | 2 | no | — |
| 542 | C2×C4 | — | 52 | 1 | no | — |
| 543 | C2×C4 | — | 52 | 1 | no | — |
| 544 | C2×C4 | #88184 | 1 | 2 | yes | — |
| 545 | C2×C4 | C22×D52 | 1 | 1 | yes | characteristic |
| 546 | C2×C4 | C2×D4×D13 | 1 | 2 | yes | — |
| 547 | C2×C4 | #88251 | 1 | 2 | yes | — |
| 548 | C2×C4 | C22×C22⋊D13 | 1 | 1 | yes | characteristic |
| 549 | C8 | — | 2 | 4 | no | — |
| 550 | C8 | — | 4 | 2 | no | — |
| 551 | C8 | — | 26 | 4 | no | — |
| 552 | C8 | — | 52 | 1 | no | — |
| 553 | C8 | — | 52 | 1 | no | — |
| 554 | C22 | — | 2 | 2 | no | — |
| 555 | C22 | — | 2 | 2 | no | — |
| 556 | C22 | — | 4 | 1 | no | — |
| 557 | C22 | — | 4 | 2 | no | — |
| 558 | C22 | — | 8 | 1 | no | — |
| 559 | C22 | — | 52 | 2 | no | — |
| 560 | C22 | — | 104 | 2 | no | — |
| 561 | C22 | — | 208 | 2 | no | — |
| 562 | C22 | #11719195 | 1 | 2 | yes | — |
| 563 | C22 | C2×#88184 | 1 | 1 | yes | characteristic |
| 564 | C4 | — | 2 | 2 | no | — |
| 565 | C4 | — | 2 | 2 | no | — |
| 566 | C4 | — | 4 | 2 | no | — |
| 567 | C4 | — | 52 | 2 | no | — |
| 568 | C4 | — | 104 | 1 | no | — |
| 569 | C4 | — | 104 | 1 | no | — |
| 570 | C4 | C2×#88136 | 1 | 1 | yes | characteristic |
| 571 | C4 | #11719198 | 1 | 1 | yes | characteristic |
| 572 | C4 | D4×C22⋊D13 | 1 | 2 | yes | — |
| 573 | C2 | — | 2 | 1 | no | — |
| 574 | C2 | — | 2 | 2 | no | — |
| 575 | C2 | — | 4 | 2 | no | — |
| 576 | C2 | — | 4 | 2 | no | — |
| 577 | C2 | — | 104 | 2 | no | — |
| 578 | C2 | #13118204 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #13124573 | C2 | semidirect |
| 3. #13124217 | C2 | semidirect |
| 4. #13124131 | C2 | semidirect |
| 5. #13116115 | C2 | semidirect |
| 6. #13115956 | C2 | semidirect |
| 7. #13115386 | C2 | semidirect |
| 8. #13115198 | C2 | semidirect |
| 9. #13115058 | C2 | semidirect |
| 10. #13114785 | C2 | semidirect |
| 11. C13×#2889 | C2 | semidirect |
| 14. C13×#568 | C22 | semidirect |
| 18. C2×#88205 | C22 | semidirect |
| 22. C22×#6107 | C22 | semidirect |
| 30. C2×C13×#101 | C22 | semidirect |
| 33. #11718894 | C22 | semidirect |
| 35. #11718886 | C22 | semidirect |
| 39. C2×#88064 | C22 | semidirect |
| 42. #11718786 | C22 | semidirect |
| 45. #11718150 | C22 | semidirect |
| 46. #11718148 | C22 | semidirect |
| 213. #2889 | D13 | semidirect |
| 288. #568 | C2×D13 | semidirect |
| 306. C2×#101 | C2×D13 | semidirect |
| 497. C13 | #24423 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13129623 | 2 |
| #13124573 | 2 |
| #13124217 | 2 |
| #13124131 | 2 |
| #13116115 | 2 |
| #13115956 | 2 |
| #13115386 | 2 |
| #13115198 | 2 |
| #13115058 | 2 |
| #13114785 | 2 |
| C13×#2889 | 2 |
| #24423 | 13 |