← C13×#33954 #15720293
Subgroups — C13×#33954 #15720293
Order 3328.
450 conjugacy classes of subgroups.
The subgroup lattice has 310 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C13×#3383 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | Q8×C13×Q16 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C13×#2255 | C2 | 1 | 2 | yes | maximal |
| 4 | C13×#2254 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C13×#2229 | C2 | 1 | 2 | yes | maximal |
| 6 | C13×#2227 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | C13×#2225 | C2 | 1 | 2 | yes | maximal |
| 8 | C13×#2225 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | C13×#2183 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | C13×#2176 | C2 | 1 | 2 | yes | maximal |
| 11 | C4×C13×Q32 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | Q82×C13 | — | 2 | 1 | no | — |
| 13 | C13×#557 | — | 2 | 1 | no | — |
| 14 | C2×C13×Q32 | C22 | 1 | 1 | yes | characteristic |
| 15 | C13×#500 | C22 | 1 | 1 | yes | characteristic |
| 16 | C13×#500 | C22 | 1 | 1 | yes | characteristic |
| 17 | C13×#500 | C22 | 1 | 2 | yes | — |
| 18 | C13×#499 | C22 | 1 | 2 | yes | — |
| 19 | C13×#479 | — | 2 | 2 | no | — |
| 20 | C13×#477 | — | 2 | 1 | no | — |
| 21 | C13×#477 | — | 2 | 2 | no | — |
| 22 | C13×#475 | — | 2 | 1 | no | — |
| 23 | C8×Q8×C13 | C22 | 1 | 1 | yes | characteristic |
| 24 | C4×C13×Q16 | C22 | 1 | 1 | yes | characteristic |
| 25 | C4×C13×Q16 | C22 | 1 | 2 | yes | — |
| 26 | C4×C13×Q16 | C22 | 1 | 1 | yes | characteristic |
| 27 | C4×C13×Q16 | C22 | 1 | 2 | yes | — |
| 28 | C13×#367 | C22 | 1 | 2 | yes | — |
| 29 | C13×#367 | C22 | 1 | 2 | yes | — |
| 30 | C13×#367 | C22 | 1 | 2 | yes | — |
| 31 | C13×#366 | C22 | 1 | 1 | yes | characteristic |
| 32 | C13×#366 | C22 | 1 | 2 | yes | — |
| 33 | C13×C4⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 34 | C13×C4⋊C16 | C22 | 1 | 2 | yes | — |
| 35 | C13×#358 | C22 | 1 | 1 | yes | characteristic |
| 36 | C13×#358 | C22 | 1 | 1 | yes | characteristic |
| 37 | C13×#358 | C22 | 1 | 2 | yes | — |
| 38 | C13×#358 | C22 | 1 | 2 | yes | — |
| 39 | C13×#346 | C22 | 1 | 2 | yes | — |
| 40 | C4×C13×C16 | C22 | 1 | 1 | yes | characteristic |
| 41 | C2×C13×Q16 | C23 | 1 | 1 | yes | characteristic |
| 42 | C2×C13×Q16 | C23 | 1 | 1 | yes | characteristic |
| 43 | C13×C4⋊Q8 | — | 2 | 1 | no | — |
| 44 | C13×C4⋊Q8 | — | 2 | 2 | no | — |
| 45 | C13×C4⋊Q8 | — | 2 | 1 | no | — |
| 46 | C13×C4⋊Q8 | — | 4 | 1 | no | — |
| 47 | C13×C4⋊Q8 | — | 4 | 1 | no | — |
| 48 | C13×C4⋊Q8 | — | 4 | 2 | no | — |
| 49 | C13×#125 | — | 2 | 2 | no | — |
| 50 | C13×#125 | — | 4 | 2 | no | — |
| 51 | C4×Q8×C13 | — | 2 | 1 | no | — |
| 52 | C4×Q8×C13 | — | 2 | 2 | no | — |
| 53 | C4×Q8×C13 | — | 2 | 1 | no | — |
| 54 | C4×Q8×C13 | — | 2 | 2 | no | — |
| 55 | C4×Q8×C13 | — | 4 | 1 | no | — |
| 56 | C4×Q8×C13 | — | 4 | 1 | no | — |
| 57 | C4×Q8×C13 | D4 | 1 | 1 | yes | characteristic |
| 58 | C13×Q32 | Q8 | 1 | 4 | yes | complemented |
| 59 | C2×C13×C16 | C23 | 1 | 1 | yes | characteristic |
| 60 | C2×C13×C16 | C23 | 1 | 2 | yes | — |
| 61 | C2×C13×C16 | C23 | 1 | 1 | yes | characteristic |
| 62 | C13×#107 | — | 2 | 2 | no | — |
| 63 | C13×#107 | — | 2 | 1 | no | — |
| 64 | C13×#107 | — | 2 | 1 | no | — |
| 65 | C13×#107 | C23 | 1 | 1 | yes | characteristic |
| 66 | C13×#107 | C23 | 1 | 1 | yes | characteristic |
| 67 | C13×#107 | C23 | 1 | 2 | yes | — |
| 68 | C13×#107 | C23 | 1 | 2 | yes | — |
| 69 | C13×#106 | — | 2 | 2 | no | — |
| 70 | C13×C4⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 71 | C13×C4⋊C8 | D4 | 1 | 2 | yes | — |
| 72 | C13×#103 | — | 2 | 2 | no | — |
| 73 | C13×#103 | — | 2 | 2 | no | — |
| 74 | C13×#103 | — | 2 | 1 | no | — |
| 75 | C13×#103 | — | 2 | 1 | no | — |
| 76 | C4×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 77 | C4×C8×C13 | C23 | 1 | 2 | yes | — |
| 78 | #33954 | C13 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 79 | C2×Q8×C13 | — | 2 | 1 | no | — |
| 80 | C2×Q8×C13 | — | 2 | 1 | no | — |
| 81 | C2×Q8×C13 | — | 4 | 1 | no | — |
| 82 | C2×Q8×C13 | — | 4 | 2 | no | — |
| 83 | C2×Q8×C13 | — | 4 | 1 | no | — |
| 84 | C2×Q8×C13 | D8 | 1 | 1 | yes | characteristic |
| 85 | C13×Q16 | — | 2 | 1 | no | — |
| 86 | C13×Q16 | — | 2 | 1 | no | — |
| 87 | C13×Q16 | C2×Q8 | 1 | 2 | yes | — |
| 88 | C13×Q16 | C2×Q8 | 1 | 2 | yes | — |
| 89 | C2×C8×C13 | C2×D4 | 1 | 2 | yes | — |
| 90 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 91 | C2×C8×C13 | C24 | 1 | 1 | yes | characteristic |
| 92 | C13×C4⋊C4 | — | 2 | 1 | no | — |
| 93 | C13×C4⋊C4 | — | 2 | 2 | no | — |
| 94 | C13×C4⋊C4 | — | 2 | 2 | no | — |
| 95 | C13×C4⋊C4 | — | 2 | 1 | no | — |
| 96 | C13×C4⋊C4 | — | 4 | 1 | no | — |
| 97 | C13×C4⋊C4 | — | 4 | 2 | no | — |
| 98 | C13×C4⋊C4 | — | 4 | 2 | no | — |
| 99 | C13×C4⋊C4 | — | 4 | 1 | no | — |
| 100 | C13×C4⋊C4 | — | 4 | 2 | no | — |
| 101 | C13×C4⋊C4 | — | 4 | 2 | no | — |
| 102 | C13×C4⋊C4 | — | 4 | 1 | no | — |
| 103 | C13×C4⋊C4 | — | 4 | 2 | no | — |
| 104 | C13×C4⋊C4 | — | 4 | 1 | no | — |
| 105 | C13×C4⋊C4 | D8 | 1 | 1 | yes | characteristic |
| 106 | C13×C4⋊C4 | D8 | 1 | 2 | yes | — |
| 107 | C42×C13 | — | 4 | 2 | no | — |
| 108 | C42×C13 | — | 4 | 1 | no | — |
| 109 | C42×C13 | — | 4 | 2 | no | — |
| 110 | C42×C13 | — | 4 | 1 | no | — |
| 111 | C42×C13 | C2×D4 | 1 | 2 | yes | — |
| 112 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 113 | C13×C16 | — | 2 | 1 | no | — |
| 114 | C13×C16 | — | 2 | 2 | no | — |
| 115 | C13×C16 | C2×Q8 | 1 | 2 | yes | — |
| 116 | #3383 | C2×C13 | 1 | 1 | yes | characteristic |
| 117 | Q8×Q16 | C2×C13 | 1 | 1 | yes | characteristic |
| 118 | #2255 | C2×C13 | 1 | 2 | yes | — |
| 119 | #2254 | C2×C13 | 1 | 1 | yes | characteristic |
| 120 | #2229 | C2×C13 | 1 | 2 | yes | — |
| 121 | #2227 | C2×C13 | 1 | 1 | yes | characteristic |
| 122 | #2225 | C2×C13 | 1 | 2 | yes | — |
| 123 | #2225 | C2×C13 | 1 | 1 | yes | characteristic |
| 124 | #2183 | C2×C13 | 1 | 1 | yes | characteristic |
| 125 | #2176 | C2×C13 | 1 | 2 | yes | — |
| 126 | C4×Q32 | C2×C13 | 1 | 1 | yes | characteristic |
| 127 | Q8×C13 | — | 2 | 2 | no | — |
| 128 | Q8×C13 | — | 2 | 2 | no | — |
| 129 | Q8×C13 | — | 2 | 2 | no | — |
| 130 | Q8×C13 | — | 4 | 1 | no | — |
| 131 | Q8×C13 | — | 4 | 1 | no | — |
| 132 | Q8×C13 | — | 8 | 2 | no | — |
| 133 | Q8×C13 | — | 16 | 2 | no | — |
| 134 | Q8×C13 | — | 16 | 1 | no | — |
| 135 | C2×C4×C13 | — | 4 | 1 | no | — |
| 136 | C2×C4×C13 | — | 4 | 1 | no | — |
| 137 | C2×C4×C13 | — | 4 | 1 | no | — |
| 138 | C2×C4×C13 | — | 4 | 2 | no | — |
| 139 | C2×C4×C13 | — | 4 | 2 | no | — |
| 140 | C2×C4×C13 | — | 4 | 1 | no | — |
| 141 | C2×C4×C13 | C2×D8 | 1 | 2 | yes | — |
| 142 | C2×C4×C13 | C2×D8 | 1 | 2 | yes | — |
| 143 | C2×C4×C13 | C2×D8 | 1 | 1 | yes | characteristic |
| 144 | C2×C4×C13 | C2×D8 | 1 | 1 | yes | characteristic |
| 145 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 146 | C8×C13 | — | 2 | 2 | no | — |
| 147 | C8×C13 | — | 2 | 1 | no | — |
| 148 | C8×C13 | C22×Q8 | 1 | 1 | yes | characteristic |
| 149 | C8×C13 | 2−1+4 | 1 | 1 | yes | characteristic |
| 150 | Q82 | — | 2 | 1 | no | — |
| 151 | #557 | — | 2 | 1 | no | — |
| 152 | C2×Q32 | C22×C13 | 1 | 1 | yes | characteristic |
| 153 | #500 | C22×C13 | 1 | 2 | yes | — |
| 154 | #500 | C22×C13 | 1 | 1 | yes | characteristic |
| 155 | #500 | C22×C13 | 1 | 1 | yes | characteristic |
| 156 | #499 | C22×C13 | 1 | 2 | yes | — |
| 157 | #479 | — | 2 | 2 | no | — |
| 158 | #477 | — | 2 | 1 | no | — |
| 159 | #477 | — | 2 | 2 | no | — |
| 160 | #475 | — | 2 | 1 | no | — |
| 161 | C8×Q8 | C22×C13 | 1 | 1 | yes | characteristic |
| 162 | C4×Q16 | C22×C13 | 1 | 1 | yes | characteristic |
| 163 | C4×Q16 | C22×C13 | 1 | 2 | yes | — |
| 164 | C4×Q16 | C22×C13 | 1 | 1 | yes | characteristic |
| 165 | C4×Q16 | C22×C13 | 1 | 2 | yes | — |
| 166 | #367 | C22×C13 | 1 | 2 | yes | — |
| 167 | #367 | C22×C13 | 1 | 2 | yes | — |
| 168 | #367 | C22×C13 | 1 | 2 | yes | — |
| 169 | #366 | C22×C13 | 1 | 1 | yes | characteristic |
| 170 | #366 | C22×C13 | 1 | 2 | yes | — |
| 171 | C4⋊C16 | C22×C13 | 1 | 1 | yes | characteristic |
| 172 | C4⋊C16 | C22×C13 | 1 | 2 | yes | — |
| 173 | #358 | C22×C13 | 1 | 1 | yes | characteristic |
| 174 | #358 | C22×C13 | 1 | 1 | yes | characteristic |
| 175 | #358 | C22×C13 | 1 | 2 | yes | — |
| 176 | #358 | C22×C13 | 1 | 2 | yes | — |
| 177 | #346 | C22×C13 | 1 | 2 | yes | — |
| 178 | C4×C16 | C22×C13 | 1 | 1 | yes | characteristic |
| 179 | C22×C13 | C22×D8 | 1 | 1 | yes | characteristic |
| 180 | C4×C13 | — | 2 | 2 | no | — |
| 181 | C4×C13 | — | 2 | 2 | no | — |
| 182 | C4×C13 | — | 2 | 1 | no | — |
| 183 | C4×C13 | — | 4 | 2 | no | — |
| 184 | C4×C13 | — | 4 | 2 | no | — |
| 185 | C4×C13 | — | 8 | 2 | no | — |
| 186 | C4×C13 | — | 8 | 1 | no | — |
| 187 | C4×C13 | — | 8 | 2 | no | — |
| 188 | C4×C13 | — | 8 | 1 | no | — |
| 189 | C4×C13 | #510 | 1 | 2 | yes | — |
| 190 | C4×C13 | D4×Q8 | 1 | 1 | yes | characteristic |
| 191 | C4×C13 | #578 | 1 | 1 | yes | characteristic |
| 192 | C2×Q16 | C23×C13 | 1 | 1 | yes | characteristic |
| 193 | C2×Q16 | C23×C13 | 1 | 1 | yes | characteristic |
| 194 | C4⋊Q8 | — | 2 | 1 | no | — |
| 195 | C4⋊Q8 | — | 2 | 2 | no | — |
| 196 | C4⋊Q8 | — | 2 | 1 | no | — |
| 197 | C4⋊Q8 | — | 4 | 1 | no | — |
| 198 | C4⋊Q8 | — | 4 | 1 | no | — |
| 199 | C4⋊Q8 | — | 4 | 2 | no | — |
| 200 | #125 | — | 2 | 2 | no | — |
| 201 | #125 | — | 4 | 2 | no | — |
| 202 | C4×Q8 | — | 2 | 1 | no | — |
| 203 | C4×Q8 | — | 2 | 2 | no | — |
| 204 | C4×Q8 | — | 2 | 2 | no | — |
| 205 | C4×Q8 | — | 2 | 1 | no | — |
| 206 | C4×Q8 | — | 4 | 1 | no | — |
| 207 | C4×Q8 | — | 4 | 1 | no | — |
| 208 | C4×Q8 | D4×C13 | 1 | 1 | yes | characteristic |
| 209 | Q32 | Q8×C13 | 1 | 4 | yes | complemented |
| 210 | C2×C16 | C23×C13 | 1 | 1 | yes | characteristic |
| 211 | C2×C16 | C23×C13 | 1 | 2 | yes | — |
| 212 | C2×C16 | C23×C13 | 1 | 1 | yes | characteristic |
| 213 | #107 | — | 2 | 2 | no | — |
| 214 | #107 | — | 2 | 1 | no | — |
| 215 | #107 | — | 2 | 1 | no | — |
| 216 | #107 | C23×C13 | 1 | 1 | yes | characteristic |
| 217 | #107 | C23×C13 | 1 | 1 | yes | characteristic |
| 218 | #107 | C23×C13 | 1 | 2 | yes | — |
| 219 | #107 | C23×C13 | 1 | 2 | yes | — |
| 220 | #106 | — | 2 | 2 | no | — |
| 221 | C4⋊C8 | D4×C13 | 1 | 1 | yes | characteristic |
| 222 | C4⋊C8 | D4×C13 | 1 | 2 | yes | — |
| 223 | #103 | — | 2 | 2 | no | — |
| 224 | #103 | — | 2 | 2 | no | — |
| 225 | #103 | — | 2 | 1 | no | — |
| 226 | #103 | — | 2 | 1 | no | — |
| 227 | C4×C8 | C23×C13 | 1 | 1 | yes | characteristic |
| 228 | C4×C8 | C23×C13 | 1 | 2 | yes | — |
| 229 | C2×C13 | Q8×D8 | 1 | 1 | yes | characteristic |
| 230 | C2×C13 | C2×#510 | 1 | 1 | yes | characteristic |
| 231 | C2×C13 | #3416 | 1 | 1 | yes | characteristic |
| 232 | C2×Q8 | — | 2 | 1 | no | — |
| 233 | C2×Q8 | — | 2 | 1 | no | — |
| 234 | C2×Q8 | — | 4 | 1 | no | — |
| 235 | C2×Q8 | — | 4 | 2 | no | — |
| 236 | C2×Q8 | — | 4 | 1 | no | — |
| 237 | C2×Q8 | C13×D8 | 1 | 1 | yes | characteristic |
| 238 | Q16 | — | 2 | 1 | no | — |
| 239 | Q16 | — | 2 | 1 | no | — |
| 240 | Q16 | C2×Q8×C13 | 1 | 2 | yes | — |
| 241 | Q16 | C2×Q8×C13 | 1 | 2 | yes | — |
| 242 | C2×C8 | C2×D4×C13 | 1 | 2 | yes | — |
| 243 | C2×C8 | C2×D4×C13 | 1 | 1 | yes | characteristic |
| 244 | C2×C8 | C24×C13 | 1 | 1 | yes | characteristic |
| 245 | C4⋊C4 | — | 2 | 1 | no | — |
| 246 | C4⋊C4 | — | 2 | 2 | no | — |
| 247 | C4⋊C4 | — | 2 | 2 | no | — |
| 248 | C4⋊C4 | — | 2 | 1 | no | — |
| 249 | C4⋊C4 | — | 4 | 1 | no | — |
| 250 | C4⋊C4 | — | 4 | 2 | no | — |
| 251 | C4⋊C4 | — | 4 | 2 | no | — |
| 252 | C4⋊C4 | — | 4 | 1 | no | — |
| 253 | C4⋊C4 | — | 4 | 2 | no | — |
| 254 | C4⋊C4 | — | 4 | 2 | no | — |
| 255 | C4⋊C4 | — | 4 | 1 | no | — |
| 256 | C4⋊C4 | — | 4 | 2 | no | — |
| 257 | C4⋊C4 | — | 4 | 1 | no | — |
| 258 | C4⋊C4 | C13×D8 | 1 | 1 | yes | characteristic |
| 259 | C4⋊C4 | C13×D8 | 1 | 2 | yes | — |
| 260 | C42 | — | 4 | 2 | no | — |
| 261 | C42 | — | 4 | 1 | no | — |
| 262 | C42 | — | 4 | 2 | no | — |
| 263 | C42 | — | 4 | 1 | no | — |
| 264 | C42 | C2×D4×C13 | 1 | 2 | yes | — |
| 265 | C42 | C2×D4×C13 | 1 | 1 | yes | characteristic |
| 266 | C16 | — | 2 | 1 | no | — |
| 267 | C16 | — | 2 | 2 | no | — |
| 268 | C16 | C2×Q8×C13 | 1 | 2 | yes | — |
| 269 | C13 | #33954 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 270 | Q8 | — | 2 | 2 | no | — |
| 271 | Q8 | — | 2 | 2 | no | — |
| 272 | Q8 | — | 2 | 2 | no | — |
| 273 | Q8 | — | 4 | 1 | no | — |
| 274 | Q8 | — | 4 | 1 | no | — |
| 275 | Q8 | — | 8 | 2 | no | — |
| 276 | Q8 | — | 16 | 2 | no | — |
| 277 | Q8 | — | 16 | 1 | no | — |
| 278 | C2×C4 | — | 4 | 1 | no | — |
| 279 | C2×C4 | — | 4 | 1 | no | — |
| 280 | C2×C4 | — | 4 | 1 | no | — |
| 281 | C2×C4 | — | 4 | 2 | no | — |
| 282 | C2×C4 | — | 4 | 2 | no | — |
| 283 | C2×C4 | — | 4 | 1 | no | — |
| 284 | C2×C4 | C2×C13×D8 | 1 | 2 | yes | — |
| 285 | C2×C4 | C2×C13×D8 | 1 | 2 | yes | — |
| 286 | C2×C4 | C2×C13×D8 | 1 | 1 | yes | characteristic |
| 287 | C2×C4 | C2×C13×D8 | 1 | 1 | yes | characteristic |
| 288 | C2×C4 | C22×D4×C13 | 1 | 1 | yes | characteristic |
| 289 | C8 | — | 2 | 2 | no | — |
| 290 | C8 | — | 2 | 1 | no | — |
| 291 | C8 | C22×Q8×C13 | 1 | 1 | yes | characteristic |
| 292 | C8 | C13×2−1+4 | 1 | 1 | yes | characteristic |
| 293 | C22 | C22×C13×D8 | 1 | 1 | yes | characteristic |
| 294 | C4 | — | 2 | 2 | no | — |
| 295 | C4 | — | 2 | 2 | no | — |
| 296 | C4 | — | 2 | 1 | no | — |
| 297 | C4 | — | 4 | 2 | no | — |
| 298 | C4 | — | 4 | 2 | no | — |
| 299 | C4 | — | 8 | 2 | no | — |
| 300 | C4 | — | 8 | 1 | no | — |
| 301 | C4 | — | 8 | 2 | no | — |
| 302 | C4 | — | 8 | 1 | no | — |
| 303 | C4 | C13×#510 | 1 | 2 | yes | — |
| 304 | C4 | D4×Q8×C13 | 1 | 1 | yes | characteristic |
| 305 | C4 | C13×#578 | 1 | 1 | yes | characteristic |
| 306 | C2 | Q8×C13×D8 | 1 | 1 | yes | characteristic |
| 307 | C2 | C2×C13×#510 | 1 | 1 | yes | characteristic |
| 308 | C2 | C13×#3416 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta