Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
800 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | D13×H(5,𝔽2) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11719294 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | C13×B(4,𝔽2) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11718904 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11718693 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | D13×#99 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #11718403 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | C13×H(5,𝔽2) | C22 | 1 | 1 | yes | characteristic |
| 9 | C22×C22⋊D13 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | #88256 | — | 2 | 3 | no | — |
| 11 | #41×D13 | — | 2 | 3 | no | — |
| 12 | #88251 | — | 2 | 3 | no | — |
| 13 | #88251 | C22 | 1 | 3 | yes | — |
| 14 | C2×D4×D13 | — | 2 | 3 | no | — |
| 15 | C2×D4×D13 | C22 | 1 | 3 | yes | — |
| 16 | C13×#120 | C22 | 1 | 3 | yes | complemented |
| 17 | #88207 | C22 | 1 | 3 | yes | complemented |
| 18 | #88192 | — | 2 | 3 | no | — |
| 19 | #88191 | — | 2 | 3 | no | — |
| 20 | #88189 | C22 | 1 | 3 | yes | complemented |
| 21 | #88140 | C22 | 1 | 3 | yes | complemented |
| 22 | #88138 | — | 2 | 3 | no | — |
| 23 | #88137 | — | 2 | 3 | no | — |
| 24 | C22⋊C4×D13 | C22 | 1 | 3 | yes | complemented |
| 25 | C13×#99 | C22 | 1 | 3 | yes | complemented |
| 26 | #88074 | C22 | 1 | 3 | yes | complemented |
| 27 | #88046 | C22 | 1 | 6 | yes | complemented |
| 28 | C24×C13 | C23 | 1 | 1 | yes | characteristic, complemented |
| 29 | C23×D13 | — | 2 | 1 | no | — |
| 30 | C23×D13 | D4 | 1 | 3 | yes | complemented |
| 31 | C23×D13 | C23 | 1 | 1 | yes | characteristic |
| 32 | C13×#41 | — | 2 | 3 | no | — |
| 33 | C2×D4×C13 | — | 2 | 3 | no | — |
| 34 | C2×D4×C13 | — | 2 | 3 | no | — |
| 35 | C2×D4×C13 | C23 | 1 | 3 | yes | — |
| 36 | C2×C22⋊D13 | — | 2 | 3 | no | — |
| 37 | C2×C22⋊D13 | — | 2 | 3 | no | — |
| 38 | C2×C22⋊D13 | — | 2 | 3 | no | — |
| 39 | C2×C22⋊D13 | — | 2 | 3 | no | — |
| 40 | C2×C22⋊D13 | — | 2 | 3 | no | — |
| 41 | C2×C22⋊D13 | D4 | 1 | 3 | yes | complemented |
| 42 | C2×C22⋊D13 | C23 | 1 | 3 | yes | — |
| 43 | C22×Dic13 | C23 | 1 | 1 | yes | characteristic, complemented |
| 44 | #6131 | — | 2 | 3 | no | — |
| 45 | Q8×D13 | — | 2 | 1 | no | — |
| 46 | #6129 | — | 2 | 3 | no | — |
| 47 | #6129 | — | 2 | 6 | no | — |
| 48 | D4×D13 | — | 2 | 3 | no | — |
| 49 | D4×D13 | — | 2 | 6 | no | — |
| 50 | D4×D13 | — | 2 | 6 | no | — |
| 51 | D4×D13 | — | 2 | 6 | no | — |
| 52 | D4×D13 | — | 2 | 6 | no | — |
| 53 | #6127 | — | 2 | 6 | no | — |
| 54 | #6127 | — | 2 | 3 | no | — |
| 55 | C2×D52 | — | 2 | 3 | no | — |
| 56 | C2×D52 | D4 | 1 | 3 | yes | complemented |
| 57 | C2×C4×D13 | — | 2 | 3 | no | — |
| 58 | C2×C4×D13 | — | 2 | 3 | no | — |
| 59 | C2×C4×D13 | D4 | 1 | 3 | yes | complemented |
| 60 | C13×C22⋊C4 | — | 2 | 3 | no | — |
| 61 | C13×C22⋊C4 | C23 | 1 | 3 | yes | complemented |
| 62 | C22⋊Dic13 | — | 2 | 3 | no | — |
| 63 | C22⋊Dic13 | — | 2 | 3 | no | — |
| 64 | C22⋊Dic13 | C23 | 1 | 3 | yes | complemented |
| 65 | #6103 | — | 2 | 3 | no | — |
| 66 | #6103 | — | 2 | 3 | no | — |
| 67 | C4⋊Dic13 | — | 2 | 3 | no | — |
| 68 | #6101 | — | 2 | 3 | no | — |
| 69 | #3026 | — | 13 | 1 | no | maximal, Sylow |
| 70 | C23×C13 | — | 2 | 1 | no | — |
| 71 | C23×C13 | — | 2 | 3 | no | — |
| 72 | C23×C13 | — | 8 | 1 | no | — |
| 73 | C23×C13 | C2×D4 | 1 | 3 | yes | — |
| 74 | C23×C13 | C24 | 1 | 1 | yes | characteristic |
| 75 | C22×D13 | — | 2 | 3 | no | — |
| 76 | C22×D13 | — | 2 | 3 | no | — |
| 77 | C22×D13 | — | 2 | 3 | no | — |
| 78 | C22×D13 | — | 8 | 1 | no | — |
| 79 | C22×D13 | — | 8 | 3 | no | — |
| 80 | C22×D13 | — | 8 | 2 | no | — |
| 81 | C22×D13 | C2×D4 | 1 | 3 | yes | — |
| 82 | C22×D13 | C2×D4 | 1 | 3 | yes | — |
| 83 | C22×D13 | C2×D4 | 1 | 3 | yes | — |
| 84 | Q8×C13 | — | 2 | 1 | no | — |
| 85 | D4×C13 | — | 2 | 3 | no | — |
| 86 | D4×C13 | — | 2 | 6 | no | — |
| 87 | D4×C13 | — | 8 | 3 | no | — |
| 88 | C2×C4×C13 | — | 2 | 3 | no | — |
| 89 | C2×C4×C13 | — | 2 | 3 | no | — |
| 90 | C2×C4×C13 | C2×D4 | 1 | 3 | yes | — |
| 91 | C22⋊D13 | — | 2 | 6 | no | — |
| 92 | C22⋊D13 | — | 2 | 6 | no | — |
| 93 | C22⋊D13 | — | 2 | 6 | no | — |
| 94 | C22⋊D13 | — | 4 | 1 | no | — |
| 95 | C22⋊D13 | — | 4 | 3 | no | — |
| 96 | C22⋊D13 | — | 8 | 3 | no | — |
| 97 | C2×Dic13 | — | 2 | 3 | no | — |
| 98 | C2×Dic13 | — | 2 | 3 | no | — |
| 99 | C2×Dic13 | — | 2 | 3 | no | — |
| 100 | C2×Dic13 | C2×D4 | 1 | 3 | yes | — |
| 101 | D52 | — | 2 | 3 | no | — |
| 102 | D52 | — | 2 | 6 | no | — |
| 103 | C4×D13 | — | 2 | 6 | no | — |
| 104 | C4×D13 | — | 2 | 3 | no | — |
| 105 | C4×D13 | — | 2 | 3 | no | — |
| 106 | C4×D13 | — | 8 | 3 | no | — |
| 107 | Dic26 | — | 2 | 3 | no | — |
| 108 | C2×H(5,𝔽2) | — | 13 | 1 | no | — |
| 109 | #534 | — | 13 | 3 | no | — |
| 110 | #458 | — | 13 | 1 | no | — |
| 111 | #458 | — | 13 | 3 | no | — |
| 112 | B(4,𝔽2) | — | 13 | 3 | no | — |
| 113 | B(4,𝔽2) | D13 | 1 | 1 | yes | characteristic, complemented |
| 114 | C2×#99 | — | 13 | 3 | no | — |
| 115 | C22×C13 | — | 2 | 3 | no | — |
| 116 | C22×C13 | — | 4 | 1 | no | — |
| 117 | C22×C13 | — | 4 | 3 | no | — |
| 118 | C22×C13 | — | 4 | 3 | no | — |
| 119 | C22×C13 | — | 4 | 3 | no | — |
| 120 | C22×C13 | — | 4 | 1 | no | — |
| 121 | C22×C13 | — | 8 | 1 | no | — |
| 122 | C22×C13 | C22×D4 | 1 | 3 | yes | — |
| 123 | C2×D13 | — | 2 | 3 | no | — |
| 124 | C2×D13 | — | 4 | 3 | no | — |
| 125 | C2×D13 | — | 4 | 3 | no | — |
| 126 | C2×D13 | — | 4 | 6 | no | — |
| 127 | C2×D13 | — | 4 | 3 | no | — |
| 128 | C2×D13 | — | 8 | 3 | no | — |
| 129 | C2×D13 | — | 8 | 3 | no | — |
| 130 | C2×D13 | #120 | 1 | 1 | yes | characteristic |
| 131 | C2×D13 | #120 | 1 | 3 | yes | — |
| 132 | C4×C13 | — | 2 | 3 | no | — |
| 133 | C4×C13 | — | 4 | 3 | no | — |
| 134 | Dic13 | — | 2 | 3 | no | — |
| 135 | Dic13 | — | 4 | 3 | no | — |
| 136 | Dic13 | — | 4 | 1 | no | — |
| 137 | H(5,𝔽2) | — | 13 | 3 | no | — |
| 138 | H(5,𝔽2) | — | 26 | 3 | no | — |
| 139 | H(5,𝔽2) | — | 26 | 3 | no | — |
| 140 | H(5,𝔽2) | C2×D13 | 1 | 1 | yes | characteristic |
| 141 | C2×#41 | — | 26 | 3 | no | — |
| 142 | C22×D4 | — | 13 | 3 | no | — |
| 143 | C22×D4 | — | 13 | 1 | no | — |
| 144 | C22×D4 | — | 26 | 3 | no | — |
| 145 | #123 | — | 13 | 3 | no | — |
| 146 | #123 | — | 13 | 3 | no | — |
| 147 | #123 | — | 26 | 3 | no | — |
| 148 | #121 | — | 26 | 3 | no | — |
| 149 | #121 | — | 26 | 3 | no | — |
| 150 | #120 | — | 13 | 3 | no | — |
| 151 | #120 | — | 26 | 3 | no | — |
| 152 | #120 | C2×D13 | 1 | 3 | yes | complemented |
| 153 | C2×C22⋊C4 | — | 13 | 3 | no | — |
| 154 | #99 | — | 13 | 3 | no | — |
| 155 | #99 | — | 13 | 6 | no | — |
| 156 | #99 | C2×D13 | 1 | 3 | yes | complemented |
| 157 | C2×C13 | — | 2 | 3 | no | — |
| 158 | C2×C13 | — | 4 | 3 | no | — |
| 159 | C2×C13 | — | 8 | 1 | no | — |
| 160 | C2×C13 | C2×#120 | 1 | 1 | yes | characteristic |
| 161 | D13 | — | 2 | 1 | no | — |
| 162 | D13 | — | 2 | 3 | no | — |
| 163 | D13 | — | 4 | 3 | no | — |
| 164 | C24 | — | 13 | 1 | no | — |
| 165 | C24 | — | 13 | 3 | no | — |
| 166 | C24 | — | 26 | 1 | no | — |
| 167 | C24 | C22×D13 | 1 | 1 | yes | characteristic, complemented |
| 168 | #41 | — | 2 | 3 | no | — |
| 169 | #41 | — | 26 | 6 | no | — |
| 170 | #41 | — | 26 | 6 | no | — |
| 171 | #41 | — | 26 | 3 | no | — |
| 172 | #41 | — | 26 | 3 | no | — |
| 173 | #41 | — | 26 | 3 | no | — |
| 174 | C2×Q8 | — | 26 | 1 | no | — |
| 175 | C2×D4 | — | 2 | 3 | no | — |
| 176 | C2×D4 | — | 2 | 3 | no | — |
| 177 | C2×D4 | — | 13 | 3 | no | — |
| 178 | C2×D4 | — | 13 | 3 | no | — |
| 179 | C2×D4 | — | 13 | 3 | no | — |
| 180 | C2×D4 | — | 26 | 3 | no | — |
| 181 | C2×D4 | — | 26 | 6 | no | — |
| 182 | C2×D4 | — | 26 | 6 | no | — |
| 183 | C2×D4 | — | 26 | 6 | no | — |
| 184 | C2×D4 | — | 26 | 3 | no | — |
| 185 | C2×D4 | — | 26 | 6 | no | — |
| 186 | C2×D4 | — | 26 | 3 | no | — |
| 187 | C2×D4 | — | 26 | 3 | no | — |
| 188 | C2×D4 | — | 26 | 3 | no | — |
| 189 | C2×D4 | — | 26 | 3 | no | — |
| 190 | C2×D4 | — | 26 | 3 | no | — |
| 191 | C2×D4 | C22×D13 | 1 | 3 | yes | — |
| 192 | C22×C4 | — | 13 | 3 | no | — |
| 193 | C22×C4 | — | 13 | 1 | no | — |
| 194 | C22×C4 | — | 26 | 3 | no | — |
| 195 | C22×C4 | — | 26 | 3 | no | — |
| 196 | C4⋊C4 | — | 26 | 3 | no | — |
| 197 | C4⋊C4 | — | 26 | 3 | no | — |
| 198 | C22⋊C4 | — | 2 | 3 | no | — |
| 199 | C22⋊C4 | — | 13 | 3 | no | — |
| 200 | C22⋊C4 | — | 26 | 3 | no | — |
| 201 | C22⋊C4 | — | 26 | 3 | no | — |
| 202 | C22⋊C4 | — | 26 | 3 | no | — |
| 203 | C22⋊C4 | — | 26 | 3 | no | — |
| 204 | C22⋊C4 | C22×D13 | 1 | 3 | yes | complemented |
| 205 | C13 | #3026 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 206 | C23 | — | 2 | 1 | no | — |
| 207 | C23 | — | 2 | 3 | no | — |
| 208 | C23 | — | 8 | 1 | no | — |
| 209 | C23 | — | 13 | 3 | no | — |
| 210 | C23 | — | 13 | 3 | no | — |
| 211 | C23 | — | 13 | 3 | no | — |
| 212 | C23 | — | 26 | 3 | no | — |
| 213 | C23 | — | 26 | 3 | no | — |
| 214 | C23 | — | 26 | 3 | no | — |
| 215 | C23 | — | 104 | 1 | no | — |
| 216 | C23 | — | 104 | 3 | no | — |
| 217 | C23 | — | 104 | 2 | no | — |
| 218 | C23 | D4×D13 | 1 | 3 | yes | — |
| 219 | C23 | C23×D13 | 1 | 1 | yes | characteristic |
| 220 | Q8 | — | 2 | 1 | no | — |
| 221 | Q8 | — | 26 | 3 | no | — |
| 222 | D4 | — | 2 | 3 | no | — |
| 223 | D4 | — | 2 | 6 | no | — |
| 224 | D4 | — | 8 | 3 | no | — |
| 225 | D4 | — | 26 | 6 | no | — |
| 226 | D4 | — | 26 | 3 | no | — |
| 227 | D4 | — | 26 | 6 | no | — |
| 228 | D4 | — | 26 | 6 | no | — |
| 229 | D4 | — | 26 | 6 | no | — |
| 230 | D4 | — | 52 | 1 | no | — |
| 231 | D4 | — | 52 | 3 | no | — |
| 232 | D4 | — | 104 | 3 | no | — |
| 233 | C2×C4 | — | 2 | 3 | no | — |
| 234 | C2×C4 | — | 2 | 3 | no | — |
| 235 | C2×C4 | — | 13 | 3 | no | — |
| 236 | C2×C4 | — | 26 | 3 | no | — |
| 237 | C2×C4 | — | 26 | 3 | no | — |
| 238 | C2×C4 | — | 26 | 6 | no | — |
| 239 | C2×C4 | — | 26 | 3 | no | — |
| 240 | C2×C4 | — | 26 | 3 | no | — |
| 241 | C2×C4 | — | 26 | 3 | no | — |
| 242 | C2×C4 | — | 104 | 3 | no | — |
| 243 | C2×C4 | D4×D13 | 1 | 3 | yes | — |
| 244 | C22 | — | 2 | 3 | no | — |
| 245 | C22 | — | 4 | 1 | no | — |
| 246 | C22 | — | 4 | 3 | no | — |
| 247 | C22 | — | 4 | 3 | no | — |
| 248 | C22 | — | 4 | 3 | no | — |
| 249 | C22 | — | 4 | 1 | no | — |
| 250 | C22 | — | 8 | 1 | no | — |
| 251 | C22 | — | 13 | 1 | no | — |
| 252 | C22 | — | 13 | 3 | no | — |
| 253 | C22 | — | 26 | 3 | no | — |
| 254 | C22 | — | 52 | 3 | no | — |
| 255 | C22 | — | 52 | 3 | no | — |
| 256 | C22 | — | 52 | 3 | no | — |
| 257 | C22 | — | 52 | 6 | no | — |
| 258 | C22 | — | 104 | 3 | no | — |
| 259 | C22 | — | 104 | 3 | no | — |
| 260 | C22 | C2×D4×D13 | 1 | 3 | yes | — |
| 261 | C4 | — | 2 | 3 | no | — |
| 262 | C4 | — | 4 | 3 | no | — |
| 263 | C4 | — | 26 | 3 | no | — |
| 264 | C4 | — | 52 | 3 | no | — |
| 265 | C4 | — | 52 | 1 | no | — |
| 266 | C2 | — | 2 | 3 | no | — |
| 267 | C2 | — | 4 | 3 | no | — |
| 268 | C2 | — | 8 | 1 | no | — |
| 269 | C2 | — | 26 | 1 | no | — |
| 270 | C2 | — | 26 | 3 | no | — |
| 271 | C2 | — | 52 | 3 | no | — |
| 272 | C2 | D13×#120 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D13×H(5,𝔽2) | C2 | semidirect |
| 2. #11719294 | C2 | semidirect |
| 3. C13×B(4,𝔽2) | C2 | semidirect |
| 4. #11718904 | C2 | semidirect |
| 5. #11718693 | C2 | semidirect |
| 6. D13×#99 | C2 | semidirect |
| 7. #11718403 | C2 | semidirect |
| 9. C22×C22⋊D13 | C22 | semidirect |
| 16. C13×#120 | C22 | semidirect |
| 17. #88207 | C22 | semidirect |
| 20. #88189 | C22 | semidirect |
| 21. #88140 | C22 | semidirect |
| 24. C22⋊C4×D13 | C22 | semidirect |
| 25. C13×#99 | C22 | semidirect |
| 26. #88074 | C22 | semidirect |
| 27. #88046 | C22 | semidirect |
| 28. C24×C13 | C23 | semidirect |
| 30. C23×D13 | D4 | semidirect |
| 41. C2×C22⋊D13 | D4 | semidirect |
| 43. C22×Dic13 | C23 | semidirect |
| 56. C2×D52 | D4 | semidirect |
| 59. C2×C4×D13 | D4 | semidirect |
| 61. C13×C22⋊C4 | C23 | semidirect |
| 64. C22⋊Dic13 | C23 | semidirect |
| 113. B(4,𝔽2) | D13 | semidirect |
| 152. #120 | C2×D13 | semidirect |
| 156. #99 | C2×D13 | semidirect |
| 167. C24 | C22×D13 | semidirect |
| 204. C22⋊C4 | C22×D13 | semidirect |
| 205. C13 | #3026 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D13×H(5,𝔽2) | 2 |
| #11719294 | 2 |
| C13×B(4,𝔽2) | 2 |
| #11718904 | 2 |
| #11718693 | 2 |
| D13×#99 | 2 |
| #11718403 | 2 |
| #3026 | 13 |