Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
366 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 61 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 | #10611626 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C5×#2213 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10602088 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10602068 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10598257 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10598063 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10598059 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #66105 | — | 2 | 1 | no | — |
| 9 | #66087 | — | 2 | 1 | no | — |
| 10 | C5×#509 | — | 2 | 1 | no | — |
| 11 | C5×#493 | C22 | 1 | 1 | yes | characteristic |
| 12 | C5×#443 | C22 | 1 | 1 | yes | characteristic |
| 13 | #65436 | — | 2 | 1 | no | — |
| 14 | #65432 | — | 2 | 1 | no | — |
| 15 | #65359 | — | 2 | 2 | no | — |
| 16 | #65185 | — | 2 | 1 | no | — |
| 17 | #65115 | — | 2 | 2 | no | — |
| 18 | #64989 | C22 | 1 | 1 | yes | characteristic |
| 19 | #64988 | C22 | 1 | 1 | yes | characteristic |
| 20 | C5×#364 | C22 | 1 | 1 | yes | characteristic |
| 21 | C5×#361 | — | 2 | 1 | no | — |
| 22 | #64783 | — | 2 | 1 | no | — |
| 23 | #64683 | C22 | 1 | 1 | yes | characteristic |
| 24 | C8×#168 | C22 | 1 | 1 | yes | characteristic |
| 25 | #12311 | — | 5 | 1 | no | maximal, Sylow |
| 26 | #4150 | — | 2 | 2 | no | — |
| 27 | C5×#135 | D4 | 1 | 1 | yes | characteristic |
| 28 | C2×C5×D8 | — | 2 | 1 | no | — |
| 29 | C2×C5×D8 | — | 2 | 1 | no | — |
| 30 | C5×#131 | — | 2 | 1 | no | — |
| 31 | C5×#127 | — | 2 | 1 | no | — |
| 32 | #4097 | — | 2 | 2 | no | — |
| 33 | D5×Q16 | — | 4 | 1 | no | — |
| 34 | #4061 | — | 4 | 2 | no | — |
| 35 | #4058 | — | 4 | 1 | no | — |
| 36 | #4055 | — | 2 | 2 | no | — |
| 37 | #4055 | — | 4 | 2 | no | — |
| 38 | C2×Dic20 | — | 2 | 1 | no | — |
| 39 | C2×Dic20 | — | 2 | 1 | no | — |
| 40 | C2×Dic20 | — | 4 | 1 | no | — |
| 41 | #4050 | — | 4 | 1 | no | — |
| 42 | #4050 | D4 | 1 | 1 | yes | characteristic |
| 43 | #4047 | — | 2 | 1 | no | — |
| 44 | #4015 | D4 | 1 | 2 | yes | — |
| 45 | C5×SD32 | — | 4 | 1 | no | — |
| 46 | C5×D16 | — | 4 | 1 | no | — |
| 47 | C5×M32 | — | 2 | 1 | no | — |
| 48 | C5×#108 | D4 | 1 | 1 | yes | characteristic |
| 49 | C5×#104 | — | 2 | 1 | no | — |
| 50 | C4×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 51 | #3964 | — | 4 | 4 | no | — |
| 52 | #3959 | — | 4 | 1 | no | — |
| 53 | #3958 | — | 4 | 1 | no | — |
| 54 | #3956 | — | 2 | 2 | no | — |
| 55 | #3951 | D4 | 1 | 1 | yes | characteristic |
| 56 | #3944 | — | 2 | 1 | no | — |
| 57 | #3937 | — | 2 | 1 | no | — |
| 58 | C4×#168 | — | 2 | 1 | no | — |
| 59 | #3293 | — | 5 | 1 | no | — |
| 60 | #2213 | — | 5 | 1 | no | — |
| 61 | #2213 | D5 | 1 | 1 | yes | characteristic, complemented |
| 62 | #1709 | — | 5 | 1 | no | — |
| 63 | #1358 | — | 5 | 1 | no | — |
| 64 | #1335 | — | 5 | 1 | no | — |
| 65 | #1335 | — | 5 | 1 | no | — |
| 66 | C5×#41 | — | 2 | 1 | no | — |
| 67 | C2×C5×D4 | — | 4 | 2 | no | — |
| 68 | C2×C5×D4 | — | 4 | 1 | no | — |
| 69 | Q8×D5 | — | 4 | 2 | no | — |
| 70 | #711 | — | 4 | 2 | no | — |
| 71 | #711 | — | 8 | 2 | no | — |
| 72 | #709 | — | 2 | 1 | no | — |
| 73 | #709 | — | 4 | 2 | no | — |
| 74 | C2×Dic10 | — | 2 | 2 | no | — |
| 75 | C2×Dic10 | — | 4 | 2 | no | — |
| 76 | C5×Q16 | D8 | 1 | 1 | yes | characteristic |
| 77 | C5×SD16 | — | 2 | 1 | no | — |
| 78 | C5×D8 | — | 4 | 1 | no | — |
| 79 | C5×D8 | — | 4 | 1 | no | — |
| 80 | C5×D8 | — | 4 | 1 | no | — |
| 81 | C5×D8 | — | 4 | 1 | no | — |
| 82 | C5×D8 | D8 | 1 | 1 | yes | characteristic |
| 83 | C5×M16 | — | 2 | 1 | no | — |
| 84 | C5×M16 | — | 4 | 1 | no | — |
| 85 | C2×C5×C8 | — | 4 | 1 | no | — |
| 86 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 87 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 88 | C42×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 89 | #689 | — | 4 | 2 | no | — |
| 90 | #687 | — | 4 | 2 | no | — |
| 91 | C4⋊Dic5 | — | 4 | 2 | no | — |
| 92 | #681 | — | 2 | 1 | no | — |
| 93 | C2×#168 | — | 2 | 2 | no | — |
| 94 | Dic20 | — | 4 | 2 | no | — |
| 95 | Dic20 | — | 4 | 1 | no | — |
| 96 | Dic20 | — | 4 | 1 | no | — |
| 97 | Dic20 | — | 4 | 1 | no | — |
| 98 | Dic20 | — | 4 | 1 | no | — |
| 99 | Dic20 | D8 | 1 | 1 | yes | characteristic |
| 100 | D40 | D8 | 1 | 1 | yes | characteristic |
| 101 | #677 | — | 2 | 1 | no | — |
| 102 | #677 | — | 4 | 2 | no | — |
| 103 | #676 | — | 4 | 1 | no | — |
| 104 | C8×D5 | — | 4 | 1 | no | — |
| 105 | C5×C16 | — | 4 | 1 | no | — |
| 106 | #672 | — | 4 | 1 | no | — |
| 107 | #578 | — | 10 | 1 | no | — |
| 108 | #578 | — | 10 | 1 | no | — |
| 109 | #509 | — | 2 | 1 | no | — |
| 110 | #509 | — | 10 | 1 | no | — |
| 111 | #494 | — | 5 | 1 | no | — |
| 112 | #493 | C2×D5 | 1 | 1 | yes | characteristic |
| 113 | #486 | — | 10 | 2 | no | — |
| 114 | #473 | — | 10 | 1 | no | — |
| 115 | #473 | — | 10 | 1 | no | — |
| 116 | #456 | — | 10 | 2 | no | — |
| 117 | #443 | — | 5 | 1 | no | — |
| 118 | #443 | C2×D5 | 1 | 1 | yes | characteristic |
| 119 | #364 | — | 5 | 1 | no | — |
| 120 | #364 | C2×D5 | 1 | 1 | yes | characteristic |
| 121 | #361 | — | 2 | 1 | no | — |
| 122 | #361 | — | 10 | 1 | no | — |
| 123 | C82 | — | 5 | 1 | no | — |
| 124 | C23×C5 | — | 8 | 1 | no | — |
| 125 | C5×Q8 | — | 2 | 1 | no | — |
| 126 | C5×D4 | — | 2 | 1 | no | — |
| 127 | C5×D4 | — | 4 | 1 | no | — |
| 128 | C5×D4 | — | 8 | 4 | no | — |
| 129 | C5×D4 | — | 8 | 1 | no | — |
| 130 | C5×D4 | — | 8 | 1 | no | — |
| 131 | C2×C4×C5 | — | 2 | 1 | no | — |
| 132 | C2×C4×C5 | — | 4 | 1 | no | — |
| 133 | C2×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 134 | C22⋊D5 | — | 4 | 1 | no | — |
| 135 | C22⋊D5 | — | 8 | 2 | no | — |
| 136 | C2×Dic5 | — | 4 | 2 | no | — |
| 137 | C2×Dic5 | — | 8 | 2 | no | — |
| 138 | D20 | — | 2 | 1 | no | — |
| 139 | C4×D5 | — | 4 | 1 | no | — |
| 140 | C4×D5 | — | 8 | 2 | no | — |
| 141 | Dic10 | — | 2 | 1 | no | — |
| 142 | Dic10 | — | 4 | 2 | no | — |
| 143 | Dic10 | — | 4 | 2 | no | — |
| 144 | Dic10 | — | 8 | 2 | no | — |
| 145 | C5×C8 | — | 4 | 1 | no | — |
| 146 | C5×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 147 | C5×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 148 | C5×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 149 | C5×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 150 | #168 | — | 4 | 2 | no | — |
| 151 | #168 | — | 4 | 1 | no | — |
| 152 | 2−1+4 | — | 10 | 2 | no | — |
| 153 | #137 | — | 10 | 2 | no | — |
| 154 | #137 | — | 10 | 2 | no | — |
| 155 | #137 | — | 20 | 2 | no | — |
| 156 | #137 | — | 20 | 2 | no | — |
| 157 | #135 | — | 5 | 1 | no | — |
| 158 | #135 | — | 20 | 1 | no | — |
| 159 | #135 | — | 20 | 1 | no | — |
| 160 | #135 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 161 | C2×Q16 | — | 10 | 1 | no | — |
| 162 | C2×Q16 | — | 10 | 1 | no | — |
| 163 | C2×Q16 | — | 20 | 1 | no | — |
| 164 | C2×Q16 | — | 20 | 1 | no | — |
| 165 | C2×D8 | — | 2 | 1 | no | — |
| 166 | C2×D8 | — | 2 | 1 | no | — |
| 167 | #131 | — | 2 | 1 | no | — |
| 168 | #131 | — | 10 | 1 | no | — |
| 169 | C4⋊Q8 | — | 5 | 2 | no | — |
| 170 | #127 | — | 2 | 1 | no | — |
| 171 | SD32 | — | 4 | 1 | no | — |
| 172 | SD32 | — | 20 | 1 | no | — |
| 173 | D16 | — | 4 | 1 | no | — |
| 174 | D16 | — | 20 | 1 | no | — |
| 175 | M32 | — | 2 | 1 | no | — |
| 176 | M32 | — | 10 | 1 | no | — |
| 177 | #108 | — | 5 | 1 | no | — |
| 178 | #108 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 179 | #104 | — | 2 | 1 | no | — |
| 180 | #104 | — | 10 | 1 | no | — |
| 181 | #102 | — | 20 | 4 | no | — |
| 182 | #101 | — | 10 | 2 | no | — |
| 183 | C4×C8 | — | 10 | 1 | no | — |
| 184 | C4×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 185 | C22×C5 | — | 4 | 1 | no | — |
| 186 | C22×C5 | — | 16 | 2 | no | — |
| 187 | C22×C5 | — | 16 | 1 | no | — |
| 188 | C22×C5 | #453 | 1 | 1 | yes | characteristic |
| 189 | C2×D5 | — | 4 | 1 | no | — |
| 190 | C4×C5 | — | 2 | 2 | no | — |
| 191 | C4×C5 | — | 4 | 1 | no | — |
| 192 | C4×C5 | #447 | 1 | 1 | yes | characteristic |
| 193 | C4×C5 | #447 | 1 | 1 | yes | characteristic |
| 194 | Dic5 | — | 4 | 1 | no | — |
| 195 | Dic5 | — | 8 | 2 | no | — |
| 196 | #41 | — | 2 | 1 | no | — |
| 197 | #41 | — | 10 | 1 | no | — |
| 198 | #41 | — | 20 | 2 | no | — |
| 199 | #41 | — | 20 | 2 | no | — |
| 200 | #41 | — | 40 | 2 | no | — |
| 201 | C2×Q8 | — | 10 | 2 | no | — |
| 202 | C2×Q8 | — | 20 | 2 | no | — |
| 203 | C2×Q8 | — | 20 | 2 | no | — |
| 204 | C2×D4 | — | 4 | 2 | no | — |
| 205 | C2×D4 | — | 4 | 1 | no | — |
| 206 | Q16 | — | 5 | 1 | no | — |
| 207 | Q16 | — | 20 | 2 | no | — |
| 208 | Q16 | — | 20 | 2 | no | — |
| 209 | Q16 | — | 20 | 1 | no | — |
| 210 | Q16 | — | 20 | 1 | no | — |
| 211 | Q16 | — | 20 | 1 | no | — |
| 212 | Q16 | — | 20 | 1 | no | — |
| 213 | Q16 | #686 | 1 | 1 | yes | characteristic |
| 214 | SD16 | — | 2 | 1 | no | — |
| 215 | SD16 | — | 10 | 1 | no | — |
| 216 | SD16 | — | 20 | 2 | no | — |
| 217 | SD16 | — | 20 | 2 | no | — |
| 218 | D8 | — | 4 | 1 | no | — |
| 219 | D8 | — | 4 | 1 | no | — |
| 220 | D8 | — | 4 | 1 | no | — |
| 221 | D8 | — | 4 | 1 | no | — |
| 222 | D8 | — | 5 | 1 | no | — |
| 223 | D8 | #686 | 1 | 1 | yes | characteristic |
| 224 | M16 | — | 2 | 1 | no | — |
| 225 | M16 | — | 4 | 1 | no | — |
| 226 | M16 | — | 10 | 1 | no | — |
| 227 | M16 | — | 20 | 1 | no | — |
| 228 | C2×C8 | — | 4 | 1 | no | — |
| 229 | C2×C8 | — | 10 | 2 | no | — |
| 230 | C2×C8 | — | 20 | 1 | no | — |
| 231 | C2×C8 | D4×D5 | 1 | 1 | yes | characteristic |
| 232 | C2×C8 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 233 | C4⋊C4 | — | 20 | 2 | no | — |
| 234 | C42 | D4×D5 | 1 | 1 | yes | characteristic |
| 235 | C16 | — | 4 | 1 | no | — |
| 236 | C16 | — | 20 | 1 | no | — |
| 237 | C2×C5 | — | 2 | 1 | no | — |
| 238 | C2×C5 | — | 8 | 1 | no | — |
| 239 | C2×C5 | — | 32 | 1 | no | — |
| 240 | C2×C5 | #1619 | 1 | 1 | yes | characteristic |
| 241 | D5 | — | 8 | 1 | no | — |
| 242 | C23 | — | 8 | 1 | no | — |
| 243 | Q8 | — | 2 | 1 | no | — |
| 244 | Q8 | — | 10 | 1 | no | — |
| 245 | Q8 | — | 20 | 2 | no | — |
| 246 | Q8 | — | 20 | 2 | no | — |
| 247 | Q8 | — | 40 | 2 | no | — |
| 248 | D4 | — | 2 | 1 | no | — |
| 249 | D4 | — | 4 | 1 | no | — |
| 250 | D4 | — | 8 | 4 | no | — |
| 251 | D4 | — | 8 | 1 | no | — |
| 252 | D4 | — | 8 | 1 | no | — |
| 253 | D4 | — | 10 | 1 | no | — |
| 254 | D4 | — | 20 | 1 | no | — |
| 255 | D4 | — | 40 | 2 | no | — |
| 256 | C2×C4 | — | 2 | 1 | no | — |
| 257 | C2×C4 | — | 4 | 1 | no | — |
| 258 | C2×C4 | — | 20 | 1 | no | — |
| 259 | C2×C4 | — | 20 | 2 | no | — |
| 260 | C2×C4 | — | 40 | 2 | no | — |
| 261 | C2×C4 | — | 40 | 2 | no | — |
| 262 | C2×C4 | #4083 | 1 | 1 | yes | characteristic |
| 263 | C8 | — | 4 | 1 | no | — |
| 264 | C8 | — | 20 | 2 | no | — |
| 265 | C8 | — | 20 | 1 | no | — |
| 266 | C8 | D5×D8 | 1 | 1 | yes | characteristic |
| 267 | C8 | #4057 | 1 | 1 | yes | characteristic |
| 268 | C8 | C2×#686 | 1 | 1 | yes | characteristic |
| 269 | C8 | #4095 | 1 | 1 | yes | characteristic |
| 270 | C5 | #12311 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 271 | C22 | — | 4 | 1 | no | — |
| 272 | C22 | — | 16 | 2 | no | — |
| 273 | C22 | — | 16 | 1 | no | — |
| 274 | C22 | — | 20 | 1 | no | — |
| 275 | C22 | #65487 | 1 | 1 | yes | characteristic |
| 276 | C4 | — | 2 | 2 | no | — |
| 277 | C4 | — | 4 | 1 | no | — |
| 278 | C4 | — | 20 | 1 | no | — |
| 279 | C4 | — | 40 | 2 | no | — |
| 280 | C4 | #65325 | 1 | 1 | yes | characteristic |
| 281 | C4 | #65445 | 1 | 1 | yes | characteristic |
| 282 | C2 | — | 2 | 1 | no | — |
| 283 | C2 | — | 8 | 1 | no | — |
| 284 | C2 | — | 32 | 1 | no | — |
| 285 | C2 | — | 40 | 1 | no | — |
| 286 | C2 | #10601808 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10611626 | C2 | semidirect |
| 2. C5×#2213 | C2 | semidirect |
| 3. #10602088 | C2 | semidirect |
| 4. #10602068 | C2 | semidirect |
| 5. #10598257 | C2 | semidirect |
| 6. #10598063 | C2 | semidirect |
| 7. #10598059 | C2 | semidirect |
| 61. #2213 | D5 | semidirect |
| 270. C5 | #12311 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611626 | 2 |
| C5×#2213 | 2 |
| #10602088 | 2 |
| #10602068 | 2 |
| #10598257 | 2 |
| #10598063 | 2 |
| #10598059 | 2 |
| #12311 | 5 |