Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
336 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 336 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 |
| 2 | C5×#2230 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10602143 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10602131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10598258 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10598063 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10598060 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #66105 | — | 2 | 1 | no | — |
| 9 | #66087 | — | 2 | 1 | no | — |
| 10 | C5×#498 | C22 | 1 | 1 | yes | characteristic |
| 11 | C5×#443 | C22 | 1 | 1 | yes | characteristic |
| 12 | #65432 | — | 2 | 1 | no | — |
| 13 | #65370 | — | 2 | 1 | no | — |
| 14 | #65368 | — | 2 | 1 | no | — |
| 15 | #65185 | — | 2 | 1 | no | — |
| 16 | #65115 | — | 2 | 1 | no | — |
| 17 | #65115 | — | 2 | 1 | no | — |
| 18 | #64989 | C22 | 1 | 1 | yes | characteristic |
| 19 | #64988 | C22 | 1 | 1 | yes | characteristic |
| 20 | C5×#365 | — | 2 | 1 | no | — |
| 21 | C5×#364 | C22 | 1 | 1 | yes | characteristic |
| 22 | C5×#360 | — | 2 | 1 | no | — |
| 23 | #64708 | — | 2 | 1 | no | — |
| 24 | #64707 | — | 2 | 1 | no | — |
| 25 | #64683 | C22 | 1 | 1 | yes | characteristic |
| 26 | #64675 | C22 | 1 | 1 | yes | characteristic |
| 27 | #12367 | — | 5 | 1 | no | maximal, Sylow |
| 28 | #4150 | — | 2 | 1 | no | — |
| 29 | #4150 | — | 2 | 1 | no | — |
| 30 | C5×#135 | D4 | 1 | 1 | yes | characteristic |
| 31 | C5×#131 | — | 2 | 1 | no | — |
| 32 | C5×C4⋊Q8 | — | 2 | 1 | no | — |
| 33 | #4097 | — | 2 | 1 | no | — |
| 34 | #4097 | — | 2 | 1 | no | — |
| 35 | D5×Q16 | — | 4 | 1 | no | — |
| 36 | #4061 | — | 4 | 1 | no | — |
| 37 | #4061 | — | 4 | 1 | no | — |
| 38 | #4058 | — | 4 | 1 | no | — |
| 39 | #4055 | — | 2 | 1 | no | — |
| 40 | #4055 | — | 2 | 1 | no | — |
| 41 | #4055 | — | 4 | 1 | no | — |
| 42 | #4055 | — | 4 | 1 | no | — |
| 43 | C2×Dic20 | — | 2 | 1 | no | — |
| 44 | C2×Dic20 | — | 2 | 1 | no | — |
| 45 | C2×Dic20 | — | 4 | 1 | no | — |
| 46 | #4050 | — | 4 | 1 | no | — |
| 47 | #4050 | D4 | 1 | 1 | yes | characteristic |
| 48 | #4047 | — | 2 | 1 | no | — |
| 49 | #4015 | D4 | 1 | 1 | yes | characteristic |
| 50 | #4015 | D4 | 1 | 1 | yes | characteristic |
| 51 | C5×M32 | — | 2 | 1 | no | — |
| 52 | C5×#108 | D4 | 1 | 1 | yes | characteristic |
| 53 | C5×#106 | — | 2 | 1 | no | — |
| 54 | C5×#106 | — | 2 | 1 | no | — |
| 55 | C5×#104 | — | 2 | 1 | no | — |
| 56 | C4×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 57 | #3967 | — | 4 | 2 | no | — |
| 58 | #3956 | — | 2 | 1 | no | — |
| 59 | #3956 | — | 2 | 1 | no | — |
| 60 | #3951 | D4 | 1 | 1 | yes | characteristic |
| 61 | #3944 | — | 2 | 1 | no | — |
| 62 | #3940 | — | 4 | 2 | no | — |
| 63 | #3937 | — | 2 | 1 | no | — |
| 64 | C4×#168 | — | 2 | 1 | no | — |
| 65 | #3293 | — | 5 | 1 | no | — |
| 66 | #2230 | — | 5 | 1 | no | — |
| 67 | #2230 | D5 | 1 | 1 | yes | characteristic, complemented |
| 68 | #1716 | — | 5 | 1 | no | — |
| 69 | #1358 | — | 5 | 1 | no | — |
| 70 | #1336 | — | 5 | 1 | no | — |
| 71 | #1336 | — | 5 | 1 | no | — |
| 72 | C5×#41 | — | 2 | 1 | no | — |
| 73 | C2×C5×Q8 | — | 4 | 1 | no | — |
| 74 | Q8×D5 | — | 4 | 1 | no | — |
| 75 | Q8×D5 | — | 4 | 1 | no | — |
| 76 | #711 | — | 4 | 1 | no | — |
| 77 | #711 | — | 4 | 1 | no | — |
| 78 | #711 | — | 8 | 1 | no | — |
| 79 | #711 | — | 8 | 1 | no | — |
| 80 | #709 | — | 2 | 1 | no | — |
| 81 | #709 | — | 4 | 1 | no | — |
| 82 | #709 | — | 4 | 1 | no | — |
| 83 | C2×Dic10 | — | 2 | 1 | no | — |
| 84 | C2×Dic10 | — | 2 | 1 | no | — |
| 85 | C2×Dic10 | — | 4 | 1 | no | — |
| 86 | C2×Dic10 | — | 4 | 1 | no | — |
| 87 | C5×Q16 | SD16 | 1 | 1 | yes | characteristic |
| 88 | C5×SD16 | — | 2 | 1 | no | — |
| 89 | C5×D8 | SD16 | 1 | 1 | yes | characteristic |
| 90 | C5×M16 | — | 2 | 1 | no | — |
| 91 | C5×M16 | — | 4 | 1 | no | — |
| 92 | C2×C5×C8 | — | 4 | 1 | no | — |
| 93 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 94 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 95 | C5×C4⋊C4 | — | 4 | 1 | no | — |
| 96 | C5×C4⋊C4 | — | 4 | 1 | no | — |
| 97 | C42×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 98 | #689 | — | 4 | 1 | no | — |
| 99 | #689 | — | 4 | 1 | no | — |
| 100 | #687 | — | 4 | 1 | no | — |
| 101 | #687 | — | 4 | 1 | no | — |
| 102 | C4⋊Dic5 | — | 4 | 1 | no | — |
| 103 | C4⋊Dic5 | — | 4 | 1 | no | — |
| 104 | #681 | — | 2 | 1 | no | — |
| 105 | C2×#168 | — | 2 | 2 | no | — |
| 106 | Dic20 | — | 4 | 1 | no | — |
| 107 | Dic20 | — | 4 | 1 | no | — |
| 108 | Dic20 | — | 4 | 1 | no | — |
| 109 | Dic20 | — | 4 | 1 | no | — |
| 110 | Dic20 | — | 4 | 1 | no | — |
| 111 | Dic20 | — | 4 | 1 | no | — |
| 112 | Dic20 | SD16 | 1 | 1 | yes | characteristic |
| 113 | D40 | SD16 | 1 | 1 | yes | characteristic |
| 114 | #677 | — | 2 | 1 | no | — |
| 115 | #677 | — | 4 | 1 | no | — |
| 116 | #677 | — | 4 | 1 | no | — |
| 117 | #676 | — | 4 | 1 | no | — |
| 118 | C8×D5 | — | 4 | 1 | no | — |
| 119 | C5×C16 | — | 4 | 1 | no | — |
| 120 | #672 | — | 4 | 1 | no | — |
| 121 | #578 | — | 10 | 1 | no | — |
| 122 | #578 | — | 10 | 1 | no | — |
| 123 | #498 | — | 10 | 1 | no | — |
| 124 | #498 | C2×D5 | 1 | 1 | yes | characteristic |
| 125 | #494 | — | 5 | 1 | no | — |
| 126 | #487 | — | 10 | 1 | no | — |
| 127 | #473 | — | 10 | 1 | no | — |
| 128 | #473 | — | 10 | 1 | no | — |
| 129 | #456 | — | 10 | 1 | no | — |
| 130 | #456 | — | 10 | 1 | no | — |
| 131 | #443 | — | 5 | 1 | no | — |
| 132 | #443 | C2×D5 | 1 | 1 | yes | characteristic |
| 133 | #365 | — | 2 | 1 | no | — |
| 134 | #365 | — | 10 | 1 | no | — |
| 135 | #364 | — | 5 | 1 | no | — |
| 136 | #364 | C2×D5 | 1 | 1 | yes | characteristic |
| 137 | #360 | — | 2 | 1 | no | — |
| 138 | #360 | — | 10 | 1 | no | — |
| 139 | #322 | — | 5 | 1 | no | — |
| 140 | C5×Q8 | — | 2 | 1 | no | — |
| 141 | C5×Q8 | — | 8 | 2 | no | — |
| 142 | C5×D4 | — | 2 | 1 | no | — |
| 143 | C5×D4 | — | 4 | 1 | no | — |
| 144 | C2×C4×C5 | — | 2 | 1 | no | — |
| 145 | C2×C4×C5 | — | 4 | 1 | no | — |
| 146 | C2×C4×C5 | — | 8 | 1 | no | — |
| 147 | C2×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 148 | C22⋊D5 | — | 4 | 1 | no | — |
| 149 | C22⋊D5 | — | 8 | 1 | no | — |
| 150 | C22⋊D5 | — | 8 | 1 | no | — |
| 151 | C2×Dic5 | — | 4 | 1 | no | — |
| 152 | C2×Dic5 | — | 4 | 1 | no | — |
| 153 | C2×Dic5 | — | 8 | 1 | no | — |
| 154 | C2×Dic5 | — | 8 | 1 | no | — |
| 155 | D20 | — | 2 | 1 | no | — |
| 156 | C4×D5 | — | 4 | 1 | no | — |
| 157 | C4×D5 | — | 8 | 1 | no | — |
| 158 | C4×D5 | — | 8 | 1 | no | — |
| 159 | Dic10 | — | 2 | 1 | no | — |
| 160 | Dic10 | — | 4 | 1 | no | — |
| 161 | Dic10 | — | 4 | 1 | no | — |
| 162 | Dic10 | — | 4 | 1 | no | — |
| 163 | Dic10 | — | 4 | 1 | no | — |
| 164 | Dic10 | — | 8 | 1 | no | — |
| 165 | Dic10 | — | 8 | 1 | no | — |
| 166 | C5×C8 | — | 4 | 1 | no | — |
| 167 | C5×C8 | C2×SD16 | 1 | 1 | yes | characteristic |
| 168 | C5×C8 | C2×SD16 | 1 | 1 | yes | characteristic |
| 169 | C5×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 170 | C5×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 171 | #168 | — | 4 | 2 | no | — |
| 172 | #168 | — | 4 | 1 | no | — |
| 173 | 2−1+4 | — | 10 | 1 | no | — |
| 174 | 2−1+4 | — | 10 | 1 | no | — |
| 175 | #137 | — | 10 | 1 | no | — |
| 176 | #137 | — | 10 | 1 | no | — |
| 177 | #137 | — | 10 | 1 | no | — |
| 178 | #137 | — | 10 | 1 | no | — |
| 179 | #137 | — | 20 | 1 | no | — |
| 180 | #137 | — | 20 | 1 | no | — |
| 181 | #137 | — | 20 | 1 | no | — |
| 182 | #137 | — | 20 | 1 | no | — |
| 183 | #135 | — | 5 | 1 | no | — |
| 184 | #135 | — | 20 | 1 | no | — |
| 185 | #135 | — | 20 | 1 | no | — |
| 186 | #135 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 187 | C2×Q16 | — | 10 | 1 | no | — |
| 188 | C2×Q16 | — | 10 | 1 | no | — |
| 189 | C2×Q16 | — | 20 | 1 | no | — |
| 190 | C2×Q16 | — | 20 | 1 | no | — |
| 191 | #131 | — | 2 | 1 | no | — |
| 192 | #131 | — | 10 | 1 | no | — |
| 193 | C4⋊Q8 | — | 2 | 1 | no | — |
| 194 | C4⋊Q8 | — | 5 | 1 | no | — |
| 195 | C4⋊Q8 | — | 5 | 1 | no | — |
| 196 | M32 | — | 2 | 1 | no | — |
| 197 | M32 | — | 10 | 1 | no | — |
| 198 | #108 | — | 5 | 1 | no | — |
| 199 | #108 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 200 | #106 | — | 2 | 1 | no | — |
| 201 | #106 | — | 2 | 1 | no | — |
| 202 | #106 | — | 20 | 2 | no | — |
| 203 | #104 | — | 2 | 1 | no | — |
| 204 | #104 | — | 10 | 1 | no | — |
| 205 | #103 | — | 20 | 2 | no | — |
| 206 | #101 | — | 10 | 1 | no | — |
| 207 | #101 | — | 10 | 1 | no | — |
| 208 | C4×C8 | — | 10 | 1 | no | — |
| 209 | C4×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 210 | C22×C5 | — | 4 | 1 | no | — |
| 211 | C22×C5 | #453 | 1 | 1 | yes | characteristic |
| 212 | C2×D5 | — | 4 | 1 | no | — |
| 213 | C4×C5 | — | 2 | 2 | no | — |
| 214 | C4×C5 | — | 4 | 1 | no | — |
| 215 | C4×C5 | — | 16 | 1 | no | — |
| 216 | C4×C5 | #450 | 1 | 1 | yes | characteristic |
| 217 | C4×C5 | #450 | 1 | 1 | yes | characteristic |
| 218 | Dic5 | — | 4 | 1 | no | — |
| 219 | Dic5 | — | 8 | 1 | no | — |
| 220 | Dic5 | — | 8 | 1 | no | — |
| 221 | #41 | — | 2 | 1 | no | — |
| 222 | #41 | — | 10 | 1 | no | — |
| 223 | #41 | — | 20 | 1 | no | — |
| 224 | #41 | — | 20 | 1 | no | — |
| 225 | #41 | — | 20 | 1 | no | — |
| 226 | #41 | — | 20 | 1 | no | — |
| 227 | #41 | — | 40 | 1 | no | — |
| 228 | #41 | — | 40 | 1 | no | — |
| 229 | C2×Q8 | — | 4 | 1 | no | — |
| 230 | C2×Q8 | — | 10 | 1 | no | — |
| 231 | C2×Q8 | — | 10 | 1 | no | — |
| 232 | C2×Q8 | — | 20 | 1 | no | — |
| 233 | C2×Q8 | — | 20 | 1 | no | — |
| 234 | C2×Q8 | — | 20 | 1 | no | — |
| 235 | C2×Q8 | — | 20 | 1 | no | — |
| 236 | Q16 | — | 5 | 1 | no | — |
| 237 | Q16 | — | 20 | 1 | no | — |
| 238 | Q16 | — | 20 | 1 | no | — |
| 239 | Q16 | — | 20 | 1 | no | — |
| 240 | Q16 | — | 20 | 1 | no | — |
| 241 | Q16 | — | 20 | 1 | no | — |
| 242 | Q16 | — | 20 | 1 | no | — |
| 243 | Q16 | — | 20 | 1 | no | — |
| 244 | Q16 | — | 20 | 1 | no | — |
| 245 | Q16 | #688 | 1 | 1 | yes | characteristic |
| 246 | SD16 | — | 2 | 1 | no | — |
| 247 | SD16 | — | 10 | 1 | no | — |
| 248 | SD16 | — | 20 | 1 | no | — |
| 249 | SD16 | — | 20 | 1 | no | — |
| 250 | SD16 | — | 20 | 1 | no | — |
| 251 | SD16 | — | 20 | 1 | no | — |
| 252 | D8 | — | 5 | 1 | no | — |
| 253 | D8 | #688 | 1 | 1 | yes | characteristic |
| 254 | M16 | — | 2 | 1 | no | — |
| 255 | M16 | — | 4 | 1 | no | — |
| 256 | M16 | — | 10 | 1 | no | — |
| 257 | M16 | — | 20 | 1 | no | — |
| 258 | C2×C8 | — | 4 | 1 | no | — |
| 259 | C2×C8 | — | 10 | 2 | no | — |
| 260 | C2×C8 | — | 20 | 1 | no | — |
| 261 | C2×C8 | D4×D5 | 1 | 1 | yes | characteristic |
| 262 | C2×C8 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 263 | C4⋊C4 | — | 4 | 1 | no | — |
| 264 | C4⋊C4 | — | 4 | 1 | no | — |
| 265 | C4⋊C4 | — | 20 | 1 | no | — |
| 266 | C4⋊C4 | — | 20 | 1 | no | — |
| 267 | C42 | D4×D5 | 1 | 1 | yes | characteristic |
| 268 | C16 | — | 4 | 1 | no | — |
| 269 | C16 | — | 20 | 1 | no | — |
| 270 | C2×C5 | — | 2 | 1 | no | — |
| 271 | C2×C5 | — | 8 | 1 | no | — |
| 272 | C2×C5 | #1629 | 1 | 1 | yes | characteristic |
| 273 | D5 | — | 8 | 1 | no | — |
| 274 | Q8 | — | 2 | 1 | no | — |
| 275 | Q8 | — | 8 | 2 | no | — |
| 276 | Q8 | — | 10 | 1 | no | — |
| 277 | Q8 | — | 20 | 1 | no | — |
| 278 | Q8 | — | 20 | 1 | no | — |
| 279 | Q8 | — | 20 | 1 | no | — |
| 280 | Q8 | — | 20 | 1 | no | — |
| 281 | Q8 | — | 40 | 1 | no | — |
| 282 | Q8 | — | 40 | 1 | no | — |
| 283 | D4 | — | 2 | 1 | no | — |
| 284 | D4 | — | 4 | 1 | no | — |
| 285 | D4 | — | 10 | 1 | no | — |
| 286 | D4 | — | 20 | 1 | no | — |
| 287 | D4 | — | 40 | 1 | no | — |
| 288 | D4 | — | 40 | 1 | no | — |
| 289 | C2×C4 | — | 2 | 1 | no | — |
| 290 | C2×C4 | — | 4 | 1 | no | — |
| 291 | C2×C4 | — | 8 | 1 | no | — |
| 292 | C2×C4 | — | 20 | 1 | no | — |
| 293 | C2×C4 | — | 20 | 1 | no | — |
| 294 | C2×C4 | — | 20 | 1 | no | — |
| 295 | C2×C4 | — | 40 | 1 | no | — |
| 296 | C2×C4 | — | 40 | 1 | no | — |
| 297 | C2×C4 | — | 40 | 1 | no | — |
| 298 | C2×C4 | — | 40 | 1 | no | — |
| 299 | C2×C4 | #4083 | 1 | 1 | yes | characteristic |
| 300 | C8 | — | 4 | 1 | no | — |
| 301 | C8 | — | 20 | 2 | no | — |
| 302 | C8 | — | 20 | 1 | no | — |
| 303 | C8 | D5×SD16 | 1 | 1 | yes | characteristic |
| 304 | C8 | #4060 | 1 | 1 | yes | characteristic |
| 305 | C8 | C2×#688 | 1 | 1 | yes | characteristic |
| 306 | C8 | #4095 | 1 | 1 | yes | characteristic |
| 307 | C5 | #12367 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 308 | C22 | — | 4 | 1 | no | — |
| 309 | C22 | — | 20 | 1 | no | — |
| 310 | C22 | #65487 | 1 | 1 | yes | characteristic |
| 311 | C4 | — | 2 | 2 | no | — |
| 312 | C4 | — | 4 | 1 | no | — |
| 313 | C4 | — | 16 | 1 | no | — |
| 314 | C4 | — | 20 | 1 | no | — |
| 315 | C4 | — | 40 | 1 | no | — |
| 316 | C4 | — | 40 | 1 | no | — |
| 317 | C4 | #65335 | 1 | 1 | yes | characteristic |
| 318 | C4 | #65458 | 1 | 1 | yes | characteristic |
| 319 | C2 | — | 2 | 1 | no | — |
| 320 | C2 | — | 8 | 1 | no | — |
| 321 | C2 | — | 40 | 1 | no | — |
| 322 | C2 | #10601936 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#2230 | C2 | semidirect |
| 3. #10602143 | C2 | semidirect |
| 4. #10602131 | C2 | semidirect |
| 5. #10598258 | C2 | semidirect |
| 6. #10598063 | C2 | semidirect |
| 7. #10598060 | C2 | semidirect |
| 67. #2230 | D5 | semidirect |
| 307. C5 | #12367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611626 | 2 |
| C5×#2230 | 2 |
| #10602143 | 2 |
| #10602131 | 2 |
| #10598258 | 2 |
| #10598063 | 2 |
| #10598060 | 2 |
| #12367 | 5 |