Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
392 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 72 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 | #10615567 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10604733 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10604713 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10598804 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | C22×C5×D8 | C4 | 1 | 1 | yes | characteristic |
| 6 | #66139 | — | 2 | 1 | no | — |
| 7 | C2×#4047 | C22 | 1 | 1 | yes | characteristic |
| 8 | #65761 | — | 2 | 1 | no | — |
| 9 | D5⋊#108 | — | 2 | 1 | no | — |
| 10 | D5⋊M32 | — | 2 | 1 | no | — |
| 11 | #65504 | — | 2 | 1 | no | — |
| 12 | #65448 | C4 | 1 | 2 | yes | — |
| 13 | #65448 | C22 | 1 | 2 | yes | — |
| 14 | #65446 | — | 2 | 1 | no | — |
| 15 | #65446 | — | 2 | 1 | no | — |
| 16 | #65395 | C4 | 1 | 1 | yes | characteristic |
| 17 | #64912 | — | 2 | 1 | no | — |
| 18 | #64897 | C22 | 1 | 2 | yes | complemented |
| 19 | #64891 | C22 | 1 | 2 | yes | complemented |
| 20 | #11870 | — | 5 | 1 | no | maximal, Sylow |
| 21 | C22×C5×D4 | — | 2 | 1 | no | — |
| 22 | C2×#709 | D4 | 1 | 1 | yes | characteristic |
| 23 | D5⋊M16 | — | 2 | 2 | no | — |
| 24 | C2×C5×D8 | — | 2 | 1 | no | — |
| 25 | C2×C5×D8 | — | 4 | 1 | no | — |
| 26 | C2×C5×D8 | — | 4 | 1 | no | — |
| 27 | C2×C5×D8 | C2×C4 | 1 | 2 | yes | — |
| 28 | C22×C5×C8 | C2×C4 | 1 | 1 | yes | characteristic |
| 29 | #4099 | — | 4 | 1 | no | — |
| 30 | #4099 | — | 4 | 1 | no | — |
| 31 | #4086 | — | 4 | 1 | no | — |
| 32 | #4084 | — | 2 | 2 | no | — |
| 33 | #4084 | — | 2 | 2 | no | — |
| 34 | #4082 | — | 4 | 1 | no | — |
| 35 | #4072 | — | 2 | 1 | no | — |
| 36 | C2×#681 | D4 | 1 | 1 | yes | characteristic |
| 37 | #4047 | — | 4 | 1 | no | — |
| 38 | #4047 | — | 4 | 1 | no | — |
| 39 | C2×#676 | C2×C4 | 1 | 1 | yes | characteristic |
| 40 | C2×#676 | C23 | 1 | 1 | yes | characteristic |
| 41 | C2×C8×D5 | D4 | 1 | 1 | yes | characteristic |
| 42 | C2×C8×D5 | D4 | 1 | 1 | yes | characteristic |
| 43 | #4013 | — | 4 | 1 | no | — |
| 44 | #4005 | — | 4 | 1 | no | — |
| 45 | #3998 | — | 2 | 2 | no | — |
| 46 | #3996 | — | 4 | 1 | no | — |
| 47 | #3995 | — | 4 | 1 | no | — |
| 48 | #3990 | — | 4 | 1 | no | — |
| 49 | D5⋊C16 | — | 4 | 1 | no | — |
| 50 | #3964 | — | 2 | 2 | no | — |
| 51 | #3964 | — | 2 | 2 | no | — |
| 52 | #3950 | — | 2 | 1 | no | — |
| 53 | #3949 | C2×C4 | 1 | 2 | yes | — |
| 54 | #3058 | — | 5 | 1 | no | — |
| 55 | #2115 | — | 5 | 1 | no | — |
| 56 | #1813 | — | 5 | 1 | no | — |
| 57 | #1341 | — | 5 | 4 | no | — |
| 58 | C24×C5 | — | 4 | 1 | no | — |
| 59 | C2×C5×D4 | — | 2 | 2 | no | — |
| 60 | C2×C5×D4 | — | 4 | 2 | no | — |
| 61 | C2×C5×D4 | — | 4 | 2 | no | — |
| 62 | C2×C5×D4 | — | 4 | 1 | no | — |
| 63 | C22×C4×C5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 64 | C2×C22⋊D5 | — | 4 | 2 | no | — |
| 65 | C2×C22⋊D5 | — | 4 | 2 | no | — |
| 66 | C2×C22⋊D5 | D8 | 1 | 1 | yes | characteristic |
| 67 | C2×C22⋊D5 | SD16 | 1 | 1 | yes | characteristic |
| 68 | #709 | — | 4 | 1 | no | — |
| 69 | #709 | — | 4 | 1 | no | — |
| 70 | C2×D20 | SD16 | 1 | 1 | yes | characteristic |
| 71 | C2×C4×D5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 72 | C2×C4×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 73 | C2×Dic10 | D8 | 1 | 1 | yes | characteristic |
| 74 | #704 | — | 4 | 2 | no | — |
| 75 | #700 | — | 4 | 2 | no | — |
| 76 | D5⋊C8 | — | 4 | 2 | no | — |
| 77 | C5×D8 | — | 4 | 2 | no | — |
| 78 | C5×D8 | — | 4 | 1 | no | — |
| 79 | C5×D8 | — | 4 | 1 | no | — |
| 80 | C2×C5×C8 | — | 2 | 1 | no | — |
| 81 | C2×C5×C8 | — | 2 | 1 | no | — |
| 82 | C2×C5×C8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 83 | C2×C5×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 84 | C22⋊Dic5 | — | 4 | 1 | no | — |
| 85 | C22⋊Dic5 | — | 4 | 2 | no | — |
| 86 | C22⋊Dic5 | — | 4 | 2 | no | — |
| 87 | C4⋊Dic5 | — | 2 | 2 | no | — |
| 88 | C4×Dic5 | — | 4 | 1 | no | — |
| 89 | #681 | — | 4 | 1 | no | — |
| 90 | C2×#168 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 91 | C2×#168 | C2×D4 | 1 | 1 | yes | characteristic |
| 92 | #676 | — | 4 | 1 | no | — |
| 93 | #676 | — | 4 | 1 | no | — |
| 94 | C8×D5 | — | 2 | 1 | no | — |
| 95 | C8×D5 | — | 2 | 1 | no | — |
| 96 | C8×D5 | — | 2 | 1 | no | — |
| 97 | C8×D5 | — | 2 | 1 | no | — |
| 98 | #674 | — | 4 | 2 | no | — |
| 99 | C22×D8 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 100 | C2×#131 | — | 5 | 1 | no | — |
| 101 | #535 | — | 10 | 1 | no | — |
| 102 | C2×M32 | — | 10 | 1 | no | — |
| 103 | #469 | — | 5 | 2 | no | — |
| 104 | #469 | — | 5 | 2 | no | — |
| 105 | #466 | — | 10 | 1 | no | — |
| 106 | #466 | — | 10 | 1 | no | — |
| 107 | C2×#108 | — | 10 | 1 | no | — |
| 108 | #427 | — | 5 | 1 | no | — |
| 109 | #418 | — | 10 | 1 | no | — |
| 110 | #413 | — | 10 | 1 | no | — |
| 111 | #349 | — | 5 | 2 | no | — |
| 112 | #349 | — | 10 | 1 | no | — |
| 113 | #338 | — | 5 | 2 | no | — |
| 114 | C23×C5 | — | 4 | 2 | no | — |
| 115 | C23×C5 | — | 8 | 2 | no | — |
| 116 | C23×C5 | — | 16 | 2 | no | — |
| 117 | C23×C5 | #102 | 1 | 1 | yes | characteristic |
| 118 | C22×D5 | #102 | 1 | 1 | yes | characteristic |
| 119 | C22×D5 | C2×SD16 | 1 | 1 | yes | characteristic |
| 120 | C5×D4 | — | 4 | 2 | no | — |
| 121 | C5×D4 | — | 4 | 2 | no | — |
| 122 | C5×D4 | — | 8 | 2 | no | — |
| 123 | C2×C4×C5 | — | 2 | 1 | no | — |
| 124 | C2×C4×C5 | — | 2 | 1 | no | — |
| 125 | C2×C4×C5 | #102 | 1 | 1 | yes | characteristic |
| 126 | C2×C4×C5 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 127 | C22⋊D5 | — | 4 | 1 | no | — |
| 128 | C22⋊D5 | — | 4 | 1 | no | — |
| 129 | C22⋊D5 | — | 16 | 2 | no | — |
| 130 | C22⋊D5 | — | 16 | 2 | no | — |
| 131 | C2×Dic5 | — | 4 | 2 | no | — |
| 132 | C2×Dic5 | #102 | 1 | 1 | yes | characteristic |
| 133 | C2×Dic5 | C2×D8 | 1 | 1 | yes | characteristic |
| 134 | D20 | — | 4 | 1 | no | — |
| 135 | C4×D5 | — | 2 | 1 | no | — |
| 136 | C4×D5 | — | 2 | 1 | no | — |
| 137 | C4×D5 | — | 2 | 1 | no | — |
| 138 | C4×D5 | — | 2 | 1 | no | — |
| 139 | Dic10 | — | 4 | 1 | no | — |
| 140 | #170 | — | 8 | 2 | no | — |
| 141 | C5×C8 | — | 2 | 1 | no | — |
| 142 | C5×C8 | #99 | 1 | 1 | yes | characteristic |
| 143 | C5×C8 | #99 | 1 | 1 | yes | characteristic |
| 144 | #168 | — | 2 | 1 | no | — |
| 145 | #168 | — | 2 | 1 | no | — |
| 146 | C2×#41 | — | 5 | 1 | no | — |
| 147 | C22×D4 | — | 2 | 1 | no | — |
| 148 | C2×D8 | — | 2 | 1 | no | — |
| 149 | C2×D8 | — | 4 | 1 | no | — |
| 150 | C2×D8 | — | 4 | 1 | no | — |
| 151 | C2×D8 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 152 | #131 | — | 20 | 1 | no | — |
| 153 | #131 | — | 20 | 1 | no | — |
| 154 | C2×M16 | — | 5 | 1 | no | — |
| 155 | C2×M16 | — | 5 | 1 | no | — |
| 156 | C2×M16 | — | 5 | 1 | no | — |
| 157 | C2×M16 | — | 10 | 2 | no | — |
| 158 | C22×C8 | — | 5 | 1 | no | — |
| 159 | C22×C8 | — | 5 | 1 | no | — |
| 160 | C22×C8 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 161 | #127 | — | 20 | 1 | no | — |
| 162 | #124 | — | 20 | 1 | no | — |
| 163 | #121 | — | 10 | 2 | no | — |
| 164 | #121 | — | 10 | 2 | no | — |
| 165 | #120 | — | 20 | 1 | no | — |
| 166 | #120 | — | 20 | 1 | no | — |
| 167 | #117 | — | 10 | 1 | no | — |
| 168 | M32 | — | 10 | 2 | no | — |
| 169 | M32 | — | 20 | 1 | no | — |
| 170 | C2×C16 | — | 20 | 1 | no | — |
| 171 | #108 | — | 20 | 1 | no | — |
| 172 | #108 | — | 20 | 1 | no | — |
| 173 | #107 | — | 10 | 1 | no | — |
| 174 | #106 | — | 5 | 2 | no | — |
| 175 | #102 | — | 10 | 2 | no | — |
| 176 | #102 | — | 10 | 2 | no | — |
| 177 | #101 | — | 20 | 1 | no | — |
| 178 | #100 | — | 20 | 1 | no | — |
| 179 | C22×C5 | — | 2 | 1 | no | — |
| 180 | C22×C5 | — | 4 | 1 | no | — |
| 181 | C22×C5 | — | 8 | 2 | no | — |
| 182 | C22×C5 | — | 8 | 2 | no | — |
| 183 | C22×C5 | — | 8 | 2 | no | — |
| 184 | C22×C5 | — | 16 | 4 | no | — |
| 185 | C22×C5 | C2×#102 | 1 | 1 | yes | characteristic |
| 186 | C2×D5 | — | 2 | 1 | no | — |
| 187 | C2×D5 | — | 2 | 1 | no | — |
| 188 | C2×D5 | — | 4 | 1 | no | — |
| 189 | C2×D5 | — | 4 | 1 | no | — |
| 190 | C4×C5 | — | 2 | 1 | no | — |
| 191 | C4×C5 | C2×#99 | 1 | 1 | yes | characteristic |
| 192 | C4×C5 | #421 | 1 | 1 | yes | characteristic |
| 193 | Dic5 | — | 2 | 1 | no | — |
| 194 | Dic5 | — | 2 | 1 | no | — |
| 195 | Dic5 | — | 8 | 2 | no | — |
| 196 | C24 | — | 4 | 1 | no | — |
| 197 | #41 | — | 20 | 1 | no | — |
| 198 | #41 | — | 20 | 1 | no | — |
| 199 | C2×Q8 | — | 5 | 1 | no | — |
| 200 | C2×D4 | — | 2 | 2 | no | — |
| 201 | C2×D4 | — | 4 | 2 | no | — |
| 202 | C2×D4 | — | 4 | 2 | no | — |
| 203 | C2×D4 | — | 4 | 1 | no | — |
| 204 | C2×D4 | — | 5 | 1 | no | — |
| 205 | C2×D4 | — | 5 | 1 | no | — |
| 206 | C2×D4 | — | 5 | 1 | no | — |
| 207 | C2×D4 | — | 20 | 2 | no | — |
| 208 | C2×D4 | — | 20 | 2 | no | — |
| 209 | C22×C4 | — | 5 | 1 | no | — |
| 210 | C22×C4 | — | 5 | 1 | no | — |
| 211 | C22×C4 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 212 | D8 | — | 4 | 2 | no | — |
| 213 | D8 | — | 4 | 1 | no | — |
| 214 | D8 | — | 4 | 1 | no | — |
| 215 | M16 | — | 20 | 1 | no | — |
| 216 | M16 | — | 20 | 1 | no | — |
| 217 | M16 | — | 20 | 1 | no | — |
| 218 | M16 | — | 20 | 2 | no | — |
| 219 | M16 | — | 20 | 2 | no | — |
| 220 | C2×C8 | — | 2 | 1 | no | — |
| 221 | C2×C8 | — | 2 | 1 | no | — |
| 222 | C2×C8 | — | 5 | 1 | no | — |
| 223 | C2×C8 | — | 5 | 1 | no | — |
| 224 | C2×C8 | — | 10 | 1 | no | — |
| 225 | C2×C8 | — | 10 | 1 | no | — |
| 226 | C2×C8 | — | 10 | 1 | no | — |
| 227 | C2×C8 | — | 10 | 1 | no | — |
| 228 | C2×C8 | — | 20 | 2 | no | — |
| 229 | C2×C8 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 230 | C2×C8 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 231 | C4⋊C4 | — | 10 | 2 | no | — |
| 232 | C22⋊C4 | — | 20 | 2 | no | — |
| 233 | C22⋊C4 | — | 20 | 2 | no | — |
| 234 | C22⋊C4 | — | 20 | 1 | no | — |
| 235 | C42 | — | 20 | 1 | no | — |
| 236 | C16 | — | 20 | 2 | no | — |
| 237 | C2×C5 | — | 2 | 1 | no | — |
| 238 | C2×C5 | — | 4 | 1 | no | — |
| 239 | C2×C5 | — | 16 | 2 | no | — |
| 240 | C2×C5 | #1519 | 1 | 1 | yes | characteristic |
| 241 | D5 | — | 4 | 1 | no | — |
| 242 | D5 | — | 4 | 1 | no | — |
| 243 | C23 | — | 4 | 2 | no | — |
| 244 | C23 | — | 5 | 1 | no | — |
| 245 | C23 | — | 5 | 1 | no | — |
| 246 | C23 | — | 8 | 2 | no | — |
| 247 | C23 | — | 16 | 2 | no | — |
| 248 | C23 | #4007 | 1 | 1 | yes | characteristic |
| 249 | Q8 | — | 20 | 1 | no | — |
| 250 | D4 | — | 4 | 2 | no | — |
| 251 | D4 | — | 4 | 2 | no | — |
| 252 | D4 | — | 8 | 2 | no | — |
| 253 | D4 | — | 20 | 1 | no | — |
| 254 | D4 | — | 20 | 1 | no | — |
| 255 | D4 | — | 20 | 1 | no | — |
| 256 | D4 | — | 80 | 2 | no | — |
| 257 | D4 | — | 80 | 2 | no | — |
| 258 | C2×C4 | — | 2 | 1 | no | — |
| 259 | C2×C4 | — | 2 | 1 | no | — |
| 260 | C2×C4 | — | 5 | 1 | no | — |
| 261 | C2×C4 | — | 5 | 1 | no | — |
| 262 | C2×C4 | — | 10 | 1 | no | — |
| 263 | C2×C4 | — | 10 | 1 | no | — |
| 264 | C2×C4 | — | 10 | 1 | no | — |
| 265 | C2×C4 | — | 10 | 1 | no | — |
| 266 | C2×C4 | — | 20 | 2 | no | — |
| 267 | C2×C4 | #4007 | 1 | 1 | yes | characteristic |
| 268 | C2×C4 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 269 | C8 | — | 2 | 1 | no | — |
| 270 | C8 | — | 10 | 1 | no | — |
| 271 | C8 | — | 10 | 1 | no | — |
| 272 | C8 | — | 40 | 2 | no | — |
| 273 | C8 | #4011 | 1 | 1 | yes | characteristic |
| 274 | C8 | #4011 | 1 | 1 | yes | characteristic |
| 275 | C5 | #11870 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 276 | C22 | — | 2 | 1 | no | — |
| 277 | C22 | — | 4 | 1 | no | — |
| 278 | C22 | — | 8 | 2 | no | — |
| 279 | C22 | — | 8 | 2 | no | — |
| 280 | C22 | — | 8 | 2 | no | — |
| 281 | C22 | — | 10 | 1 | no | — |
| 282 | C22 | — | 10 | 1 | no | — |
| 283 | C22 | — | 16 | 4 | no | — |
| 284 | C22 | — | 20 | 1 | no | — |
| 285 | C22 | — | 20 | 1 | no | — |
| 286 | C22 | C2×#4007 | 1 | 1 | yes | characteristic |
| 287 | C4 | — | 2 | 1 | no | — |
| 288 | C4 | — | 10 | 1 | no | — |
| 289 | C4 | — | 10 | 1 | no | — |
| 290 | C4 | — | 40 | 2 | no | — |
| 291 | C4 | #65769 | 1 | 1 | yes | characteristic |
| 292 | C4 | C2×#4011 | 1 | 1 | yes | characteristic |
| 293 | C2 | — | 2 | 1 | no | — |
| 294 | C2 | — | 4 | 1 | no | — |
| 295 | C2 | — | 16 | 2 | no | — |
| 296 | C2 | — | 20 | 1 | no | — |
| 297 | C2 | — | 20 | 1 | no | — |
| 298 | C2 | #10604913 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10604733 | C2 | semidirect |
| 3. #10604713 | C2 | semidirect |
| 4. #10598804 | C2 | semidirect |
| 18. #64897 | C22 | semidirect |
| 19. #64891 | C22 | semidirect |
| 275. C5 | #11870 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615567 | 2 |
| #10604733 | 2 |
| #10604713 | 2 |
| #10598804 | 2 |
| #11870 | 5 |