Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1328 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1328 conjugacy classes of subgroups — too many to draw. Only its 251 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 | #10619197 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10615856 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #10610386 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | C5×#1791 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10600929 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #10600926 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #10600795 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | C5×#585 | C22 | 1 | 1 | yes | characteristic |
| 9 | #66162 | C22 | 1 | 3 | yes | — |
| 10 | #66153 | — | 2 | 6 | no | — |
| 11 | #66153 | C22 | 1 | 3 | yes | — |
| 12 | C2×#4094 | — | 2 | 6 | no | — |
| 13 | C2×#4094 | C22 | 1 | 3 | yes | — |
| 14 | C22×C8×D5 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | C5×#413 | C22 | 1 | 3 | yes | — |
| 16 | C5×#408 | C22 | 1 | 3 | yes | — |
| 17 | #65533 | C4 | 1 | 4 | yes | — |
| 18 | #65532 | C4 | 1 | 4 | yes | — |
| 19 | #65529 | C22 | 1 | 3 | yes | — |
| 20 | #65415 | C22 | 1 | 3 | yes | complemented |
| 21 | #65411 | C22 | 1 | 3 | yes | complemented |
| 22 | #65391 | C22 | 1 | 3 | yes | complemented |
| 23 | #65017 | — | 2 | 6 | no | — |
| 24 | #65014 | — | 2 | 6 | no | — |
| 25 | #64779 | C22 | 1 | 6 | yes | complemented |
| 26 | #21483 | — | 5 | 1 | no | maximal, Sylow |
| 27 | C5×2−1+4 | — | 2 | 3 | no | — |
| 28 | C5×H(5,𝔽2) | — | 2 | 3 | no | — |
| 29 | C5×H(5,𝔽2) | C2×C4 | 1 | 4 | yes | — |
| 30 | C2×C5×#41 | — | 2 | 6 | no | — |
| 31 | C2×C5×#41 | C23 | 1 | 3 | yes | — |
| 32 | C22×C4×D5 | C23 | 1 | 1 | yes | characteristic |
| 33 | C2×C5×M16 | C23 | 1 | 3 | yes | — |
| 34 | C22×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 35 | #4094 | — | 2 | 4 | no | — |
| 36 | #4094 | — | 2 | 12 | no | — |
| 37 | #4094 | — | 2 | 6 | no | — |
| 38 | #4094 | — | 2 | 12 | no | — |
| 39 | #4094 | — | 2 | 6 | no | — |
| 40 | #4092 | — | 2 | 3 | no | — |
| 41 | #4084 | — | 2 | 3 | no | — |
| 42 | #4083 | C2×C4 | 1 | 6 | yes | — |
| 43 | #4081 | C2×C4 | 1 | 6 | yes | — |
| 44 | C4×C22⋊D5 | — | 2 | 6 | no | — |
| 45 | #4072 | C23 | 1 | 3 | yes | — |
| 46 | C2×#681 | — | 2 | 12 | no | — |
| 47 | C2×#681 | — | 2 | 6 | no | — |
| 48 | C2×#681 | D4 | 1 | 6 | yes | complemented |
| 49 | C2×#681 | C23 | 1 | 3 | yes | — |
| 50 | C22×#168 | — | 2 | 4 | no | — |
| 51 | C22×#168 | D4 | 1 | 6 | yes | complemented |
| 52 | C22×#168 | C23 | 1 | 1 | yes | characteristic |
| 53 | C2×C8×D5 | — | 2 | 3 | no | — |
| 54 | C2×C8×D5 | — | 2 | 3 | no | — |
| 55 | C5×#101 | — | 2 | 3 | no | — |
| 56 | C5×#100 | — | 2 | 3 | no | — |
| 57 | C5×C22⋊C8 | — | 2 | 6 | no | — |
| 58 | #3966 | C2×C4 | 1 | 12 | yes | — |
| 59 | #3952 | — | 2 | 6 | no | — |
| 60 | #3947 | — | 2 | 3 | no | — |
| 61 | #3946 | — | 2 | 6 | no | — |
| 62 | C8×Dic5 | — | 2 | 3 | no | — |
| 63 | #3573 | — | 5 | 1 | no | — |
| 64 | #3025 | — | 5 | 1 | no | — |
| 65 | #2929 | — | 5 | 3 | no | — |
| 66 | #1891 | — | 5 | 3 | no | — |
| 67 | #1868 | — | 5 | 3 | no | — |
| 68 | #1791 | D5 | 1 | 1 | yes | characteristic, complemented |
| 69 | #1757 | — | 5 | 3 | no | — |
| 70 | C23×D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 71 | C5×#41 | — | 2 | 4 | no | — |
| 72 | C5×#41 | — | 2 | 12 | no | — |
| 73 | C5×#41 | — | 2 | 12 | no | — |
| 74 | C5×#41 | — | 2 | 6 | no | — |
| 75 | C5×#41 | — | 2 | 6 | no | — |
| 76 | C2×C5×Q8 | — | 2 | 6 | no | — |
| 77 | C2×C5×Q8 | #41 | 1 | 3 | yes | — |
| 78 | C2×C5×D4 | — | 2 | 6 | no | — |
| 79 | C2×C5×D4 | — | 2 | 12 | no | — |
| 80 | C2×C5×D4 | C22×C4 | 1 | 6 | yes | — |
| 81 | C2×C5×D4 | #41 | 1 | 3 | yes | — |
| 82 | C22×C4×C5 | — | 2 | 4 | no | — |
| 83 | C22×C4×C5 | C2×D4 | 1 | 6 | yes | — |
| 84 | C22×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 85 | C2×C22⋊D5 | — | 2 | 6 | no | — |
| 86 | C22×Dic5 | C22×C4 | 1 | 1 | yes | characteristic |
| 87 | C2×C4×D5 | — | 2 | 3 | no | — |
| 88 | C2×C4×D5 | — | 2 | 3 | no | — |
| 89 | C5×M16 | — | 2 | 6 | no | — |
| 90 | C2×C5×C8 | — | 2 | 3 | no | — |
| 91 | C2×C5×C8 | — | 2 | 3 | no | — |
| 92 | C22⋊Dic5 | — | 2 | 6 | no | — |
| 93 | C22⋊Dic5 | C22×C4 | 1 | 6 | yes | — |
| 94 | #685 | — | 2 | 6 | no | — |
| 95 | C4⋊Dic5 | — | 2 | 3 | no | — |
| 96 | #683 | — | 2 | 6 | no | — |
| 97 | C4×Dic5 | — | 2 | 3 | no | — |
| 98 | #681 | — | 2 | 12 | no | — |
| 99 | #681 | — | 2 | 6 | no | — |
| 100 | #681 | — | 2 | 12 | no | — |
| 101 | C2×#168 | — | 2 | 12 | no | — |
| 102 | C2×#168 | — | 2 | 6 | no | — |
| 103 | C2×#168 | — | 2 | 6 | no | — |
| 104 | C2×#168 | C2×D4 | 1 | 6 | yes | — |
| 105 | C2×#168 | C2×D4 | 1 | 3 | yes | — |
| 106 | C2×#168 | C2×D4 | 1 | 3 | yes | — |
| 107 | C8×D5 | — | 4 | 1 | no | — |
| 108 | C8×D5 | — | 4 | 3 | no | — |
| 109 | #585 | C2×D5 | 1 | 1 | yes | characteristic |
| 110 | #568 | — | 5 | 3 | no | — |
| 111 | #568 | — | 10 | 6 | no | — |
| 112 | C2×#131 | — | 5 | 3 | no | — |
| 113 | C2×#131 | — | 10 | 6 | no | — |
| 114 | C23×C8 | — | 5 | 1 | no | — |
| 115 | #525 | — | 5 | 3 | no | — |
| 116 | #458 | — | 5 | 4 | no | — |
| 117 | B(4,𝔽2) | — | 5 | 4 | no | — |
| 118 | #435 | — | 10 | 6 | no | — |
| 119 | C8×D4 | — | 10 | 6 | no | — |
| 120 | #424 | — | 5 | 3 | no | — |
| 121 | #413 | C2×D5 | 1 | 3 | yes | — |
| 122 | #410 | — | 5 | 3 | no | — |
| 123 | #408 | C2×D5 | 1 | 3 | yes | — |
| 124 | #407 | — | 5 | 3 | no | — |
| 125 | #405 | — | 5 | 3 | no | — |
| 126 | #344 | — | 5 | 6 | no | — |
| 127 | C23×C5 | — | 2 | 4 | no | — |
| 128 | C23×C5 | C4×D4 | 1 | 6 | yes | — |
| 129 | C23×C5 | C23×C4 | 1 | 1 | yes | characteristic |
| 130 | C22×D5 | — | 2 | 3 | no | — |
| 131 | C22×D5 | — | 4 | 2 | no | — |
| 132 | C5×Q8 | — | 2 | 4 | no | — |
| 133 | C5×Q8 | — | 2 | 6 | no | — |
| 134 | C5×D4 | — | 2 | 12 | no | — |
| 135 | C5×D4 | — | 2 | 12 | no | — |
| 136 | C5×D4 | — | 2 | 6 | no | — |
| 137 | C2×C4×C5 | — | 2 | 12 | no | — |
| 138 | C2×C4×C5 | — | 2 | 6 | no | — |
| 139 | C2×C4×C5 | — | 2 | 6 | no | — |
| 140 | C2×C4×C5 | C4×D4 | 1 | 6 | yes | — |
| 141 | C2×C4×C5 | C22×D4 | 1 | 3 | yes | — |
| 142 | C2×C4×C5 | C2×#41 | 1 | 3 | yes | — |
| 143 | C22⋊D5 | — | 4 | 12 | no | — |
| 144 | C2×Dic5 | — | 2 | 6 | no | — |
| 145 | C2×Dic5 | — | 2 | 3 | no | — |
| 146 | C4×D5 | — | 4 | 1 | no | — |
| 147 | C4×D5 | — | 4 | 3 | no | — |
| 148 | C5×C8 | — | 4 | 1 | no | — |
| 149 | C5×C8 | — | 4 | 3 | no | — |
| 150 | #168 | — | 2 | 6 | no | — |
| 151 | #168 | #120 | 1 | 1 | yes | characteristic |
| 152 | #168 | #120 | 1 | 3 | yes | — |
| 153 | 2−1+4 | — | 2 | 3 | no | — |
| 154 | H(5,𝔽2) | — | 2 | 3 | no | — |
| 155 | H(5,𝔽2) | C4×D5 | 1 | 4 | yes | — |
| 156 | C2×#41 | — | 2 | 6 | no | — |
| 157 | C2×#41 | C22×D5 | 1 | 3 | yes | — |
| 158 | C23×C4 | — | 5 | 1 | no | — |
| 159 | #131 | — | 10 | 6 | no | — |
| 160 | #131 | — | 10 | 6 | no | — |
| 161 | #131 | — | 10 | 12 | no | — |
| 162 | #131 | — | 10 | 4 | no | — |
| 163 | #131 | — | 10 | 12 | no | — |
| 164 | C2×M16 | — | 5 | 6 | no | — |
| 165 | C2×M16 | — | 5 | 3 | no | — |
| 166 | C2×M16 | — | 10 | 12 | no | — |
| 167 | C2×M16 | — | 10 | 6 | no | — |
| 168 | C2×M16 | C22×D5 | 1 | 3 | yes | — |
| 169 | C22×C8 | — | 5 | 1 | no | — |
| 170 | C22×C8 | — | 5 | 6 | no | — |
| 171 | C22×C8 | — | 10 | 3 | no | — |
| 172 | C22×C8 | — | 10 | 3 | no | — |
| 173 | C22×C8 | — | 10 | 4 | no | — |
| 174 | C22×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 175 | #123 | — | 5 | 6 | no | — |
| 176 | C22⋊Q8 | — | 10 | 3 | no | — |
| 177 | #121 | — | 10 | 3 | no | — |
| 178 | #120 | — | 5 | 6 | no | — |
| 179 | C4×D4 | — | 10 | 6 | no | — |
| 180 | #117 | — | 5 | 3 | no | — |
| 181 | C4⋊C8 | — | 10 | 6 | no | — |
| 182 | #101 | — | 2 | 3 | no | — |
| 183 | #100 | — | 2 | 3 | no | — |
| 184 | #99 | — | 5 | 12 | no | — |
| 185 | C22⋊C8 | — | 2 | 6 | no | — |
| 186 | C22⋊C8 | — | 10 | 6 | no | — |
| 187 | #97 | — | 10 | 3 | no | — |
| 188 | C4×C8 | — | 10 | 3 | no | — |
| 189 | C22×C5 | — | 2 | 6 | no | — |
| 190 | C22×C5 | — | 4 | 1 | no | — |
| 191 | C22×C5 | — | 4 | 6 | no | — |
| 192 | C22×C5 | — | 8 | 4 | no | — |
| 193 | C22×C5 | C2×C4×D4 | 1 | 3 | yes | — |
| 194 | C2×D5 | — | 2 | 6 | no | — |
| 195 | C2×D5 | — | 4 | 3 | no | — |
| 196 | C2×D5 | — | 4 | 1 | no | — |
| 197 | C4×C5 | — | 2 | 6 | no | — |
| 198 | C4×C5 | C2×#120 | 1 | 1 | yes | characteristic |
| 199 | C4×C5 | #525 | 1 | 3 | yes | — |
| 200 | Dic5 | — | 4 | 6 | no | — |
| 201 | Dic5 | — | 4 | 1 | no | — |
| 202 | C24 | — | 5 | 1 | no | — |
| 203 | #41 | — | 2 | 4 | no | — |
| 204 | #41 | — | 2 | 12 | no | — |
| 205 | #41 | — | 2 | 6 | no | — |
| 206 | #41 | — | 2 | 6 | no | — |
| 207 | #41 | — | 2 | 12 | no | — |
| 208 | C2×Q8 | — | 2 | 6 | no | — |
| 209 | C2×Q8 | #711 | 1 | 3 | yes | — |
| 210 | C2×D4 | — | 2 | 6 | no | — |
| 211 | C2×D4 | — | 2 | 12 | no | — |
| 212 | C2×D4 | — | 10 | 6 | no | — |
| 213 | C2×D4 | C2×C4×D5 | 1 | 6 | yes | — |
| 214 | C2×D4 | #711 | 1 | 3 | yes | — |
| 215 | C22×C4 | — | 2 | 4 | no | — |
| 216 | C22×C4 | — | 5 | 1 | no | — |
| 217 | C22×C4 | — | 10 | 3 | no | — |
| 218 | C22×C4 | — | 10 | 3 | no | — |
| 219 | C22×C4 | D4×D5 | 1 | 6 | yes | — |
| 220 | C22×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 221 | M16 | — | 2 | 6 | no | — |
| 222 | M16 | — | 10 | 12 | no | — |
| 223 | M16 | — | 10 | 12 | no | — |
| 224 | M16 | — | 10 | 6 | no | — |
| 225 | C2×C8 | — | 2 | 3 | no | — |
| 226 | C2×C8 | — | 2 | 3 | no | — |
| 227 | C2×C8 | — | 5 | 3 | no | — |
| 228 | C2×C8 | — | 5 | 3 | no | — |
| 229 | C2×C8 | — | 5 | 6 | no | — |
| 230 | C2×C8 | — | 10 | 6 | no | — |
| 231 | C2×C8 | — | 10 | 6 | no | — |
| 232 | C2×C8 | — | 10 | 12 | no | — |
| 233 | C2×C8 | — | 20 | 1 | no | — |
| 234 | C2×C8 | — | 20 | 3 | no | — |
| 235 | C4⋊C4 | — | 10 | 3 | no | — |
| 236 | C4⋊C4 | — | 10 | 6 | no | — |
| 237 | C22⋊C4 | — | 5 | 6 | no | — |
| 238 | C22⋊C4 | — | 10 | 6 | no | — |
| 239 | C22⋊C4 | — | 10 | 6 | no | — |
| 240 | C42 | — | 10 | 3 | no | — |
| 241 | C2×C5 | — | 2 | 3 | no | — |
| 242 | C2×C5 | — | 4 | 6 | no | — |
| 243 | C2×C5 | C4×#120 | 1 | 1 | yes | characteristic |
| 244 | D5 | — | 4 | 2 | no | — |
| 245 | C23 | — | 2 | 4 | no | — |
| 246 | C23 | — | 10 | 3 | no | — |
| 247 | C23 | — | 20 | 2 | no | — |
| 248 | C23 | #4027 | 1 | 6 | yes | — |
| 249 | C23 | C22×C4×D5 | 1 | 1 | yes | characteristic |
| 250 | Q8 | — | 2 | 4 | no | — |
| 251 | Q8 | — | 2 | 6 | no | — |
| 252 | D4 | — | 2 | 12 | no | — |
| 253 | D4 | — | 2 | 12 | no | — |
| 254 | D4 | — | 2 | 6 | no | — |
| 255 | D4 | — | 20 | 12 | no | — |
| 256 | C2×C4 | — | 2 | 12 | no | — |
| 257 | C2×C4 | — | 2 | 6 | no | — |
| 258 | C2×C4 | — | 2 | 6 | no | — |
| 259 | C2×C4 | — | 10 | 6 | no | — |
| 260 | C2×C4 | — | 10 | 3 | no | — |
| 261 | C2×C4 | — | 20 | 3 | no | — |
| 262 | C2×C4 | — | 20 | 1 | no | — |
| 263 | C2×C4 | #4027 | 1 | 6 | yes | — |
| 264 | C2×C4 | C2×D4×D5 | 1 | 3 | yes | — |
| 265 | C2×C4 | C2×#711 | 1 | 3 | yes | — |
| 266 | C8 | — | 4 | 3 | no | — |
| 267 | C8 | — | 4 | 1 | no | — |
| 268 | C8 | — | 5 | 1 | no | — |
| 269 | C8 | — | 5 | 3 | no | — |
| 270 | C8 | — | 10 | 6 | no | — |
| 271 | C5 | #21483 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 272 | C22 | — | 2 | 6 | no | — |
| 273 | C22 | — | 4 | 1 | no | — |
| 274 | C22 | — | 4 | 6 | no | — |
| 275 | C22 | — | 8 | 4 | no | — |
| 276 | C22 | — | 10 | 6 | no | — |
| 277 | C22 | — | 20 | 3 | no | — |
| 278 | C22 | — | 20 | 1 | no | — |
| 279 | C22 | C2×#4027 | 1 | 3 | yes | — |
| 280 | C4 | — | 2 | 6 | no | — |
| 281 | C4 | — | 20 | 6 | no | — |
| 282 | C4 | — | 20 | 1 | no | — |
| 283 | C4 | #65920 | 1 | 3 | yes | — |
| 284 | C4 | D5×#120 | 1 | 1 | yes | characteristic |
| 285 | C2 | — | 2 | 3 | no | — |
| 286 | C2 | — | 4 | 6 | no | — |
| 287 | C2 | — | 20 | 2 | no | — |
| 288 | C2 | #10605549 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10619197 | C2 | semidirect |
| 3. #10610386 | C2 | semidirect |
| 4. C5×#1791 | C2 | semidirect |
| 5. #10600929 | C2 | semidirect |
| 6. #10600926 | C2 | semidirect |
| 7. #10600795 | C2 | semidirect |
| 14. C22×C8×D5 | C22 | semidirect |
| 20. #65415 | C22 | semidirect |
| 21. #65411 | C22 | semidirect |
| 22. #65391 | C22 | semidirect |
| 25. #64779 | C22 | semidirect |
| 48. C2×#681 | D4 | semidirect |
| 51. C22×#168 | D4 | semidirect |
| 68. #1791 | D5 | semidirect |
| 271. C5 | #21483 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10619197 | 2 |
| #10615856 | 2 |
| #10610386 | 2 |
| C5×#1791 | 2 |
| #10600929 | 2 |
| #10600926 | 2 |
| #10600795 | 2 |
| #21483 | 5 |