← #12963648
Subgroups — #12963648
Order 1280.
2604 conjugacy classes of subgroups.
The subgroup lattice has 340 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #10619064 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10619061 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C5×#2875 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10615520 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10614267 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #10610311 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #10610310 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #10610272 | C2 | 1 | 6 | yes | maximal, complemented |
| 9 | C2×#65006 | C2 | 1 | 6 | yes | maximal, complemented |
| 10 | #66283 | C22 | 1 | 2 | yes | — |
| 11 | C2×C5×#131 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×C5×#131 | C22 | 1 | 1 | yes | characteristic |
| 13 | C4×C5×#41 | C22 | 1 | 1 | yes | characteristic |
| 14 | #66153 | C22 | 1 | 2 | yes | — |
| 15 | #66087 | C4 | 1 | 4 | yes | complemented |
| 16 | #66086 | C4 | 1 | 4 | yes | complemented |
| 17 | #66085 | C4 | 1 | 8 | yes | complemented |
| 18 | #66084 | — | 2 | 8 | no | — |
| 19 | D5×#131 | — | 2 | 8 | no | — |
| 20 | #66082 | C22 | 1 | 6 | yes | — |
| 21 | #66079 | C22 | 1 | 12 | yes | complemented |
| 22 | C2×#4050 | C22 | 1 | 6 | yes | — |
| 23 | C2×#4047 | C22 | 1 | 12 | yes | complemented |
| 24 | C5×#405 | C22 | 1 | 3 | yes | complemented |
| 25 | C5×#405 | C22 | 1 | 3 | yes | complemented |
| 26 | C4×C5×M16 | C22 | 1 | 3 | yes | complemented |
| 27 | C2×C5×#97 | C22 | 1 | 3 | yes | complemented |
| 28 | #65414 | C22 | 1 | 6 | yes | complemented |
| 29 | C2×#3951 | C22 | 1 | 6 | yes | complemented |
| 30 | #65294 | C22 | 1 | 12 | yes | complemented |
| 31 | C2×#3937 | C22 | 1 | 12 | yes | complemented |
| 32 | #65006 | C22 | 1 | 4 | yes | complemented |
| 33 | #65006 | C22 | 1 | 12 | yes | complemented |
| 34 | #65006 | C22 | 1 | 12 | yes | complemented |
| 35 | #65006 | C22 | 1 | 12 | yes | complemented |
| 36 | #64989 | C22 | 1 | 24 | yes | complemented |
| 37 | #60184 | — | 5 | 1 | no | maximal, Sylow |
| 38 | C2×C5×#41 | C23 | 1 | 1 | yes | characteristic |
| 39 | #4150 | C2×C4 | 1 | 8 | yes | — |
| 40 | #4149 | C2×C4 | 1 | 8 | yes | — |
| 41 | D5×#41 | — | 2 | 8 | no | — |
| 42 | #4147 | — | 2 | 2 | no | — |
| 43 | #4144 | — | 2 | 6 | no | — |
| 44 | C2×#709 | C23 | 1 | 12 | yes | — |
| 45 | C5×#131 | C2×C4 | 1 | 4 | yes | — |
| 46 | C5×#131 | C2×C4 | 1 | 4 | yes | — |
| 47 | C5×#131 | D4 | 1 | 8 | yes | — |
| 48 | C2×C5×M16 | C23 | 1 | 3 | yes | — |
| 49 | C2×C5×M16 | C23 | 1 | 3 | yes | — |
| 50 | C22×C5×C8 | C23 | 1 | 3 | yes | — |
| 51 | C22×C5×C8 | C23 | 1 | 3 | yes | — |
| 52 | C4×C5×Q8 | — | 2 | 1 | no | — |
| 53 | C4×C5×D4 | — | 2 | 3 | no | — |
| 54 | C5×#117 | C23 | 1 | 3 | yes | — |
| 55 | C2×C42×C5 | C23 | 1 | 3 | yes | — |
| 56 | #4094 | — | 2 | 8 | no | — |
| 57 | C2×#681 | C23 | 1 | 12 | yes | — |
| 58 | #4055 | C2×C4 | 1 | 24 | yes | complemented |
| 59 | #4054 | C2×C4 | 1 | 24 | yes | complemented |
| 60 | #4053 | — | 2 | 24 | no | — |
| 61 | D5×M16 | — | 2 | 24 | no | — |
| 62 | C2×Dic20 | C2×C4 | 1 | 6 | yes | complemented |
| 63 | #4050 | C2×C4 | 1 | 12 | yes | complemented |
| 64 | #4050 | C2×C4 | 1 | 12 | yes | complemented |
| 65 | #4050 | C23 | 1 | 4 | yes | — |
| 66 | #4050 | C23 | 1 | 12 | yes | — |
| 67 | C2×D40 | C2×C4 | 1 | 6 | yes | complemented |
| 68 | C2×#677 | C2×C4 | 1 | 12 | yes | complemented |
| 69 | #4047 | — | 2 | 12 | no | — |
| 70 | #4047 | — | 2 | 12 | no | — |
| 71 | #4047 | C23 | 1 | 8 | yes | — |
| 72 | #4047 | C23 | 1 | 24 | yes | — |
| 73 | C2×#676 | — | 2 | 12 | no | — |
| 74 | C2×C8×D5 | — | 2 | 12 | no | — |
| 75 | C5×#97 | C23 | 1 | 1 | yes | characteristic |
| 76 | C5×#97 | C23 | 1 | 3 | yes | — |
| 77 | C5×#97 | C23 | 1 | 3 | yes | — |
| 78 | C5×#97 | C23 | 1 | 3 | yes | — |
| 79 | C4×C5×C8 | C23 | 1 | 6 | yes | — |
| 80 | #3951 | C23 | 1 | 4 | yes | — |
| 81 | #3951 | C23 | 1 | 12 | yes | — |
| 82 | #3937 | C23 | 1 | 24 | yes | — |
| 83 | #3937 | C23 | 1 | 8 | yes | — |
| 84 | #3584 | — | 5 | 1 | no | — |
| 85 | #3573 | — | 5 | 2 | no | — |
| 86 | #2957 | — | 5 | 6 | no | — |
| 87 | #2956 | — | 5 | 6 | no | — |
| 88 | #2955 | — | 5 | 6 | no | — |
| 89 | C2×#444 | — | 5 | 6 | no | — |
| 90 | #2916 | — | 5 | 1 | no | — |
| 91 | #2901 | — | 5 | 2 | no | — |
| 92 | #2875 | D5 | 1 | 1 | yes | characteristic, complemented |
| 93 | C5×#41 | C22×C4 | 1 | 4 | yes | — |
| 94 | C5×#41 | C2×D4 | 1 | 4 | yes | — |
| 95 | C2×C5×Q8 | #41 | 1 | 1 | yes | characteristic |
| 96 | C2×C5×D4 | #41 | 1 | 3 | yes | — |
| 97 | C22×C4×C5 | — | 2 | 3 | no | — |
| 98 | C22×C4×C5 | C24 | 1 | 3 | yes | — |
| 99 | C2×C22⋊D5 | — | 2 | 12 | no | — |
| 100 | #713 | — | 2 | 8 | no | — |
| 101 | Q8×D5 | — | 2 | 8 | no | — |
| 102 | #711 | — | 2 | 24 | no | — |
| 103 | D4×D5 | — | 2 | 24 | no | — |
| 104 | #709 | — | 2 | 12 | no | — |
| 105 | #709 | — | 2 | 12 | no | — |
| 106 | #709 | C22×C4 | 1 | 24 | yes | — |
| 107 | #709 | C24 | 1 | 8 | yes | — |
| 108 | C2×D20 | C22×C4 | 1 | 12 | yes | — |
| 109 | C2×C4×D5 | — | 2 | 12 | no | — |
| 110 | C2×Dic10 | C22×C4 | 1 | 12 | yes | — |
| 111 | C5×M16 | C22×C4 | 1 | 12 | yes | — |
| 112 | C5×M16 | C2×D4 | 1 | 12 | yes | — |
| 113 | C2×C5×C8 | C22×C4 | 1 | 6 | yes | — |
| 114 | C2×C5×C8 | C22×C4 | 1 | 6 | yes | — |
| 115 | C2×C5×C8 | C2×D4 | 1 | 12 | yes | — |
| 116 | C2×C5×C8 | C24 | 1 | 1 | yes | characteristic |
| 117 | C2×C5×C8 | C24 | 1 | 3 | yes | — |
| 118 | C2×C5×C8 | C24 | 1 | 1 | yes | characteristic |
| 119 | C2×C5×C8 | C24 | 1 | 3 | yes | — |
| 120 | C5×C4⋊C4 | — | 2 | 3 | no | — |
| 121 | C5×C22⋊C4 | — | 2 | 3 | no | — |
| 122 | C42×C5 | — | 2 | 3 | no | — |
| 123 | C42×C5 | C24 | 1 | 1 | yes | characteristic |
| 124 | C42×C5 | C24 | 1 | 3 | yes | — |
| 125 | #681 | — | 2 | 12 | no | — |
| 126 | #681 | C24 | 1 | 8 | yes | — |
| 127 | C2×#168 | — | 2 | 12 | no | — |
| 128 | Dic20 | C22×C4 | 1 | 4 | yes | — |
| 129 | Dic20 | C22×C4 | 1 | 12 | yes | — |
| 130 | D40 | C22×C4 | 1 | 4 | yes | — |
| 131 | D40 | C22×C4 | 1 | 12 | yes | — |
| 132 | #677 | C22×C4 | 1 | 8 | yes | — |
| 133 | #677 | C22×C4 | 1 | 24 | yes | — |
| 134 | #676 | — | 2 | 8 | no | — |
| 135 | #676 | — | 2 | 24 | no | — |
| 136 | C8×D5 | — | 2 | 8 | no | — |
| 137 | C8×D5 | — | 2 | 24 | no | — |
| 138 | #585 | — | 5 | 2 | no | — |
| 139 | #578 | — | 5 | 4 | no | — |
| 140 | #577 | — | 5 | 8 | no | — |
| 141 | #576 | — | 5 | 4 | no | — |
| 142 | #575 | — | 5 | 6 | no | — |
| 143 | C2×#135 | — | 5 | 6 | no | — |
| 144 | #568 | — | 5 | 2 | no | — |
| 145 | #568 | — | 5 | 12 | no | — |
| 146 | #568 | — | 10 | 8 | no | — |
| 147 | C2×#131 | — | 5 | 12 | no | — |
| 148 | C2×#131 | — | 10 | 8 | no | — |
| 149 | C2×#131 | C2×D5 | 1 | 1 | yes | characteristic |
| 150 | C2×#131 | C2×D5 | 1 | 1 | yes | characteristic |
| 151 | C4×#41 | C2×D5 | 1 | 1 | yes | characteristic |
| 152 | #444 | — | 5 | 4 | no | — |
| 153 | #444 | — | 5 | 12 | no | — |
| 154 | #444 | — | 5 | 12 | no | — |
| 155 | #444 | — | 5 | 12 | no | — |
| 156 | #443 | — | 5 | 24 | no | — |
| 157 | #430 | — | 5 | 6 | no | — |
| 158 | C2×#108 | — | 5 | 6 | no | — |
| 159 | #421 | — | 5 | 12 | no | — |
| 160 | C2×#104 | — | 5 | 12 | no | — |
| 161 | #405 | C2×D5 | 1 | 3 | yes | complemented |
| 162 | #405 | C2×D5 | 1 | 3 | yes | complemented |
| 163 | C4×M16 | C2×D5 | 1 | 3 | yes | complemented |
| 164 | C2×#97 | C2×D5 | 1 | 3 | yes | complemented |
| 165 | C23×C5 | C2×#41 | 1 | 3 | yes | — |
| 166 | C22×D5 | — | 2 | 12 | no | — |
| 167 | C5×Q8 | C4×D4 | 1 | 4 | yes | — |
| 168 | C5×D4 | C4×D4 | 1 | 12 | yes | — |
| 169 | C2×C4×C5 | — | 2 | 1 | no | — |
| 170 | C2×C4×C5 | — | 2 | 3 | no | — |
| 171 | C2×C4×C5 | — | 8 | 3 | no | — |
| 172 | C2×C4×C5 | C23×C4 | 1 | 6 | yes | — |
| 173 | C2×C4×C5 | C22×D4 | 1 | 6 | yes | — |
| 174 | C2×C4×C5 | C2×#41 | 1 | 3 | yes | — |
| 175 | C2×C4×C5 | C25 | 1 | 1 | yes | characteristic |
| 176 | C22⋊D5 | — | 2 | 24 | no | — |
| 177 | C22⋊D5 | — | 2 | 8 | no | — |
| 178 | C2×Dic5 | — | 2 | 12 | no | — |
| 179 | D20 | — | 2 | 12 | no | — |
| 180 | D20 | C23×C4 | 1 | 8 | yes | — |
| 181 | C4×D5 | — | 2 | 24 | no | — |
| 182 | C4×D5 | — | 2 | 8 | no | — |
| 183 | Dic10 | — | 2 | 12 | no | — |
| 184 | Dic10 | C23×C4 | 1 | 8 | yes | — |
| 185 | C5×C8 | C23×C4 | 1 | 1 | yes | characteristic |
| 186 | C5×C8 | C23×C4 | 1 | 6 | yes | — |
| 187 | C5×C8 | C23×C4 | 1 | 1 | yes | characteristic |
| 188 | C5×C8 | C22×D4 | 1 | 2 | yes | — |
| 189 | C5×C8 | C22×D4 | 1 | 6 | yes | — |
| 190 | #168 | — | 2 | 8 | no | — |
| 191 | 2−1+4 | — | 5 | 8 | no | — |
| 192 | 2−1+4 | — | 10 | 2 | no | — |
| 193 | H(5,𝔽2) | — | 5 | 8 | no | — |
| 194 | H(5,𝔽2) | — | 10 | 6 | no | — |
| 195 | C2×#41 | — | 5 | 12 | no | — |
| 196 | C2×#41 | — | 10 | 8 | no | — |
| 197 | C2×#41 | C22×D5 | 1 | 1 | yes | characteristic |
| 198 | #137 | — | 5 | 24 | no | — |
| 199 | AGL(1,ℤ/8) | — | 5 | 24 | no | — |
| 200 | #135 | — | 5 | 12 | no | — |
| 201 | #135 | — | 5 | 12 | no | — |
| 202 | #135 | — | 5 | 4 | no | — |
| 203 | #135 | — | 5 | 12 | no | — |
| 204 | C2×Q16 | — | 5 | 6 | no | — |
| 205 | C2×SD16 | — | 5 | 12 | no | — |
| 206 | C2×D8 | — | 5 | 6 | no | — |
| 207 | #131 | — | 5 | 8 | no | — |
| 208 | #131 | — | 5 | 24 | no | — |
| 209 | #131 | — | 10 | 8 | no | — |
| 210 | #131 | — | 10 | 24 | no | — |
| 211 | #131 | — | 10 | 12 | no | — |
| 212 | #131 | — | 10 | 12 | no | — |
| 213 | #131 | C4×D5 | 1 | 4 | yes | — |
| 214 | #131 | C4×D5 | 1 | 4 | yes | — |
| 215 | #131 | D20 | 1 | 8 | yes | — |
| 216 | C2×M16 | — | 5 | 12 | no | — |
| 217 | C2×M16 | — | 10 | 24 | no | — |
| 218 | C2×M16 | — | 10 | 12 | no | — |
| 219 | C2×M16 | C22×D5 | 1 | 3 | yes | — |
| 220 | C2×M16 | C22×D5 | 1 | 3 | yes | — |
| 221 | C22×C8 | — | 10 | 12 | no | — |
| 222 | C22×C8 | C22×D5 | 1 | 3 | yes | — |
| 223 | C22×C8 | C22×D5 | 1 | 3 | yes | — |
| 224 | C4×Q8 | — | 2 | 1 | no | — |
| 225 | C4×D4 | — | 2 | 3 | no | — |
| 226 | #117 | C22×D5 | 1 | 3 | yes | — |
| 227 | C2×C42 | C22×D5 | 1 | 3 | yes | — |
| 228 | #108 | — | 5 | 4 | no | — |
| 229 | #108 | — | 5 | 12 | no | — |
| 230 | #104 | — | 5 | 8 | no | — |
| 231 | #104 | — | 5 | 24 | no | — |
| 232 | #97 | C22×D5 | 1 | 1 | yes | characteristic |
| 233 | #97 | C22×D5 | 1 | 3 | yes | — |
| 234 | #97 | C22×D5 | 1 | 3 | yes | — |
| 235 | #97 | C22×D5 | 1 | 3 | yes | — |
| 236 | C4×C8 | C22×D5 | 1 | 6 | yes | — |
| 237 | C22×C5 | — | 4 | 3 | no | — |
| 238 | C22×C5 | C2×C4×D4 | 1 | 6 | yes | — |
| 239 | C22×C5 | C22×#41 | 1 | 1 | yes | characteristic |
| 240 | C2×D5 | — | 2 | 8 | no | — |
| 241 | C2×D5 | — | 8 | 12 | no | — |
| 242 | C4×C5 | — | 4 | 3 | no | — |
| 243 | C4×C5 | — | 4 | 1 | no | — |
| 244 | C4×C5 | C2×C4×D4 | 1 | 6 | yes | — |
| 245 | C4×C5 | C24×C4 | 1 | 1 | yes | characteristic |
| 246 | C4×C5 | C23×D4 | 1 | 1 | yes | characteristic |
| 247 | Dic5 | — | 2 | 8 | no | — |
| 248 | #41 | — | 5 | 24 | no | — |
| 249 | #41 | — | 5 | 8 | no | — |
| 250 | #41 | — | 10 | 8 | no | — |
| 251 | #41 | — | 10 | 24 | no | — |
| 252 | #41 | — | 10 | 12 | no | — |
| 253 | #41 | — | 10 | 12 | no | — |
| 254 | #41 | C2×C4×D5 | 1 | 4 | yes | — |
| 255 | #41 | C2×D20 | 1 | 4 | yes | — |
| 256 | C2×Q8 | — | 5 | 12 | no | — |
| 257 | C2×Q8 | — | 10 | 8 | no | — |
| 258 | C2×Q8 | #709 | 1 | 1 | yes | characteristic |
| 259 | C2×D4 | — | 5 | 12 | no | — |
| 260 | C2×D4 | — | 10 | 12 | no | — |
| 261 | C2×D4 | — | 10 | 24 | no | — |
| 262 | C2×D4 | #709 | 1 | 3 | yes | — |
| 263 | C22×C4 | — | 2 | 3 | no | — |
| 264 | C22×C4 | — | 10 | 12 | no | — |
| 265 | C22×C4 | C23×D5 | 1 | 3 | yes | — |
| 266 | Q16 | — | 5 | 4 | no | — |
| 267 | Q16 | — | 5 | 12 | no | — |
| 268 | SD16 | — | 5 | 8 | no | — |
| 269 | SD16 | — | 5 | 24 | no | — |
| 270 | D8 | — | 5 | 4 | no | — |
| 271 | D8 | — | 5 | 12 | no | — |
| 272 | M16 | — | 5 | 8 | no | — |
| 273 | M16 | — | 10 | 12 | no | — |
| 274 | M16 | — | 10 | 8 | no | — |
| 275 | M16 | — | 10 | 24 | no | — |
| 276 | M16 | C2×C4×D5 | 1 | 12 | yes | — |
| 277 | M16 | C2×D20 | 1 | 12 | yes | — |
| 278 | C2×C8 | — | 10 | 12 | no | — |
| 279 | C2×C8 | — | 10 | 8 | no | — |
| 280 | C2×C8 | — | 10 | 24 | no | — |
| 281 | C2×C8 | C2×C4×D5 | 1 | 6 | yes | — |
| 282 | C2×C8 | C2×C4×D5 | 1 | 6 | yes | — |
| 283 | C2×C8 | C2×D20 | 1 | 12 | yes | — |
| 284 | C2×C8 | C23×D5 | 1 | 3 | yes | — |
| 285 | C2×C8 | C23×D5 | 1 | 1 | yes | characteristic |
| 286 | C2×C8 | C23×D5 | 1 | 3 | yes | — |
| 287 | C2×C8 | C23×D5 | 1 | 1 | yes | characteristic |
| 288 | C4⋊C4 | — | 2 | 3 | no | — |
| 289 | C22⋊C4 | — | 2 | 3 | no | — |
| 290 | C42 | — | 2 | 3 | no | — |
| 291 | C42 | C23×D5 | 1 | 3 | yes | — |
| 292 | C42 | C23×D5 | 1 | 1 | yes | characteristic |
| 293 | C2×C5 | — | 2 | 1 | no | — |
| 294 | C2×C5 | — | 2 | 6 | no | — |
| 295 | C2×C5 | C22×C4×D4 | 1 | 1 | yes | characteristic |
| 296 | D5 | — | 4 | 8 | no | — |
| 297 | C23 | — | 10 | 12 | no | — |
| 298 | C23 | C2×#709 | 1 | 3 | yes | — |
| 299 | Q8 | — | 5 | 8 | no | — |
| 300 | Q8 | — | 10 | 12 | no | — |
| 301 | Q8 | C4×D20 | 1 | 4 | yes | — |
| 302 | D4 | — | 5 | 8 | no | — |
| 303 | D4 | — | 10 | 24 | no | — |
| 304 | D4 | — | 10 | 8 | no | — |
| 305 | D4 | — | 10 | 12 | no | — |
| 306 | D4 | C4×D20 | 1 | 12 | yes | — |
| 307 | C2×C4 | — | 2 | 1 | no | — |
| 308 | C2×C4 | — | 2 | 3 | no | — |
| 309 | C2×C4 | — | 8 | 3 | no | — |
| 310 | C2×C4 | — | 10 | 12 | no | — |
| 311 | C2×C4 | — | 10 | 24 | no | — |
| 312 | C2×C4 | — | 10 | 8 | no | — |
| 313 | C2×C4 | C22×C4×D5 | 1 | 6 | yes | — |
| 314 | C2×C4 | C22×D20 | 1 | 6 | yes | — |
| 315 | C2×C4 | C2×#709 | 1 | 3 | yes | — |
| 316 | C2×C4 | C24×D5 | 1 | 1 | yes | characteristic |
| 317 | C8 | — | 10 | 8 | no | — |
| 318 | C8 | C22×C4×D5 | 1 | 1 | yes | characteristic |
| 319 | C8 | C22×C4×D5 | 1 | 1 | yes | characteristic |
| 320 | C8 | C22×C4×D5 | 1 | 6 | yes | — |
| 321 | C8 | C22×D20 | 1 | 2 | yes | — |
| 322 | C8 | C22×D20 | 1 | 6 | yes | — |
| 323 | C5 | #60184 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 324 | C22 | — | 4 | 3 | no | — |
| 325 | C22 | — | 10 | 8 | no | — |
| 326 | C22 | — | 40 | 12 | no | — |
| 327 | C22 | C2×C4×D20 | 1 | 6 | yes | — |
| 328 | C22 | C22×#709 | 1 | 1 | yes | characteristic |
| 329 | C4 | — | 4 | 1 | no | — |
| 330 | C4 | — | 4 | 3 | no | — |
| 331 | C4 | — | 10 | 8 | no | — |
| 332 | C4 | C2×C4×D20 | 1 | 6 | yes | — |
| 333 | C4 | C23×C4×D5 | 1 | 1 | yes | characteristic |
| 334 | C4 | C23×D20 | 1 | 1 | yes | characteristic |
| 335 | C2 | — | 2 | 1 | no | — |
| 336 | C2 | — | 2 | 6 | no | — |
| 337 | C2 | — | 20 | 8 | no | — |
| 338 | C2 | C22×C4×D20 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta