Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1688 conjugacy classes of subgroups.
The subgroup lattice has 588 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×D4×D20 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C5×#3100 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10615033 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10615028 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10602391 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10601901 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #10601808 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #10601567 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #10601549 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C22×D4×D5 | — | 2 | 1 | no | — |
| 11 | C23×D20 | — | 2 | 1 | no | — |
| 12 | C5×#532 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | C2×C4×C5×D4 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×#4095 | — | 2 | 1 | no | — |
| 15 | C2×#4076 | — | 2 | 1 | no | — |
| 16 | D4×D20 | — | 2 | 2 | no | — |
| 17 | D4×D20 | — | 2 | 2 | no | — |
| 18 | D4×D20 | — | 2 | 2 | no | — |
| 19 | D4×D20 | C22 | 1 | 4 | yes | — |
| 20 | C2×#4041 | — | 2 | 1 | no | — |
| 21 | C2×#4028 | — | 2 | 2 | no | — |
| 22 | C2×#4020 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×C4×D20 | C22 | 1 | 1 | yes | characteristic |
| 24 | C5×#480 | — | 2 | 1 | no | — |
| 25 | C5×#474 | C22 | 1 | 2 | yes | complemented |
| 26 | C5×#459 | C22 | 1 | 2 | yes | complemented |
| 27 | C5×#447 | — | 2 | 1 | no | — |
| 28 | C4×C5×D8 | — | 2 | 2 | no | — |
| 29 | C5×#431 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | #65521 | — | 2 | 1 | no | — |
| 31 | #65377 | C22 | 1 | 2 | yes | complemented |
| 32 | #65372 | C22 | 1 | 2 | yes | complemented |
| 33 | #65362 | C22 | 1 | 2 | yes | complemented |
| 34 | #65361 | C22 | 1 | 2 | yes | complemented |
| 35 | #65346 | — | 2 | 2 | no | — |
| 36 | #65325 | — | 2 | 2 | no | — |
| 37 | #65304 | — | 2 | 2 | no | — |
| 38 | #65214 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | #65213 | C22 | 1 | 1 | yes | characteristic, complemented |
| 40 | D4⋊#168 | C22 | 1 | 4 | yes | complemented |
| 41 | #64705 | C22 | 1 | 4 | yes | complemented |
| 42 | #64703 | C22 | 1 | 4 | yes | complemented |
| 43 | #18746 | — | 5 | 1 | no | maximal, Sylow |
| 44 | C24×D5 | — | 2 | 2 | no | — |
| 45 | C2×C5×#41 | — | 2 | 1 | no | — |
| 46 | C22×C5×D4 | D4 | 1 | 1 | yes | characteristic |
| 47 | C23×C4×C5 | — | 2 | 1 | no | — |
| 48 | C22×C22⋊D5 | — | 2 | 2 | no | — |
| 49 | C2×D4×D5 | — | 2 | 4 | no | — |
| 50 | C2×D4×D5 | — | 2 | 4 | no | — |
| 51 | C2×D4×D5 | — | 4 | 8 | no | — |
| 52 | C22×D20 | — | 2 | 2 | no | — |
| 53 | C22×D20 | — | 2 | 4 | no | — |
| 54 | C22×D20 | — | 2 | 1 | no | — |
| 55 | C22×D20 | — | 2 | 1 | no | — |
| 56 | C22×D20 | — | 2 | 4 | no | — |
| 57 | C22×D20 | — | 4 | 4 | no | — |
| 58 | C22×D20 | — | 4 | 4 | no | — |
| 59 | C22×D20 | D4 | 1 | 1 | yes | characteristic |
| 60 | C22×D20 | D4 | 1 | 2 | yes | — |
| 61 | C22×C4×D5 | — | 2 | 1 | no | — |
| 62 | C2×C5×D8 | — | 2 | 2 | no | — |
| 63 | C5×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic, complemented |
| 64 | C5×#127 | C23 | 1 | 1 | yes | characteristic, complemented |
| 65 | C5×#124 | — | 2 | 1 | no | — |
| 66 | C5×#121 | — | 2 | 1 | no | — |
| 67 | C5×#121 | — | 2 | 1 | no | — |
| 68 | C4×C5×D4 | — | 2 | 1 | no | — |
| 69 | C4×C5×D4 | — | 2 | 1 | no | — |
| 70 | C4×C5×D4 | — | 2 | 1 | no | — |
| 71 | C4×C5×D4 | — | 2 | 1 | no | — |
| 72 | C4×C5×D4 | D4 | 1 | 2 | yes | — |
| 73 | C4×C5×D4 | C23 | 1 | 2 | yes | — |
| 74 | C2×C5×C4⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 75 | C2×C5×C22⋊C4 | — | 2 | 1 | no | — |
| 76 | C2×C42×C5 | C23 | 1 | 1 | yes | characteristic |
| 77 | #4095 | — | 4 | 4 | no | — |
| 78 | C2×#688 | — | 2 | 2 | no | — |
| 79 | C2×#686 | — | 2 | 2 | no | — |
| 80 | C2×#686 | — | 2 | 4 | no | — |
| 81 | #4076 | — | 2 | 4 | no | — |
| 82 | #4076 | — | 2 | 4 | no | — |
| 83 | C2×#685 | — | 2 | 2 | no | — |
| 84 | C2×#685 | — | 2 | 1 | no | — |
| 85 | C2×C4⋊Dic5 | D4 | 1 | 1 | yes | characteristic |
| 86 | C2×#681 | — | 2 | 1 | no | — |
| 87 | #4041 | — | 2 | 4 | no | — |
| 88 | #4041 | — | 2 | 4 | no | — |
| 89 | #4028 | — | 2 | 8 | no | — |
| 90 | #4028 | — | 2 | 8 | no | — |
| 91 | #4020 | — | 2 | 1 | no | — |
| 92 | #4020 | — | 2 | 1 | no | — |
| 93 | #4020 | D4 | 1 | 2 | yes | — |
| 94 | #4020 | C23 | 1 | 2 | yes | — |
| 95 | C4×D20 | — | 2 | 1 | no | — |
| 96 | C4×D20 | — | 2 | 1 | no | — |
| 97 | C4×D20 | D4 | 1 | 2 | yes | — |
| 98 | C4×D20 | C23 | 1 | 2 | yes | — |
| 99 | C5×#107 | — | 2 | 2 | no | — |
| 100 | C5×C4⋊C8 | C23 | 1 | 2 | yes | complemented |
| 101 | C5×#102 | — | 2 | 2 | no | — |
| 102 | C5×#102 | — | 2 | 2 | no | — |
| 103 | C5×C22⋊C8 | — | 2 | 1 | no | — |
| 104 | C4×C5×C8 | — | 2 | 1 | no | — |
| 105 | #3967 | — | 2 | 2 | no | — |
| 106 | #3964 | — | 2 | 2 | no | — |
| 107 | C22⋊#168 | — | 2 | 1 | no | — |
| 108 | #3941 | — | 2 | 4 | no | — |
| 109 | C4⋊#168 | — | 2 | 1 | no | — |
| 110 | C4⋊#168 | — | 2 | 1 | no | — |
| 111 | C4⋊#168 | C23 | 1 | 2 | yes | complemented |
| 112 | C4×#168 | C23 | 1 | 2 | yes | complemented |
| 113 | C2×D42 | — | 5 | 1 | no | — |
| 114 | #3205 | — | 5 | 1 | no | — |
| 115 | #3100 | D5 | 1 | 1 | yes | characteristic, complemented |
| 116 | #3036 | — | 5 | 1 | no | — |
| 117 | #1639 | — | 5 | 4 | no | — |
| 118 | #1619 | — | 5 | 4 | no | — |
| 119 | #1545 | — | 5 | 1 | no | — |
| 120 | #1486 | — | 5 | 1 | no | — |
| 121 | #1478 | — | 5 | 1 | no | — |
| 122 | C24×C5 | — | 2 | 1 | no | — |
| 123 | C23×D5 | — | 2 | 1 | no | — |
| 124 | C23×D5 | — | 2 | 2 | no | — |
| 125 | C23×D5 | — | 2 | 8 | no | — |
| 126 | C23×D5 | — | 4 | 8 | no | — |
| 127 | C23×D5 | — | 4 | 8 | no | — |
| 128 | C23×D5 | — | 8 | 4 | no | — |
| 129 | C5×#41 | — | 4 | 2 | no | — |
| 130 | C5×#41 | — | 4 | 2 | no | — |
| 131 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 132 | C2×C5×D4 | — | 2 | 4 | no | — |
| 133 | C2×C5×D4 | — | 2 | 1 | no | — |
| 134 | C2×C5×D4 | — | 2 | 1 | no | — |
| 135 | C2×C5×D4 | — | 2 | 1 | no | — |
| 136 | C2×C5×D4 | — | 2 | 1 | no | — |
| 137 | C2×C5×D4 | — | 4 | 1 | no | — |
| 138 | C2×C5×D4 | C2×D4 | 1 | 2 | yes | — |
| 139 | C22×C4×C5 | — | 2 | 1 | no | — |
| 140 | C22×C4×C5 | — | 2 | 2 | no | — |
| 141 | C22×C4×C5 | — | 2 | 2 | no | — |
| 142 | C22×C4×C5 | — | 4 | 2 | no | — |
| 143 | C22×C4×C5 | — | 4 | 2 | no | — |
| 144 | C22×C4×C5 | — | 4 | 1 | no | — |
| 145 | C22×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 146 | C22×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 147 | C22×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 148 | C2×C22⋊D5 | — | 2 | 8 | no | — |
| 149 | C2×C22⋊D5 | — | 4 | 8 | no | — |
| 150 | C22×Dic5 | — | 2 | 1 | no | — |
| 151 | D4×D5 | — | 4 | 16 | no | — |
| 152 | D4×D5 | — | 4 | 8 | no | — |
| 153 | D4×D5 | — | 4 | 8 | no | — |
| 154 | C2×D20 | — | 2 | 1 | no | — |
| 155 | C2×D20 | — | 2 | 2 | no | — |
| 156 | C2×D20 | — | 2 | 8 | no | — |
| 157 | C2×D20 | — | 2 | 2 | no | — |
| 158 | C2×D20 | — | 2 | 2 | no | — |
| 159 | C2×D20 | — | 2 | 2 | no | — |
| 160 | C2×D20 | — | 2 | 2 | no | — |
| 161 | C2×D20 | — | 2 | 2 | no | — |
| 162 | C2×D20 | — | 4 | 8 | no | — |
| 163 | C2×D20 | — | 4 | 16 | no | — |
| 164 | C2×D20 | — | 4 | 4 | no | — |
| 165 | C2×D20 | — | 4 | 8 | no | — |
| 166 | C2×D20 | — | 4 | 2 | no | — |
| 167 | C2×D20 | — | 4 | 2 | no | — |
| 168 | C2×D20 | — | 4 | 8 | no | — |
| 169 | C2×D20 | — | 8 | 2 | no | — |
| 170 | C2×D20 | D8 | 1 | 4 | yes | complemented |
| 171 | C2×D20 | C2×D4 | 1 | 2 | yes | — |
| 172 | C2×D20 | C2×D4 | 1 | 4 | yes | — |
| 173 | C2×C4×D5 | — | 2 | 2 | no | — |
| 174 | C2×C4×D5 | — | 2 | 2 | no | — |
| 175 | C2×C4×D5 | — | 4 | 4 | no | — |
| 176 | C5×D8 | — | 4 | 4 | no | — |
| 177 | C2×C5×C8 | — | 2 | 2 | no | — |
| 178 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 179 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 180 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 181 | C5×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 182 | C5×C22⋊C4 | — | 2 | 2 | no | — |
| 183 | C5×C22⋊C4 | — | 2 | 2 | no | — |
| 184 | C5×C22⋊C4 | — | 4 | 1 | no | — |
| 185 | C5×C22⋊C4 | — | 4 | 1 | no | — |
| 186 | C42×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 187 | C42×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 188 | C42×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 189 | C42×C5 | C24 | 1 | 1 | yes | characteristic |
| 190 | #688 | — | 4 | 4 | no | — |
| 191 | #686 | — | 4 | 4 | no | — |
| 192 | #686 | — | 8 | 4 | no | — |
| 193 | #685 | — | 2 | 8 | no | — |
| 194 | #685 | — | 2 | 2 | no | — |
| 195 | #685 | — | 2 | 2 | no | — |
| 196 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 197 | C4⋊Dic5 | C2×D4 | 1 | 2 | yes | — |
| 198 | #681 | — | 4 | 2 | no | — |
| 199 | C2×#168 | — | 2 | 2 | no | — |
| 200 | C2×#168 | — | 2 | 2 | no | — |
| 201 | C23×D4 | — | 10 | 1 | no | — |
| 202 | C23×D4 | — | 10 | 1 | no | — |
| 203 | C2×AGL(1,ℤ/8) | — | 10 | 1 | no | — |
| 204 | D42 | — | 5 | 4 | no | — |
| 205 | D42 | — | 10 | 2 | no | — |
| 206 | D42 | — | 10 | 2 | no | — |
| 207 | D42 | — | 10 | 2 | no | — |
| 208 | #532 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 209 | C2×#127 | — | 5 | 1 | no | — |
| 210 | C2×#121 | — | 10 | 1 | no | — |
| 211 | C2×#121 | — | 10 | 1 | no | — |
| 212 | C2×#120 | — | 10 | 2 | no | — |
| 213 | C2×C4×D4 | — | 5 | 1 | no | — |
| 214 | C2×C4×D4 | C2×D5 | 1 | 1 | yes | characteristic |
| 215 | #493 | — | 5 | 2 | no | — |
| 216 | #486 | — | 5 | 2 | no | — |
| 217 | #480 | — | 2 | 1 | no | — |
| 218 | #474 | C2×D5 | 1 | 2 | yes | complemented |
| 219 | #463 | — | 10 | 2 | no | — |
| 220 | #461 | — | 5 | 2 | no | — |
| 221 | #459 | — | 5 | 2 | no | — |
| 222 | #459 | — | 10 | 2 | no | — |
| 223 | #459 | C2×D5 | 1 | 2 | yes | complemented |
| 224 | #447 | — | 2 | 1 | no | — |
| 225 | #447 | — | 10 | 2 | no | — |
| 226 | C4×D8 | — | 2 | 2 | no | — |
| 227 | #431 | — | 5 | 1 | no | — |
| 228 | #431 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 229 | #423 | — | 5 | 1 | no | — |
| 230 | #417 | — | 10 | 1 | no | — |
| 231 | #331 | — | 5 | 4 | no | — |
| 232 | D4⋊C8 | — | 5 | 4 | no | — |
| 233 | D4⋊C8 | — | 5 | 4 | no | — |
| 234 | C23×C5 | — | 2 | 4 | no | — |
| 235 | C23×C5 | — | 2 | 2 | no | — |
| 236 | C23×C5 | — | 4 | 2 | no | — |
| 237 | C23×C5 | — | 4 | 2 | no | — |
| 238 | C23×C5 | — | 4 | 1 | no | — |
| 239 | C23×C5 | #120 | 1 | 1 | yes | characteristic |
| 240 | C22×D5 | — | 2 | 2 | no | — |
| 241 | C22×D5 | — | 2 | 4 | no | — |
| 242 | C22×D5 | — | 2 | 4 | no | — |
| 243 | C22×D5 | — | 4 | 16 | no | — |
| 244 | C22×D5 | — | 4 | 2 | no | — |
| 245 | C22×D5 | — | 4 | 2 | no | — |
| 246 | C22×D5 | — | 4 | 4 | no | — |
| 247 | C22×D5 | — | 4 | 4 | no | — |
| 248 | C22×D5 | — | 4 | 16 | no | — |
| 249 | C22×D5 | — | 4 | 4 | no | — |
| 250 | C22×D5 | — | 8 | 8 | no | — |
| 251 | C22×D5 | — | 8 | 32 | no | — |
| 252 | C5×Q8 | — | 4 | 1 | no | — |
| 253 | C5×Q8 | — | 4 | 1 | no | — |
| 254 | C5×D4 | — | 2 | 4 | no | — |
| 255 | C5×D4 | — | 2 | 2 | no | — |
| 256 | C5×D4 | — | 4 | 2 | no | — |
| 257 | C5×D4 | — | 4 | 1 | no | — |
| 258 | C5×D4 | — | 4 | 2 | no | — |
| 259 | C5×D4 | — | 4 | 1 | no | — |
| 260 | C5×D4 | — | 8 | 2 | no | — |
| 261 | C5×D4 | AGL(1,ℤ/8) | 1 | 4 | yes | complemented |
| 262 | C2×C4×C5 | — | 2 | 2 | no | — |
| 263 | C2×C4×C5 | — | 2 | 2 | no | — |
| 264 | C2×C4×C5 | — | 4 | 1 | no | — |
| 265 | C2×C4×C5 | — | 4 | 2 | no | — |
| 266 | C2×C4×C5 | — | 4 | 2 | no | — |
| 267 | C2×C4×C5 | — | 4 | 2 | no | — |
| 268 | C2×C4×C5 | — | 4 | 4 | no | — |
| 269 | C2×C4×C5 | — | 4 | 1 | no | — |
| 270 | C2×C4×C5 | — | 8 | 2 | no | — |
| 271 | C2×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 272 | C2×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 273 | C2×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 274 | C2×C4×C5 | C2×D8 | 1 | 2 | yes | — |
| 275 | C2×C4×C5 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 276 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 277 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 278 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 279 | C22⋊D5 | — | 4 | 16 | no | — |
| 280 | C2×Dic5 | — | 2 | 2 | no | — |
| 281 | C2×Dic5 | — | 4 | 2 | no | — |
| 282 | D20 | — | 2 | 2 | no | — |
| 283 | D20 | — | 2 | 4 | no | — |
| 284 | D20 | — | 4 | 4 | no | — |
| 285 | D20 | — | 4 | 4 | no | — |
| 286 | D20 | — | 4 | 16 | no | — |
| 287 | D20 | — | 4 | 2 | no | — |
| 288 | D20 | — | 4 | 2 | no | — |
| 289 | D20 | — | 4 | 4 | no | — |
| 290 | D20 | — | 4 | 4 | no | — |
| 291 | D20 | — | 8 | 2 | no | — |
| 292 | D20 | C2×D8 | 1 | 4 | yes | — |
| 293 | C4×D5 | — | 4 | 4 | no | — |
| 294 | C4×D5 | — | 4 | 4 | no | — |
| 295 | C5×C8 | — | 4 | 2 | no | — |
| 296 | #168 | — | 4 | 2 | no | — |
| 297 | #168 | — | 4 | 2 | no | — |
| 298 | C25 | — | 10 | 2 | no | — |
| 299 | C2×#41 | — | 2 | 1 | no | — |
| 300 | C22×D4 | — | 5 | 1 | no | — |
| 301 | C22×D4 | — | 5 | 2 | no | — |
| 302 | C22×D4 | — | 10 | 4 | no | — |
| 303 | C22×D4 | — | 10 | 2 | no | — |
| 304 | C22×D4 | — | 10 | 4 | no | — |
| 305 | C22×D4 | — | 10 | 4 | no | — |
| 306 | C22×D4 | — | 10 | 2 | no | — |
| 307 | C22×D4 | — | 10 | 4 | no | — |
| 308 | C22×D4 | — | 10 | 1 | no | — |
| 309 | C22×D4 | — | 10 | 1 | no | — |
| 310 | C22×D4 | — | 20 | 4 | no | — |
| 311 | C22×D4 | — | 20 | 4 | no | — |
| 312 | C22×D4 | — | 20 | 8 | no | — |
| 313 | C22×D4 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 314 | C23×C4 | — | 2 | 1 | no | — |
| 315 | C23×C4 | — | 10 | 1 | no | — |
| 316 | AGL(1,ℤ/8) | — | 20 | 4 | no | — |
| 317 | C2×SD16 | — | 10 | 2 | no | — |
| 318 | C2×D8 | — | 2 | 2 | no | — |
| 319 | C2×D8 | — | 10 | 2 | no | — |
| 320 | C2×D8 | — | 10 | 4 | no | — |
| 321 | C2×M16 | — | 10 | 1 | no | — |
| 322 | C4⋊Q8 | C22×D5 | 1 | 1 | yes | characteristic, complemented |
| 323 | #127 | — | 5 | 2 | no | — |
| 324 | #127 | — | 5 | 2 | no | — |
| 325 | #127 | — | 10 | 1 | no | — |
| 326 | #127 | — | 10 | 1 | no | — |
| 327 | #127 | C22×D5 | 1 | 1 | yes | characteristic, complemented |
| 328 | #124 | — | 2 | 1 | no | — |
| 329 | #121 | — | 2 | 1 | no | — |
| 330 | #121 | — | 2 | 1 | no | — |
| 331 | #121 | — | 10 | 4 | no | — |
| 332 | #121 | — | 10 | 4 | no | — |
| 333 | #121 | — | 10 | 4 | no | — |
| 334 | #121 | — | 10 | 4 | no | — |
| 335 | #120 | — | 10 | 8 | no | — |
| 336 | #120 | — | 10 | 8 | no | — |
| 337 | C4×D4 | — | 2 | 1 | no | — |
| 338 | C4×D4 | — | 2 | 1 | no | — |
| 339 | C4×D4 | — | 2 | 1 | no | — |
| 340 | C4×D4 | — | 2 | 1 | no | — |
| 341 | C4×D4 | — | 5 | 2 | no | — |
| 342 | C4×D4 | — | 5 | 2 | no | — |
| 343 | C4×D4 | — | 10 | 1 | no | — |
| 344 | C4×D4 | — | 10 | 1 | no | — |
| 345 | C4×D4 | C22⋊D5 | 1 | 2 | yes | — |
| 346 | C4×D4 | C22×D5 | 1 | 2 | yes | — |
| 347 | C2×C4⋊C4 | — | 5 | 1 | no | — |
| 348 | C2×C4⋊C4 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 349 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 350 | C2×C22⋊C4 | — | 10 | 2 | no | — |
| 351 | C2×C22⋊C4 | — | 10 | 1 | no | — |
| 352 | C2×C42 | C22×D5 | 1 | 1 | yes | characteristic |
| 353 | #107 | — | 2 | 2 | no | — |
| 354 | C4⋊C8 | — | 5 | 2 | no | — |
| 355 | C4⋊C8 | — | 10 | 1 | no | — |
| 356 | C4⋊C8 | — | 10 | 1 | no | — |
| 357 | C4⋊C8 | C22×D5 | 1 | 2 | yes | complemented |
| 358 | #103 | — | 10 | 2 | no | — |
| 359 | #102 | — | 2 | 2 | no | — |
| 360 | #102 | — | 2 | 2 | no | — |
| 361 | #102 | — | 10 | 4 | no | — |
| 362 | #102 | — | 10 | 2 | no | — |
| 363 | C22⋊C8 | — | 2 | 1 | no | — |
| 364 | C22⋊C8 | — | 10 | 1 | no | — |
| 365 | C4×C8 | — | 2 | 1 | no | — |
| 366 | C4×C8 | — | 5 | 2 | no | — |
| 367 | C22×C5 | — | 2 | 1 | no | — |
| 368 | C22×C5 | — | 2 | 1 | no | — |
| 369 | C22×C5 | — | 2 | 4 | no | — |
| 370 | C22×C5 | — | 4 | 8 | no | — |
| 371 | C22×C5 | — | 4 | 2 | no | — |
| 372 | C22×C5 | — | 4 | 2 | no | — |
| 373 | C22×C5 | — | 8 | 1 | no | — |
| 374 | C22×C5 | — | 8 | 1 | no | — |
| 375 | C22×C5 | — | 8 | 1 | no | — |
| 376 | C22×C5 | #447 | 1 | 2 | yes | — |
| 377 | C22×C5 | C2×#120 | 1 | 1 | yes | characteristic |
| 378 | C2×D5 | — | 2 | 4 | no | — |
| 379 | C2×D5 | — | 4 | 8 | no | — |
| 380 | C2×D5 | — | 4 | 2 | no | — |
| 381 | C2×D5 | — | 4 | 2 | no | — |
| 382 | C2×D5 | — | 4 | 4 | no | — |
| 383 | C2×D5 | — | 4 | 4 | no | — |
| 384 | C2×D5 | — | 4 | 4 | no | — |
| 385 | C2×D5 | — | 8 | 32 | no | — |
| 386 | C2×D5 | — | 8 | 8 | no | — |
| 387 | C4×C5 | — | 2 | 1 | no | — |
| 388 | C4×C5 | — | 2 | 1 | no | — |
| 389 | C4×C5 | — | 2 | 1 | no | — |
| 390 | C4×C5 | — | 4 | 2 | no | — |
| 391 | C4×C5 | — | 8 | 1 | no | — |
| 392 | C4×C5 | #447 | 1 | 2 | yes | — |
| 393 | C4×C5 | C22×D8 | 1 | 1 | yes | characteristic |
| 394 | C4×C5 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 395 | C4×C5 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 396 | Dic5 | — | 4 | 2 | no | — |
| 397 | C24 | — | 2 | 1 | no | — |
| 398 | C24 | — | 10 | 8 | no | — |
| 399 | C24 | — | 10 | 1 | no | — |
| 400 | C24 | — | 10 | 2 | no | — |
| 401 | C24 | — | 20 | 8 | no | — |
| 402 | C24 | — | 20 | 8 | no | — |
| 403 | C24 | — | 40 | 4 | no | — |
| 404 | #41 | — | 4 | 2 | no | — |
| 405 | #41 | — | 4 | 2 | no | — |
| 406 | C2×Q8 | — | 2 | 1 | no | — |
| 407 | C2×D4 | — | 2 | 4 | no | — |
| 408 | C2×D4 | — | 2 | 1 | no | — |
| 409 | C2×D4 | — | 2 | 1 | no | — |
| 410 | C2×D4 | — | 2 | 1 | no | — |
| 411 | C2×D4 | — | 2 | 1 | no | — |
| 412 | C2×D4 | — | 4 | 1 | no | — |
| 413 | C2×D4 | — | 5 | 2 | no | — |
| 414 | C2×D4 | — | 5 | 4 | no | — |
| 415 | C2×D4 | — | 5 | 4 | no | — |
| 416 | C2×D4 | — | 10 | 8 | no | — |
| 417 | C2×D4 | — | 10 | 8 | no | — |
| 418 | C2×D4 | — | 10 | 2 | no | — |
| 419 | C2×D4 | — | 10 | 2 | no | — |
| 420 | C2×D4 | — | 10 | 2 | no | — |
| 421 | C2×D4 | — | 10 | 1 | no | — |
| 422 | C2×D4 | — | 10 | 2 | no | — |
| 423 | C2×D4 | — | 10 | 2 | no | — |
| 424 | C2×D4 | — | 10 | 2 | no | — |
| 425 | C2×D4 | — | 20 | 4 | no | — |
| 426 | C2×D4 | — | 20 | 8 | no | — |
| 427 | C2×D4 | — | 20 | 8 | no | — |
| 428 | C2×D4 | — | 20 | 16 | no | — |
| 429 | C2×D4 | — | 20 | 8 | no | — |
| 430 | C2×D4 | — | 20 | 16 | no | — |
| 431 | C2×D4 | — | 20 | 8 | no | — |
| 432 | C2×D4 | — | 20 | 8 | no | — |
| 433 | C2×D4 | — | 20 | 8 | no | — |
| 434 | C2×D4 | — | 20 | 2 | no | — |
| 435 | C2×D4 | — | 20 | 2 | no | — |
| 436 | C2×D4 | — | 40 | 2 | no | — |
| 437 | C2×D4 | C2×C22⋊D5 | 1 | 2 | yes | — |
| 438 | C22×C4 | — | 2 | 1 | no | — |
| 439 | C22×C4 | — | 2 | 2 | no | — |
| 440 | C22×C4 | — | 2 | 2 | no | — |
| 441 | C22×C4 | — | 4 | 2 | no | — |
| 442 | C22×C4 | — | 4 | 2 | no | — |
| 443 | C22×C4 | — | 4 | 1 | no | — |
| 444 | C22×C4 | — | 10 | 1 | no | — |
| 445 | C22×C4 | — | 10 | 2 | no | — |
| 446 | C22×C4 | — | 10 | 2 | no | — |
| 447 | C22×C4 | — | 20 | 4 | no | — |
| 448 | C22×C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 449 | C22×C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 450 | C22×C4 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 451 | SD16 | — | 20 | 4 | no | — |
| 452 | D8 | — | 4 | 4 | no | — |
| 453 | D8 | — | 20 | 4 | no | — |
| 454 | D8 | — | 40 | 4 | no | — |
| 455 | M16 | — | 20 | 2 | no | — |
| 456 | C2×C8 | — | 2 | 2 | no | — |
| 457 | C2×C8 | — | 10 | 2 | no | — |
| 458 | C2×C8 | — | 10 | 2 | no | — |
| 459 | C4⋊C4 | — | 2 | 1 | no | — |
| 460 | C4⋊C4 | — | 2 | 1 | no | — |
| 461 | C4⋊C4 | — | 2 | 1 | no | — |
| 462 | C4⋊C4 | — | 5 | 2 | no | — |
| 463 | C4⋊C4 | — | 10 | 1 | no | — |
| 464 | C4⋊C4 | C2×C22⋊D5 | 1 | 2 | yes | — |
| 465 | C22⋊C4 | — | 2 | 2 | no | — |
| 466 | C22⋊C4 | — | 2 | 2 | no | — |
| 467 | C22⋊C4 | — | 4 | 1 | no | — |
| 468 | C22⋊C4 | — | 4 | 1 | no | — |
| 469 | C22⋊C4 | — | 10 | 8 | no | — |
| 470 | C22⋊C4 | — | 10 | 2 | no | — |
| 471 | C22⋊C4 | — | 10 | 2 | no | — |
| 472 | C42 | D4×D5 | 1 | 1 | yes | characteristic |
| 473 | C42 | D4×D5 | 1 | 1 | yes | characteristic |
| 474 | C42 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 475 | C42 | C23×D5 | 1 | 1 | yes | characteristic |
| 476 | C2×C5 | — | 2 | 2 | no | — |
| 477 | C2×C5 | — | 4 | 4 | no | — |
| 478 | C2×C5 | — | 16 | 1 | no | — |
| 479 | C2×C5 | C2×#447 | 1 | 1 | yes | characteristic |
| 480 | C2×C5 | #3003 | 1 | 1 | yes | characteristic |
| 481 | C2×C5 | #3019 | 1 | 1 | yes | characteristic |
| 482 | D5 | — | 4 | 4 | no | — |
| 483 | D5 | — | 8 | 4 | no | — |
| 484 | C23 | — | 2 | 4 | no | — |
| 485 | C23 | — | 2 | 2 | no | — |
| 486 | C23 | — | 4 | 2 | no | — |
| 487 | C23 | — | 4 | 2 | no | — |
| 488 | C23 | — | 4 | 1 | no | — |
| 489 | C23 | — | 10 | 2 | no | — |
| 490 | C23 | — | 10 | 4 | no | — |
| 491 | C23 | — | 10 | 4 | no | — |
| 492 | C23 | — | 20 | 2 | no | — |
| 493 | C23 | — | 20 | 2 | no | — |
| 494 | C23 | — | 20 | 4 | no | — |
| 495 | C23 | — | 20 | 16 | no | — |
| 496 | C23 | — | 20 | 4 | no | — |
| 497 | C23 | — | 20 | 16 | no | — |
| 498 | C23 | — | 20 | 4 | no | — |
| 499 | C23 | — | 40 | 8 | no | — |
| 500 | C23 | — | 40 | 32 | no | — |
| 501 | C23 | #4083 | 1 | 1 | yes | characteristic |
| 502 | Q8 | — | 4 | 1 | no | — |
| 503 | Q8 | — | 4 | 1 | no | — |
| 504 | D4 | — | 2 | 4 | no | — |
| 505 | D4 | — | 2 | 2 | no | — |
| 506 | D4 | — | 4 | 2 | no | — |
| 507 | D4 | — | 4 | 1 | no | — |
| 508 | D4 | — | 4 | 1 | no | — |
| 509 | D4 | — | 4 | 2 | no | — |
| 510 | D4 | — | 5 | 4 | no | — |
| 511 | D4 | — | 8 | 2 | no | — |
| 512 | D4 | — | 10 | 2 | no | — |
| 513 | D4 | — | 10 | 4 | no | — |
| 514 | D4 | — | 20 | 4 | no | — |
| 515 | D4 | — | 20 | 4 | no | — |
| 516 | D4 | — | 20 | 16 | no | — |
| 517 | D4 | — | 20 | 16 | no | — |
| 518 | D4 | — | 20 | 2 | no | — |
| 519 | D4 | — | 20 | 2 | no | — |
| 520 | D4 | — | 20 | 4 | no | — |
| 521 | D4 | — | 20 | 4 | no | — |
| 522 | D4 | — | 40 | 2 | no | — |
| 523 | D4 | #4095 | 1 | 4 | yes | complemented |
| 524 | C2×C4 | — | 2 | 2 | no | — |
| 525 | C2×C4 | — | 2 | 2 | no | — |
| 526 | C2×C4 | — | 4 | 1 | no | — |
| 527 | C2×C4 | — | 4 | 2 | no | — |
| 528 | C2×C4 | — | 4 | 2 | no | — |
| 529 | C2×C4 | — | 4 | 2 | no | — |
| 530 | C2×C4 | — | 4 | 4 | no | — |
| 531 | C2×C4 | — | 4 | 1 | no | — |
| 532 | C2×C4 | — | 8 | 2 | no | — |
| 533 | C2×C4 | — | 10 | 2 | no | — |
| 534 | C2×C4 | — | 20 | 4 | no | — |
| 535 | C2×C4 | — | 20 | 2 | no | — |
| 536 | C2×C4 | — | 20 | 4 | no | — |
| 537 | C2×C4 | D5×D8 | 1 | 2 | yes | — |
| 538 | C2×C4 | #4057 | 1 | 2 | yes | — |
| 539 | C2×C4 | #4083 | 1 | 1 | yes | characteristic |
| 540 | C2×C4 | #4083 | 1 | 1 | yes | characteristic |
| 541 | C2×C4 | #4083 | 1 | 1 | yes | characteristic |
| 542 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 543 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 544 | C2×C4 | C22×C22⋊D5 | 1 | 1 | yes | characteristic |
| 545 | C8 | — | 4 | 2 | no | — |
| 546 | C8 | — | 20 | 2 | no | — |
| 547 | C8 | — | 20 | 2 | no | — |
| 548 | C5 | #18746 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 549 | C22 | — | 2 | 1 | no | — |
| 550 | C22 | — | 2 | 1 | no | — |
| 551 | C22 | — | 2 | 4 | no | — |
| 552 | C22 | — | 4 | 8 | no | — |
| 553 | C22 | — | 4 | 2 | no | — |
| 554 | C22 | — | 4 | 2 | no | — |
| 555 | C22 | — | 8 | 1 | no | — |
| 556 | C22 | — | 8 | 1 | no | — |
| 557 | C22 | — | 8 | 1 | no | — |
| 558 | C22 | — | 10 | 4 | no | — |
| 559 | C22 | — | 20 | 8 | no | — |
| 560 | C22 | — | 20 | 2 | no | — |
| 561 | C22 | — | 20 | 2 | no | — |
| 562 | C22 | — | 20 | 4 | no | — |
| 563 | C22 | — | 20 | 4 | no | — |
| 564 | C22 | — | 20 | 4 | no | — |
| 565 | C22 | — | 40 | 8 | no | — |
| 566 | C22 | — | 40 | 32 | no | — |
| 567 | C22 | #65445 | 1 | 2 | yes | — |
| 568 | C22 | C2×#4083 | 1 | 1 | yes | characteristic |
| 569 | C4 | — | 2 | 1 | no | — |
| 570 | C4 | — | 2 | 1 | no | — |
| 571 | C4 | — | 2 | 1 | no | — |
| 572 | C4 | — | 4 | 2 | no | — |
| 573 | C4 | — | 8 | 1 | no | — |
| 574 | C4 | — | 20 | 2 | no | — |
| 575 | C4 | #65445 | 1 | 2 | yes | — |
| 576 | C4 | C2×D5×D8 | 1 | 1 | yes | characteristic |
| 577 | C4 | C2×#4057 | 1 | 1 | yes | characteristic |
| 578 | C4 | C2×#4095 | 1 | 2 | yes | — |
| 579 | C2 | — | 2 | 2 | no | — |
| 580 | C2 | — | 4 | 4 | no | — |
| 581 | C2 | — | 16 | 1 | no | — |
| 582 | C2 | — | 20 | 4 | no | — |
| 583 | C2 | — | 40 | 4 | no | — |
| 584 | C2 | #10614658 | 1 | 1 | yes | characteristic |
| 585 | C2 | C2×#65445 | 1 | 1 | yes | characteristic |
| 586 | C2 | #10615736 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×#4083 |
| commutator, cosocle | C42×C5 | C24 |
| Frattini | C42 | C23×D5 |
| Fitting | C5×#3100 | C2 |
| socle | C22×C5 | C2×#120 |
| hypercenter | #3100 | D5 |
| hypocenter | C5 | #18746 |
| LCS | G ▷ C42×C5 ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #3100 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D4×D20 | C2 | semidirect |
| 2. C5×#3100 | C2 | semidirect |
| 3. #10615033 | C2 | semidirect |
| 4. #10615028 | C2 | semidirect |
| 5. #10602391 | C2 | semidirect |
| 6. #10601901 | C2 | semidirect |
| 7. #10601808 | C2 | semidirect |
| 8. #10601567 | C2 | semidirect |
| 9. #10601549 | C2 | semidirect |
| 12. C5×#532 | C22 | semidirect |
| 25. C5×#474 | C22 | semidirect |
| 26. C5×#459 | C22 | semidirect |
| 29. C5×#431 | C22 | semidirect |
| 31. #65377 | C22 | semidirect |
| 32. #65372 | C22 | semidirect |
| 33. #65362 | C22 | semidirect |
| 34. #65361 | C22 | semidirect |
| 38. #65214 | C22 | semidirect |
| 39. #65213 | C22 | semidirect |
| 40. D4⋊#168 | C22 | semidirect |
| 41. #64705 | C22 | semidirect |
| 42. #64703 | C22 | semidirect |
| 63. C5×C4⋊Q8 | C23 | semidirect |
| 64. C5×#127 | C23 | semidirect |
| 100. C5×C4⋊C8 | C23 | semidirect |
| 111. C4⋊#168 | C23 | semidirect |
| 112. C4×#168 | C23 | semidirect |
| 115. #3100 | D5 | semidirect |
| 170. C2×D20 | D8 | semidirect |
| 208. #532 | C2×D5 | semidirect |
| 218. #474 | C2×D5 | semidirect |
| 223. #459 | C2×D5 | semidirect |
| 228. #431 | C2×D5 | semidirect |
| 261. C5×D4 | AGL(1,ℤ/8) | semidirect |
| 322. C4⋊Q8 | C22×D5 | semidirect |
| 327. #127 | C22×D5 | semidirect |
| 357. C4⋊C8 | C22×D5 | semidirect |
| 523. D4 | #4095 | semidirect |
| 548. C5 | #18746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D20 | 2 |
| C5×#3100 | 2 |
| #10615033 | 2 |
| #10615028 | 2 |
| #10602391 | 2 |
| #10601901 | 2 |
| #10601808 | 2 |
| #10601567 | 2 |
| #10601549 | 2 |
| #18746 | 5 |