Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
4874 conjugacy classes of subgroups.
The subgroup lattice has 506 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10619436 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C5×#3498 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10619178 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10615831 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10615126 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #10615125 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #10615053 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | C2×#65366 | C2 | 1 | 6 | yes | maximal, complemented |
| 9 | #10614267 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | C2×C5×H(5,𝔽2) | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×C5×H(5,𝔽2) | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | #66285 | — | 2 | 8 | no | — |
| 13 | D5×H(5,𝔽2) | — | 2 | 8 | no | — |
| 14 | #66283 | — | 2 | 2 | no | — |
| 15 | #66283 | C22 | 1 | 2 | yes | — |
| 16 | #66283 | C22 | 1 | 6 | yes | complemented |
| 17 | C2×#4144 | — | 2 | 6 | no | — |
| 18 | C2×#4144 | C22 | 1 | 6 | yes | complemented |
| 19 | C5×#550 | — | 2 | 2 | no | — |
| 20 | C5×D42 | — | 2 | 6 | no | — |
| 21 | C5×#535 | C22 | 1 | 3 | yes | complemented |
| 22 | C5×#535 | C22 | 1 | 3 | yes | complemented |
| 23 | C5×#532 | C22 | 1 | 3 | yes | complemented |
| 24 | C2×C5×#127 | C22 | 1 | 3 | yes | complemented |
| 25 | C4×C5×#41 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | #66170 | — | 2 | 8 | no | — |
| 27 | #66169 | — | 2 | 8 | no | — |
| 28 | #66156 | C22 | 1 | 12 | yes | complemented |
| 29 | #66153 | C22 | 1 | 2 | yes | complemented |
| 30 | C2×#4078 | C22 | 1 | 12 | yes | complemented |
| 31 | #65526 | C22 | 1 | 6 | yes | complemented |
| 32 | C2×#3965 | C22 | 1 | 6 | yes | complemented |
| 33 | #65384 | C22 | 1 | 4 | yes | complemented |
| 34 | #65366 | C22 | 1 | 12 | yes | complemented |
| 35 | #65366 | C22 | 1 | 24 | yes | complemented |
| 36 | #65351 | C22 | 1 | 12 | yes | complemented |
| 37 | #65350 | C22 | 1 | 12 | yes | complemented |
| 38 | #65294 | C22 | 1 | 12 | yes | complemented |
| 39 | C2×#3937 | C22 | 1 | 12 | yes | complemented |
| 40 | #60388 | — | 5 | 1 | no | maximal, Sylow |
| 41 | C5×H(5,𝔽2) | — | 2 | 8 | no | — |
| 42 | C5×H(5,𝔽2) | — | 2 | 8 | no | — |
| 43 | C2×C5×#41 | — | 2 | 1 | no | — |
| 44 | C2×C5×#41 | D4 | 1 | 2 | yes | — |
| 45 | C2×C5×#41 | C23 | 1 | 3 | yes | — |
| 46 | C2×C5×#41 | C23 | 1 | 1 | yes | characteristic |
| 47 | C2×C5×#41 | C23 | 1 | 3 | yes | complemented |
| 48 | C22×C5×D4 | — | 2 | 6 | no | — |
| 49 | C22×C5×D4 | — | 2 | 3 | no | — |
| 50 | C22×C5×D4 | D4 | 1 | 6 | yes | — |
| 51 | C22×C5×D4 | C23 | 1 | 3 | yes | — |
| 52 | C22×C5×D4 | C23 | 1 | 3 | yes | complemented |
| 53 | C22×C22⋊D5 | — | 2 | 12 | no | — |
| 54 | #4150 | — | 2 | 8 | no | — |
| 55 | #4150 | — | 2 | 12 | no | — |
| 56 | #4150 | D4 | 1 | 8 | yes | complemented |
| 57 | #4149 | — | 2 | 8 | no | — |
| 58 | #4149 | — | 2 | 12 | no | — |
| 59 | #4149 | D4 | 1 | 8 | yes | complemented |
| 60 | D5×#41 | — | 2 | 16 | no | — |
| 61 | D5×#41 | — | 2 | 8 | no | — |
| 62 | D5×#41 | — | 2 | 24 | no | — |
| 63 | #4147 | — | 2 | 2 | no | — |
| 64 | #4147 | C23 | 1 | 4 | yes | — |
| 65 | #4144 | — | 2 | 48 | no | — |
| 66 | #4144 | — | 2 | 6 | no | — |
| 67 | #4144 | — | 2 | 12 | no | — |
| 68 | #4144 | — | 2 | 12 | no | — |
| 69 | #4144 | — | 2 | 24 | no | — |
| 70 | #4144 | C23 | 1 | 12 | yes | — |
| 71 | C2×#711 | — | 2 | 24 | no | — |
| 72 | C2×#711 | — | 2 | 12 | no | — |
| 73 | C2×D4×D5 | — | 2 | 24 | no | — |
| 74 | C2×D4×D5 | — | 2 | 12 | no | — |
| 75 | C2×#709 | — | 2 | 12 | no | — |
| 76 | C2×#709 | C23 | 1 | 12 | yes | — |
| 77 | C5×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic, complemented |
| 78 | C5×#127 | — | 2 | 6 | no | — |
| 79 | C5×#127 | C23 | 1 | 3 | yes | complemented |
| 80 | C5×#127 | C23 | 1 | 6 | yes | complemented |
| 81 | C5×#124 | C23 | 1 | 3 | yes | complemented |
| 82 | C5×#124 | C23 | 1 | 3 | yes | complemented |
| 83 | C5×#121 | — | 2 | 6 | no | — |
| 84 | C5×#121 | — | 2 | 6 | no | — |
| 85 | C5×#121 | — | 2 | 6 | no | — |
| 86 | C5×#120 | — | 2 | 6 | no | — |
| 87 | C5×#120 | — | 2 | 6 | no | — |
| 88 | C4×C5×Q8 | — | 2 | 1 | no | — |
| 89 | C4×C5×D4 | — | 2 | 3 | no | — |
| 90 | C4×C5×D4 | — | 2 | 6 | no | — |
| 91 | C5×#117 | C23 | 1 | 3 | yes | complemented |
| 92 | C2×C42×C5 | C23 | 1 | 3 | yes | complemented |
| 93 | #4097 | — | 2 | 12 | no | — |
| 94 | #4096 | — | 2 | 24 | no | — |
| 95 | #4095 | — | 2 | 12 | no | — |
| 96 | #4094 | — | 2 | 8 | no | — |
| 97 | #4088 | C23 | 1 | 8 | yes | complemented |
| 98 | C2×#687 | — | 2 | 12 | no | — |
| 99 | #4078 | — | 2 | 24 | no | — |
| 100 | #4078 | C23 | 1 | 24 | yes | complemented |
| 101 | C2×#686 | — | 2 | 12 | no | — |
| 102 | C2×#681 | C23 | 1 | 12 | yes | complemented |
| 103 | #3968 | C23 | 1 | 4 | yes | complemented |
| 104 | #3965 | C23 | 1 | 12 | yes | complemented |
| 105 | #3937 | C23 | 1 | 24 | yes | complemented |
| 106 | #3937 | C23 | 1 | 8 | yes | complemented |
| 107 | H(7,𝔽2) | — | 5 | 1 | no | — |
| 108 | #3585 | — | 5 | 2 | no | — |
| 109 | #3498 | D5 | 1 | 1 | yes | characteristic, complemented |
| 110 | #3021 | — | 5 | 6 | no | — |
| 111 | #3019 | — | 5 | 6 | no | — |
| 112 | #3018 | — | 5 | 6 | no | — |
| 113 | C2×#453 | — | 5 | 6 | no | — |
| 114 | #2901 | — | 5 | 2 | no | — |
| 115 | #2888 | — | 5 | 1 | no | — |
| 116 | C24×C5 | — | 2 | 3 | no | — |
| 117 | C24×C5 | C2×D4 | 1 | 6 | yes | — |
| 118 | C23×D5 | — | 2 | 12 | no | — |
| 119 | C5×#41 | — | 2 | 8 | no | — |
| 120 | C5×#41 | — | 2 | 12 | no | — |
| 121 | C5×#41 | — | 2 | 12 | no | — |
| 122 | C5×#41 | — | 4 | 4 | no | — |
| 123 | C5×#41 | C2×D4 | 1 | 8 | yes | — |
| 124 | C2×C5×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 125 | C2×C5×Q8 | C24 | 1 | 1 | yes | characteristic |
| 126 | C2×C5×Q8 | C24 | 1 | 1 | yes | characteristic |
| 127 | C2×C5×D4 | — | 2 | 24 | no | — |
| 128 | C2×C5×D4 | — | 2 | 6 | no | — |
| 129 | C2×C5×D4 | — | 2 | 3 | no | — |
| 130 | C2×C5×D4 | — | 2 | 12 | no | — |
| 131 | C2×C5×D4 | — | 2 | 12 | no | — |
| 132 | C2×C5×D4 | — | 2 | 12 | no | — |
| 133 | C2×C5×D4 | — | 2 | 3 | no | — |
| 134 | C2×C5×D4 | — | 4 | 12 | no | — |
| 135 | C2×C5×D4 | — | 8 | 12 | no | — |
| 136 | C2×C5×D4 | C2×D4 | 1 | 6 | yes | — |
| 137 | C2×C5×D4 | C2×D4 | 1 | 6 | yes | — |
| 138 | C2×C5×D4 | C2×D4 | 1 | 3 | yes | — |
| 139 | C2×C5×D4 | C24 | 1 | 3 | yes | — |
| 140 | C2×C5×D4 | C24 | 1 | 3 | yes | — |
| 141 | C22×C4×C5 | — | 2 | 3 | no | — |
| 142 | C22×C4×C5 | — | 2 | 3 | no | — |
| 143 | C22×C4×C5 | C2×D4 | 1 | 6 | yes | — |
| 144 | C22×C4×C5 | C24 | 1 | 3 | yes | — |
| 145 | C2×C22⋊D5 | — | 2 | 48 | no | — |
| 146 | C2×C22⋊D5 | — | 2 | 24 | no | — |
| 147 | C2×C22⋊D5 | — | 2 | 24 | no | — |
| 148 | C2×C22⋊D5 | — | 2 | 12 | no | — |
| 149 | C22×Dic5 | — | 2 | 12 | no | — |
| 150 | #713 | — | 2 | 8 | no | — |
| 151 | #713 | — | 2 | 8 | no | — |
| 152 | Q8×D5 | — | 2 | 8 | no | — |
| 153 | Q8×D5 | — | 2 | 8 | no | — |
| 154 | #711 | — | 2 | 48 | no | — |
| 155 | #711 | — | 2 | 48 | no | — |
| 156 | #711 | — | 2 | 24 | no | — |
| 157 | #711 | — | 2 | 24 | no | — |
| 158 | D4×D5 | — | 2 | 48 | no | — |
| 159 | D4×D5 | — | 2 | 48 | no | — |
| 160 | D4×D5 | — | 2 | 24 | no | — |
| 161 | D4×D5 | — | 2 | 24 | no | — |
| 162 | #709 | — | 2 | 24 | no | — |
| 163 | #709 | — | 2 | 24 | no | — |
| 164 | #709 | — | 2 | 8 | no | — |
| 165 | #709 | — | 2 | 12 | no | — |
| 166 | #709 | — | 2 | 12 | no | — |
| 167 | #709 | C2×D4 | 1 | 24 | yes | complemented |
| 168 | #709 | C24 | 1 | 8 | yes | — |
| 169 | C2×D20 | — | 2 | 12 | no | — |
| 170 | C2×D20 | C2×D4 | 1 | 12 | yes | complemented |
| 171 | C2×C4×D5 | — | 2 | 24 | no | — |
| 172 | C2×C4×D5 | — | 2 | 12 | no | — |
| 173 | C2×Dic10 | — | 2 | 12 | no | — |
| 174 | C2×Dic10 | C2×D4 | 1 | 12 | yes | complemented |
| 175 | C5×C4⋊C4 | — | 2 | 3 | no | — |
| 176 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 177 | C5×C22⋊C4 | — | 2 | 3 | no | — |
| 178 | C5×C22⋊C4 | — | 2 | 6 | no | — |
| 179 | C5×C22⋊C4 | — | 2 | 6 | no | — |
| 180 | C42×C5 | — | 2 | 3 | no | — |
| 181 | C42×C5 | C24 | 1 | 1 | yes | characteristic |
| 182 | C42×C5 | C24 | 1 | 3 | yes | — |
| 183 | #689 | — | 2 | 8 | no | — |
| 184 | #688 | — | 2 | 8 | no | — |
| 185 | #687 | — | 2 | 24 | no | — |
| 186 | #686 | — | 2 | 24 | no | — |
| 187 | #681 | — | 2 | 12 | no | — |
| 188 | #681 | C24 | 1 | 8 | yes | — |
| 189 | C2×#168 | — | 2 | 12 | no | — |
| 190 | #585 | — | 5 | 2 | no | — |
| 191 | #585 | — | 5 | 6 | no | — |
| 192 | #585 | — | 10 | 8 | no | — |
| 193 | #585 | — | 10 | 2 | no | — |
| 194 | C2×H(5,𝔽2) | — | 5 | 6 | no | — |
| 195 | C2×H(5,𝔽2) | — | 10 | 8 | no | — |
| 196 | C2×H(5,𝔽2) | — | 10 | 6 | no | — |
| 197 | C2×H(5,𝔽2) | C2×D5 | 1 | 1 | yes | characteristic |
| 198 | C2×H(5,𝔽2) | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 199 | #577 | — | 10 | 8 | no | — |
| 200 | #576 | — | 10 | 8 | no | — |
| 201 | #575 | — | 5 | 12 | no | — |
| 202 | C2×AGL(1,ℤ/8) | — | 5 | 12 | no | — |
| 203 | #568 | — | 5 | 2 | no | — |
| 204 | #550 | — | 2 | 2 | no | — |
| 205 | D42 | — | 2 | 6 | no | — |
| 206 | #535 | C2×D5 | 1 | 3 | yes | complemented |
| 207 | #535 | C2×D5 | 1 | 3 | yes | complemented |
| 208 | #532 | C2×D5 | 1 | 3 | yes | complemented |
| 209 | C2×#127 | C2×D5 | 1 | 3 | yes | complemented |
| 210 | C4×#41 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 211 | #456 | — | 5 | 4 | no | — |
| 212 | #455 | — | 5 | 12 | no | — |
| 213 | #454 | — | 5 | 12 | no | — |
| 214 | #453 | — | 5 | 12 | no | — |
| 215 | #453 | — | 5 | 24 | no | — |
| 216 | #421 | — | 5 | 12 | no | — |
| 217 | C2×#104 | — | 5 | 12 | no | — |
| 218 | #413 | — | 5 | 6 | no | — |
| 219 | C2×#100 | — | 5 | 6 | no | — |
| 220 | C23×C5 | — | 2 | 12 | no | — |
| 221 | C23×C5 | — | 2 | 3 | no | — |
| 222 | C23×C5 | — | 4 | 6 | no | — |
| 223 | C23×C5 | — | 8 | 6 | no | — |
| 224 | C23×C5 | — | 8 | 6 | no | — |
| 225 | C23×C5 | C22×D4 | 1 | 6 | yes | — |
| 226 | C23×C5 | C22×D4 | 1 | 3 | yes | — |
| 227 | C22×D5 | — | 2 | 24 | no | — |
| 228 | C22×D5 | — | 2 | 12 | no | — |
| 229 | C22×D5 | — | 16 | 12 | no | — |
| 230 | C5×Q8 | — | 2 | 2 | no | — |
| 231 | C5×Q8 | — | 2 | 2 | no | — |
| 232 | C5×Q8 | #120 | 1 | 4 | yes | — |
| 233 | C5×D4 | — | 2 | 12 | no | — |
| 234 | C5×D4 | — | 2 | 12 | no | — |
| 235 | C5×D4 | — | 2 | 6 | no | — |
| 236 | C5×D4 | — | 2 | 6 | no | — |
| 237 | C5×D4 | — | 4 | 12 | no | — |
| 238 | C5×D4 | — | 4 | 6 | no | — |
| 239 | C5×D4 | — | 4 | 6 | no | — |
| 240 | C5×D4 | — | 8 | 12 | no | — |
| 241 | C5×D4 | #120 | 1 | 12 | yes | — |
| 242 | C2×C4×C5 | — | 2 | 1 | no | — |
| 243 | C2×C4×C5 | — | 2 | 12 | no | — |
| 244 | C2×C4×C5 | — | 2 | 3 | no | — |
| 245 | C2×C4×C5 | — | 2 | 1 | no | — |
| 246 | C2×C4×C5 | — | 4 | 6 | no | — |
| 247 | C2×C4×C5 | — | 4 | 6 | no | — |
| 248 | C2×C4×C5 | C22×D4 | 1 | 12 | yes | — |
| 249 | C2×C4×C5 | C22×D4 | 1 | 2 | yes | — |
| 250 | C2×C4×C5 | C22×D4 | 1 | 3 | yes | — |
| 251 | C2×C4×C5 | C25 | 1 | 1 | yes | characteristic |
| 252 | C22⋊D5 | — | 2 | 48 | no | — |
| 253 | C22⋊D5 | — | 2 | 24 | no | — |
| 254 | C22⋊D5 | — | 2 | 8 | no | — |
| 255 | C2×Dic5 | — | 2 | 24 | no | — |
| 256 | C2×Dic5 | — | 2 | 12 | no | — |
| 257 | D20 | — | 2 | 8 | no | — |
| 258 | D20 | — | 2 | 12 | no | — |
| 259 | D20 | C22×D4 | 1 | 8 | yes | — |
| 260 | C4×D5 | — | 2 | 16 | no | — |
| 261 | C4×D5 | — | 2 | 24 | no | — |
| 262 | C4×D5 | — | 2 | 8 | no | — |
| 263 | Dic10 | — | 2 | 8 | no | — |
| 264 | Dic10 | — | 2 | 12 | no | — |
| 265 | Dic10 | C22×D4 | 1 | 8 | yes | — |
| 266 | #168 | — | 2 | 8 | no | — |
| 267 | 2−1+4 | — | 5 | 8 | no | — |
| 268 | 2−1+4 | — | 5 | 4 | no | — |
| 269 | 2−1+4 | — | 10 | 12 | no | — |
| 270 | 2−1+4 | — | 10 | 8 | no | — |
| 271 | 2−1+4 | — | 10 | 2 | no | — |
| 272 | H(5,𝔽2) | — | 2 | 8 | no | — |
| 273 | H(5,𝔽2) | — | 2 | 8 | no | — |
| 274 | H(5,𝔽2) | — | 5 | 8 | no | — |
| 275 | H(5,𝔽2) | — | 5 | 12 | no | — |
| 276 | H(5,𝔽2) | — | 10 | 24 | no | — |
| 277 | H(5,𝔽2) | — | 10 | 48 | no | — |
| 278 | H(5,𝔽2) | — | 10 | 12 | no | — |
| 279 | H(5,𝔽2) | — | 10 | 8 | no | — |
| 280 | H(5,𝔽2) | — | 10 | 12 | no | — |
| 281 | H(5,𝔽2) | — | 10 | 12 | no | — |
| 282 | H(5,𝔽2) | — | 10 | 6 | no | — |
| 283 | C2×#41 | — | 2 | 1 | no | — |
| 284 | C2×#41 | — | 5 | 12 | no | — |
| 285 | C2×#41 | — | 10 | 12 | no | — |
| 286 | C2×#41 | — | 10 | 24 | no | — |
| 287 | C2×#41 | — | 10 | 24 | no | — |
| 288 | C2×#41 | — | 10 | 16 | no | — |
| 289 | C2×#41 | — | 10 | 8 | no | — |
| 290 | C2×#41 | — | 10 | 12 | no | — |
| 291 | C2×#41 | C22⋊D5 | 1 | 2 | yes | — |
| 292 | C2×#41 | C22×D5 | 1 | 3 | yes | — |
| 293 | C2×#41 | C22×D5 | 1 | 1 | yes | characteristic |
| 294 | C2×#41 | C22×D5 | 1 | 3 | yes | complemented |
| 295 | C22×D4 | — | 2 | 6 | no | — |
| 296 | C22×D4 | — | 2 | 3 | no | — |
| 297 | C22×D4 | — | 10 | 12 | no | — |
| 298 | C22×D4 | — | 10 | 24 | no | — |
| 299 | C22×D4 | — | 10 | 12 | no | — |
| 300 | C22×D4 | C22⋊D5 | 1 | 6 | yes | — |
| 301 | C22×D4 | C22×D5 | 1 | 3 | yes | — |
| 302 | C22×D4 | C22×D5 | 1 | 3 | yes | complemented |
| 303 | #137 | — | 5 | 8 | no | — |
| 304 | #137 | — | 10 | 12 | no | — |
| 305 | AGL(1,ℤ/8) | — | 5 | 24 | no | — |
| 306 | AGL(1,ℤ/8) | — | 10 | 24 | no | — |
| 307 | AGL(1,ℤ/8) | — | 10 | 12 | no | — |
| 308 | #135 | — | 10 | 24 | no | — |
| 309 | C2×SD16 | — | 10 | 12 | no | — |
| 310 | C2×D8 | — | 10 | 12 | no | — |
| 311 | #131 | — | 10 | 8 | no | — |
| 312 | C2×M16 | — | 5 | 12 | no | — |
| 313 | C4⋊Q8 | C22×D5 | 1 | 1 | yes | characteristic, complemented |
| 314 | #127 | — | 2 | 6 | no | — |
| 315 | #127 | C22×D5 | 1 | 3 | yes | complemented |
| 316 | #127 | C22×D5 | 1 | 6 | yes | complemented |
| 317 | #124 | C22×D5 | 1 | 3 | yes | complemented |
| 318 | #124 | C22×D5 | 1 | 3 | yes | complemented |
| 319 | #121 | — | 2 | 6 | no | — |
| 320 | #121 | — | 2 | 6 | no | — |
| 321 | #121 | — | 2 | 6 | no | — |
| 322 | #120 | — | 2 | 6 | no | — |
| 323 | #120 | — | 2 | 6 | no | — |
| 324 | C4×Q8 | — | 2 | 1 | no | — |
| 325 | C4×D4 | — | 2 | 3 | no | — |
| 326 | C4×D4 | — | 2 | 6 | no | — |
| 327 | #117 | C22×D5 | 1 | 3 | yes | complemented |
| 328 | C2×C42 | C22×D5 | 1 | 3 | yes | complemented |
| 329 | #104 | — | 5 | 8 | no | — |
| 330 | #104 | — | 5 | 24 | no | — |
| 331 | #101 | — | 5 | 4 | no | — |
| 332 | #100 | — | 5 | 12 | no | — |
| 333 | C22×C5 | — | 2 | 6 | no | — |
| 334 | C22×C5 | — | 4 | 3 | no | — |
| 335 | C22×C5 | — | 4 | 6 | no | — |
| 336 | C22×C5 | — | 4 | 6 | no | — |
| 337 | C22×C5 | — | 4 | 3 | no | — |
| 338 | C22×C5 | — | 8 | 12 | no | — |
| 339 | C22×C5 | — | 16 | 6 | no | — |
| 340 | C22×C5 | C2×#120 | 1 | 6 | yes | — |
| 341 | C22×C5 | C23×D4 | 1 | 1 | yes | characteristic |
| 342 | C2×D5 | — | 2 | 8 | no | — |
| 343 | C2×D5 | — | 8 | 12 | no | — |
| 344 | C2×D5 | — | 8 | 24 | no | — |
| 345 | C4×C5 | — | 2 | 2 | no | — |
| 346 | C4×C5 | — | 2 | 2 | no | — |
| 347 | C4×C5 | — | 4 | 3 | no | — |
| 348 | C4×C5 | — | 4 | 1 | no | — |
| 349 | C4×C5 | C2×#120 | 1 | 6 | yes | — |
| 350 | C4×C5 | C23×D4 | 1 | 2 | yes | — |
| 351 | Dic5 | — | 2 | 8 | no | — |
| 352 | C24 | — | 2 | 3 | no | — |
| 353 | C24 | — | 10 | 12 | no | — |
| 354 | C24 | C2×C22⋊D5 | 1 | 6 | yes | — |
| 355 | #41 | — | 2 | 8 | no | — |
| 356 | #41 | — | 2 | 12 | no | — |
| 357 | #41 | — | 2 | 12 | no | — |
| 358 | #41 | — | 4 | 4 | no | — |
| 359 | #41 | — | 5 | 24 | no | — |
| 360 | #41 | — | 5 | 8 | no | — |
| 361 | #41 | — | 10 | 24 | no | — |
| 362 | #41 | — | 10 | 24 | no | — |
| 363 | #41 | — | 10 | 24 | no | — |
| 364 | #41 | — | 10 | 48 | no | — |
| 365 | #41 | — | 10 | 48 | no | — |
| 366 | #41 | — | 10 | 8 | no | — |
| 367 | #41 | — | 10 | 8 | no | — |
| 368 | #41 | — | 10 | 24 | no | — |
| 369 | #41 | — | 10 | 12 | no | — |
| 370 | #41 | — | 10 | 12 | no | — |
| 371 | #41 | — | 10 | 8 | no | — |
| 372 | #41 | D4×D5 | 1 | 8 | yes | — |
| 373 | C2×Q8 | — | 5 | 12 | no | — |
| 374 | C2×Q8 | — | 10 | 12 | no | — |
| 375 | C2×Q8 | — | 10 | 8 | no | — |
| 376 | C2×Q8 | — | 10 | 8 | no | — |
| 377 | C2×Q8 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 378 | C2×Q8 | C23×D5 | 1 | 1 | yes | characteristic |
| 379 | C2×Q8 | C23×D5 | 1 | 1 | yes | characteristic |
| 380 | C2×D4 | — | 2 | 24 | no | — |
| 381 | C2×D4 | — | 2 | 6 | no | — |
| 382 | C2×D4 | — | 2 | 3 | no | — |
| 383 | C2×D4 | — | 2 | 12 | no | — |
| 384 | C2×D4 | — | 2 | 12 | no | — |
| 385 | C2×D4 | — | 2 | 12 | no | — |
| 386 | C2×D4 | — | 2 | 3 | no | — |
| 387 | C2×D4 | — | 4 | 12 | no | — |
| 388 | C2×D4 | — | 5 | 12 | no | — |
| 389 | C2×D4 | — | 8 | 12 | no | — |
| 390 | C2×D4 | — | 10 | 12 | no | — |
| 391 | C2×D4 | — | 10 | 24 | no | — |
| 392 | C2×D4 | — | 10 | 48 | no | — |
| 393 | C2×D4 | — | 10 | 48 | no | — |
| 394 | C2×D4 | — | 10 | 48 | no | — |
| 395 | C2×D4 | — | 10 | 24 | no | — |
| 396 | C2×D4 | — | 10 | 12 | no | — |
| 397 | C2×D4 | — | 10 | 24 | no | — |
| 398 | C2×D4 | — | 10 | 24 | no | — |
| 399 | C2×D4 | C2×C22⋊D5 | 1 | 6 | yes | — |
| 400 | C2×D4 | C2×C22⋊D5 | 1 | 6 | yes | — |
| 401 | C2×D4 | C2×C22⋊D5 | 1 | 3 | yes | — |
| 402 | C2×D4 | C23×D5 | 1 | 3 | yes | — |
| 403 | C2×D4 | C23×D5 | 1 | 3 | yes | — |
| 404 | C22×C4 | — | 2 | 3 | no | — |
| 405 | C22×C4 | — | 2 | 3 | no | — |
| 406 | C22×C4 | — | 10 | 24 | no | — |
| 407 | C22×C4 | — | 10 | 12 | no | — |
| 408 | C22×C4 | — | 10 | 12 | no | — |
| 409 | C22×C4 | C2×C22⋊D5 | 1 | 6 | yes | — |
| 410 | C22×C4 | C23×D5 | 1 | 3 | yes | — |
| 411 | Q16 | — | 10 | 8 | no | — |
| 412 | SD16 | — | 10 | 24 | no | — |
| 413 | SD16 | — | 10 | 8 | no | — |
| 414 | D8 | — | 10 | 24 | no | — |
| 415 | M16 | — | 5 | 8 | no | — |
| 416 | M16 | — | 10 | 12 | no | — |
| 417 | C2×C8 | — | 10 | 12 | no | — |
| 418 | C4⋊C4 | — | 2 | 3 | no | — |
| 419 | C4⋊C4 | — | 2 | 2 | no | — |
| 420 | C22⋊C4 | — | 2 | 3 | no | — |
| 421 | C22⋊C4 | — | 2 | 6 | no | — |
| 422 | C22⋊C4 | — | 2 | 6 | no | — |
| 423 | C42 | — | 2 | 3 | no | — |
| 424 | C42 | C23×D5 | 1 | 1 | yes | characteristic |
| 425 | C42 | C23×D5 | 1 | 3 | yes | — |
| 426 | C2×C5 | — | 2 | 1 | no | — |
| 427 | C2×C5 | — | 2 | 6 | no | — |
| 428 | C2×C5 | — | 4 | 6 | no | — |
| 429 | C2×C5 | — | 8 | 3 | no | — |
| 430 | C2×C5 | C22×#120 | 1 | 1 | yes | characteristic |
| 431 | D5 | — | 4 | 8 | no | — |
| 432 | C23 | — | 2 | 12 | no | — |
| 433 | C23 | — | 2 | 3 | no | — |
| 434 | C23 | — | 4 | 6 | no | — |
| 435 | C23 | — | 8 | 6 | no | — |
| 436 | C23 | — | 8 | 6 | no | — |
| 437 | C23 | — | 10 | 24 | no | — |
| 438 | C23 | — | 10 | 12 | no | — |
| 439 | C23 | — | 80 | 12 | no | — |
| 440 | C23 | C22×C22⋊D5 | 1 | 6 | yes | — |
| 441 | C23 | C22×C22⋊D5 | 1 | 3 | yes | — |
| 442 | Q8 | — | 2 | 2 | no | — |
| 443 | Q8 | — | 2 | 2 | no | — |
| 444 | Q8 | — | 5 | 8 | no | — |
| 445 | Q8 | — | 10 | 8 | no | — |
| 446 | Q8 | — | 10 | 12 | no | — |
| 447 | Q8 | #4083 | 1 | 4 | yes | — |
| 448 | D4 | — | 2 | 12 | no | — |
| 449 | D4 | — | 2 | 12 | no | — |
| 450 | D4 | — | 2 | 6 | no | — |
| 451 | D4 | — | 2 | 6 | no | — |
| 452 | D4 | — | 4 | 12 | no | — |
| 453 | D4 | — | 4 | 6 | no | — |
| 454 | D4 | — | 4 | 6 | no | — |
| 455 | D4 | — | 5 | 8 | no | — |
| 456 | D4 | — | 8 | 12 | no | — |
| 457 | D4 | — | 10 | 8 | no | — |
| 458 | D4 | — | 10 | 48 | no | — |
| 459 | D4 | — | 10 | 24 | no | — |
| 460 | D4 | — | 10 | 8 | no | — |
| 461 | D4 | — | 10 | 12 | no | — |
| 462 | D4 | #4083 | 1 | 12 | yes | — |
| 463 | C2×C4 | — | 2 | 1 | no | — |
| 464 | C2×C4 | — | 2 | 12 | no | — |
| 465 | C2×C4 | — | 2 | 3 | no | — |
| 466 | C2×C4 | — | 2 | 1 | no | — |
| 467 | C2×C4 | — | 4 | 6 | no | — |
| 468 | C2×C4 | — | 4 | 6 | no | — |
| 469 | C2×C4 | — | 10 | 16 | no | — |
| 470 | C2×C4 | — | 10 | 24 | no | — |
| 471 | C2×C4 | — | 10 | 12 | no | — |
| 472 | C2×C4 | — | 10 | 24 | no | — |
| 473 | C2×C4 | — | 10 | 8 | no | — |
| 474 | C2×C4 | C2×D4×D5 | 1 | 12 | yes | — |
| 475 | C2×C4 | C22×C22⋊D5 | 1 | 2 | yes | — |
| 476 | C2×C4 | C22×C22⋊D5 | 1 | 3 | yes | — |
| 477 | C2×C4 | C24×D5 | 1 | 1 | yes | characteristic |
| 478 | C8 | — | 10 | 8 | no | — |
| 479 | C5 | #60388 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 480 | C22 | — | 2 | 6 | no | — |
| 481 | C22 | — | 4 | 3 | no | — |
| 482 | C22 | — | 4 | 6 | no | — |
| 483 | C22 | — | 4 | 6 | no | — |
| 484 | C22 | — | 4 | 3 | no | — |
| 485 | C22 | — | 8 | 12 | no | — |
| 486 | C22 | — | 10 | 8 | no | — |
| 487 | C22 | — | 16 | 6 | no | — |
| 488 | C22 | — | 40 | 12 | no | — |
| 489 | C22 | — | 40 | 24 | no | — |
| 490 | C22 | C2×#4083 | 1 | 6 | yes | — |
| 491 | C22 | C23×C22⋊D5 | 1 | 1 | yes | characteristic |
| 492 | C4 | — | 2 | 2 | no | — |
| 493 | C4 | — | 2 | 2 | no | — |
| 494 | C4 | — | 4 | 3 | no | — |
| 495 | C4 | — | 4 | 1 | no | — |
| 496 | C4 | — | 10 | 8 | no | — |
| 497 | C4 | C2×#4083 | 1 | 6 | yes | — |
| 498 | C4 | C22×D4×D5 | 1 | 2 | yes | — |
| 499 | C2 | — | 2 | 1 | no | — |
| 500 | C2 | — | 2 | 6 | no | — |
| 501 | C2 | — | 4 | 6 | no | — |
| 502 | C2 | — | 8 | 3 | no | — |
| 503 | C2 | — | 20 | 8 | no | — |
| 504 | C2 | C22×#4083 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10619436 | C2 | semidirect |
| 2. C5×#3498 | C2 | semidirect |
| 3. #10619178 | C2 | semidirect |
| 4. #10615831 | C2 | semidirect |
| 5. #10615126 | C2 | semidirect |
| 6. #10615125 | C2 | semidirect |
| 7. #10615053 | C2 | semidirect |
| 8. C2×#65366 | C2 | semidirect |
| 9. #10614267 | C2 | semidirect |
| 11. C2×C5×H(5,𝔽2) | C22 | semidirect |
| 16. #66283 | C22 | semidirect |
| 18. C2×#4144 | C22 | semidirect |
| 21. C5×#535 | C22 | semidirect |
| 22. C5×#535 | C22 | semidirect |
| 23. C5×#532 | C22 | semidirect |
| 24. C2×C5×#127 | C22 | semidirect |
| 25. C4×C5×#41 | C22 | semidirect |
| 28. #66156 | C22 | semidirect |
| 29. #66153 | C22 | semidirect |
| 30. C2×#4078 | C22 | semidirect |
| 31. #65526 | C22 | semidirect |
| 32. C2×#3965 | C22 | semidirect |
| 33. #65384 | C22 | semidirect |
| 34. #65366 | C22 | semidirect |
| 35. #65366 | C22 | semidirect |
| 36. #65351 | C22 | semidirect |
| 37. #65350 | C22 | semidirect |
| 38. #65294 | C22 | semidirect |
| 39. C2×#3937 | C22 | semidirect |
| 47. C2×C5×#41 | C23 | semidirect |
| 52. C22×C5×D4 | C23 | semidirect |
| 56. #4150 | D4 | semidirect |
| 59. #4149 | D4 | semidirect |
| 77. C5×C4⋊Q8 | C23 | semidirect |
| 79. C5×#127 | C23 | semidirect |
| 80. C5×#127 | C23 | semidirect |
| 81. C5×#124 | C23 | semidirect |
| 82. C5×#124 | C23 | semidirect |
| 91. C5×#117 | C23 | semidirect |
| 92. C2×C42×C5 | C23 | semidirect |
| 97. #4088 | C23 | semidirect |
| 100. #4078 | C23 | semidirect |
| 102. C2×#681 | C23 | semidirect |
| 103. #3968 | C23 | semidirect |
| 104. #3965 | C23 | semidirect |
| 105. #3937 | C23 | semidirect |
| 106. #3937 | C23 | semidirect |
| 109. #3498 | D5 | semidirect |
| 167. #709 | C2×D4 | semidirect |
| 170. C2×D20 | C2×D4 | semidirect |
| 174. C2×Dic10 | C2×D4 | semidirect |
| 198. C2×H(5,𝔽2) | C2×D5 | semidirect |
| 206. #535 | C2×D5 | semidirect |
| 207. #535 | C2×D5 | semidirect |
| 208. #532 | C2×D5 | semidirect |
| 209. C2×#127 | C2×D5 | semidirect |
| 210. C4×#41 | C2×D5 | semidirect |
| 294. C2×#41 | C22×D5 | semidirect |
| 302. C22×D4 | C22×D5 | semidirect |
| 313. C4⋊Q8 | C22×D5 | semidirect |
| 315. #127 | C22×D5 | semidirect |
| 316. #127 | C22×D5 | semidirect |
| 317. #124 | C22×D5 | semidirect |
| 318. #124 | C22×D5 | semidirect |
| 327. #117 | C22×D5 | semidirect |
| 328. C2×C42 | C22×D5 | semidirect |
| 479. C5 | #60388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10619436 | 2 |
| C5×#3498 | 2 |
| #10619178 | 2 |
| #10615831 | 2 |
| #10615126 | 2 |
| #10615125 | 2 |
| #10615053 | 2 |
| C2×#65366 | 2 |
| #10614267 | 2 |
| #60388 | 5 |