Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1284 conjugacy classes of subgroups.
The subgroup lattice has 580 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10619188 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C5×#3011 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10615843 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10615709 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10615147 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10602867 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #10602659 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10601145 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10601086 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #10600802 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #10600794 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×C5×2−1+4 | C22 | 1 | 1 | yes | characteristic |
| 13 | #66283 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C5×#137 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | C22×C5×Q16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | C5×#536 | C22 | 1 | 1 | yes | characteristic |
| 17 | #66172 | — | 2 | 4 | no | — |
| 18 | #66171 | — | 2 | 4 | no | — |
| 19 | #66156 | — | 2 | 2 | no | — |
| 20 | #66156 | C22 | 1 | 2 | yes | — |
| 21 | #66153 | C22 | 1 | 1 | yes | characteristic |
| 22 | #66153 | C22 | 1 | 2 | yes | complemented |
| 23 | C2×#4088 | — | 2 | 2 | no | — |
| 24 | C2×#4088 | C22 | 1 | 2 | yes | — |
| 25 | C2×#4088 | C22 | 1 | 2 | yes | — |
| 26 | C5×#452 | — | 2 | 2 | no | — |
| 27 | C5×#451 | — | 2 | 2 | no | — |
| 28 | C5×#419 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | C5×#416 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | C5×#408 | C22 | 1 | 1 | yes | characteristic |
| 31 | #65526 | — | 2 | 2 | no | — |
| 32 | #65526 | C22 | 1 | 1 | yes | characteristic |
| 33 | #65526 | C22 | 1 | 1 | yes | characteristic |
| 34 | C2×#3968 | — | 2 | 2 | no | — |
| 35 | C2×#3968 | C22 | 1 | 2 | yes | complemented |
| 36 | C2×#3968 | C22 | 1 | 2 | yes | complemented |
| 37 | #65493 | — | 2 | 4 | no | — |
| 38 | #65492 | — | 2 | 4 | no | — |
| 39 | #65421 | C22 | 1 | 2 | yes | — |
| 40 | #65413 | C22 | 1 | 2 | yes | complemented |
| 41 | #65399 | C22 | 1 | 2 | yes | — |
| 42 | #65384 | — | 2 | 2 | no | — |
| 43 | #65350 | — | 2 | 2 | no | — |
| 44 | #65294 | C22 | 1 | 2 | yes | — |
| 45 | #64772 | C22 | 1 | 2 | yes | complemented |
| 46 | #64753 | C22 | 1 | 2 | yes | complemented |
| 47 | #24423 | — | 5 | 1 | no | maximal, Sylow |
| 48 | C5×2−1+4 | — | 2 | 4 | no | — |
| 49 | C5×2−1+4 | — | 4 | 2 | no | — |
| 50 | C2×C5×#41 | — | 2 | 1 | no | — |
| 51 | C2×C5×#41 | — | 2 | 2 | no | — |
| 52 | C2×C5×#41 | D4 | 1 | 2 | yes | — |
| 53 | C2×C5×#41 | C23 | 1 | 1 | yes | characteristic |
| 54 | C2×C5×#41 | C23 | 1 | 1 | yes | characteristic |
| 55 | C22×C5×Q8 | — | 2 | 1 | no | — |
| 56 | C22×C5×Q8 | D4 | 1 | 2 | yes | — |
| 57 | C22×C5×Q8 | C23 | 1 | 1 | yes | characteristic |
| 58 | C22×C5×Q8 | C23 | 1 | 1 | yes | characteristic |
| 59 | #4150 | — | 2 | 2 | no | — |
| 60 | #4149 | — | 2 | 2 | no | — |
| 61 | D5×#41 | — | 4 | 2 | no | — |
| 62 | #4147 | — | 2 | 1 | no | — |
| 63 | #4144 | — | 2 | 1 | no | — |
| 64 | #4144 | — | 2 | 2 | no | — |
| 65 | C2×#709 | — | 2 | 2 | no | — |
| 66 | C2×#709 | C23 | 1 | 2 | yes | — |
| 67 | C5×#137 | — | 2 | 4 | no | — |
| 68 | C2×C5×Q16 | — | 2 | 1 | no | — |
| 69 | C2×C5×Q16 | — | 2 | 2 | no | — |
| 70 | C2×C5×Q16 | — | 4 | 2 | no | — |
| 71 | C2×C5×SD16 | — | 2 | 1 | no | — |
| 72 | C2×C5×M16 | C23 | 1 | 1 | yes | characteristic |
| 73 | C22×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 74 | C5×C4⋊Q8 | — | 2 | 1 | no | — |
| 75 | C5×#124 | — | 2 | 1 | no | — |
| 76 | C5×#123 | — | 2 | 2 | no | — |
| 77 | C5×C22⋊Q8 | — | 2 | 2 | no | — |
| 78 | C5×#117 | C23 | 1 | 1 | yes | characteristic |
| 79 | #4097 | — | 2 | 4 | no | — |
| 80 | #4097 | D4 | 1 | 4 | yes | — |
| 81 | #4096 | — | 2 | 8 | no | — |
| 82 | #4096 | — | 2 | 4 | no | — |
| 83 | #4095 | — | 2 | 4 | no | — |
| 84 | #4095 | D4 | 1 | 4 | yes | — |
| 85 | #4094 | — | 2 | 4 | no | — |
| 86 | #4094 | — | 2 | 4 | no | — |
| 87 | #4094 | — | 4 | 2 | no | — |
| 88 | C2×#689 | — | 2 | 4 | no | — |
| 89 | C2×#689 | — | 2 | 2 | no | — |
| 90 | C2×#689 | — | 2 | 2 | no | — |
| 91 | #4088 | — | 2 | 8 | no | — |
| 92 | #4088 | — | 2 | 2 | no | — |
| 93 | #4088 | — | 2 | 4 | no | — |
| 94 | #4088 | — | 2 | 4 | no | — |
| 95 | #4088 | — | 2 | 4 | no | — |
| 96 | #4088 | — | 4 | 2 | no | — |
| 97 | C2×#688 | — | 2 | 4 | no | — |
| 98 | C2×#688 | — | 2 | 2 | no | — |
| 99 | C2×#688 | — | 2 | 2 | no | — |
| 100 | #4078 | — | 2 | 2 | no | — |
| 101 | C2×#681 | — | 2 | 2 | no | — |
| 102 | C2×#681 | — | 2 | 4 | no | — |
| 103 | C2×#681 | C23 | 1 | 2 | yes | — |
| 104 | C2×#681 | C23 | 1 | 2 | yes | — |
| 105 | C2×#681 | C23 | 1 | 2 | yes | — |
| 106 | C5×#103 | — | 2 | 1 | no | — |
| 107 | C5×#103 | — | 2 | 2 | no | — |
| 108 | C5×#102 | — | 2 | 1 | no | — |
| 109 | C5×C22⋊C8 | — | 2 | 2 | no | — |
| 110 | #3968 | — | 2 | 1 | no | — |
| 111 | #3968 | — | 2 | 4 | no | — |
| 112 | #3968 | — | 2 | 4 | no | — |
| 113 | #3968 | D4 | 1 | 2 | yes | — |
| 114 | #3965 | — | 2 | 1 | no | — |
| 115 | #3965 | D4 | 1 | 2 | yes | — |
| 116 | #3956 | — | 2 | 2 | no | — |
| 117 | #3955 | — | 2 | 2 | no | — |
| 118 | #3954 | — | 2 | 4 | no | — |
| 119 | #3952 | — | 4 | 2 | no | — |
| 120 | #3937 | — | 2 | 4 | no | — |
| 121 | #3586 | — | 5 | 1 | no | — |
| 122 | #3069 | — | 5 | 2 | no | — |
| 123 | #3022 | — | 5 | 1 | no | — |
| 124 | #3011 | D5 | 1 | 1 | yes | characteristic, complemented |
| 125 | #2889 | — | 5 | 1 | no | — |
| 126 | #2049 | — | 5 | 2 | no | — |
| 127 | #2020 | — | 5 | 2 | no | — |
| 128 | #1915 | — | 5 | 1 | no | — |
| 129 | #1881 | — | 5 | 2 | no | — |
| 130 | #1858 | — | 5 | 1 | no | — |
| 131 | #1791 | — | 5 | 1 | no | — |
| 132 | C5×#41 | — | 2 | 2 | no | — |
| 133 | C5×#41 | — | 2 | 2 | no | — |
| 134 | C5×#41 | — | 2 | 2 | no | — |
| 135 | C5×#41 | — | 2 | 4 | no | — |
| 136 | C5×#41 | — | 4 | 2 | no | — |
| 137 | C5×#41 | — | 4 | 4 | no | — |
| 138 | C5×#41 | — | 4 | 8 | no | — |
| 139 | C5×#41 | C2×D4 | 1 | 4 | yes | — |
| 140 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 141 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 142 | C2×C5×Q8 | — | 2 | 4 | no | — |
| 143 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 144 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 145 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 146 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 147 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 148 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 149 | C2×C5×Q8 | — | 4 | 2 | no | — |
| 150 | C2×C5×Q8 | — | 4 | 4 | no | — |
| 151 | C2×C5×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 152 | C2×C5×Q8 | C2×D4 | 1 | 2 | yes | — |
| 153 | C2×C5×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 154 | C2×C5×D4 | — | 2 | 1 | no | — |
| 155 | C2×C5×D4 | — | 2 | 2 | no | — |
| 156 | C2×C5×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 157 | C2×C5×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 158 | C2×C5×D4 | #41 | 1 | 2 | yes | — |
| 159 | C22×C4×C5 | — | 2 | 1 | no | — |
| 160 | C22×C4×C5 | — | 2 | 2 | no | — |
| 161 | C22×C4×C5 | — | 2 | 1 | no | — |
| 162 | C22×C4×C5 | — | 2 | 2 | no | — |
| 163 | C22×C4×C5 | — | 2 | 1 | no | — |
| 164 | C22×C4×C5 | C2×D4 | 1 | 2 | yes | — |
| 165 | C22×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 166 | C2×C22⋊D5 | — | 2 | 2 | no | — |
| 167 | C2×C22⋊D5 | — | 4 | 2 | no | — |
| 168 | #713 | — | 4 | 2 | no | — |
| 169 | Q8×D5 | — | 4 | 2 | no | — |
| 170 | #711 | — | 4 | 2 | no | — |
| 171 | #711 | — | 4 | 4 | no | — |
| 172 | D4×D5 | — | 4 | 2 | no | — |
| 173 | D4×D5 | — | 4 | 4 | no | — |
| 174 | #709 | — | 2 | 4 | no | — |
| 175 | #709 | — | 2 | 2 | no | — |
| 176 | #709 | — | 2 | 2 | no | — |
| 177 | #709 | — | 2 | 2 | no | — |
| 178 | #709 | — | 2 | 2 | no | — |
| 179 | #709 | — | 4 | 2 | no | — |
| 180 | #709 | — | 4 | 2 | no | — |
| 181 | C2×D20 | — | 2 | 2 | no | — |
| 182 | C2×D20 | C2×D4 | 1 | 2 | yes | — |
| 183 | C2×C4×D5 | — | 2 | 2 | no | — |
| 184 | C2×C4×D5 | — | 4 | 2 | no | — |
| 185 | C2×Dic10 | — | 2 | 2 | no | — |
| 186 | C2×Dic10 | C2×D4 | 1 | 2 | yes | — |
| 187 | C5×Q16 | — | 4 | 4 | no | — |
| 188 | C5×Q16 | — | 4 | 2 | no | — |
| 189 | C5×SD16 | — | 4 | 2 | no | — |
| 190 | C5×M16 | — | 2 | 2 | no | — |
| 191 | C2×C5×C8 | — | 2 | 1 | no | — |
| 192 | C2×C5×C8 | — | 2 | 1 | no | — |
| 193 | C2×C5×C8 | — | 2 | 2 | no | — |
| 194 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 195 | C5×C4⋊C4 | — | 4 | 2 | no | — |
| 196 | C5×C22⋊C4 | — | 2 | 1 | no | — |
| 197 | C5×C22⋊C4 | — | 4 | 2 | no | — |
| 198 | C42×C5 | — | 2 | 1 | no | — |
| 199 | #689 | — | 2 | 8 | no | — |
| 200 | #689 | — | 2 | 4 | no | — |
| 201 | #689 | — | 4 | 4 | no | — |
| 202 | #688 | — | 2 | 8 | no | — |
| 203 | #688 | — | 2 | 4 | no | — |
| 204 | #688 | — | 4 | 4 | no | — |
| 205 | #687 | — | 2 | 4 | no | — |
| 206 | #686 | — | 2 | 4 | no | — |
| 207 | #681 | — | 2 | 4 | no | — |
| 208 | #681 | — | 2 | 2 | no | — |
| 209 | #681 | — | 2 | 2 | no | — |
| 210 | #681 | — | 2 | 2 | no | — |
| 211 | #681 | — | 2 | 2 | no | — |
| 212 | #681 | — | 4 | 4 | no | — |
| 213 | #681 | C2×D4 | 1 | 4 | yes | — |
| 214 | #681 | C2×D4 | 1 | 4 | yes | — |
| 215 | C2×#168 | — | 2 | 4 | no | — |
| 216 | C2×#168 | — | 2 | 2 | no | — |
| 217 | C2×#168 | — | 2 | 2 | no | — |
| 218 | C2×#168 | — | 2 | 2 | no | — |
| 219 | C2×#168 | — | 4 | 4 | no | — |
| 220 | #585 | — | 5 | 1 | no | — |
| 221 | C2×2−1+4 | C2×D5 | 1 | 1 | yes | characteristic |
| 222 | #578 | — | 10 | 4 | no | — |
| 223 | #577 | — | 10 | 4 | no | — |
| 224 | #575 | — | 5 | 2 | no | — |
| 225 | #575 | — | 10 | 2 | no | — |
| 226 | C2×#137 | — | 5 | 2 | no | — |
| 227 | C2×#137 | — | 5 | 2 | no | — |
| 228 | C2×#137 | — | 10 | 2 | no | — |
| 229 | C2×#137 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 230 | C22×Q16 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 231 | #568 | — | 5 | 1 | no | — |
| 232 | #568 | — | 5 | 2 | no | — |
| 233 | #536 | C2×D5 | 1 | 1 | yes | characteristic |
| 234 | #473 | — | 10 | 4 | no | — |
| 235 | #471 | — | 10 | 4 | no | — |
| 236 | #456 | — | 10 | 2 | no | — |
| 237 | #455 | — | 10 | 2 | no | — |
| 238 | #452 | — | 2 | 2 | no | — |
| 239 | #451 | — | 2 | 2 | no | — |
| 240 | #430 | — | 5 | 2 | no | — |
| 241 | #421 | — | 5 | 2 | no | — |
| 242 | #419 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 243 | #416 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 244 | #413 | — | 5 | 1 | no | — |
| 245 | #413 | — | 5 | 1 | no | — |
| 246 | #413 | — | 5 | 2 | no | — |
| 247 | #413 | — | 10 | 2 | no | — |
| 248 | C2×#101 | — | 5 | 2 | no | — |
| 249 | C2×#101 | — | 5 | 2 | no | — |
| 250 | C2×#101 | — | 10 | 2 | no | — |
| 251 | #408 | — | 5 | 2 | no | — |
| 252 | #408 | C2×D5 | 1 | 1 | yes | characteristic |
| 253 | #344 | — | 5 | 2 | no | — |
| 254 | #341 | — | 5 | 2 | no | — |
| 255 | C23×C5 | — | 2 | 1 | no | — |
| 256 | C23×C5 | #121 | 1 | 2 | yes | — |
| 257 | C23×C5 | C2×#41 | 1 | 1 | yes | characteristic |
| 258 | C22×D5 | — | 2 | 2 | no | — |
| 259 | C22×D5 | — | 4 | 2 | no | — |
| 260 | C5×Q8 | — | 2 | 1 | no | — |
| 261 | C5×Q8 | — | 2 | 2 | no | — |
| 262 | C5×Q8 | — | 2 | 2 | no | — |
| 263 | C5×Q8 | — | 2 | 2 | no | — |
| 264 | C5×Q8 | — | 4 | 4 | no | — |
| 265 | C5×Q8 | — | 4 | 2 | no | — |
| 266 | C5×Q8 | — | 4 | 1 | no | — |
| 267 | C5×Q8 | — | 4 | 1 | no | — |
| 268 | C5×Q8 | — | 4 | 2 | no | — |
| 269 | C5×Q8 | #120 | 1 | 2 | yes | — |
| 270 | C5×D4 | — | 2 | 4 | no | — |
| 271 | C5×D4 | — | 2 | 4 | no | — |
| 272 | C5×D4 | — | 2 | 1 | no | — |
| 273 | C5×D4 | — | 2 | 2 | no | — |
| 274 | C5×D4 | — | 4 | 4 | no | — |
| 275 | C5×D4 | #120 | 1 | 2 | yes | — |
| 276 | C2×C4×C5 | — | 2 | 1 | no | — |
| 277 | C2×C4×C5 | — | 2 | 2 | no | — |
| 278 | C2×C4×C5 | — | 2 | 2 | no | — |
| 279 | C2×C4×C5 | — | 2 | 4 | no | — |
| 280 | C2×C4×C5 | — | 2 | 2 | no | — |
| 281 | C2×C4×C5 | — | 4 | 4 | no | — |
| 282 | C2×C4×C5 | — | 4 | 4 | no | — |
| 283 | C2×C4×C5 | — | 4 | 2 | no | — |
| 284 | C2×C4×C5 | — | 4 | 1 | no | — |
| 285 | C2×C4×C5 | — | 4 | 1 | no | — |
| 286 | C2×C4×C5 | — | 4 | 2 | no | — |
| 287 | C2×C4×C5 | #121 | 1 | 2 | yes | — |
| 288 | C2×C4×C5 | C22×D4 | 1 | 2 | yes | — |
| 289 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 290 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 291 | C2×C4×C5 | H(5,𝔽2) | 1 | 2 | yes | — |
| 292 | C22⋊D5 | — | 4 | 4 | no | — |
| 293 | C22⋊D5 | — | 4 | 2 | no | — |
| 294 | C22⋊D5 | — | 4 | 2 | no | — |
| 295 | C2×Dic5 | — | 2 | 2 | no | — |
| 296 | C2×Dic5 | — | 4 | 2 | no | — |
| 297 | D20 | — | 2 | 2 | no | — |
| 298 | D20 | — | 2 | 2 | no | — |
| 299 | D20 | — | 4 | 2 | no | — |
| 300 | C4×D5 | — | 4 | 4 | no | — |
| 301 | C4×D5 | — | 4 | 2 | no | — |
| 302 | C4×D5 | — | 4 | 2 | no | — |
| 303 | Dic10 | — | 2 | 2 | no | — |
| 304 | Dic10 | — | 2 | 2 | no | — |
| 305 | Dic10 | — | 4 | 2 | no | — |
| 306 | C5×C8 | — | 4 | 1 | no | — |
| 307 | C5×C8 | — | 4 | 1 | no | — |
| 308 | #168 | — | 2 | 4 | no | — |
| 309 | #168 | — | 2 | 4 | no | — |
| 310 | #168 | — | 4 | 2 | no | — |
| 311 | 2−1+4 | — | 2 | 4 | no | — |
| 312 | 2−1+4 | — | 4 | 2 | no | — |
| 313 | 2−1+4 | — | 10 | 2 | no | — |
| 314 | 2−1+4 | — | 10 | 1 | no | — |
| 315 | H(5,𝔽2) | — | 10 | 2 | no | — |
| 316 | H(5,𝔽2) | — | 10 | 2 | no | — |
| 317 | H(5,𝔽2) | — | 10 | 1 | no | — |
| 318 | C2×#41 | — | 2 | 1 | no | — |
| 319 | C2×#41 | — | 2 | 2 | no | — |
| 320 | C2×#41 | — | 5 | 2 | no | — |
| 321 | C2×#41 | — | 10 | 2 | no | — |
| 322 | C2×#41 | — | 20 | 2 | no | — |
| 323 | C2×#41 | C22⋊D5 | 1 | 2 | yes | — |
| 324 | C2×#41 | C22×D5 | 1 | 1 | yes | characteristic |
| 325 | C2×#41 | C22×D5 | 1 | 1 | yes | characteristic |
| 326 | C22×Q8 | — | 2 | 1 | no | — |
| 327 | C22×Q8 | C22⋊D5 | 1 | 2 | yes | — |
| 328 | C22×Q8 | C22×D5 | 1 | 1 | yes | characteristic |
| 329 | C22×Q8 | C22×D5 | 1 | 1 | yes | characteristic |
| 330 | #137 | — | 2 | 4 | no | — |
| 331 | #137 | — | 5 | 4 | no | — |
| 332 | #137 | — | 10 | 4 | no | — |
| 333 | #137 | — | 10 | 4 | no | — |
| 334 | #137 | — | 10 | 8 | no | — |
| 335 | #137 | — | 10 | 4 | no | — |
| 336 | #137 | — | 10 | 4 | no | — |
| 337 | #137 | — | 10 | 2 | no | — |
| 338 | #137 | — | 20 | 2 | no | — |
| 339 | AGL(1,ℤ/8) | — | 5 | 4 | no | — |
| 340 | AGL(1,ℤ/8) | — | 10 | 4 | no | — |
| 341 | AGL(1,ℤ/8) | — | 10 | 2 | no | — |
| 342 | #135 | — | 10 | 8 | no | — |
| 343 | #135 | — | 10 | 4 | no | — |
| 344 | C2×Q16 | — | 2 | 2 | no | — |
| 345 | C2×Q16 | — | 2 | 1 | no | — |
| 346 | C2×Q16 | — | 4 | 2 | no | — |
| 347 | C2×Q16 | — | 10 | 2 | no | — |
| 348 | C2×Q16 | — | 10 | 4 | no | — |
| 349 | C2×Q16 | — | 10 | 2 | no | — |
| 350 | C2×SD16 | — | 2 | 1 | no | — |
| 351 | C2×SD16 | — | 10 | 2 | no | — |
| 352 | C2×SD16 | — | 10 | 4 | no | — |
| 353 | C2×SD16 | — | 10 | 2 | no | — |
| 354 | #131 | — | 10 | 4 | no | — |
| 355 | #131 | — | 10 | 4 | no | — |
| 356 | #131 | — | 20 | 2 | no | — |
| 357 | C2×M16 | — | 5 | 2 | no | — |
| 358 | C2×M16 | — | 5 | 2 | no | — |
| 359 | C2×M16 | — | 5 | 2 | no | — |
| 360 | C2×M16 | — | 10 | 2 | no | — |
| 361 | C2×M16 | — | 10 | 4 | no | — |
| 362 | C2×M16 | C22×D5 | 1 | 1 | yes | characteristic |
| 363 | C22×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 364 | C4⋊Q8 | — | 2 | 1 | no | — |
| 365 | #124 | — | 2 | 1 | no | — |
| 366 | #123 | — | 2 | 2 | no | — |
| 367 | C22⋊Q8 | — | 2 | 2 | no | — |
| 368 | #117 | C22×D5 | 1 | 1 | yes | characteristic |
| 369 | #108 | — | 10 | 4 | no | — |
| 370 | #104 | — | 10 | 4 | no | — |
| 371 | #103 | — | 2 | 1 | no | — |
| 372 | #103 | — | 2 | 2 | no | — |
| 373 | #102 | — | 2 | 1 | no | — |
| 374 | #101 | — | 5 | 2 | no | — |
| 375 | #101 | — | 10 | 2 | no | — |
| 376 | #101 | — | 10 | 4 | no | — |
| 377 | #101 | — | 10 | 4 | no | — |
| 378 | #101 | — | 10 | 1 | no | — |
| 379 | #100 | — | 5 | 2 | no | — |
| 380 | #100 | — | 10 | 2 | no | — |
| 381 | #100 | — | 10 | 1 | no | — |
| 382 | C22⋊C8 | — | 2 | 2 | no | — |
| 383 | C22⋊C8 | — | 20 | 2 | no | — |
| 384 | C22×C5 | — | 2 | 2 | no | — |
| 385 | C22×C5 | — | 2 | 2 | no | — |
| 386 | C22×C5 | — | 4 | 1 | no | — |
| 387 | C22×C5 | — | 4 | 2 | no | — |
| 388 | C22×C5 | — | 8 | 1 | no | — |
| 389 | C22×C5 | C2×#121 | 1 | 1 | yes | characteristic |
| 390 | C22×C5 | #546 | 1 | 2 | yes | — |
| 391 | C2×D5 | — | 4 | 2 | no | — |
| 392 | C2×D5 | — | 8 | 2 | no | — |
| 393 | C2×D5 | — | 16 | 2 | no | — |
| 394 | C4×C5 | — | 2 | 2 | no | — |
| 395 | C4×C5 | — | 2 | 2 | no | — |
| 396 | C4×C5 | — | 4 | 2 | no | — |
| 397 | C4×C5 | — | 8 | 1 | no | — |
| 398 | C4×C5 | — | 8 | 1 | no | — |
| 399 | C4×C5 | C2×#120 | 1 | 1 | yes | characteristic |
| 400 | C4×C5 | #534 | 1 | 1 | yes | characteristic |
| 401 | C4×C5 | D42 | 1 | 2 | yes | — |
| 402 | Dic5 | — | 4 | 2 | no | — |
| 403 | #41 | — | 2 | 2 | no | — |
| 404 | #41 | — | 2 | 2 | no | — |
| 405 | #41 | — | 2 | 2 | no | — |
| 406 | #41 | — | 2 | 4 | no | — |
| 407 | #41 | — | 4 | 2 | no | — |
| 408 | #41 | — | 4 | 4 | no | — |
| 409 | #41 | — | 4 | 8 | no | — |
| 410 | #41 | — | 10 | 4 | no | — |
| 411 | #41 | — | 10 | 2 | no | — |
| 412 | #41 | — | 10 | 2 | no | — |
| 413 | #41 | — | 10 | 2 | no | — |
| 414 | #41 | — | 10 | 2 | no | — |
| 415 | #41 | — | 20 | 2 | no | — |
| 416 | #41 | — | 20 | 4 | no | — |
| 417 | #41 | — | 20 | 2 | no | — |
| 418 | #41 | — | 20 | 2 | no | — |
| 419 | #41 | — | 20 | 2 | no | — |
| 420 | #41 | D4×D5 | 1 | 4 | yes | — |
| 421 | C2×Q8 | — | 2 | 1 | no | — |
| 422 | C2×Q8 | — | 2 | 2 | no | — |
| 423 | C2×Q8 | — | 2 | 4 | no | — |
| 424 | C2×Q8 | — | 2 | 2 | no | — |
| 425 | C2×Q8 | — | 2 | 2 | no | — |
| 426 | C2×Q8 | — | 2 | 1 | no | — |
| 427 | C2×Q8 | — | 2 | 2 | no | — |
| 428 | C2×Q8 | — | 2 | 2 | no | — |
| 429 | C2×Q8 | — | 2 | 1 | no | — |
| 430 | C2×Q8 | — | 4 | 2 | no | — |
| 431 | C2×Q8 | — | 4 | 4 | no | — |
| 432 | C2×Q8 | — | 5 | 2 | no | — |
| 433 | C2×Q8 | — | 10 | 2 | no | — |
| 434 | C2×Q8 | — | 20 | 2 | no | — |
| 435 | C2×Q8 | D4×D5 | 1 | 1 | yes | characteristic |
| 436 | C2×Q8 | C2×C22⋊D5 | 1 | 2 | yes | — |
| 437 | C2×Q8 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 438 | C2×D4 | — | 2 | 1 | no | — |
| 439 | C2×D4 | — | 2 | 2 | no | — |
| 440 | C2×D4 | — | 5 | 2 | no | — |
| 441 | C2×D4 | — | 10 | 2 | no | — |
| 442 | C2×D4 | — | 10 | 2 | no | — |
| 443 | C2×D4 | — | 20 | 2 | no | — |
| 444 | C2×D4 | — | 20 | 4 | no | — |
| 445 | C2×D4 | — | 20 | 2 | no | — |
| 446 | C2×D4 | D4×D5 | 1 | 1 | yes | characteristic |
| 447 | C2×D4 | #711 | 1 | 2 | yes | — |
| 448 | C2×D4 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 449 | C22×C4 | — | 2 | 1 | no | — |
| 450 | C22×C4 | — | 2 | 1 | no | — |
| 451 | C22×C4 | — | 2 | 2 | no | — |
| 452 | C22×C4 | — | 2 | 2 | no | — |
| 453 | C22×C4 | — | 2 | 1 | no | — |
| 454 | C22×C4 | — | 10 | 2 | no | — |
| 455 | C22×C4 | — | 20 | 2 | no | — |
| 456 | C22×C4 | C2×C22⋊D5 | 1 | 2 | yes | — |
| 457 | C22×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 458 | Q16 | — | 4 | 4 | no | — |
| 459 | Q16 | — | 4 | 2 | no | — |
| 460 | Q16 | — | 10 | 8 | no | — |
| 461 | Q16 | — | 10 | 4 | no | — |
| 462 | Q16 | — | 20 | 4 | no | — |
| 463 | SD16 | — | 4 | 2 | no | — |
| 464 | SD16 | — | 10 | 8 | no | — |
| 465 | SD16 | — | 10 | 4 | no | — |
| 466 | SD16 | — | 10 | 4 | no | — |
| 467 | SD16 | — | 20 | 4 | no | — |
| 468 | D8 | — | 10 | 4 | no | — |
| 469 | M16 | — | 2 | 2 | no | — |
| 470 | M16 | — | 5 | 4 | no | — |
| 471 | M16 | — | 5 | 4 | no | — |
| 472 | M16 | — | 10 | 4 | no | — |
| 473 | M16 | — | 10 | 2 | no | — |
| 474 | M16 | — | 10 | 2 | no | — |
| 475 | M16 | — | 10 | 2 | no | — |
| 476 | M16 | — | 10 | 2 | no | — |
| 477 | M16 | — | 20 | 4 | no | — |
| 478 | C2×C8 | — | 2 | 2 | no | — |
| 479 | C2×C8 | — | 2 | 1 | no | — |
| 480 | C2×C8 | — | 2 | 1 | no | — |
| 481 | C2×C8 | — | 10 | 4 | no | — |
| 482 | C2×C8 | — | 10 | 2 | no | — |
| 483 | C2×C8 | — | 10 | 2 | no | — |
| 484 | C2×C8 | — | 10 | 2 | no | — |
| 485 | C2×C8 | — | 20 | 4 | no | — |
| 486 | C4⋊C4 | — | 2 | 1 | no | — |
| 487 | C4⋊C4 | — | 4 | 2 | no | — |
| 488 | C22⋊C4 | — | 2 | 1 | no | — |
| 489 | C22⋊C4 | — | 4 | 2 | no | — |
| 490 | C42 | — | 2 | 1 | no | — |
| 491 | C2×C5 | — | 2 | 1 | no | — |
| 492 | C2×C5 | — | 2 | 2 | no | — |
| 493 | C2×C5 | — | 4 | 2 | no | — |
| 494 | C2×C5 | — | 4 | 2 | no | — |
| 495 | C2×C5 | #2410 | 1 | 1 | yes | characteristic |
| 496 | D5 | — | 8 | 2 | no | — |
| 497 | C23 | — | 2 | 1 | no | — |
| 498 | C23 | — | 10 | 2 | no | — |
| 499 | C23 | — | 20 | 2 | no | — |
| 500 | C23 | #4085 | 1 | 2 | yes | — |
| 501 | C23 | C2×#711 | 1 | 1 | yes | characteristic |
| 502 | Q8 | — | 2 | 1 | no | — |
| 503 | Q8 | — | 2 | 2 | no | — |
| 504 | Q8 | — | 2 | 2 | no | — |
| 505 | Q8 | — | 2 | 2 | no | — |
| 506 | Q8 | — | 4 | 4 | no | — |
| 507 | Q8 | — | 4 | 2 | no | — |
| 508 | Q8 | — | 4 | 1 | no | — |
| 509 | Q8 | — | 4 | 1 | no | — |
| 510 | Q8 | — | 4 | 2 | no | — |
| 511 | Q8 | — | 10 | 2 | no | — |
| 512 | Q8 | — | 10 | 2 | no | — |
| 513 | Q8 | — | 20 | 2 | no | — |
| 514 | Q8 | #4083 | 1 | 2 | yes | — |
| 515 | D4 | — | 2 | 4 | no | — |
| 516 | D4 | — | 2 | 4 | no | — |
| 517 | D4 | — | 2 | 1 | no | — |
| 518 | D4 | — | 2 | 2 | no | — |
| 519 | D4 | — | 4 | 4 | no | — |
| 520 | D4 | — | 10 | 2 | no | — |
| 521 | D4 | — | 10 | 2 | no | — |
| 522 | D4 | — | 20 | 2 | no | — |
| 523 | D4 | — | 20 | 4 | no | — |
| 524 | D4 | — | 20 | 2 | no | — |
| 525 | D4 | — | 20 | 2 | no | — |
| 526 | D4 | #4083 | 1 | 2 | yes | — |
| 527 | C2×C4 | — | 2 | 1 | no | — |
| 528 | C2×C4 | — | 2 | 2 | no | — |
| 529 | C2×C4 | — | 2 | 2 | no | — |
| 530 | C2×C4 | — | 2 | 4 | no | — |
| 531 | C2×C4 | — | 2 | 2 | no | — |
| 532 | C2×C4 | — | 4 | 4 | no | — |
| 533 | C2×C4 | — | 4 | 4 | no | — |
| 534 | C2×C4 | — | 4 | 2 | no | — |
| 535 | C2×C4 | — | 4 | 1 | no | — |
| 536 | C2×C4 | — | 4 | 1 | no | — |
| 537 | C2×C4 | — | 4 | 2 | no | — |
| 538 | C2×C4 | — | 10 | 2 | no | — |
| 539 | C2×C4 | — | 20 | 4 | no | — |
| 540 | C2×C4 | — | 20 | 2 | no | — |
| 541 | C2×C4 | — | 20 | 2 | no | — |
| 542 | C2×C4 | — | 20 | 2 | no | — |
| 543 | C2×C4 | #4085 | 1 | 2 | yes | — |
| 544 | C2×C4 | C2×D4×D5 | 1 | 2 | yes | — |
| 545 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 546 | C2×C4 | #4144 | 1 | 2 | yes | — |
| 547 | C2×C4 | C22×C22⋊D5 | 1 | 1 | yes | characteristic |
| 548 | C8 | — | 4 | 1 | no | — |
| 549 | C8 | — | 4 | 1 | no | — |
| 550 | C8 | — | 10 | 4 | no | — |
| 551 | C8 | — | 10 | 4 | no | — |
| 552 | C8 | — | 20 | 2 | no | — |
| 553 | C5 | #24423 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 554 | C22 | — | 2 | 2 | no | — |
| 555 | C22 | — | 2 | 2 | no | — |
| 556 | C22 | — | 4 | 1 | no | — |
| 557 | C22 | — | 4 | 2 | no | — |
| 558 | C22 | — | 8 | 1 | no | — |
| 559 | C22 | — | 20 | 2 | no | — |
| 560 | C22 | — | 40 | 2 | no | — |
| 561 | C22 | — | 80 | 2 | no | — |
| 562 | C22 | #65925 | 1 | 2 | yes | — |
| 563 | C22 | C2×#4085 | 1 | 1 | yes | characteristic |
| 564 | C4 | — | 2 | 2 | no | — |
| 565 | C4 | — | 2 | 2 | no | — |
| 566 | C4 | — | 4 | 2 | no | — |
| 567 | C4 | — | 8 | 1 | no | — |
| 568 | C4 | — | 8 | 1 | no | — |
| 569 | C4 | — | 20 | 2 | no | — |
| 570 | C4 | #65924 | 1 | 2 | yes | — |
| 571 | C4 | C2×#4083 | 1 | 1 | yes | characteristic |
| 572 | C4 | #66138 | 1 | 1 | yes | characteristic |
| 573 | C2 | — | 2 | 1 | no | — |
| 574 | C2 | — | 2 | 2 | no | — |
| 575 | C2 | — | 4 | 2 | no | — |
| 576 | C2 | — | 4 | 2 | no | — |
| 577 | C2 | — | 40 | 2 | no | — |
| 578 | C2 | #10614337 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#3011 | C2 | semidirect |
| 3. #10615843 | C2 | semidirect |
| 4. #10615709 | C2 | semidirect |
| 5. #10615147 | C2 | semidirect |
| 6. #10602867 | C2 | semidirect |
| 7. #10602659 | C2 | semidirect |
| 8. #10601145 | C2 | semidirect |
| 9. #10601086 | C2 | semidirect |
| 10. #10600802 | C2 | semidirect |
| 11. #10600794 | C2 | semidirect |
| 14. C2×C5×#137 | C22 | semidirect |
| 15. C22×C5×Q16 | C22 | semidirect |
| 22. #66153 | C22 | semidirect |
| 28. C5×#419 | C22 | semidirect |
| 29. C5×#416 | C22 | semidirect |
| 35. C2×#3968 | C22 | semidirect |
| 36. C2×#3968 | C22 | semidirect |
| 40. #65413 | C22 | semidirect |
| 45. #64772 | C22 | semidirect |
| 46. #64753 | C22 | semidirect |
| 124. #3011 | D5 | semidirect |
| 229. C2×#137 | C2×D5 | semidirect |
| 230. C22×Q16 | C2×D5 | semidirect |
| 242. #419 | C2×D5 | semidirect |
| 243. #416 | C2×D5 | semidirect |
| 553. C5 | #24423 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10619188 | 2 |
| C5×#3011 | 2 |
| #10615843 | 2 |
| #10615709 | 2 |
| #10615147 | 2 |
| #10602867 | 2 |
| #10602659 | 2 |
| #10601145 | 2 |
| #10601086 | 2 |
| #10600802 | 2 |
| #10600794 | 2 |
| #24423 | 5 |