Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1334 conjugacy classes of subgroups.
The subgroup lattice has 662 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#66103 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10615659 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10610914 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10610724 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10610310 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C5×#1976 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10601458 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10601195 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10600843 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #10600841 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #10600696 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#4149 | C22 | 1 | 2 | yes | — |
| 13 | C2×C5×#135 | C22 | 1 | 1 | yes | characteristic |
| 14 | #66156 | C22 | 1 | 2 | yes | complemented |
| 15 | C2×#4095 | C22 | 1 | 2 | yes | — |
| 16 | #66103 | — | 2 | 2 | no | — |
| 17 | #66103 | — | 2 | 2 | no | — |
| 18 | #66103 | — | 2 | 2 | no | — |
| 19 | #66103 | — | 2 | 2 | no | — |
| 20 | C2×#4065 | — | 2 | 1 | no | — |
| 21 | C2×#4060 | — | 2 | 2 | no | — |
| 22 | C2×D5×D8 | — | 2 | 1 | no | — |
| 23 | #66082 | C22 | 1 | 1 | yes | characteristic |
| 24 | C22×D40 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#4047 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×#4047 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | #65859 | C22 | 1 | 2 | yes | complemented |
| 28 | C5×#427 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | C5×#421 | C22 | 1 | 2 | yes | complemented |
| 30 | C5×#410 | C22 | 1 | 2 | yes | complemented |
| 31 | C5×#405 | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | #65526 | C22 | 1 | 2 | yes | complemented |
| 33 | #65481 | — | 2 | 1 | no | — |
| 34 | #65466 | — | 2 | 2 | no | — |
| 35 | #65449 | — | 2 | 1 | no | — |
| 36 | C2×#3955 | C22 | 1 | 2 | yes | complemented |
| 37 | #65414 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | C2×#3951 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | #65294 | C22 | 1 | 2 | yes | — |
| 40 | #65294 | C22 | 1 | 1 | yes | characteristic |
| 41 | #65294 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | #65290 | C22 | 1 | 2 | yes | complemented |
| 43 | #65290 | C22 | 1 | 2 | yes | complemented |
| 44 | #65172 | — | 2 | 2 | no | — |
| 45 | #65154 | — | 2 | 2 | no | — |
| 46 | #65114 | — | 2 | 4 | no | — |
| 47 | #65111 | — | 2 | 4 | no | — |
| 48 | #65006 | — | 2 | 2 | no | — |
| 49 | #64989 | — | 2 | 2 | no | — |
| 50 | #64753 | C22 | 1 | 2 | yes | complemented |
| 51 | #24297 | — | 5 | 1 | no | maximal, Sylow |
| 52 | C2×C5×#41 | C23 | 1 | 2 | yes | — |
| 53 | #4149 | — | 2 | 4 | no | — |
| 54 | #4149 | — | 2 | 4 | no | — |
| 55 | #4149 | — | 2 | 4 | no | — |
| 56 | #4149 | — | 4 | 2 | no | — |
| 57 | C2×#713 | — | 2 | 2 | no | — |
| 58 | C2×D4×D5 | — | 2 | 2 | no | — |
| 59 | C2×D4×D5 | — | 4 | 2 | no | — |
| 60 | C2×#709 | — | 2 | 2 | no | — |
| 61 | C2×#709 | C23 | 1 | 1 | yes | characteristic |
| 62 | C2×#709 | C23 | 1 | 1 | yes | characteristic |
| 63 | C22×D20 | — | 2 | 2 | no | — |
| 64 | C22×D20 | C23 | 1 | 2 | yes | — |
| 65 | C5×#135 | — | 2 | 1 | no | — |
| 66 | C5×#135 | — | 2 | 1 | no | — |
| 67 | C5×#135 | — | 2 | 1 | no | — |
| 68 | C5×#135 | — | 2 | 1 | no | — |
| 69 | C2×C5×Q16 | D4 | 1 | 1 | yes | characteristic, complemented |
| 70 | C2×C5×SD16 | D4 | 1 | 2 | yes | complemented |
| 71 | C2×C5×D8 | D4 | 1 | 1 | yes | characteristic, complemented |
| 72 | C2×C5×M16 | C23 | 1 | 1 | yes | characteristic |
| 73 | C22×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 74 | C5×#117 | C23 | 1 | 1 | yes | characteristic |
| 75 | C5×#117 | C23 | 1 | 2 | yes | — |
| 76 | #4097 | — | 2 | 2 | no | — |
| 77 | #4096 | — | 4 | 2 | no | — |
| 78 | #4095 | — | 2 | 4 | no | — |
| 79 | #4095 | — | 2 | 2 | no | — |
| 80 | #4095 | — | 2 | 4 | no | — |
| 81 | #4088 | — | 2 | 2 | no | — |
| 82 | C2×#688 | — | 2 | 2 | no | — |
| 83 | #4078 | — | 2 | 2 | no | — |
| 84 | C2×#686 | — | 2 | 2 | no | — |
| 85 | C2×#681 | C23 | 1 | 1 | yes | characteristic |
| 86 | C2×#681 | C23 | 1 | 2 | yes | — |
| 87 | C2×#681 | C23 | 1 | 1 | yes | characteristic |
| 88 | #4065 | — | 2 | 4 | no | — |
| 89 | #4065 | — | 2 | 4 | no | — |
| 90 | #4060 | — | 2 | 8 | no | — |
| 91 | #4060 | — | 2 | 8 | no | — |
| 92 | D5×D8 | — | 2 | 4 | no | — |
| 93 | D5×D8 | — | 2 | 4 | no | — |
| 94 | #4055 | — | 2 | 1 | no | — |
| 95 | #4055 | D4 | 1 | 2 | yes | — |
| 96 | #4054 | — | 2 | 1 | no | — |
| 97 | #4054 | D4 | 1 | 2 | yes | — |
| 98 | #4050 | — | 2 | 2 | no | — |
| 99 | C2×D40 | — | 2 | 1 | no | — |
| 100 | C2×D40 | — | 2 | 1 | no | — |
| 101 | C2×D40 | — | 2 | 1 | no | — |
| 102 | C2×D40 | — | 2 | 1 | no | — |
| 103 | C2×D40 | D4 | 1 | 2 | yes | — |
| 104 | C2×D40 | D4 | 1 | 2 | yes | — |
| 105 | #4047 | — | 2 | 1 | no | — |
| 106 | #4047 | — | 2 | 1 | no | — |
| 107 | #4047 | — | 2 | 1 | no | — |
| 108 | #4047 | — | 2 | 1 | no | — |
| 109 | #4047 | — | 2 | 1 | no | — |
| 110 | #4047 | — | 2 | 1 | no | — |
| 111 | #4047 | D4 | 1 | 2 | yes | complemented |
| 112 | #4047 | D4 | 1 | 2 | yes | complemented |
| 113 | C2×#676 | — | 2 | 1 | no | — |
| 114 | C2×#676 | — | 2 | 1 | no | — |
| 115 | C2×C8×D5 | — | 2 | 1 | no | — |
| 116 | C2×C8×D5 | — | 2 | 1 | no | — |
| 117 | #4041 | — | 2 | 4 | no | — |
| 118 | #4028 | — | 4 | 2 | no | — |
| 119 | #4021 | — | 2 | 2 | no | — |
| 120 | #4020 | — | 2 | 2 | no | — |
| 121 | C5×#107 | — | 2 | 1 | no | — |
| 122 | C5×#106 | — | 2 | 1 | no | — |
| 123 | C5×#104 | — | 2 | 4 | no | — |
| 124 | C5×#99 | — | 4 | 2 | no | — |
| 125 | C5×#97 | — | 2 | 1 | no | — |
| 126 | C4×C5×C8 | — | 2 | 1 | no | — |
| 127 | #3968 | — | 2 | 2 | no | — |
| 128 | #3965 | — | 2 | 2 | no | — |
| 129 | #3955 | — | 2 | 4 | no | — |
| 130 | #3951 | — | 2 | 1 | no | — |
| 131 | #3951 | — | 2 | 1 | no | — |
| 132 | #3951 | — | 2 | 2 | no | — |
| 133 | #3941 | — | 2 | 4 | no | — |
| 134 | #3941 | — | 4 | 2 | no | — |
| 135 | #3937 | — | 2 | 4 | no | — |
| 136 | #3937 | — | 2 | 2 | no | — |
| 137 | #3937 | — | 2 | 2 | no | — |
| 138 | C2×#576 | — | 5 | 1 | no | — |
| 139 | #3067 | — | 5 | 1 | no | — |
| 140 | #3058 | — | 5 | 1 | no | — |
| 141 | #3019 | — | 5 | 2 | no | — |
| 142 | #2955 | — | 5 | 1 | no | — |
| 143 | #2048 | — | 5 | 2 | no | — |
| 144 | #2008 | — | 5 | 2 | no | — |
| 145 | #1978 | — | 5 | 1 | no | — |
| 146 | #1976 | D5 | 1 | 1 | yes | characteristic, complemented |
| 147 | #1814 | — | 5 | 1 | no | — |
| 148 | #1795 | — | 5 | 2 | no | — |
| 149 | C23×D5 | — | 2 | 2 | no | — |
| 150 | C23×D5 | — | 4 | 2 | no | — |
| 151 | C5×#41 | — | 2 | 2 | no | — |
| 152 | C5×#41 | — | 2 | 2 | no | — |
| 153 | C5×#41 | — | 2 | 2 | no | — |
| 154 | C5×#41 | — | 2 | 2 | no | — |
| 155 | C2×C5×Q8 | C2×D4 | 1 | 2 | yes | — |
| 156 | C2×C5×D4 | — | 2 | 2 | no | — |
| 157 | C2×C5×D4 | C2×D4 | 1 | 2 | yes | — |
| 158 | C22×C4×C5 | — | 2 | 2 | no | — |
| 159 | C22×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 160 | C2×C22⋊D5 | — | 2 | 1 | no | — |
| 161 | C2×C22⋊D5 | — | 2 | 1 | no | — |
| 162 | C2×C22⋊D5 | — | 4 | 2 | no | — |
| 163 | #713 | — | 2 | 8 | no | — |
| 164 | #713 | — | 4 | 4 | no | — |
| 165 | D4×D5 | — | 2 | 8 | no | — |
| 166 | D4×D5 | — | 4 | 4 | no | — |
| 167 | D4×D5 | — | 4 | 8 | no | — |
| 168 | D4×D5 | — | 4 | 8 | no | — |
| 169 | #709 | — | 2 | 1 | no | — |
| 170 | #709 | — | 2 | 1 | no | — |
| 171 | #709 | — | 2 | 1 | no | — |
| 172 | #709 | — | 2 | 1 | no | — |
| 173 | #709 | — | 2 | 1 | no | — |
| 174 | #709 | — | 2 | 1 | no | — |
| 175 | #709 | — | 4 | 4 | no | — |
| 176 | #709 | — | 4 | 4 | no | — |
| 177 | #709 | C2×D4 | 1 | 2 | yes | — |
| 178 | #709 | C2×D4 | 1 | 2 | yes | — |
| 179 | C2×D20 | — | 2 | 2 | no | — |
| 180 | C2×D20 | — | 2 | 2 | no | — |
| 181 | C2×D20 | — | 2 | 2 | no | — |
| 182 | C2×D20 | — | 2 | 2 | no | — |
| 183 | C2×D20 | — | 2 | 2 | no | — |
| 184 | C2×D20 | — | 4 | 4 | no | — |
| 185 | C2×D20 | — | 4 | 2 | no | — |
| 186 | C2×D20 | — | 4 | 4 | no | — |
| 187 | C2×D20 | — | 4 | 4 | no | — |
| 188 | C2×D20 | C2×D4 | 1 | 4 | yes | — |
| 189 | C2×D20 | C2×D4 | 1 | 1 | yes | characteristic |
| 190 | C2×D20 | #41 | 1 | 1 | yes | characteristic |
| 191 | C2×C4×D5 | — | 2 | 1 | no | — |
| 192 | C2×C4×D5 | — | 2 | 1 | no | — |
| 193 | C2×C4×D5 | — | 4 | 2 | no | — |
| 194 | C2×Dic10 | C2×D4 | 1 | 1 | yes | characteristic |
| 195 | C2×Dic10 | #41 | 1 | 1 | yes | characteristic |
| 196 | C5×Q16 | — | 2 | 1 | no | — |
| 197 | C5×Q16 | — | 2 | 1 | no | — |
| 198 | C5×SD16 | — | 2 | 2 | no | — |
| 199 | C5×SD16 | — | 2 | 2 | no | — |
| 200 | C5×D8 | — | 2 | 1 | no | — |
| 201 | C5×D8 | — | 2 | 1 | no | — |
| 202 | C5×M16 | — | 2 | 1 | no | — |
| 203 | C5×M16 | C2×D4 | 1 | 2 | yes | — |
| 204 | C2×C5×C8 | — | 2 | 1 | no | — |
| 205 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 206 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 207 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 208 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 209 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 210 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 211 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 212 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 213 | C5×C22⋊C4 | — | 2 | 1 | no | — |
| 214 | C5×C22⋊C4 | — | 2 | 2 | no | — |
| 215 | C42×C5 | — | 2 | 1 | no | — |
| 216 | C42×C5 | — | 2 | 2 | no | — |
| 217 | #689 | — | 4 | 2 | no | — |
| 218 | #688 | — | 2 | 8 | no | — |
| 219 | #688 | — | 4 | 2 | no | — |
| 220 | #687 | — | 4 | 2 | no | — |
| 221 | #686 | — | 2 | 8 | no | — |
| 222 | #686 | — | 4 | 2 | no | — |
| 223 | #685 | — | 4 | 4 | no | — |
| 224 | #681 | — | 2 | 1 | no | — |
| 225 | #681 | — | 2 | 2 | no | — |
| 226 | #681 | — | 2 | 1 | no | — |
| 227 | #681 | — | 2 | 2 | no | — |
| 228 | #681 | — | 2 | 1 | no | — |
| 229 | #681 | C2×D4 | 1 | 2 | yes | — |
| 230 | C2×#168 | — | 2 | 1 | no | — |
| 231 | C2×#168 | — | 2 | 1 | no | — |
| 232 | C2×#168 | — | 2 | 2 | no | — |
| 233 | Dic20 | — | 2 | 2 | no | — |
| 234 | D40 | — | 2 | 2 | no | — |
| 235 | D40 | — | 2 | 2 | no | — |
| 236 | D40 | — | 2 | 2 | no | — |
| 237 | D40 | — | 2 | 2 | no | — |
| 238 | D40 | — | 2 | 2 | no | — |
| 239 | #677 | — | 2 | 2 | no | — |
| 240 | #677 | — | 2 | 2 | no | — |
| 241 | #676 | — | 2 | 2 | no | — |
| 242 | #676 | — | 2 | 2 | no | — |
| 243 | #676 | — | 4 | 1 | no | — |
| 244 | #676 | — | 4 | 1 | no | — |
| 245 | C8×D5 | — | 2 | 2 | no | — |
| 246 | C8×D5 | — | 2 | 2 | no | — |
| 247 | C8×D5 | — | 4 | 1 | no | — |
| 248 | C8×D5 | — | 4 | 1 | no | — |
| 249 | C2×H(5,𝔽2) | — | 5 | 2 | no | — |
| 250 | #576 | — | 10 | 2 | no | — |
| 251 | #576 | — | 10 | 2 | no | — |
| 252 | #576 | — | 10 | 2 | no | — |
| 253 | #576 | — | 10 | 2 | no | — |
| 254 | #575 | — | 5 | 2 | no | — |
| 255 | #575 | — | 5 | 1 | no | — |
| 256 | C2×AGL(1,ℤ/8) | — | 5 | 2 | no | — |
| 257 | C2×AGL(1,ℤ/8) | — | 10 | 2 | no | — |
| 258 | C2×#135 | — | 10 | 1 | no | — |
| 259 | C2×#135 | C2×D5 | 1 | 1 | yes | characteristic |
| 260 | C22×D8 | — | 5 | 1 | no | — |
| 261 | C22×D8 | — | 10 | 1 | no | — |
| 262 | C2×#131 | — | 5 | 1 | no | — |
| 263 | C2×#131 | — | 5 | 1 | no | — |
| 264 | #535 | — | 5 | 2 | no | — |
| 265 | #473 | — | 10 | 1 | no | — |
| 266 | #472 | — | 10 | 1 | no | — |
| 267 | #471 | — | 10 | 2 | no | — |
| 268 | #469 | — | 10 | 2 | no | — |
| 269 | #466 | — | 10 | 2 | no | — |
| 270 | #455 | — | 10 | 4 | no | — |
| 271 | #453 | — | 10 | 4 | no | — |
| 272 | #444 | — | 10 | 2 | no | — |
| 273 | #443 | — | 10 | 2 | no | — |
| 274 | #430 | — | 5 | 1 | no | — |
| 275 | C2×#108 | — | 5 | 1 | no | — |
| 276 | #427 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 277 | #421 | — | 5 | 1 | no | — |
| 278 | #421 | — | 5 | 2 | no | — |
| 279 | #421 | — | 5 | 1 | no | — |
| 280 | #421 | C2×D5 | 1 | 2 | yes | complemented |
| 281 | #418 | — | 5 | 2 | no | — |
| 282 | #418 | — | 5 | 2 | no | — |
| 283 | #413 | — | 5 | 2 | no | — |
| 284 | C2×#100 | — | 5 | 2 | no | — |
| 285 | #410 | C2×D5 | 1 | 2 | yes | complemented |
| 286 | #405 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 287 | #344 | — | 5 | 2 | no | — |
| 288 | C23×C5 | — | 2 | 2 | no | — |
| 289 | C23×C5 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 290 | C22×D5 | — | 2 | 1 | no | — |
| 291 | C22×D5 | — | 2 | 1 | no | — |
| 292 | C22×D5 | — | 2 | 4 | no | — |
| 293 | C22×D5 | — | 4 | 8 | no | — |
| 294 | C22×D5 | — | 4 | 2 | no | — |
| 295 | C22×D5 | — | 4 | 2 | no | — |
| 296 | C22×D5 | — | 16 | 4 | no | — |
| 297 | C22×D5 | — | 16 | 2 | no | — |
| 298 | C5×Q8 | — | 2 | 2 | no | — |
| 299 | C5×Q8 | — | 2 | 2 | no | — |
| 300 | C5×D4 | — | 2 | 2 | no | — |
| 301 | C5×D4 | — | 2 | 2 | no | — |
| 302 | C5×D4 | — | 4 | 2 | no | — |
| 303 | C5×D4 | — | 4 | 2 | no | — |
| 304 | C2×C4×C5 | — | 2 | 2 | no | — |
| 305 | C2×C4×C5 | — | 4 | 2 | no | — |
| 306 | C2×C4×C5 | — | 4 | 2 | no | — |
| 307 | C2×C4×C5 | — | 4 | 1 | no | — |
| 308 | C2×C4×C5 | — | 4 | 2 | no | — |
| 309 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 310 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 311 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 312 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 313 | C2×C4×C5 | C2×#41 | 1 | 1 | yes | characteristic |
| 314 | C2×C4×C5 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 315 | C22⋊D5 | — | 2 | 2 | no | — |
| 316 | C22⋊D5 | — | 2 | 2 | no | — |
| 317 | C22⋊D5 | — | 4 | 8 | no | — |
| 318 | C22⋊D5 | — | 4 | 1 | no | — |
| 319 | C22⋊D5 | — | 4 | 1 | no | — |
| 320 | C2×Dic5 | — | 2 | 1 | no | — |
| 321 | C2×Dic5 | — | 2 | 1 | no | — |
| 322 | D20 | — | 2 | 4 | no | — |
| 323 | D20 | — | 2 | 1 | no | — |
| 324 | D20 | — | 2 | 1 | no | — |
| 325 | D20 | — | 2 | 1 | no | — |
| 326 | D20 | — | 2 | 4 | no | — |
| 327 | D20 | — | 4 | 8 | no | — |
| 328 | D20 | — | 4 | 2 | no | — |
| 329 | D20 | — | 4 | 2 | no | — |
| 330 | D20 | — | 16 | 4 | no | — |
| 331 | D20 | #121 | 1 | 2 | yes | — |
| 332 | C4×D5 | — | 2 | 2 | no | — |
| 333 | C4×D5 | — | 2 | 2 | no | — |
| 334 | C4×D5 | — | 4 | 8 | no | — |
| 335 | C4×D5 | — | 4 | 1 | no | — |
| 336 | C4×D5 | — | 4 | 1 | no | — |
| 337 | Dic10 | — | 2 | 1 | no | — |
| 338 | Dic10 | — | 2 | 1 | no | — |
| 339 | Dic10 | — | 2 | 1 | no | — |
| 340 | Dic10 | #121 | 1 | 2 | yes | — |
| 341 | C5×C8 | — | 2 | 2 | no | — |
| 342 | C5×C8 | #120 | 1 | 1 | yes | characteristic |
| 343 | C5×C8 | #120 | 1 | 1 | yes | characteristic |
| 344 | C5×C8 | #120 | 1 | 1 | yes | characteristic |
| 345 | C5×C8 | #120 | 1 | 1 | yes | characteristic |
| 346 | #168 | — | 2 | 2 | no | — |
| 347 | #168 | — | 4 | 1 | no | — |
| 348 | #168 | — | 4 | 2 | no | — |
| 349 | H(5,𝔽2) | — | 10 | 4 | no | — |
| 350 | H(5,𝔽2) | — | 10 | 4 | no | — |
| 351 | H(5,𝔽2) | — | 10 | 4 | no | — |
| 352 | H(5,𝔽2) | — | 20 | 2 | no | — |
| 353 | C2×#41 | — | 5 | 1 | no | — |
| 354 | C2×#41 | — | 5 | 1 | no | — |
| 355 | C2×#41 | — | 10 | 2 | no | — |
| 356 | C2×#41 | — | 10 | 2 | no | — |
| 357 | C2×#41 | C22×D5 | 1 | 2 | yes | — |
| 358 | C22×D4 | — | 5 | 2 | no | — |
| 359 | C22×D4 | — | 10 | 2 | no | — |
| 360 | C22×D4 | — | 10 | 2 | no | — |
| 361 | C22×D4 | — | 20 | 2 | no | — |
| 362 | #137 | — | 5 | 2 | no | — |
| 363 | #137 | — | 10 | 1 | no | — |
| 364 | #137 | — | 10 | 2 | no | — |
| 365 | #137 | — | 10 | 2 | no | — |
| 366 | AGL(1,ℤ/8) | — | 5 | 2 | no | — |
| 367 | AGL(1,ℤ/8) | — | 10 | 1 | no | — |
| 368 | AGL(1,ℤ/8) | — | 10 | 4 | no | — |
| 369 | AGL(1,ℤ/8) | — | 10 | 8 | no | — |
| 370 | AGL(1,ℤ/8) | — | 10 | 8 | no | — |
| 371 | AGL(1,ℤ/8) | — | 10 | 4 | no | — |
| 372 | AGL(1,ℤ/8) | — | 10 | 2 | no | — |
| 373 | AGL(1,ℤ/8) | — | 10 | 2 | no | — |
| 374 | #135 | — | 2 | 1 | no | — |
| 375 | #135 | — | 2 | 1 | no | — |
| 376 | #135 | — | 2 | 1 | no | — |
| 377 | #135 | — | 2 | 1 | no | — |
| 378 | #135 | — | 10 | 2 | no | — |
| 379 | #135 | — | 10 | 4 | no | — |
| 380 | #135 | — | 10 | 4 | no | — |
| 381 | #135 | — | 20 | 2 | no | — |
| 382 | C2×Q16 | D20 | 1 | 1 | yes | characteristic, complemented |
| 383 | C2×SD16 | — | 10 | 2 | no | — |
| 384 | C2×SD16 | D20 | 1 | 2 | yes | complemented |
| 385 | C2×D8 | — | 5 | 2 | no | — |
| 386 | C2×D8 | — | 5 | 2 | no | — |
| 387 | C2×D8 | — | 10 | 4 | no | — |
| 388 | C2×D8 | — | 10 | 4 | no | — |
| 389 | C2×D8 | — | 10 | 2 | no | — |
| 390 | C2×D8 | — | 10 | 1 | no | — |
| 391 | C2×D8 | — | 10 | 1 | no | — |
| 392 | C2×D8 | — | 10 | 1 | no | — |
| 393 | C2×D8 | — | 10 | 1 | no | — |
| 394 | C2×D8 | D20 | 1 | 1 | yes | characteristic, complemented |
| 395 | #131 | — | 5 | 2 | no | — |
| 396 | #131 | — | 5 | 2 | no | — |
| 397 | #131 | — | 10 | 1 | no | — |
| 398 | #131 | — | 10 | 1 | no | — |
| 399 | #131 | — | 10 | 1 | no | — |
| 400 | #131 | — | 10 | 1 | no | — |
| 401 | #131 | — | 10 | 1 | no | — |
| 402 | #131 | — | 10 | 1 | no | — |
| 403 | C2×M16 | — | 5 | 1 | no | — |
| 404 | C2×M16 | — | 5 | 1 | no | — |
| 405 | C2×M16 | — | 5 | 2 | no | — |
| 406 | C2×M16 | — | 10 | 1 | no | — |
| 407 | C2×M16 | — | 10 | 1 | no | — |
| 408 | C2×M16 | C22×D5 | 1 | 1 | yes | characteristic |
| 409 | C22×C8 | — | 10 | 1 | no | — |
| 410 | C22×C8 | — | 10 | 1 | no | — |
| 411 | C22×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 412 | #127 | — | 10 | 2 | no | — |
| 413 | #124 | — | 10 | 2 | no | — |
| 414 | #121 | — | 10 | 4 | no | — |
| 415 | #120 | — | 20 | 2 | no | — |
| 416 | #117 | C22×D5 | 1 | 2 | yes | — |
| 417 | #117 | C22×D5 | 1 | 1 | yes | characteristic |
| 418 | #108 | — | 10 | 2 | no | — |
| 419 | #108 | — | 10 | 1 | no | — |
| 420 | #108 | — | 10 | 1 | no | — |
| 421 | #107 | — | 2 | 1 | no | — |
| 422 | #106 | — | 2 | 1 | no | — |
| 423 | #104 | — | 2 | 4 | no | — |
| 424 | #104 | — | 10 | 2 | no | — |
| 425 | #104 | — | 10 | 2 | no | — |
| 426 | #104 | — | 10 | 4 | no | — |
| 427 | #102 | — | 10 | 4 | no | — |
| 428 | #102 | — | 20 | 2 | no | — |
| 429 | #101 | — | 10 | 2 | no | — |
| 430 | #100 | — | 10 | 2 | no | — |
| 431 | #100 | — | 10 | 4 | no | — |
| 432 | #99 | — | 4 | 2 | no | — |
| 433 | #97 | — | 2 | 1 | no | — |
| 434 | C4×C8 | — | 2 | 1 | no | — |
| 435 | C22×C5 | — | 4 | 1 | no | — |
| 436 | C22×C5 | — | 4 | 2 | no | — |
| 437 | C22×C5 | — | 8 | 2 | no | — |
| 438 | C22×C5 | #535 | 1 | 1 | yes | characteristic |
| 439 | C22×C5 | D42 | 1 | 1 | yes | characteristic |
| 440 | C22×C5 | #546 | 1 | 1 | yes | characteristic |
| 441 | C2×D5 | — | 2 | 2 | no | — |
| 442 | C2×D5 | — | 4 | 2 | no | — |
| 443 | C2×D5 | — | 4 | 2 | no | — |
| 444 | C2×D5 | — | 4 | 4 | no | — |
| 445 | C2×D5 | — | 4 | 1 | no | — |
| 446 | C2×D5 | — | 8 | 4 | no | — |
| 447 | C2×D5 | — | 8 | 4 | no | — |
| 448 | C2×D5 | — | 16 | 8 | no | — |
| 449 | C2×D5 | — | 16 | 2 | no | — |
| 450 | C4×C5 | — | 4 | 2 | no | — |
| 451 | C4×C5 | — | 8 | 2 | no | — |
| 452 | C4×C5 | — | 8 | 1 | no | — |
| 453 | C4×C5 | C2×#120 | 1 | 1 | yes | characteristic |
| 454 | C4×C5 | C2×#121 | 1 | 1 | yes | characteristic |
| 455 | C4×C5 | D42 | 1 | 1 | yes | characteristic |
| 456 | C4×C5 | #546 | 1 | 1 | yes | characteristic |
| 457 | Dic5 | — | 2 | 2 | no | — |
| 458 | Dic5 | — | 4 | 1 | no | — |
| 459 | C24 | — | 10 | 2 | no | — |
| 460 | C24 | — | 20 | 2 | no | — |
| 461 | #41 | — | 2 | 2 | no | — |
| 462 | #41 | — | 2 | 2 | no | — |
| 463 | #41 | — | 2 | 2 | no | — |
| 464 | #41 | — | 2 | 2 | no | — |
| 465 | #41 | — | 5 | 2 | no | — |
| 466 | #41 | — | 5 | 2 | no | — |
| 467 | #41 | — | 10 | 1 | no | — |
| 468 | #41 | — | 10 | 1 | no | — |
| 469 | #41 | — | 10 | 8 | no | — |
| 470 | #41 | — | 10 | 1 | no | — |
| 471 | #41 | — | 10 | 1 | no | — |
| 472 | #41 | — | 10 | 1 | no | — |
| 473 | #41 | — | 10 | 1 | no | — |
| 474 | #41 | — | 20 | 4 | no | — |
| 475 | #41 | — | 20 | 4 | no | — |
| 476 | #41 | — | 20 | 4 | no | — |
| 477 | C2×Q8 | — | 5 | 1 | no | — |
| 478 | C2×Q8 | — | 5 | 1 | no | — |
| 479 | C2×Q8 | C2×D20 | 1 | 2 | yes | — |
| 480 | C2×D4 | — | 2 | 2 | no | — |
| 481 | C2×D4 | — | 5 | 4 | no | — |
| 482 | C2×D4 | — | 5 | 1 | no | — |
| 483 | C2×D4 | — | 5 | 1 | no | — |
| 484 | C2×D4 | — | 10 | 8 | no | — |
| 485 | C2×D4 | — | 10 | 1 | no | — |
| 486 | C2×D4 | — | 10 | 1 | no | — |
| 487 | C2×D4 | — | 10 | 2 | no | — |
| 488 | C2×D4 | — | 10 | 2 | no | — |
| 489 | C2×D4 | — | 10 | 2 | no | — |
| 490 | C2×D4 | — | 10 | 2 | no | — |
| 491 | C2×D4 | — | 10 | 2 | no | — |
| 492 | C2×D4 | — | 20 | 2 | no | — |
| 493 | C2×D4 | — | 20 | 4 | no | — |
| 494 | C2×D4 | — | 20 | 4 | no | — |
| 495 | C2×D4 | — | 20 | 4 | no | — |
| 496 | C2×D4 | — | 20 | 4 | no | — |
| 497 | C2×D4 | — | 20 | 2 | no | — |
| 498 | C2×D4 | — | 20 | 8 | no | — |
| 499 | C2×D4 | — | 20 | 8 | no | — |
| 500 | C2×D4 | C2×D20 | 1 | 2 | yes | — |
| 501 | C22×C4 | — | 2 | 2 | no | — |
| 502 | C22×C4 | — | 10 | 1 | no | — |
| 503 | C22×C4 | — | 10 | 1 | no | — |
| 504 | C22×C4 | — | 20 | 2 | no | — |
| 505 | C22×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 506 | Q16 | — | 2 | 1 | no | — |
| 507 | Q16 | — | 2 | 1 | no | — |
| 508 | Q16 | — | 10 | 2 | no | — |
| 509 | Q16 | — | 20 | 2 | no | — |
| 510 | SD16 | — | 2 | 2 | no | — |
| 511 | SD16 | — | 2 | 2 | no | — |
| 512 | SD16 | — | 10 | 2 | no | — |
| 513 | SD16 | — | 10 | 2 | no | — |
| 514 | SD16 | — | 10 | 8 | no | — |
| 515 | SD16 | — | 20 | 2 | no | — |
| 516 | SD16 | — | 20 | 2 | no | — |
| 517 | D8 | — | 2 | 1 | no | — |
| 518 | D8 | — | 2 | 1 | no | — |
| 519 | D8 | — | 10 | 2 | no | — |
| 520 | D8 | — | 10 | 8 | no | — |
| 521 | D8 | — | 10 | 2 | no | — |
| 522 | D8 | — | 10 | 2 | no | — |
| 523 | D8 | — | 10 | 2 | no | — |
| 524 | D8 | — | 10 | 2 | no | — |
| 525 | D8 | — | 20 | 2 | no | — |
| 526 | M16 | — | 2 | 1 | no | — |
| 527 | M16 | — | 5 | 2 | no | — |
| 528 | M16 | — | 10 | 1 | no | — |
| 529 | M16 | — | 10 | 2 | no | — |
| 530 | M16 | — | 10 | 2 | no | — |
| 531 | M16 | — | 10 | 1 | no | — |
| 532 | M16 | — | 10 | 2 | no | — |
| 533 | M16 | — | 10 | 2 | no | — |
| 534 | M16 | — | 10 | 1 | no | — |
| 535 | M16 | — | 20 | 1 | no | — |
| 536 | M16 | — | 20 | 1 | no | — |
| 537 | M16 | D4×D5 | 1 | 2 | yes | — |
| 538 | C2×C8 | — | 2 | 1 | no | — |
| 539 | C2×C8 | — | 10 | 1 | no | — |
| 540 | C2×C8 | — | 10 | 2 | no | — |
| 541 | C2×C8 | — | 10 | 2 | no | — |
| 542 | C2×C8 | — | 10 | 1 | no | — |
| 543 | C2×C8 | — | 10 | 2 | no | — |
| 544 | C2×C8 | — | 20 | 1 | no | — |
| 545 | C2×C8 | — | 20 | 1 | no | — |
| 546 | C2×C8 | C2×D20 | 1 | 1 | yes | characteristic |
| 547 | C2×C8 | C2×D20 | 1 | 1 | yes | characteristic |
| 548 | C2×C8 | D4×D5 | 1 | 1 | yes | characteristic |
| 549 | C2×C8 | D4×D5 | 1 | 1 | yes | characteristic |
| 550 | C2×C8 | D4×D5 | 1 | 1 | yes | characteristic |
| 551 | C2×C8 | D4×D5 | 1 | 1 | yes | characteristic |
| 552 | C4⋊C4 | — | 2 | 2 | no | — |
| 553 | C4⋊C4 | — | 2 | 1 | no | — |
| 554 | C22⋊C4 | — | 2 | 1 | no | — |
| 555 | C22⋊C4 | — | 2 | 2 | no | — |
| 556 | C22⋊C4 | — | 20 | 4 | no | — |
| 557 | C42 | — | 2 | 1 | no | — |
| 558 | C42 | — | 2 | 2 | no | — |
| 559 | C2×C5 | — | 2 | 1 | no | — |
| 560 | C2×C5 | — | 2 | 1 | no | — |
| 561 | C2×C5 | — | 2 | 1 | no | — |
| 562 | C2×C5 | — | 8 | 2 | no | — |
| 563 | C2×C5 | #2408 | 1 | 1 | yes | characteristic |
| 564 | D5 | — | 4 | 2 | no | — |
| 565 | D5 | — | 8 | 1 | no | — |
| 566 | D5 | — | 8 | 4 | no | — |
| 567 | C23 | — | 2 | 2 | no | — |
| 568 | C23 | — | 10 | 1 | no | — |
| 569 | C23 | — | 10 | 1 | no | — |
| 570 | C23 | — | 10 | 4 | no | — |
| 571 | C23 | — | 20 | 8 | no | — |
| 572 | C23 | — | 20 | 2 | no | — |
| 573 | C23 | — | 20 | 2 | no | — |
| 574 | C23 | — | 80 | 2 | no | — |
| 575 | C23 | — | 80 | 4 | no | — |
| 576 | C23 | #4144 | 1 | 1 | yes | characteristic |
| 577 | Q8 | — | 2 | 2 | no | — |
| 578 | Q8 | — | 2 | 2 | no | — |
| 579 | Q8 | — | 5 | 2 | no | — |
| 580 | Q8 | — | 10 | 1 | no | — |
| 581 | Q8 | — | 10 | 1 | no | — |
| 582 | Q8 | — | 10 | 1 | no | — |
| 583 | D4 | — | 2 | 2 | no | — |
| 584 | D4 | — | 2 | 2 | no | — |
| 585 | D4 | — | 4 | 2 | no | — |
| 586 | D4 | — | 4 | 2 | no | — |
| 587 | D4 | — | 5 | 2 | no | — |
| 588 | D4 | — | 10 | 2 | no | — |
| 589 | D4 | — | 10 | 2 | no | — |
| 590 | D4 | — | 10 | 4 | no | — |
| 591 | D4 | — | 10 | 1 | no | — |
| 592 | D4 | — | 10 | 1 | no | — |
| 593 | D4 | — | 10 | 1 | no | — |
| 594 | D4 | — | 10 | 4 | no | — |
| 595 | D4 | — | 20 | 8 | no | — |
| 596 | D4 | — | 20 | 8 | no | — |
| 597 | D4 | — | 20 | 1 | no | — |
| 598 | D4 | — | 20 | 1 | no | — |
| 599 | D4 | — | 20 | 2 | no | — |
| 600 | D4 | — | 20 | 2 | no | — |
| 601 | D4 | — | 80 | 4 | no | — |
| 602 | C2×C4 | — | 2 | 2 | no | — |
| 603 | C2×C4 | — | 4 | 2 | no | — |
| 604 | C2×C4 | — | 4 | 2 | no | — |
| 605 | C2×C4 | — | 4 | 2 | no | — |
| 606 | C2×C4 | — | 4 | 1 | no | — |
| 607 | C2×C4 | — | 10 | 1 | no | — |
| 608 | C2×C4 | — | 10 | 2 | no | — |
| 609 | C2×C4 | — | 10 | 2 | no | — |
| 610 | C2×C4 | — | 10 | 1 | no | — |
| 611 | C2×C4 | — | 20 | 8 | no | — |
| 612 | C2×C4 | — | 20 | 1 | no | — |
| 613 | C2×C4 | — | 20 | 1 | no | — |
| 614 | C2×C4 | C22×D20 | 1 | 1 | yes | characteristic |
| 615 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 616 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 617 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 618 | C2×C4 | D5×#41 | 1 | 1 | yes | characteristic |
| 619 | C2×C4 | #4149 | 1 | 1 | yes | characteristic |
| 620 | C8 | — | 2 | 2 | no | — |
| 621 | C8 | — | 10 | 2 | no | — |
| 622 | C8 | — | 20 | 1 | no | — |
| 623 | C8 | — | 20 | 2 | no | — |
| 624 | C8 | #4028 | 1 | 1 | yes | characteristic |
| 625 | C8 | #4028 | 1 | 1 | yes | characteristic |
| 626 | C8 | #4028 | 1 | 1 | yes | characteristic |
| 627 | C8 | #4028 | 1 | 1 | yes | characteristic |
| 628 | C5 | #24297 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 629 | C22 | — | 4 | 1 | no | — |
| 630 | C22 | — | 4 | 2 | no | — |
| 631 | C22 | — | 8 | 2 | no | — |
| 632 | C22 | — | 10 | 2 | no | — |
| 633 | C22 | — | 20 | 2 | no | — |
| 634 | C22 | — | 20 | 2 | no | — |
| 635 | C22 | — | 20 | 4 | no | — |
| 636 | C22 | — | 20 | 1 | no | — |
| 637 | C22 | — | 40 | 4 | no | — |
| 638 | C22 | — | 40 | 4 | no | — |
| 639 | C22 | — | 80 | 2 | no | — |
| 640 | C22 | — | 80 | 8 | no | — |
| 641 | C22 | #65888 | 1 | 1 | yes | characteristic |
| 642 | C22 | #65941 | 1 | 1 | yes | characteristic |
| 643 | C22 | #66051 | 1 | 1 | yes | characteristic |
| 644 | C4 | — | 4 | 2 | no | — |
| 645 | C4 | — | 8 | 2 | no | — |
| 646 | C4 | — | 8 | 1 | no | — |
| 647 | C4 | — | 10 | 2 | no | — |
| 648 | C4 | — | 20 | 1 | no | — |
| 649 | C4 | C2×#4028 | 1 | 1 | yes | characteristic |
| 650 | C4 | D4×D20 | 1 | 1 | yes | characteristic |
| 651 | C4 | D5×#121 | 1 | 1 | yes | characteristic |
| 652 | C4 | #66010 | 1 | 1 | yes | characteristic |
| 653 | C2 | — | 2 | 1 | no | — |
| 654 | C2 | — | 2 | 1 | no | — |
| 655 | C2 | — | 2 | 1 | no | — |
| 656 | C2 | — | 8 | 2 | no | — |
| 657 | C2 | — | 20 | 2 | no | — |
| 658 | C2 | — | 40 | 1 | no | — |
| 659 | C2 | — | 40 | 4 | no | — |
| 660 | C2 | #10608167 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#66103 | C2 | semidirect |
| 2. #10615659 | C2 | semidirect |
| 3. #10610914 | C2 | semidirect |
| 4. #10610724 | C2 | semidirect |
| 5. #10610310 | C2 | semidirect |
| 6. C5×#1976 | C2 | semidirect |
| 7. #10601458 | C2 | semidirect |
| 8. #10601195 | C2 | semidirect |
| 9. #10600843 | C2 | semidirect |
| 10. #10600841 | C2 | semidirect |
| 11. #10600696 | C2 | semidirect |
| 14. #66156 | C22 | semidirect |
| 26. C2×#4047 | C22 | semidirect |
| 27. #65859 | C22 | semidirect |
| 28. C5×#427 | C22 | semidirect |
| 29. C5×#421 | C22 | semidirect |
| 30. C5×#410 | C22 | semidirect |
| 31. C5×#405 | C22 | semidirect |
| 32. #65526 | C22 | semidirect |
| 36. C2×#3955 | C22 | semidirect |
| 37. #65414 | C22 | semidirect |
| 38. C2×#3951 | C22 | semidirect |
| 41. #65294 | C22 | semidirect |
| 42. #65290 | C22 | semidirect |
| 43. #65290 | C22 | semidirect |
| 50. #64753 | C22 | semidirect |
| 69. C2×C5×Q16 | D4 | semidirect |
| 70. C2×C5×SD16 | D4 | semidirect |
| 71. C2×C5×D8 | D4 | semidirect |
| 111. #4047 | D4 | semidirect |
| 112. #4047 | D4 | semidirect |
| 146. #1976 | D5 | semidirect |
| 276. #427 | C2×D5 | semidirect |
| 280. #421 | C2×D5 | semidirect |
| 285. #410 | C2×D5 | semidirect |
| 286. #405 | C2×D5 | semidirect |
| 382. C2×Q16 | D20 | semidirect |
| 384. C2×SD16 | D20 | semidirect |
| 394. C2×D8 | D20 | semidirect |
| 628. C5 | #24297 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66103 | 2 |
| #10615659 | 2 |
| #10610914 | 2 |
| #10610724 | 2 |
| #10610310 | 2 |
| C5×#1976 | 2 |
| #10601458 | 2 |
| #10601195 | 2 |
| #10600843 | 2 |
| #10600841 | 2 |
| #10600696 | 2 |
| #24297 | 5 |