Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
2616 conjugacy classes of subgroups.
The subgroup lattice has 666 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10619088 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #10619064 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C2×C5×#444 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10615536 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10611632 | C2 | 1 | 8 | yes | maximal, complemented |
| 6 | #10611631 | C2 | 1 | 8 | yes | maximal, complemented |
| 7 | #10610987 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #10610717 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | C2×#65006 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #10610230 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #66283 | C22 | 1 | 4 | yes | complemented |
| 12 | C2×C5×#135 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×C5×#131 | C22 | 1 | 2 | yes | complemented |
| 14 | #66156 | C22 | 1 | 4 | yes | complemented |
| 15 | #66105 | C22 | 1 | 4 | yes | complemented |
| 16 | #66104 | C22 | 1 | 8 | yes | complemented |
| 17 | #66103 | C22 | 1 | 4 | yes | complemented |
| 18 | #66102 | — | 2 | 4 | no | — |
| 19 | D5×#135 | — | 2 | 4 | no | — |
| 20 | #66100 | — | 2 | 2 | no | — |
| 21 | #66096 | — | 2 | 4 | no | — |
| 22 | #66091 | — | 2 | 2 | no | — |
| 23 | #66087 | — | 2 | 2 | no | — |
| 24 | #66087 | C22 | 1 | 4 | yes | complemented |
| 25 | #66086 | — | 2 | 2 | no | — |
| 26 | #66086 | C22 | 1 | 4 | yes | complemented |
| 27 | #66085 | — | 2 | 4 | no | — |
| 28 | #66085 | C22 | 1 | 8 | yes | complemented |
| 29 | #66082 | — | 2 | 4 | no | — |
| 30 | #66082 | C22 | 1 | 4 | yes | complemented |
| 31 | C2×#4050 | — | 2 | 4 | no | — |
| 32 | C2×#4050 | C22 | 1 | 1 | yes | characteristic |
| 33 | C2×#4050 | C22 | 1 | 2 | yes | complemented |
| 34 | C2×#4050 | C22 | 1 | 2 | yes | complemented |
| 35 | C2×#4047 | C22 | 1 | 2 | yes | complemented |
| 36 | #65811 | C22 | 1 | 2 | yes | complemented |
| 37 | C5×#444 | C22 | 1 | 8 | yes | complemented |
| 38 | C2×C5×#108 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | C2×C5×#104 | C22 | 1 | 2 | yes | complemented |
| 40 | C2×C5×#97 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | #65432 | C22 | 1 | 4 | yes | complemented |
| 42 | #65431 | C22 | 1 | 4 | yes | complemented |
| 43 | #65430 | C22 | 1 | 8 | yes | complemented |
| 44 | #65421 | C22 | 1 | 4 | yes | complemented |
| 45 | C2×#3951 | C22 | 1 | 1 | yes | characteristic, complemented |
| 46 | C2×#3937 | C22 | 1 | 2 | yes | complemented |
| 47 | #65187 | C22 | 1 | 8 | yes | complemented |
| 48 | #65186 | C22 | 1 | 4 | yes | complemented |
| 49 | #65185 | C22 | 1 | 4 | yes | complemented |
| 50 | #65116 | C22 | 1 | 8 | yes | complemented |
| 51 | #65115 | C22 | 1 | 8 | yes | complemented |
| 52 | #65114 | C22 | 1 | 8 | yes | complemented |
| 53 | #65111 | C22 | 1 | 8 | yes | complemented |
| 54 | #65006 | C22 | 1 | 8 | yes | complemented |
| 55 | #65004 | C22 | 1 | 4 | yes | complemented |
| 56 | #65001 | C22 | 1 | 4 | yes | complemented |
| 57 | #61100 | — | 5 | 1 | no | maximal, Sylow |
| 58 | C2×C5×#41 | C23 | 1 | 2 | yes | — |
| 59 | #4150 | — | 2 | 4 | no | — |
| 60 | #4150 | C23 | 1 | 8 | yes | — |
| 61 | #4149 | — | 2 | 4 | no | — |
| 62 | #4149 | C23 | 1 | 8 | yes | — |
| 63 | D5×#41 | — | 2 | 8 | no | — |
| 64 | D5×#41 | — | 4 | 4 | no | — |
| 65 | #4147 | — | 2 | 4 | no | — |
| 66 | #4144 | — | 2 | 4 | no | — |
| 67 | #4144 | — | 4 | 4 | no | — |
| 68 | C2×#709 | — | 2 | 8 | no | — |
| 69 | C2×#709 | C23 | 1 | 2 | yes | — |
| 70 | C2×#709 | C23 | 1 | 4 | yes | — |
| 71 | C5×#135 | D4 | 1 | 4 | yes | complemented |
| 72 | C5×#135 | C23 | 1 | 4 | yes | — |
| 73 | C2×C5×Q16 | D4 | 1 | 1 | yes | characteristic, complemented |
| 74 | C2×C5×SD16 | D4 | 1 | 2 | yes | complemented |
| 75 | C2×C5×D8 | D4 | 1 | 1 | yes | characteristic, complemented |
| 76 | C5×#131 | — | 2 | 2 | no | — |
| 77 | C5×#131 | — | 2 | 2 | no | — |
| 78 | C5×#131 | C23 | 1 | 4 | yes | — |
| 79 | C5×#131 | C23 | 1 | 4 | yes | — |
| 80 | C2×C5×M16 | — | 2 | 2 | no | — |
| 81 | C2×C5×M16 | C23 | 1 | 2 | yes | — |
| 82 | C22×C5×C8 | — | 2 | 2 | no | — |
| 83 | C22×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 84 | C22×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 85 | C2×C42×C5 | C23 | 1 | 1 | yes | characteristic |
| 86 | #4097 | C23 | 1 | 8 | yes | — |
| 87 | #4096 | — | 2 | 8 | no | — |
| 88 | #4095 | C23 | 1 | 8 | yes | — |
| 89 | #4088 | — | 2 | 4 | no | — |
| 90 | #4078 | — | 2 | 4 | no | — |
| 91 | #4076 | — | 4 | 2 | no | — |
| 92 | C2×#681 | C23 | 1 | 2 | yes | — |
| 93 | #4065 | — | 2 | 4 | no | — |
| 94 | #4064 | — | 2 | 8 | no | — |
| 95 | D5×Q16 | — | 2 | 4 | no | — |
| 96 | #4062 | — | 2 | 8 | no | — |
| 97 | #4061 | — | 2 | 8 | no | — |
| 98 | #4060 | — | 2 | 8 | no | — |
| 99 | D5×SD16 | — | 2 | 8 | no | — |
| 100 | #4058 | — | 2 | 4 | no | — |
| 101 | #4057 | — | 2 | 8 | no | — |
| 102 | D5×D8 | — | 2 | 4 | no | — |
| 103 | #4055 | — | 2 | 4 | no | — |
| 104 | #4055 | — | 2 | 8 | no | — |
| 105 | #4055 | — | 2 | 8 | no | — |
| 106 | #4055 | C23 | 1 | 8 | yes | — |
| 107 | #4054 | — | 2 | 4 | no | — |
| 108 | #4054 | — | 2 | 8 | no | — |
| 109 | #4054 | — | 2 | 8 | no | — |
| 110 | #4054 | C23 | 1 | 8 | yes | — |
| 111 | C2×Dic20 | — | 2 | 4 | no | — |
| 112 | C2×Dic20 | D4 | 1 | 1 | yes | characteristic, complemented |
| 113 | C2×Dic20 | C23 | 1 | 2 | yes | — |
| 114 | C2×Dic20 | C23 | 1 | 2 | yes | — |
| 115 | #4050 | — | 2 | 8 | no | — |
| 116 | #4050 | — | 2 | 2 | no | — |
| 117 | #4050 | — | 2 | 2 | no | — |
| 118 | #4050 | — | 2 | 2 | no | — |
| 119 | #4050 | — | 2 | 2 | no | — |
| 120 | #4050 | — | 2 | 2 | no | — |
| 121 | #4050 | — | 2 | 2 | no | — |
| 122 | #4050 | — | 2 | 2 | no | — |
| 123 | #4050 | — | 2 | 2 | no | — |
| 124 | #4050 | — | 2 | 4 | no | — |
| 125 | #4050 | — | 2 | 4 | no | — |
| 126 | #4050 | — | 2 | 8 | no | — |
| 127 | #4050 | D4 | 1 | 4 | yes | complemented |
| 128 | #4050 | C23 | 1 | 4 | yes | — |
| 129 | C2×D40 | — | 2 | 4 | no | — |
| 130 | C2×D40 | D4 | 1 | 1 | yes | characteristic, complemented |
| 131 | C2×D40 | C23 | 1 | 2 | yes | — |
| 132 | C2×D40 | C23 | 1 | 2 | yes | — |
| 133 | C2×#677 | — | 2 | 8 | no | — |
| 134 | C2×#677 | D4 | 1 | 2 | yes | complemented |
| 135 | C2×#677 | C23 | 1 | 4 | yes | — |
| 136 | C2×#677 | C23 | 1 | 4 | yes | — |
| 137 | #4047 | — | 2 | 2 | no | — |
| 138 | #4047 | — | 2 | 2 | no | — |
| 139 | #4047 | C23 | 1 | 4 | yes | — |
| 140 | #4047 | C23 | 1 | 4 | yes | — |
| 141 | C2×#676 | — | 2 | 2 | no | — |
| 142 | C2×C8×D5 | — | 2 | 2 | no | — |
| 143 | #4021 | C23 | 1 | 4 | yes | — |
| 144 | #4020 | C23 | 1 | 2 | yes | — |
| 145 | C4×D20 | — | 4 | 2 | no | — |
| 146 | #4015 | C23 | 1 | 2 | yes | — |
| 147 | C5×#108 | C23 | 1 | 4 | yes | — |
| 148 | C5×#104 | C23 | 1 | 8 | yes | — |
| 149 | C5×#97 | C23 | 1 | 4 | yes | — |
| 150 | #3956 | C23 | 1 | 8 | yes | — |
| 151 | #3955 | C23 | 1 | 8 | yes | — |
| 152 | #3951 | C23 | 1 | 4 | yes | — |
| 153 | #3937 | C23 | 1 | 8 | yes | — |
| 154 | #3584 | — | 5 | 2 | no | — |
| 155 | #3584 | — | 5 | 2 | no | — |
| 156 | #3289 | — | 5 | 8 | no | — |
| 157 | #3288 | — | 5 | 8 | no | — |
| 158 | #3150 | — | 5 | 1 | no | — |
| 159 | #3067 | — | 5 | 2 | no | — |
| 160 | #3067 | — | 5 | 2 | no | — |
| 161 | #3018 | — | 5 | 4 | no | — |
| 162 | C2×#444 | — | 5 | 1 | no | — |
| 163 | C2×#444 | D5 | 1 | 1 | yes | characteristic, complemented |
| 164 | C5×#41 | — | 2 | 2 | no | — |
| 165 | C5×#41 | — | 2 | 2 | no | — |
| 166 | C5×#41 | C2×D4 | 1 | 4 | yes | — |
| 167 | C5×#41 | C24 | 1 | 4 | yes | — |
| 168 | C2×C5×Q8 | C2×D4 | 1 | 2 | yes | — |
| 169 | C2×C5×D4 | — | 2 | 2 | no | — |
| 170 | C2×C5×D4 | C2×D4 | 1 | 2 | yes | — |
| 171 | C22×C4×C5 | — | 2 | 2 | no | — |
| 172 | C22×C4×C5 | — | 2 | 1 | no | — |
| 173 | C22×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 174 | C2×C22⋊D5 | — | 2 | 2 | no | — |
| 175 | C2×C22⋊D5 | — | 2 | 4 | no | — |
| 176 | C2×C22⋊D5 | — | 4 | 8 | no | — |
| 177 | #713 | — | 2 | 8 | no | — |
| 178 | #713 | — | 4 | 4 | no | — |
| 179 | Q8×D5 | — | 2 | 8 | no | — |
| 180 | Q8×D5 | — | 4 | 4 | no | — |
| 181 | #711 | — | 2 | 8 | no | — |
| 182 | #711 | — | 4 | 4 | no | — |
| 183 | #711 | — | 4 | 8 | no | — |
| 184 | #711 | — | 4 | 8 | no | — |
| 185 | D4×D5 | — | 2 | 8 | no | — |
| 186 | D4×D5 | — | 4 | 4 | no | — |
| 187 | D4×D5 | — | 4 | 8 | no | — |
| 188 | D4×D5 | — | 4 | 8 | no | — |
| 189 | #709 | — | 2 | 2 | no | — |
| 190 | #709 | — | 2 | 2 | no | — |
| 191 | #709 | — | 2 | 4 | no | — |
| 192 | #709 | — | 2 | 4 | no | — |
| 193 | #709 | — | 2 | 4 | no | — |
| 194 | #709 | — | 2 | 4 | no | — |
| 195 | #709 | — | 2 | 8 | no | — |
| 196 | #709 | — | 2 | 8 | no | — |
| 197 | #709 | — | 4 | 8 | no | — |
| 198 | #709 | — | 4 | 8 | no | — |
| 199 | #709 | C2×D4 | 1 | 4 | yes | — |
| 200 | #709 | C24 | 1 | 4 | yes | — |
| 201 | C2×D20 | — | 2 | 8 | no | — |
| 202 | C2×D20 | — | 4 | 2 | no | — |
| 203 | C2×D20 | C2×D4 | 1 | 2 | yes | — |
| 204 | C2×D20 | C24 | 1 | 4 | yes | — |
| 205 | C2×C4×D5 | — | 2 | 2 | no | — |
| 206 | C2×C4×D5 | — | 2 | 4 | no | — |
| 207 | C2×C4×D5 | — | 4 | 8 | no | — |
| 208 | C2×Dic10 | — | 2 | 8 | no | — |
| 209 | C2×Dic10 | C2×D4 | 1 | 2 | yes | — |
| 210 | C2×Dic10 | C24 | 1 | 4 | yes | — |
| 211 | C5×Q16 | C2×D4 | 1 | 4 | yes | — |
| 212 | C5×SD16 | C2×D4 | 1 | 8 | yes | — |
| 213 | C5×D8 | C2×D4 | 1 | 4 | yes | — |
| 214 | C5×M16 | — | 2 | 2 | no | — |
| 215 | C5×M16 | — | 2 | 4 | no | — |
| 216 | C5×M16 | — | 2 | 4 | no | — |
| 217 | C5×M16 | C24 | 1 | 4 | yes | — |
| 218 | C2×C5×C8 | — | 2 | 2 | no | — |
| 219 | C2×C5×C8 | — | 2 | 4 | no | — |
| 220 | C2×C5×C8 | — | 2 | 4 | no | — |
| 221 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 222 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 223 | C2×C5×C8 | C2×D4 | 1 | 2 | yes | — |
| 224 | C2×C5×C8 | C2×D4 | 1 | 2 | yes | — |
| 225 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 226 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 227 | C2×C5×C8 | C24 | 1 | 2 | yes | — |
| 228 | C2×C5×C8 | C24 | 1 | 2 | yes | — |
| 229 | C42×C5 | — | 2 | 1 | no | — |
| 230 | C42×C5 | C24 | 1 | 2 | yes | — |
| 231 | #689 | — | 2 | 8 | no | — |
| 232 | #688 | — | 2 | 8 | no | — |
| 233 | #687 | — | 2 | 8 | no | — |
| 234 | #686 | — | 2 | 8 | no | — |
| 235 | #685 | — | 4 | 4 | no | — |
| 236 | C4⋊Dic5 | — | 4 | 2 | no | — |
| 237 | #681 | — | 2 | 2 | no | — |
| 238 | #681 | C24 | 1 | 4 | yes | — |
| 239 | C2×#168 | — | 2 | 2 | no | — |
| 240 | Dic20 | — | 2 | 8 | no | — |
| 241 | Dic20 | — | 2 | 2 | no | — |
| 242 | Dic20 | — | 2 | 2 | no | — |
| 243 | Dic20 | — | 2 | 2 | no | — |
| 244 | Dic20 | — | 2 | 2 | no | — |
| 245 | Dic20 | C2×D4 | 1 | 4 | yes | — |
| 246 | D40 | — | 2 | 8 | no | — |
| 247 | D40 | — | 2 | 2 | no | — |
| 248 | D40 | — | 2 | 2 | no | — |
| 249 | D40 | — | 2 | 2 | no | — |
| 250 | D40 | — | 2 | 2 | no | — |
| 251 | D40 | C2×D4 | 1 | 4 | yes | — |
| 252 | #677 | — | 2 | 8 | no | — |
| 253 | #677 | — | 2 | 8 | no | — |
| 254 | #677 | — | 2 | 4 | no | — |
| 255 | #677 | — | 2 | 4 | no | — |
| 256 | #677 | — | 2 | 4 | no | — |
| 257 | #677 | — | 2 | 4 | no | — |
| 258 | #677 | C2×D4 | 1 | 8 | yes | — |
| 259 | #676 | — | 2 | 4 | no | — |
| 260 | #676 | — | 2 | 4 | no | — |
| 261 | C8×D5 | — | 2 | 4 | no | — |
| 262 | C8×D5 | — | 2 | 4 | no | — |
| 263 | #585 | — | 5 | 4 | no | — |
| 264 | #578 | — | 5 | 4 | no | — |
| 265 | #578 | — | 5 | 4 | no | — |
| 266 | #578 | — | 10 | 2 | no | — |
| 267 | #578 | — | 10 | 2 | no | — |
| 268 | #577 | — | 5 | 8 | no | — |
| 269 | #577 | — | 5 | 8 | no | — |
| 270 | #577 | — | 10 | 4 | no | — |
| 271 | #577 | — | 10 | 4 | no | — |
| 272 | #576 | — | 5 | 4 | no | — |
| 273 | #576 | — | 5 | 4 | no | — |
| 274 | #576 | — | 10 | 2 | no | — |
| 275 | #576 | — | 10 | 2 | no | — |
| 276 | #575 | — | 5 | 4 | no | — |
| 277 | #575 | — | 5 | 4 | no | — |
| 278 | #575 | — | 10 | 4 | no | — |
| 279 | #575 | — | 10 | 4 | no | — |
| 280 | C2×#135 | — | 5 | 1 | no | — |
| 281 | C2×#135 | — | 5 | 2 | no | — |
| 282 | C2×#135 | — | 5 | 2 | no | — |
| 283 | C2×#135 | — | 10 | 4 | no | — |
| 284 | C2×#135 | — | 10 | 4 | no | — |
| 285 | C2×#135 | C2×D5 | 1 | 1 | yes | characteristic |
| 286 | C2×#131 | — | 5 | 2 | no | — |
| 287 | C2×#131 | C2×D5 | 1 | 2 | yes | complemented |
| 288 | #532 | — | 5 | 2 | no | — |
| 289 | #497 | — | 5 | 4 | no | — |
| 290 | #496 | — | 5 | 4 | no | — |
| 291 | #473 | — | 5 | 4 | no | — |
| 292 | #473 | — | 5 | 4 | no | — |
| 293 | #472 | — | 5 | 4 | no | — |
| 294 | #472 | — | 5 | 4 | no | — |
| 295 | #471 | — | 5 | 8 | no | — |
| 296 | #471 | — | 5 | 8 | no | — |
| 297 | #456 | — | 5 | 8 | no | — |
| 298 | #455 | — | 5 | 8 | no | — |
| 299 | #454 | — | 5 | 8 | no | — |
| 300 | #453 | — | 5 | 8 | no | — |
| 301 | #444 | — | 5 | 8 | no | — |
| 302 | #444 | C2×D5 | 1 | 8 | yes | complemented |
| 303 | C2×#108 | — | 5 | 1 | no | — |
| 304 | C2×#108 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 305 | C2×#104 | — | 5 | 2 | no | — |
| 306 | C2×#104 | C2×D5 | 1 | 2 | yes | complemented |
| 307 | #413 | — | 5 | 4 | no | — |
| 308 | C2×#97 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 309 | C23×C5 | — | 2 | 2 | no | — |
| 310 | C23×C5 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 311 | C22×D5 | — | 2 | 2 | no | — |
| 312 | C22×D5 | — | 2 | 4 | no | — |
| 313 | C22×D5 | — | 4 | 8 | no | — |
| 314 | C5×Q8 | — | 2 | 2 | no | — |
| 315 | C5×Q8 | C22×D4 | 1 | 4 | yes | — |
| 316 | C5×D4 | — | 2 | 4 | no | — |
| 317 | C5×D4 | — | 2 | 4 | no | — |
| 318 | C5×D4 | — | 2 | 2 | no | — |
| 319 | C5×D4 | C22×D4 | 1 | 4 | yes | — |
| 320 | C2×C4×C5 | — | 2 | 2 | no | — |
| 321 | C2×C4×C5 | — | 2 | 4 | no | — |
| 322 | C2×C4×C5 | — | 2 | 4 | no | — |
| 323 | C2×C4×C5 | — | 2 | 2 | no | — |
| 324 | C2×C4×C5 | — | 8 | 1 | no | — |
| 325 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 326 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 327 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 328 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 329 | C2×C4×C5 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 330 | C2×C4×C5 | C25 | 1 | 1 | yes | characteristic |
| 331 | C22⋊D5 | — | 2 | 4 | no | — |
| 332 | C22⋊D5 | — | 2 | 4 | no | — |
| 333 | C22⋊D5 | — | 4 | 8 | no | — |
| 334 | C22⋊D5 | — | 4 | 8 | no | — |
| 335 | C22⋊D5 | — | 4 | 4 | no | — |
| 336 | C22⋊D5 | — | 4 | 4 | no | — |
| 337 | C2×Dic5 | — | 2 | 2 | no | — |
| 338 | C2×Dic5 | — | 2 | 4 | no | — |
| 339 | C2×Dic5 | — | 4 | 8 | no | — |
| 340 | D20 | — | 2 | 2 | no | — |
| 341 | D20 | — | 2 | 4 | no | — |
| 342 | D20 | — | 2 | 4 | no | — |
| 343 | D20 | — | 4 | 8 | no | — |
| 344 | D20 | — | 8 | 4 | no | — |
| 345 | D20 | C22×D4 | 1 | 4 | yes | — |
| 346 | C4×D5 | — | 2 | 4 | no | — |
| 347 | C4×D5 | — | 2 | 4 | no | — |
| 348 | C4×D5 | — | 4 | 8 | no | — |
| 349 | C4×D5 | — | 4 | 8 | no | — |
| 350 | C4×D5 | — | 4 | 4 | no | — |
| 351 | C4×D5 | — | 4 | 4 | no | — |
| 352 | Dic10 | — | 2 | 2 | no | — |
| 353 | Dic10 | — | 2 | 4 | no | — |
| 354 | Dic10 | — | 2 | 4 | no | — |
| 355 | Dic10 | — | 4 | 8 | no | — |
| 356 | Dic10 | C22×D4 | 1 | 4 | yes | — |
| 357 | C5×C8 | — | 2 | 4 | no | — |
| 358 | C5×C8 | C22×D4 | 1 | 2 | yes | — |
| 359 | C5×C8 | C22×D4 | 1 | 2 | yes | — |
| 360 | C5×C8 | C22×D4 | 1 | 2 | yes | — |
| 361 | C5×C8 | C22×D4 | 1 | 2 | yes | — |
| 362 | #168 | — | 2 | 4 | no | — |
| 363 | 2−1+4 | — | 5 | 8 | no | — |
| 364 | 2−1+4 | — | 10 | 4 | no | — |
| 365 | 2−1+4 | — | 10 | 4 | no | — |
| 366 | H(5,𝔽2) | — | 5 | 8 | no | — |
| 367 | H(5,𝔽2) | — | 10 | 4 | no | — |
| 368 | H(5,𝔽2) | — | 10 | 4 | no | — |
| 369 | H(5,𝔽2) | — | 20 | 4 | no | — |
| 370 | C2×#41 | — | 5 | 2 | no | — |
| 371 | C2×#41 | — | 5 | 4 | no | — |
| 372 | C2×#41 | — | 10 | 8 | no | — |
| 373 | C2×#41 | — | 10 | 8 | no | — |
| 374 | C2×#41 | — | 20 | 4 | no | — |
| 375 | C2×#41 | C22×D5 | 1 | 2 | yes | — |
| 376 | #137 | — | 5 | 8 | no | — |
| 377 | #137 | — | 5 | 8 | no | — |
| 378 | #137 | — | 10 | 8 | no | — |
| 379 | #137 | — | 10 | 8 | no | — |
| 380 | #137 | — | 10 | 4 | no | — |
| 381 | #137 | — | 10 | 4 | no | — |
| 382 | #137 | — | 10 | 8 | no | — |
| 383 | #137 | — | 10 | 8 | no | — |
| 384 | AGL(1,ℤ/8) | — | 5 | 8 | no | — |
| 385 | AGL(1,ℤ/8) | — | 5 | 8 | no | — |
| 386 | AGL(1,ℤ/8) | — | 10 | 8 | no | — |
| 387 | AGL(1,ℤ/8) | — | 10 | 8 | no | — |
| 388 | AGL(1,ℤ/8) | — | 10 | 4 | no | — |
| 389 | AGL(1,ℤ/8) | — | 10 | 4 | no | — |
| 390 | AGL(1,ℤ/8) | — | 10 | 8 | no | — |
| 391 | AGL(1,ℤ/8) | — | 10 | 8 | no | — |
| 392 | #135 | — | 5 | 4 | no | — |
| 393 | #135 | — | 5 | 4 | no | — |
| 394 | #135 | — | 10 | 4 | no | — |
| 395 | #135 | — | 10 | 8 | no | — |
| 396 | #135 | — | 10 | 4 | no | — |
| 397 | #135 | — | 10 | 8 | no | — |
| 398 | #135 | — | 10 | 8 | no | — |
| 399 | #135 | — | 10 | 4 | no | — |
| 400 | #135 | — | 10 | 8 | no | — |
| 401 | #135 | — | 10 | 4 | no | — |
| 402 | #135 | — | 10 | 2 | no | — |
| 403 | #135 | — | 10 | 2 | no | — |
| 404 | #135 | — | 10 | 2 | no | — |
| 405 | #135 | — | 10 | 2 | no | — |
| 406 | #135 | — | 10 | 2 | no | — |
| 407 | #135 | — | 10 | 2 | no | — |
| 408 | #135 | — | 10 | 2 | no | — |
| 409 | #135 | — | 10 | 2 | no | — |
| 410 | #135 | D20 | 1 | 4 | yes | complemented |
| 411 | #135 | C22×D5 | 1 | 4 | yes | — |
| 412 | C2×Q16 | — | 5 | 1 | no | — |
| 413 | C2×Q16 | — | 5 | 2 | no | — |
| 414 | C2×Q16 | — | 5 | 2 | no | — |
| 415 | C2×Q16 | — | 10 | 4 | no | — |
| 416 | C2×Q16 | — | 10 | 4 | no | — |
| 417 | C2×Q16 | D20 | 1 | 1 | yes | characteristic, complemented |
| 418 | C2×SD16 | — | 5 | 2 | no | — |
| 419 | C2×SD16 | — | 5 | 4 | no | — |
| 420 | C2×SD16 | — | 5 | 4 | no | — |
| 421 | C2×SD16 | — | 10 | 8 | no | — |
| 422 | C2×SD16 | — | 10 | 8 | no | — |
| 423 | C2×SD16 | D20 | 1 | 2 | yes | complemented |
| 424 | C2×D8 | — | 5 | 1 | no | — |
| 425 | C2×D8 | — | 5 | 2 | no | — |
| 426 | C2×D8 | — | 5 | 2 | no | — |
| 427 | C2×D8 | — | 10 | 4 | no | — |
| 428 | C2×D8 | — | 10 | 4 | no | — |
| 429 | C2×D8 | D20 | 1 | 1 | yes | characteristic, complemented |
| 430 | #131 | — | 2 | 2 | no | — |
| 431 | #131 | — | 2 | 2 | no | — |
| 432 | #131 | — | 5 | 4 | no | — |
| 433 | #131 | — | 5 | 4 | no | — |
| 434 | #131 | — | 10 | 2 | no | — |
| 435 | #131 | — | 10 | 2 | no | — |
| 436 | #131 | C22×D5 | 1 | 4 | yes | — |
| 437 | #131 | C22×D5 | 1 | 4 | yes | — |
| 438 | C2×M16 | — | 2 | 2 | no | — |
| 439 | C2×M16 | — | 5 | 2 | no | — |
| 440 | C2×M16 | — | 10 | 2 | no | — |
| 441 | C2×M16 | C22×D5 | 1 | 2 | yes | — |
| 442 | C22×C8 | — | 2 | 2 | no | — |
| 443 | C22×C8 | — | 10 | 2 | no | — |
| 444 | C22×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 445 | C22×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 446 | C4⋊Q8 | — | 5 | 2 | no | — |
| 447 | #127 | — | 5 | 2 | no | — |
| 448 | #124 | — | 5 | 4 | no | — |
| 449 | #121 | — | 20 | 2 | no | — |
| 450 | C4×D4 | — | 20 | 2 | no | — |
| 451 | C2×C42 | C22×D5 | 1 | 1 | yes | characteristic |
| 452 | #108 | — | 5 | 4 | no | — |
| 453 | #108 | C22×D5 | 1 | 4 | yes | — |
| 454 | #104 | — | 5 | 8 | no | — |
| 455 | #104 | C22×D5 | 1 | 8 | yes | — |
| 456 | #101 | — | 5 | 8 | no | — |
| 457 | #100 | — | 5 | 8 | no | — |
| 458 | #97 | C22×D5 | 1 | 4 | yes | — |
| 459 | C22×C5 | — | 2 | 4 | no | — |
| 460 | C22×C5 | — | 4 | 1 | no | — |
| 461 | C22×C5 | — | 8 | 2 | no | — |
| 462 | C22×C5 | D42 | 1 | 1 | yes | characteristic |
| 463 | C22×C5 | D42 | 1 | 1 | yes | characteristic |
| 464 | C22×C5 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 465 | C2×D5 | — | 2 | 4 | no | — |
| 466 | C2×D5 | — | 4 | 4 | no | — |
| 467 | C2×D5 | — | 8 | 2 | no | — |
| 468 | C2×D5 | — | 8 | 4 | no | — |
| 469 | C2×D5 | — | 16 | 8 | no | — |
| 470 | C4×C5 | — | 2 | 4 | no | — |
| 471 | C4×C5 | — | 4 | 2 | no | — |
| 472 | C4×C5 | D42 | 1 | 1 | yes | characteristic |
| 473 | C4×C5 | D42 | 1 | 1 | yes | characteristic |
| 474 | C4×C5 | C23×D4 | 1 | 1 | yes | characteristic |
| 475 | C4×C5 | C23×D4 | 1 | 1 | yes | characteristic |
| 476 | Dic5 | — | 2 | 4 | no | — |
| 477 | Dic5 | — | 4 | 4 | no | — |
| 478 | #41 | — | 2 | 2 | no | — |
| 479 | #41 | — | 2 | 2 | no | — |
| 480 | #41 | — | 5 | 4 | no | — |
| 481 | #41 | — | 5 | 4 | no | — |
| 482 | #41 | — | 10 | 8 | no | — |
| 483 | #41 | — | 10 | 8 | no | — |
| 484 | #41 | — | 10 | 2 | no | — |
| 485 | #41 | — | 10 | 2 | no | — |
| 486 | #41 | — | 10 | 8 | no | — |
| 487 | #41 | — | 10 | 8 | no | — |
| 488 | #41 | — | 10 | 4 | no | — |
| 489 | #41 | — | 10 | 4 | no | — |
| 490 | #41 | — | 10 | 4 | no | — |
| 491 | #41 | — | 10 | 4 | no | — |
| 492 | #41 | — | 20 | 8 | no | — |
| 493 | #41 | — | 20 | 8 | no | — |
| 494 | #41 | — | 20 | 8 | no | — |
| 495 | #41 | — | 20 | 8 | no | — |
| 496 | #41 | — | 20 | 4 | no | — |
| 497 | #41 | — | 20 | 4 | no | — |
| 498 | #41 | C2×D20 | 1 | 4 | yes | — |
| 499 | #41 | C23×D5 | 1 | 4 | yes | — |
| 500 | C2×Q8 | — | 5 | 2 | no | — |
| 501 | C2×Q8 | — | 5 | 4 | no | — |
| 502 | C2×Q8 | — | 10 | 8 | no | — |
| 503 | C2×Q8 | — | 10 | 8 | no | — |
| 504 | C2×Q8 | — | 20 | 4 | no | — |
| 505 | C2×Q8 | C2×D20 | 1 | 2 | yes | — |
| 506 | C2×D4 | — | 2 | 2 | no | — |
| 507 | C2×D4 | — | 5 | 2 | no | — |
| 508 | C2×D4 | — | 5 | 4 | no | — |
| 509 | C2×D4 | — | 10 | 8 | no | — |
| 510 | C2×D4 | — | 10 | 2 | no | — |
| 511 | C2×D4 | — | 10 | 8 | no | — |
| 512 | C2×D4 | — | 10 | 4 | no | — |
| 513 | C2×D4 | — | 20 | 2 | no | — |
| 514 | C2×D4 | — | 20 | 8 | no | — |
| 515 | C2×D4 | — | 20 | 4 | no | — |
| 516 | C2×D4 | — | 20 | 8 | no | — |
| 517 | C2×D4 | — | 20 | 8 | no | — |
| 518 | C2×D4 | C2×D20 | 1 | 2 | yes | — |
| 519 | C22×C4 | — | 2 | 2 | no | — |
| 520 | C22×C4 | — | 2 | 1 | no | — |
| 521 | C22×C4 | — | 10 | 2 | no | — |
| 522 | C22×C4 | — | 10 | 4 | no | — |
| 523 | C22×C4 | — | 20 | 8 | no | — |
| 524 | C22×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 525 | Q16 | — | 5 | 4 | no | — |
| 526 | Q16 | — | 10 | 8 | no | — |
| 527 | Q16 | — | 10 | 8 | no | — |
| 528 | Q16 | — | 10 | 2 | no | — |
| 529 | Q16 | — | 10 | 2 | no | — |
| 530 | Q16 | — | 10 | 2 | no | — |
| 531 | Q16 | — | 10 | 2 | no | — |
| 532 | Q16 | C2×D20 | 1 | 4 | yes | — |
| 533 | SD16 | — | 5 | 8 | no | — |
| 534 | SD16 | — | 10 | 8 | no | — |
| 535 | SD16 | — | 10 | 8 | no | — |
| 536 | SD16 | — | 10 | 8 | no | — |
| 537 | SD16 | — | 10 | 8 | no | — |
| 538 | SD16 | — | 10 | 4 | no | — |
| 539 | SD16 | — | 10 | 4 | no | — |
| 540 | SD16 | — | 10 | 4 | no | — |
| 541 | SD16 | — | 10 | 4 | no | — |
| 542 | SD16 | C2×D20 | 1 | 8 | yes | — |
| 543 | D8 | — | 5 | 4 | no | — |
| 544 | D8 | — | 10 | 8 | no | — |
| 545 | D8 | — | 10 | 8 | no | — |
| 546 | D8 | — | 10 | 2 | no | — |
| 547 | D8 | — | 10 | 2 | no | — |
| 548 | D8 | — | 10 | 2 | no | — |
| 549 | D8 | — | 10 | 2 | no | — |
| 550 | D8 | C2×D20 | 1 | 4 | yes | — |
| 551 | M16 | — | 2 | 2 | no | — |
| 552 | M16 | — | 2 | 4 | no | — |
| 553 | M16 | — | 2 | 4 | no | — |
| 554 | M16 | — | 5 | 4 | no | — |
| 555 | M16 | — | 10 | 2 | no | — |
| 556 | M16 | — | 10 | 4 | no | — |
| 557 | M16 | — | 10 | 4 | no | — |
| 558 | M16 | C23×D5 | 1 | 4 | yes | — |
| 559 | C2×C8 | — | 2 | 2 | no | — |
| 560 | C2×C8 | — | 2 | 4 | no | — |
| 561 | C2×C8 | — | 2 | 4 | no | — |
| 562 | C2×C8 | — | 10 | 2 | no | — |
| 563 | C2×C8 | — | 10 | 4 | no | — |
| 564 | C2×C8 | — | 10 | 4 | no | — |
| 565 | C2×C8 | C2×D20 | 1 | 2 | yes | — |
| 566 | C2×C8 | C2×D20 | 1 | 1 | yes | characteristic |
| 567 | C2×C8 | C2×D20 | 1 | 1 | yes | characteristic |
| 568 | C2×C8 | D4×D5 | 1 | 2 | yes | — |
| 569 | C2×C8 | D4×D5 | 1 | 1 | yes | characteristic |
| 570 | C2×C8 | D4×D5 | 1 | 1 | yes | characteristic |
| 571 | C2×C8 | C23×D5 | 1 | 2 | yes | — |
| 572 | C2×C8 | C23×D5 | 1 | 2 | yes | — |
| 573 | C4⋊C4 | — | 20 | 2 | no | — |
| 574 | C22⋊C4 | — | 20 | 4 | no | — |
| 575 | C42 | — | 2 | 1 | no | — |
| 576 | C42 | C23×D5 | 1 | 2 | yes | — |
| 577 | C2×C5 | — | 2 | 1 | no | — |
| 578 | C2×C5 | — | 2 | 1 | no | — |
| 579 | C2×C5 | — | 2 | 1 | no | — |
| 580 | C2×C5 | — | 4 | 4 | no | — |
| 581 | C2×C5 | C2×D42 | 1 | 1 | yes | characteristic |
| 582 | D5 | — | 4 | 4 | no | — |
| 583 | D5 | — | 8 | 4 | no | — |
| 584 | C23 | — | 2 | 2 | no | — |
| 585 | C23 | — | 10 | 2 | no | — |
| 586 | C23 | — | 10 | 4 | no | — |
| 587 | C23 | — | 20 | 8 | no | — |
| 588 | C23 | #4149 | 1 | 1 | yes | characteristic |
| 589 | Q8 | — | 2 | 2 | no | — |
| 590 | Q8 | — | 5 | 4 | no | — |
| 591 | Q8 | — | 10 | 2 | no | — |
| 592 | Q8 | — | 10 | 4 | no | — |
| 593 | Q8 | — | 10 | 4 | no | — |
| 594 | Q8 | — | 20 | 8 | no | — |
| 595 | Q8 | C22×D20 | 1 | 4 | yes | — |
| 596 | D4 | — | 2 | 4 | no | — |
| 597 | D4 | — | 2 | 4 | no | — |
| 598 | D4 | — | 2 | 2 | no | — |
| 599 | D4 | — | 5 | 4 | no | — |
| 600 | D4 | — | 10 | 4 | no | — |
| 601 | D4 | — | 10 | 4 | no | — |
| 602 | D4 | — | 10 | 2 | no | — |
| 603 | D4 | — | 10 | 4 | no | — |
| 604 | D4 | — | 10 | 4 | no | — |
| 605 | D4 | — | 20 | 8 | no | — |
| 606 | D4 | — | 20 | 8 | no | — |
| 607 | D4 | — | 20 | 8 | no | — |
| 608 | D4 | — | 20 | 4 | no | — |
| 609 | D4 | — | 20 | 4 | no | — |
| 610 | D4 | — | 40 | 4 | no | — |
| 611 | D4 | C22×D20 | 1 | 4 | yes | — |
| 612 | C2×C4 | — | 2 | 2 | no | — |
| 613 | C2×C4 | — | 2 | 4 | no | — |
| 614 | C2×C4 | — | 2 | 4 | no | — |
| 615 | C2×C4 | — | 2 | 2 | no | — |
| 616 | C2×C4 | — | 8 | 1 | no | — |
| 617 | C2×C4 | — | 10 | 2 | no | — |
| 618 | C2×C4 | — | 10 | 4 | no | — |
| 619 | C2×C4 | — | 10 | 4 | no | — |
| 620 | C2×C4 | — | 10 | 4 | no | — |
| 621 | C2×C4 | — | 20 | 8 | no | — |
| 622 | C2×C4 | — | 20 | 8 | no | — |
| 623 | C2×C4 | — | 20 | 8 | no | — |
| 624 | C2×C4 | — | 20 | 4 | no | — |
| 625 | C2×C4 | — | 20 | 4 | no | — |
| 626 | C2×C4 | C22×D20 | 1 | 1 | yes | characteristic |
| 627 | C2×C4 | C22×D20 | 1 | 1 | yes | characteristic |
| 628 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 629 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 630 | C2×C4 | #4149 | 1 | 1 | yes | characteristic |
| 631 | C2×C4 | C24×D5 | 1 | 1 | yes | characteristic |
| 632 | C8 | — | 2 | 4 | no | — |
| 633 | C8 | — | 10 | 4 | no | — |
| 634 | C8 | C22×D20 | 1 | 2 | yes | — |
| 635 | C8 | C22×D20 | 1 | 2 | yes | — |
| 636 | C8 | C2×D4×D5 | 1 | 2 | yes | — |
| 637 | C8 | C2×D4×D5 | 1 | 2 | yes | — |
| 638 | C5 | #61100 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 639 | C22 | — | 2 | 4 | no | — |
| 640 | C22 | — | 4 | 1 | no | — |
| 641 | C22 | — | 8 | 2 | no | — |
| 642 | C22 | — | 10 | 4 | no | — |
| 643 | C22 | — | 20 | 4 | no | — |
| 644 | C22 | — | 40 | 2 | no | — |
| 645 | C22 | — | 40 | 4 | no | — |
| 646 | C22 | — | 80 | 8 | no | — |
| 647 | C22 | D4×D20 | 1 | 1 | yes | characteristic |
| 648 | C22 | D4×D20 | 1 | 1 | yes | characteristic |
| 649 | C22 | C2×#4149 | 1 | 1 | yes | characteristic |
| 650 | C4 | — | 2 | 4 | no | — |
| 651 | C4 | — | 4 | 2 | no | — |
| 652 | C4 | — | 10 | 4 | no | — |
| 653 | C4 | — | 20 | 4 | no | — |
| 654 | C4 | D4×D20 | 1 | 1 | yes | characteristic |
| 655 | C4 | D4×D20 | 1 | 1 | yes | characteristic |
| 656 | C4 | C23×D20 | 1 | 1 | yes | characteristic |
| 657 | C4 | C22×D4×D5 | 1 | 1 | yes | characteristic |
| 658 | C2 | — | 2 | 1 | no | — |
| 659 | C2 | — | 2 | 1 | no | — |
| 660 | C2 | — | 2 | 1 | no | — |
| 661 | C2 | — | 4 | 4 | no | — |
| 662 | C2 | — | 20 | 4 | no | — |
| 663 | C2 | — | 40 | 4 | no | — |
| 664 | C2 | C2×D4×D20 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10619088 | C2 | semidirect |
| 2. #10619064 | C2 | semidirect |
| 3. C2×C5×#444 | C2 | semidirect |
| 4. #10615536 | C2 | semidirect |
| 5. #10611632 | C2 | semidirect |
| 6. #10611631 | C2 | semidirect |
| 7. #10610987 | C2 | semidirect |
| 8. #10610717 | C2 | semidirect |
| 9. C2×#65006 | C2 | semidirect |
| 10. #10610230 | C2 | semidirect |
| 11. #66283 | C22 | semidirect |
| 13. C2×C5×#131 | C22 | semidirect |
| 14. #66156 | C22 | semidirect |
| 15. #66105 | C22 | semidirect |
| 16. #66104 | C22 | semidirect |
| 17. #66103 | C22 | semidirect |
| 24. #66087 | C22 | semidirect |
| 26. #66086 | C22 | semidirect |
| 28. #66085 | C22 | semidirect |
| 30. #66082 | C22 | semidirect |
| 33. C2×#4050 | C22 | semidirect |
| 34. C2×#4050 | C22 | semidirect |
| 35. C2×#4047 | C22 | semidirect |
| 36. #65811 | C22 | semidirect |
| 37. C5×#444 | C22 | semidirect |
| 38. C2×C5×#108 | C22 | semidirect |
| 39. C2×C5×#104 | C22 | semidirect |
| 40. C2×C5×#97 | C22 | semidirect |
| 41. #65432 | C22 | semidirect |
| 42. #65431 | C22 | semidirect |
| 43. #65430 | C22 | semidirect |
| 44. #65421 | C22 | semidirect |
| 45. C2×#3951 | C22 | semidirect |
| 46. C2×#3937 | C22 | semidirect |
| 47. #65187 | C22 | semidirect |
| 48. #65186 | C22 | semidirect |
| 49. #65185 | C22 | semidirect |
| 50. #65116 | C22 | semidirect |
| 51. #65115 | C22 | semidirect |
| 52. #65114 | C22 | semidirect |
| 53. #65111 | C22 | semidirect |
| 54. #65006 | C22 | semidirect |
| 55. #65004 | C22 | semidirect |
| 56. #65001 | C22 | semidirect |
| 71. C5×#135 | D4 | semidirect |
| 73. C2×C5×Q16 | D4 | semidirect |
| 74. C2×C5×SD16 | D4 | semidirect |
| 75. C2×C5×D8 | D4 | semidirect |
| 112. C2×Dic20 | D4 | semidirect |
| 127. #4050 | D4 | semidirect |
| 130. C2×D40 | D4 | semidirect |
| 134. C2×#677 | D4 | semidirect |
| 163. C2×#444 | D5 | semidirect |
| 287. C2×#131 | C2×D5 | semidirect |
| 302. #444 | C2×D5 | semidirect |
| 304. C2×#108 | C2×D5 | semidirect |
| 306. C2×#104 | C2×D5 | semidirect |
| 308. C2×#97 | C2×D5 | semidirect |
| 410. #135 | D20 | semidirect |
| 417. C2×Q16 | D20 | semidirect |
| 423. C2×SD16 | D20 | semidirect |
| 429. C2×D8 | D20 | semidirect |
| 638. C5 | #61100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10619088 | 2 |
| #10619064 | 2 |
| C2×C5×#444 | 2 |
| #10615536 | 2 |
| #10611632 | 2 |
| #10611631 | 2 |
| #10610987 | 2 |
| #10610717 | 2 |
| C2×#65006 | 2 |
| #10610230 | 2 |
| #61100 | 5 |