Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1122 conjugacy classes of subgroups.
The subgroup lattice has 600 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10619088 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×C5×#509 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10615567 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#65436 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10602869 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10602309 | C2 | 1 | 8 | yes | maximal, complemented |
| 7 | #10602243 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10602228 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #66283 | — | 2 | 1 | no | — |
| 10 | C2×C5×#135 | C22 | 1 | 1 | yes | characteristic |
| 11 | C22×C5×D8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | #66156 | — | 2 | 1 | no | — |
| 13 | #66139 | — | 2 | 1 | no | — |
| 14 | #66105 | — | 2 | 1 | no | — |
| 15 | #66104 | — | 2 | 2 | no | — |
| 16 | #66103 | — | 2 | 1 | no | — |
| 17 | #66102 | C22 | 1 | 4 | yes | complemented |
| 18 | D5×#135 | — | 2 | 2 | no | — |
| 19 | #66100 | — | 2 | 1 | no | — |
| 20 | #66096 | — | 2 | 2 | no | — |
| 21 | #66091 | — | 2 | 1 | no | — |
| 22 | C2×#4050 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#4047 | C22 | 1 | 1 | yes | characteristic |
| 24 | C5×#509 | — | 2 | 2 | no | — |
| 25 | C5×#509 | C22 | 1 | 4 | yes | complemented |
| 26 | C2×C5×SD32 | — | 2 | 1 | no | — |
| 27 | C2×C5×D16 | — | 2 | 1 | no | — |
| 28 | C2×C5×M32 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | #65504 | — | 2 | 1 | no | — |
| 30 | #65448 | C22 | 1 | 4 | yes | complemented |
| 31 | #65446 | — | 2 | 2 | no | — |
| 32 | C2×#3959 | — | 2 | 1 | no | — |
| 33 | #65436 | — | 2 | 2 | no | — |
| 34 | #65436 | C22 | 1 | 4 | yes | complemented |
| 35 | C2×#3958 | — | 2 | 1 | no | — |
| 36 | #65395 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | C2×#3944 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | #64786 | C22 | 1 | 4 | yes | complemented |
| 39 | #64738 | C22 | 1 | 4 | yes | complemented |
| 40 | #64734 | C22 | 1 | 4 | yes | complemented |
| 41 | #33531 | — | 5 | 1 | no | maximal, Sylow |
| 42 | C2×C5×#41 | — | 2 | 1 | no | — |
| 43 | C22×C5×D4 | — | 2 | 1 | no | — |
| 44 | #4150 | — | 2 | 2 | no | — |
| 45 | #4150 | — | 4 | 1 | no | — |
| 46 | #4149 | — | 2 | 2 | no | — |
| 47 | #4149 | — | 4 | 1 | no | — |
| 48 | D5×#41 | — | 2 | 4 | no | — |
| 49 | D5×#41 | — | 4 | 2 | no | — |
| 50 | #4147 | — | 2 | 2 | no | — |
| 51 | #4144 | — | 2 | 2 | no | — |
| 52 | #4144 | — | 4 | 2 | no | — |
| 53 | C2×#709 | — | 2 | 1 | no | — |
| 54 | C2×#709 | — | 4 | 2 | no | — |
| 55 | C2×#709 | D4 | 1 | 1 | yes | characteristic |
| 56 | C5×#135 | — | 2 | 1 | no | — |
| 57 | C5×#135 | — | 2 | 1 | no | — |
| 58 | C5×#135 | D4 | 1 | 2 | yes | complemented |
| 59 | C5×#135 | C23 | 1 | 2 | yes | — |
| 60 | C2×C5×Q16 | D4 | 1 | 1 | yes | characteristic, complemented |
| 61 | C2×C5×SD16 | — | 2 | 1 | no | — |
| 62 | C2×C5×D8 | — | 2 | 1 | no | — |
| 63 | C2×C5×D8 | — | 2 | 1 | no | — |
| 64 | C2×C5×D8 | — | 2 | 1 | no | — |
| 65 | C2×C5×D8 | — | 2 | 1 | no | — |
| 66 | C2×C5×D8 | — | 2 | 1 | no | — |
| 67 | C2×C5×D8 | D4 | 1 | 1 | yes | characteristic, complemented |
| 68 | C2×C5×D8 | C23 | 1 | 2 | yes | — |
| 69 | C22×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 70 | #4099 | — | 4 | 2 | no | — |
| 71 | #4097 | — | 2 | 2 | no | — |
| 72 | #4096 | — | 2 | 4 | no | — |
| 73 | #4095 | — | 2 | 2 | no | — |
| 74 | #4088 | — | 2 | 2 | no | — |
| 75 | #4086 | — | 4 | 1 | no | — |
| 76 | #4084 | — | 2 | 4 | no | — |
| 77 | #4082 | — | 4 | 1 | no | — |
| 78 | #4078 | — | 2 | 2 | no | — |
| 79 | #4072 | — | 2 | 1 | no | — |
| 80 | C2×#681 | D4 | 1 | 1 | yes | characteristic |
| 81 | #4065 | — | 2 | 2 | no | — |
| 82 | #4064 | — | 2 | 4 | no | — |
| 83 | D5×Q16 | — | 2 | 2 | no | — |
| 84 | #4062 | — | 2 | 4 | no | — |
| 85 | #4061 | — | 2 | 4 | no | — |
| 86 | #4060 | — | 2 | 4 | no | — |
| 87 | D5×SD16 | — | 2 | 4 | no | — |
| 88 | #4058 | — | 2 | 2 | no | — |
| 89 | #4057 | — | 2 | 4 | no | — |
| 90 | D5×D8 | — | 2 | 2 | no | — |
| 91 | C2×Dic20 | D4 | 1 | 1 | yes | characteristic, complemented |
| 92 | #4050 | — | 2 | 1 | no | — |
| 93 | #4050 | — | 2 | 1 | no | — |
| 94 | #4050 | D4 | 1 | 2 | yes | complemented |
| 95 | #4050 | C23 | 1 | 2 | yes | — |
| 96 | C2×D40 | D4 | 1 | 1 | yes | characteristic, complemented |
| 97 | C2×#677 | — | 2 | 1 | no | — |
| 98 | #4047 | — | 2 | 1 | no | — |
| 99 | #4047 | — | 2 | 1 | no | — |
| 100 | #4047 | — | 2 | 1 | no | — |
| 101 | #4047 | — | 2 | 1 | no | — |
| 102 | C2×#676 | C23 | 1 | 2 | yes | — |
| 103 | C2×C8×D5 | D4 | 1 | 2 | yes | — |
| 104 | C5×SD32 | — | 2 | 4 | no | — |
| 105 | C5×D16 | — | 2 | 4 | no | — |
| 106 | C5×M32 | — | 2 | 1 | no | — |
| 107 | C5×M32 | C23 | 1 | 2 | yes | — |
| 108 | C2×C5×C16 | — | 2 | 1 | no | — |
| 109 | #3964 | — | 2 | 4 | no | — |
| 110 | #3959 | — | 2 | 4 | no | — |
| 111 | #3958 | — | 2 | 4 | no | — |
| 112 | #3950 | — | 2 | 1 | no | — |
| 113 | #3949 | C23 | 1 | 2 | yes | — |
| 114 | #3944 | — | 2 | 1 | no | — |
| 115 | #3944 | C23 | 1 | 2 | yes | — |
| 116 | C2×#672 | — | 2 | 1 | no | — |
| 117 | #3584 | — | 5 | 1 | no | — |
| 118 | C2×#509 | — | 5 | 1 | no | — |
| 119 | C2×#509 | D5 | 1 | 1 | yes | characteristic, complemented |
| 120 | #3058 | — | 5 | 1 | no | — |
| 121 | #2190 | — | 5 | 8 | no | — |
| 122 | #2145 | — | 5 | 1 | no | — |
| 123 | #2145 | — | 5 | 1 | no | — |
| 124 | #2115 | — | 5 | 1 | no | — |
| 125 | C24×C5 | — | 4 | 1 | no | — |
| 126 | C5×#41 | — | 2 | 2 | no | — |
| 127 | C5×#41 | — | 2 | 2 | no | — |
| 128 | C5×#41 | — | 4 | 1 | no | — |
| 129 | C5×#41 | — | 4 | 1 | no | — |
| 130 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 131 | C2×C5×D4 | — | 2 | 1 | no | — |
| 132 | C2×C5×D4 | — | 2 | 2 | no | — |
| 133 | C2×C5×D4 | — | 4 | 1 | no | — |
| 134 | C2×C5×D4 | — | 4 | 1 | no | — |
| 135 | C2×C5×D4 | — | 4 | 1 | no | — |
| 136 | C2×C5×D4 | — | 4 | 1 | no | — |
| 137 | C2×C5×D4 | — | 4 | 1 | no | — |
| 138 | C2×C5×D4 | — | 4 | 1 | no | — |
| 139 | C22×C4×C5 | — | 4 | 1 | no | — |
| 140 | C22×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 141 | C2×C22⋊D5 | — | 4 | 4 | no | — |
| 142 | C2×C22⋊D5 | — | 4 | 1 | no | — |
| 143 | C2×C22⋊D5 | — | 4 | 4 | no | — |
| 144 | C2×C22⋊D5 | D8 | 1 | 2 | yes | — |
| 145 | #713 | — | 2 | 4 | no | — |
| 146 | #713 | — | 4 | 2 | no | — |
| 147 | Q8×D5 | — | 2 | 4 | no | — |
| 148 | Q8×D5 | — | 4 | 2 | no | — |
| 149 | #711 | — | 2 | 4 | no | — |
| 150 | #711 | — | 4 | 2 | no | — |
| 151 | #711 | — | 4 | 4 | no | — |
| 152 | #711 | — | 4 | 4 | no | — |
| 153 | D4×D5 | — | 2 | 4 | no | — |
| 154 | D4×D5 | — | 4 | 2 | no | — |
| 155 | D4×D5 | — | 4 | 4 | no | — |
| 156 | D4×D5 | — | 4 | 4 | no | — |
| 157 | #709 | — | 2 | 1 | no | — |
| 158 | #709 | — | 2 | 1 | no | — |
| 159 | #709 | — | 2 | 1 | no | — |
| 160 | #709 | — | 2 | 1 | no | — |
| 161 | #709 | — | 2 | 2 | no | — |
| 162 | #709 | — | 2 | 2 | no | — |
| 163 | #709 | — | 4 | 2 | no | — |
| 164 | #709 | — | 4 | 4 | no | — |
| 165 | #709 | — | 4 | 2 | no | — |
| 166 | #709 | — | 4 | 4 | no | — |
| 167 | #709 | — | 4 | 1 | no | — |
| 168 | #709 | — | 4 | 1 | no | — |
| 169 | C2×D20 | — | 2 | 1 | no | — |
| 170 | C2×D20 | — | 4 | 2 | no | — |
| 171 | C2×D20 | D8 | 1 | 1 | yes | characteristic |
| 172 | C2×C4×D5 | — | 4 | 4 | no | — |
| 173 | C2×C4×D5 | — | 4 | 1 | no | — |
| 174 | C2×C4×D5 | C2×D4 | 1 | 2 | yes | — |
| 175 | C2×Dic10 | — | 2 | 1 | no | — |
| 176 | C2×Dic10 | — | 4 | 2 | no | — |
| 177 | C2×Dic10 | D8 | 1 | 1 | yes | characteristic |
| 178 | C5×Q16 | — | 2 | 1 | no | — |
| 179 | C5×Q16 | C2×D4 | 1 | 2 | yes | — |
| 180 | C5×SD16 | — | 2 | 2 | no | — |
| 181 | C5×SD16 | — | 2 | 2 | no | — |
| 182 | C5×D8 | — | 2 | 1 | no | — |
| 183 | C5×D8 | — | 2 | 2 | no | — |
| 184 | C5×D8 | — | 2 | 2 | no | — |
| 185 | C5×D8 | — | 4 | 1 | no | — |
| 186 | C5×D8 | — | 4 | 1 | no | — |
| 187 | C5×D8 | C2×D4 | 1 | 2 | yes | — |
| 188 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 189 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 190 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 191 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 192 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 193 | C2×C5×C8 | C24 | 1 | 1 | yes | characteristic |
| 194 | C22⋊Dic5 | — | 4 | 1 | no | — |
| 195 | C22⋊Dic5 | — | 4 | 4 | no | — |
| 196 | #689 | — | 2 | 4 | no | — |
| 197 | #688 | — | 2 | 4 | no | — |
| 198 | #687 | — | 2 | 4 | no | — |
| 199 | #686 | — | 2 | 4 | no | — |
| 200 | C4⋊Dic5 | — | 2 | 2 | no | — |
| 201 | C4×Dic5 | — | 4 | 1 | no | — |
| 202 | #681 | — | 2 | 1 | no | — |
| 203 | #681 | — | 2 | 1 | no | — |
| 204 | C2×#168 | C2×D4 | 1 | 2 | yes | — |
| 205 | Dic20 | — | 2 | 1 | no | — |
| 206 | Dic20 | C2×D4 | 1 | 2 | yes | — |
| 207 | D40 | — | 2 | 1 | no | — |
| 208 | D40 | C2×D4 | 1 | 2 | yes | — |
| 209 | #677 | — | 2 | 2 | no | — |
| 210 | #677 | — | 2 | 2 | no | — |
| 211 | #676 | — | 2 | 2 | no | — |
| 212 | #676 | — | 2 | 2 | no | — |
| 213 | C8×D5 | — | 2 | 2 | no | — |
| 214 | C8×D5 | — | 2 | 2 | no | — |
| 215 | C5×C16 | — | 2 | 2 | no | — |
| 216 | #672 | — | 2 | 2 | no | — |
| 217 | #585 | — | 10 | 1 | no | — |
| 218 | #578 | — | 10 | 1 | no | — |
| 219 | #578 | — | 10 | 1 | no | — |
| 220 | #577 | — | 10 | 2 | no | — |
| 221 | #577 | — | 10 | 2 | no | — |
| 222 | #576 | — | 10 | 1 | no | — |
| 223 | #576 | — | 10 | 1 | no | — |
| 224 | #575 | — | 5 | 4 | no | — |
| 225 | #575 | — | 10 | 1 | no | — |
| 226 | C2×#135 | — | 5 | 1 | no | — |
| 227 | C2×#135 | — | 10 | 2 | no | — |
| 228 | C2×#135 | C2×D5 | 1 | 1 | yes | characteristic |
| 229 | C22×D8 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 230 | C2×#131 | — | 5 | 1 | no | — |
| 231 | #535 | — | 10 | 1 | no | — |
| 232 | #509 | — | 2 | 2 | no | — |
| 233 | #509 | — | 5 | 4 | no | — |
| 234 | #509 | — | 10 | 2 | no | — |
| 235 | #509 | C2×D5 | 1 | 4 | yes | complemented |
| 236 | C2×SD32 | — | 2 | 1 | no | — |
| 237 | C2×SD32 | — | 10 | 1 | no | — |
| 238 | C2×D16 | — | 2 | 1 | no | — |
| 239 | C2×D16 | — | 10 | 1 | no | — |
| 240 | C2×M32 | — | 5 | 1 | no | — |
| 241 | C2×M32 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 242 | #469 | — | 5 | 4 | no | — |
| 243 | #466 | — | 10 | 2 | no | — |
| 244 | #427 | — | 5 | 1 | no | — |
| 245 | #418 | — | 10 | 1 | no | — |
| 246 | #360 | — | 5 | 4 | no | — |
| 247 | #360 | — | 5 | 4 | no | — |
| 248 | #349 | — | 5 | 4 | no | — |
| 249 | C23×C5 | — | 4 | 1 | no | — |
| 250 | C23×C5 | — | 4 | 2 | no | — |
| 251 | C23×C5 | — | 8 | 1 | no | — |
| 252 | C23×C5 | — | 8 | 1 | no | — |
| 253 | C23×C5 | — | 16 | 2 | no | — |
| 254 | C23×C5 | C2×D8 | 1 | 1 | yes | characteristic |
| 255 | C22×D5 | — | 4 | 4 | no | — |
| 256 | C22×D5 | — | 4 | 1 | no | — |
| 257 | C22×D5 | C2×D8 | 1 | 2 | yes | — |
| 258 | C5×Q8 | — | 2 | 2 | no | — |
| 259 | C5×Q8 | — | 4 | 1 | no | — |
| 260 | C5×D4 | — | 2 | 2 | no | — |
| 261 | C5×D4 | — | 4 | 2 | no | — |
| 262 | C5×D4 | — | 4 | 2 | no | — |
| 263 | C5×D4 | — | 4 | 2 | no | — |
| 264 | C5×D4 | — | 4 | 2 | no | — |
| 265 | C5×D4 | — | 4 | 1 | no | — |
| 266 | C5×D4 | — | 8 | 1 | no | — |
| 267 | C5×D4 | — | 8 | 1 | no | — |
| 268 | C2×C4×C5 | — | 4 | 1 | no | — |
| 269 | C2×C4×C5 | — | 4 | 2 | no | — |
| 270 | C2×C4×C5 | — | 4 | 2 | no | — |
| 271 | C2×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 272 | C2×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 273 | C2×C4×C5 | C2×D8 | 1 | 1 | yes | characteristic |
| 274 | C2×C4×C5 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 275 | C2×C4×C5 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 276 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 277 | C22⋊D5 | — | 2 | 2 | no | — |
| 278 | C22⋊D5 | — | 2 | 2 | no | — |
| 279 | C22⋊D5 | — | 4 | 4 | no | — |
| 280 | C22⋊D5 | — | 4 | 4 | no | — |
| 281 | C22⋊D5 | — | 4 | 2 | no | — |
| 282 | C22⋊D5 | — | 4 | 2 | no | — |
| 283 | C22⋊D5 | — | 16 | 4 | no | — |
| 284 | C2×Dic5 | — | 4 | 4 | no | — |
| 285 | C2×Dic5 | — | 4 | 1 | no | — |
| 286 | C2×Dic5 | — | 4 | 2 | no | — |
| 287 | C2×Dic5 | C2×D8 | 1 | 2 | yes | — |
| 288 | D20 | — | 2 | 2 | no | — |
| 289 | D20 | — | 2 | 1 | no | — |
| 290 | D20 | — | 2 | 1 | no | — |
| 291 | D20 | — | 4 | 4 | no | — |
| 292 | D20 | — | 4 | 1 | no | — |
| 293 | C4×D5 | — | 2 | 2 | no | — |
| 294 | C4×D5 | — | 2 | 2 | no | — |
| 295 | C4×D5 | — | 4 | 4 | no | — |
| 296 | C4×D5 | — | 4 | 4 | no | — |
| 297 | C4×D5 | — | 4 | 2 | no | — |
| 298 | C4×D5 | — | 4 | 2 | no | — |
| 299 | Dic10 | — | 2 | 1 | no | — |
| 300 | Dic10 | — | 2 | 1 | no | — |
| 301 | Dic10 | — | 2 | 2 | no | — |
| 302 | Dic10 | — | 4 | 4 | no | — |
| 303 | Dic10 | — | 4 | 1 | no | — |
| 304 | C5×C8 | #120 | 1 | 1 | yes | characteristic |
| 305 | C5×C8 | #120 | 1 | 1 | yes | characteristic |
| 306 | C5×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 307 | C5×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 308 | #168 | — | 2 | 2 | no | — |
| 309 | 2−1+4 | — | 10 | 2 | no | — |
| 310 | 2−1+4 | — | 10 | 2 | no | — |
| 311 | 2−1+4 | — | 20 | 1 | no | — |
| 312 | H(5,𝔽2) | — | 10 | 2 | no | — |
| 313 | H(5,𝔽2) | — | 10 | 2 | no | — |
| 314 | H(5,𝔽2) | — | 20 | 2 | no | — |
| 315 | H(5,𝔽2) | — | 20 | 1 | no | — |
| 316 | C2×#41 | — | 2 | 1 | no | — |
| 317 | C2×#41 | — | 5 | 1 | no | — |
| 318 | C2×#41 | — | 10 | 4 | no | — |
| 319 | C2×#41 | — | 10 | 1 | no | — |
| 320 | C2×#41 | — | 20 | 2 | no | — |
| 321 | C2×#41 | — | 20 | 2 | no | — |
| 322 | C22×D4 | — | 2 | 1 | no | — |
| 323 | #137 | — | 10 | 4 | no | — |
| 324 | #137 | — | 10 | 2 | no | — |
| 325 | #137 | — | 10 | 2 | no | — |
| 326 | #137 | — | 10 | 4 | no | — |
| 327 | AGL(1,ℤ/8) | — | 10 | 4 | no | — |
| 328 | AGL(1,ℤ/8) | — | 10 | 2 | no | — |
| 329 | AGL(1,ℤ/8) | — | 10 | 2 | no | — |
| 330 | AGL(1,ℤ/8) | — | 10 | 4 | no | — |
| 331 | #135 | — | 2 | 1 | no | — |
| 332 | #135 | — | 2 | 1 | no | — |
| 333 | #135 | — | 5 | 2 | no | — |
| 334 | #135 | — | 5 | 2 | no | — |
| 335 | #135 | — | 10 | 4 | no | — |
| 336 | #135 | — | 10 | 2 | no | — |
| 337 | #135 | — | 10 | 4 | no | — |
| 338 | #135 | — | 10 | 2 | no | — |
| 339 | #135 | — | 10 | 1 | no | — |
| 340 | #135 | — | 10 | 1 | no | — |
| 341 | #135 | C22⋊D5 | 1 | 2 | yes | complemented |
| 342 | #135 | C22×D5 | 1 | 2 | yes | — |
| 343 | C2×Q16 | — | 5 | 1 | no | — |
| 344 | C2×Q16 | — | 10 | 2 | no | — |
| 345 | C2×Q16 | C22⋊D5 | 1 | 1 | yes | characteristic, complemented |
| 346 | C2×SD16 | — | 2 | 1 | no | — |
| 347 | C2×SD16 | — | 10 | 4 | no | — |
| 348 | C2×SD16 | — | 10 | 1 | no | — |
| 349 | C2×D8 | — | 2 | 1 | no | — |
| 350 | C2×D8 | — | 2 | 1 | no | — |
| 351 | C2×D8 | — | 2 | 1 | no | — |
| 352 | C2×D8 | — | 2 | 1 | no | — |
| 353 | C2×D8 | — | 2 | 1 | no | — |
| 354 | C2×D8 | — | 5 | 1 | no | — |
| 355 | C2×D8 | — | 10 | 2 | no | — |
| 356 | C2×D8 | C22⋊D5 | 1 | 1 | yes | characteristic, complemented |
| 357 | C2×D8 | C22×D5 | 1 | 2 | yes | — |
| 358 | #131 | — | 10 | 1 | no | — |
| 359 | #131 | — | 10 | 1 | no | — |
| 360 | #131 | — | 10 | 1 | no | — |
| 361 | #131 | — | 10 | 1 | no | — |
| 362 | C2×M16 | — | 5 | 1 | no | — |
| 363 | C2×M16 | — | 5 | 2 | no | — |
| 364 | C22×C8 | — | 5 | 2 | no | — |
| 365 | C22×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 366 | #127 | — | 20 | 1 | no | — |
| 367 | #124 | — | 20 | 1 | no | — |
| 368 | #121 | — | 10 | 4 | no | — |
| 369 | #120 | — | 20 | 2 | no | — |
| 370 | #117 | — | 10 | 1 | no | — |
| 371 | SD32 | — | 2 | 4 | no | — |
| 372 | SD32 | — | 10 | 4 | no | — |
| 373 | D16 | — | 2 | 4 | no | — |
| 374 | D16 | — | 10 | 4 | no | — |
| 375 | M32 | — | 2 | 1 | no | — |
| 376 | M32 | — | 5 | 2 | no | — |
| 377 | M32 | — | 10 | 1 | no | — |
| 378 | M32 | C22×D5 | 1 | 2 | yes | — |
| 379 | C2×C16 | — | 2 | 1 | no | — |
| 380 | C2×C16 | — | 10 | 1 | no | — |
| 381 | #107 | — | 10 | 1 | no | — |
| 382 | #106 | — | 5 | 2 | no | — |
| 383 | #102 | — | 10 | 4 | no | — |
| 384 | C22×C5 | — | 4 | 1 | no | — |
| 385 | C22×C5 | — | 4 | 2 | no | — |
| 386 | C22×C5 | — | 8 | 4 | no | — |
| 387 | C22×C5 | — | 8 | 2 | no | — |
| 388 | C22×C5 | — | 16 | 1 | no | — |
| 389 | C22×C5 | — | 16 | 2 | no | — |
| 390 | C22×C5 | — | 16 | 2 | no | — |
| 391 | C22×C5 | #447 | 1 | 1 | yes | characteristic |
| 392 | C22×C5 | #447 | 1 | 1 | yes | characteristic |
| 393 | C22×C5 | C22×D8 | 1 | 1 | yes | characteristic |
| 394 | C2×D5 | — | 2 | 2 | no | — |
| 395 | C2×D5 | — | 4 | 2 | no | — |
| 396 | C2×D5 | — | 4 | 2 | no | — |
| 397 | C2×D5 | — | 16 | 4 | no | — |
| 398 | C2×D5 | — | 16 | 1 | no | — |
| 399 | C4×C5 | — | 4 | 2 | no | — |
| 400 | C4×C5 | #447 | 1 | 1 | yes | characteristic |
| 401 | C4×C5 | #447 | 1 | 1 | yes | characteristic |
| 402 | C4×C5 | C2×#120 | 1 | 1 | yes | characteristic |
| 403 | C4×C5 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 404 | Dic5 | — | 2 | 2 | no | — |
| 405 | Dic5 | — | 4 | 2 | no | — |
| 406 | Dic5 | — | 8 | 2 | no | — |
| 407 | C24 | — | 4 | 1 | no | — |
| 408 | #41 | — | 2 | 2 | no | — |
| 409 | #41 | — | 2 | 2 | no | — |
| 410 | #41 | — | 4 | 1 | no | — |
| 411 | #41 | — | 4 | 1 | no | — |
| 412 | #41 | — | 10 | 1 | no | — |
| 413 | #41 | — | 10 | 1 | no | — |
| 414 | #41 | — | 10 | 1 | no | — |
| 415 | #41 | — | 10 | 1 | no | — |
| 416 | #41 | — | 10 | 4 | no | — |
| 417 | #41 | — | 10 | 4 | no | — |
| 418 | #41 | — | 10 | 2 | no | — |
| 419 | #41 | — | 10 | 2 | no | — |
| 420 | #41 | — | 20 | 4 | no | — |
| 421 | #41 | — | 20 | 4 | no | — |
| 422 | #41 | — | 20 | 2 | no | — |
| 423 | #41 | — | 20 | 2 | no | — |
| 424 | #41 | — | 20 | 4 | no | — |
| 425 | #41 | — | 20 | 4 | no | — |
| 426 | #41 | — | 20 | 2 | no | — |
| 427 | #41 | — | 20 | 2 | no | — |
| 428 | #41 | — | 20 | 1 | no | — |
| 429 | #41 | — | 20 | 1 | no | — |
| 430 | C2×Q8 | — | 2 | 1 | no | — |
| 431 | C2×Q8 | — | 5 | 1 | no | — |
| 432 | C2×Q8 | — | 10 | 4 | no | — |
| 433 | C2×Q8 | — | 10 | 1 | no | — |
| 434 | C2×Q8 | — | 20 | 2 | no | — |
| 435 | C2×Q8 | — | 20 | 2 | no | — |
| 436 | C2×D4 | — | 2 | 2 | no | — |
| 437 | C2×D4 | — | 2 | 1 | no | — |
| 438 | C2×D4 | — | 4 | 1 | no | — |
| 439 | C2×D4 | — | 4 | 1 | no | — |
| 440 | C2×D4 | — | 4 | 1 | no | — |
| 441 | C2×D4 | — | 4 | 1 | no | — |
| 442 | C2×D4 | — | 4 | 1 | no | — |
| 443 | C2×D4 | — | 4 | 1 | no | — |
| 444 | C2×D4 | — | 5 | 2 | no | — |
| 445 | C2×D4 | — | 5 | 1 | no | — |
| 446 | C2×D4 | — | 10 | 4 | no | — |
| 447 | C2×D4 | — | 10 | 1 | no | — |
| 448 | C2×D4 | — | 20 | 2 | no | — |
| 449 | C2×D4 | — | 20 | 4 | no | — |
| 450 | C2×D4 | — | 20 | 2 | no | — |
| 451 | C2×D4 | — | 20 | 4 | no | — |
| 452 | C2×D4 | — | 20 | 4 | no | — |
| 453 | C2×D4 | — | 20 | 1 | no | — |
| 454 | C2×D4 | — | 20 | 4 | no | — |
| 455 | C22×C4 | — | 4 | 1 | no | — |
| 456 | C22×C4 | — | 5 | 2 | no | — |
| 457 | C22×C4 | — | 20 | 4 | no | — |
| 458 | C22×C4 | — | 20 | 1 | no | — |
| 459 | C22×C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 460 | Q16 | — | 2 | 1 | no | — |
| 461 | Q16 | — | 5 | 2 | no | — |
| 462 | Q16 | — | 10 | 4 | no | — |
| 463 | Q16 | — | 10 | 1 | no | — |
| 464 | Q16 | C2×C22⋊D5 | 1 | 2 | yes | — |
| 465 | SD16 | — | 2 | 2 | no | — |
| 466 | SD16 | — | 2 | 2 | no | — |
| 467 | SD16 | — | 10 | 4 | no | — |
| 468 | SD16 | — | 10 | 4 | no | — |
| 469 | SD16 | — | 10 | 2 | no | — |
| 470 | SD16 | — | 10 | 2 | no | — |
| 471 | D8 | — | 2 | 2 | no | — |
| 472 | D8 | — | 2 | 2 | no | — |
| 473 | D8 | — | 2 | 1 | no | — |
| 474 | D8 | — | 4 | 1 | no | — |
| 475 | D8 | — | 4 | 1 | no | — |
| 476 | D8 | — | 5 | 2 | no | — |
| 477 | D8 | — | 10 | 4 | no | — |
| 478 | D8 | — | 10 | 1 | no | — |
| 479 | D8 | C2×C22⋊D5 | 1 | 2 | yes | — |
| 480 | M16 | — | 10 | 1 | no | — |
| 481 | M16 | — | 10 | 1 | no | — |
| 482 | M16 | — | 10 | 2 | no | — |
| 483 | M16 | — | 10 | 2 | no | — |
| 484 | C2×C8 | — | 5 | 2 | no | — |
| 485 | C2×C8 | — | 10 | 2 | no | — |
| 486 | C2×C8 | — | 10 | 2 | no | — |
| 487 | C2×C8 | D4×D5 | 1 | 1 | yes | characteristic |
| 488 | C2×C8 | D4×D5 | 1 | 1 | yes | characteristic |
| 489 | C2×C8 | D4×D5 | 1 | 1 | yes | characteristic |
| 490 | C2×C8 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 491 | C2×C8 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 492 | C2×C8 | C23×D5 | 1 | 1 | yes | characteristic |
| 493 | C4⋊C4 | — | 10 | 2 | no | — |
| 494 | C22⋊C4 | — | 20 | 4 | no | — |
| 495 | C22⋊C4 | — | 20 | 1 | no | — |
| 496 | C42 | — | 20 | 1 | no | — |
| 497 | C16 | — | 2 | 2 | no | — |
| 498 | C16 | — | 10 | 2 | no | — |
| 499 | C2×C5 | — | 2 | 1 | no | — |
| 500 | C2×C5 | — | 2 | 1 | no | — |
| 501 | C2×C5 | — | 2 | 1 | no | — |
| 502 | C2×C5 | — | 8 | 2 | no | — |
| 503 | C2×C5 | — | 16 | 2 | no | — |
| 504 | C2×C5 | C2×#447 | 1 | 1 | yes | characteristic |
| 505 | D5 | — | 4 | 2 | no | — |
| 506 | D5 | — | 8 | 2 | no | — |
| 507 | C23 | — | 4 | 1 | no | — |
| 508 | C23 | — | 4 | 2 | no | — |
| 509 | C23 | — | 5 | 2 | no | — |
| 510 | C23 | — | 8 | 1 | no | — |
| 511 | C23 | — | 8 | 1 | no | — |
| 512 | C23 | — | 16 | 2 | no | — |
| 513 | C23 | — | 20 | 4 | no | — |
| 514 | C23 | — | 20 | 1 | no | — |
| 515 | C23 | D5×D8 | 1 | 1 | yes | characteristic |
| 516 | Q8 | — | 2 | 2 | no | — |
| 517 | Q8 | — | 4 | 1 | no | — |
| 518 | Q8 | — | 10 | 1 | no | — |
| 519 | Q8 | — | 10 | 1 | no | — |
| 520 | Q8 | — | 10 | 2 | no | — |
| 521 | Q8 | — | 20 | 4 | no | — |
| 522 | Q8 | — | 20 | 1 | no | — |
| 523 | D4 | — | 2 | 2 | no | — |
| 524 | D4 | — | 4 | 2 | no | — |
| 525 | D4 | — | 4 | 2 | no | — |
| 526 | D4 | — | 4 | 2 | no | — |
| 527 | D4 | — | 4 | 2 | no | — |
| 528 | D4 | — | 4 | 1 | no | — |
| 529 | D4 | — | 8 | 1 | no | — |
| 530 | D4 | — | 8 | 1 | no | — |
| 531 | D4 | — | 10 | 2 | no | — |
| 532 | D4 | — | 10 | 2 | no | — |
| 533 | D4 | — | 10 | 2 | no | — |
| 534 | D4 | — | 10 | 1 | no | — |
| 535 | D4 | — | 10 | 1 | no | — |
| 536 | D4 | — | 20 | 4 | no | — |
| 537 | D4 | — | 20 | 4 | no | — |
| 538 | D4 | — | 20 | 4 | no | — |
| 539 | D4 | — | 20 | 2 | no | — |
| 540 | D4 | — | 20 | 2 | no | — |
| 541 | D4 | — | 20 | 1 | no | — |
| 542 | D4 | — | 80 | 4 | no | — |
| 543 | C2×C4 | — | 4 | 1 | no | — |
| 544 | C2×C4 | — | 4 | 2 | no | — |
| 545 | C2×C4 | — | 4 | 2 | no | — |
| 546 | C2×C4 | — | 5 | 2 | no | — |
| 547 | C2×C4 | — | 10 | 2 | no | — |
| 548 | C2×C4 | — | 10 | 2 | no | — |
| 549 | C2×C4 | — | 20 | 4 | no | — |
| 550 | C2×C4 | — | 20 | 4 | no | — |
| 551 | C2×C4 | — | 20 | 4 | no | — |
| 552 | C2×C4 | — | 20 | 1 | no | — |
| 553 | C2×C4 | — | 20 | 2 | no | — |
| 554 | C2×C4 | — | 20 | 2 | no | — |
| 555 | C2×C4 | — | 20 | 2 | no | — |
| 556 | C2×C4 | D5×D8 | 1 | 1 | yes | characteristic |
| 557 | C2×C4 | #4057 | 1 | 1 | yes | characteristic |
| 558 | C2×C4 | #4057 | 1 | 1 | yes | characteristic |
| 559 | C2×C4 | #4083 | 1 | 1 | yes | characteristic |
| 560 | C2×C4 | #4083 | 1 | 1 | yes | characteristic |
| 561 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 562 | C8 | — | 10 | 2 | no | — |
| 563 | C8 | #4083 | 1 | 1 | yes | characteristic |
| 564 | C8 | #4083 | 1 | 1 | yes | characteristic |
| 565 | C8 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 566 | C8 | C22×C22⋊D5 | 1 | 1 | yes | characteristic |
| 567 | C5 | #33531 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 568 | C22 | — | 4 | 1 | no | — |
| 569 | C22 | — | 4 | 2 | no | — |
| 570 | C22 | — | 8 | 4 | no | — |
| 571 | C22 | — | 8 | 2 | no | — |
| 572 | C22 | — | 10 | 2 | no | — |
| 573 | C22 | — | 16 | 1 | no | — |
| 574 | C22 | — | 16 | 2 | no | — |
| 575 | C22 | — | 16 | 2 | no | — |
| 576 | C22 | — | 20 | 2 | no | — |
| 577 | C22 | — | 20 | 2 | no | — |
| 578 | C22 | — | 80 | 1 | no | — |
| 579 | C22 | — | 80 | 4 | no | — |
| 580 | C22 | #65445 | 1 | 1 | yes | characteristic |
| 581 | C22 | #65445 | 1 | 1 | yes | characteristic |
| 582 | C22 | C2×D5×D8 | 1 | 1 | yes | characteristic |
| 583 | C4 | — | 4 | 2 | no | — |
| 584 | C4 | — | 10 | 2 | no | — |
| 585 | C4 | — | 20 | 2 | no | — |
| 586 | C4 | — | 40 | 2 | no | — |
| 587 | C4 | #65445 | 1 | 1 | yes | characteristic |
| 588 | C4 | #65445 | 1 | 1 | yes | characteristic |
| 589 | C4 | C2×#4057 | 1 | 1 | yes | characteristic |
| 590 | C4 | C2×#4083 | 1 | 1 | yes | characteristic |
| 591 | C2 | — | 2 | 1 | no | — |
| 592 | C2 | — | 2 | 1 | no | — |
| 593 | C2 | — | 2 | 1 | no | — |
| 594 | C2 | — | 8 | 2 | no | — |
| 595 | C2 | — | 16 | 2 | no | — |
| 596 | C2 | — | 20 | 2 | no | — |
| 597 | C2 | — | 40 | 2 | no | — |
| 598 | C2 | C2×#65445 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10619088 | C2 | semidirect |
| 2. C2×C5×#509 | C2 | semidirect |
| 3. #10615567 | C2 | semidirect |
| 4. C2×#65436 | C2 | semidirect |
| 5. #10602869 | C2 | semidirect |
| 6. #10602309 | C2 | semidirect |
| 7. #10602243 | C2 | semidirect |
| 8. #10602228 | C2 | semidirect |
| 11. C22×C5×D8 | C22 | semidirect |
| 17. #66102 | C22 | semidirect |
| 25. C5×#509 | C22 | semidirect |
| 28. C2×C5×M32 | C22 | semidirect |
| 30. #65448 | C22 | semidirect |
| 34. #65436 | C22 | semidirect |
| 36. #65395 | C22 | semidirect |
| 37. C2×#3944 | C22 | semidirect |
| 38. #64786 | C22 | semidirect |
| 39. #64738 | C22 | semidirect |
| 40. #64734 | C22 | semidirect |
| 58. C5×#135 | D4 | semidirect |
| 60. C2×C5×Q16 | D4 | semidirect |
| 67. C2×C5×D8 | D4 | semidirect |
| 91. C2×Dic20 | D4 | semidirect |
| 94. #4050 | D4 | semidirect |
| 96. C2×D40 | D4 | semidirect |
| 119. C2×#509 | D5 | semidirect |
| 229. C22×D8 | C2×D5 | semidirect |
| 235. #509 | C2×D5 | semidirect |
| 241. C2×M32 | C2×D5 | semidirect |
| 341. #135 | C22⋊D5 | semidirect |
| 345. C2×Q16 | C22⋊D5 | semidirect |
| 356. C2×D8 | C22⋊D5 | semidirect |
| 567. C5 | #33531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10619088 | 2 |
| C2×C5×#509 | 2 |
| #10615567 | 2 |
| C2×#65436 | 2 |
| #10602869 | 2 |
| #10602309 | 2 |
| #10602243 | 2 |
| #10602228 | 2 |
| #33531 | 5 |