Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1740 conjugacy classes of subgroups.
The subgroup lattice has 472 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10617729 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #41×Dic10 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C5×#2988 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | Q8×Dic20 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10611664 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #10611179 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #10611146 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #10611041 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #10611003 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #10610768 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | C2×#65139 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | C4×C5×#41 | C22 | 1 | 1 | yes | characteristic |
| 13 | #66161 | — | 2 | 1 | no | — |
| 14 | #41×Dic5 | — | 2 | 1 | no | — |
| 15 | #65904 | — | 2 | 1 | no | — |
| 16 | #65904 | C22 | 1 | 1 | yes | characteristic |
| 17 | #65903 | — | 2 | 1 | no | — |
| 18 | Q8×Dic10 | C22 | 1 | 1 | yes | characteristic |
| 19 | Q8×Dic10 | C22 | 1 | 2 | yes | — |
| 20 | #65877 | C22 | 1 | 3 | yes | — |
| 21 | #65877 | C22 | 1 | 6 | yes | — |
| 22 | #65873 | — | 2 | 3 | no | — |
| 23 | D4×Dic10 | — | 2 | 3 | no | — |
| 24 | D4×Dic10 | C22 | 1 | 3 | yes | — |
| 25 | #65853 | — | 2 | 3 | no | — |
| 26 | #65851 | — | 2 | 3 | no | — |
| 27 | #65804 | C22 | 1 | 3 | yes | — |
| 28 | #65804 | C22 | 1 | 3 | yes | — |
| 29 | C2×#4015 | C22 | 1 | 3 | yes | — |
| 30 | C2×C4×Dic10 | C22 | 1 | 3 | yes | — |
| 31 | C5×C8×Q8 | C22 | 1 | 2 | yes | — |
| 32 | C5×C8×D4 | C22 | 1 | 6 | yes | — |
| 33 | C5×#431 | C22 | 1 | 3 | yes | — |
| 34 | C2×C5×C4⋊C8 | C22 | 1 | 3 | yes | — |
| 35 | #65405 | C22 | 1 | 12 | yes | — |
| 36 | C2×#3950 | C22 | 1 | 6 | yes | — |
| 37 | C2×#3948 | C22 | 1 | 6 | yes | — |
| 38 | #65139 | C22 | 1 | 3 | yes | — |
| 39 | #65139 | C22 | 1 | 6 | yes | — |
| 40 | #65139 | C22 | 1 | 3 | yes | — |
| 41 | #65139 | C22 | 1 | 6 | yes | — |
| 42 | #65139 | C22 | 1 | 6 | yes | — |
| 43 | #65139 | C22 | 1 | 6 | yes | — |
| 44 | #65138 | C22 | 1 | 3 | yes | — |
| 45 | #65138 | C22 | 1 | 6 | yes | — |
| 46 | #65138 | C22 | 1 | 1 | yes | characteristic |
| 47 | #65028 | C22 | 1 | 6 | yes | — |
| 48 | #65011 | C22 | 1 | 12 | yes | — |
| 49 | #65011 | C22 | 1 | 6 | yes | — |
| 50 | C4×Dic20 | C22 | 1 | 6 | yes | — |
| 51 | C4×Dic20 | C22 | 1 | 6 | yes | — |
| 52 | #64971 | C22 | 1 | 6 | yes | — |
| 53 | #64970 | C22 | 1 | 6 | yes | — |
| 54 | #62100 | — | 5 | 1 | no | maximal, Sylow |
| 55 | C2×C5×#41 | D4 | 1 | 1 | yes | characteristic |
| 56 | C22×Dic10 | — | 2 | 3 | no | — |
| 57 | C22×Dic10 | C23 | 1 | 3 | yes | — |
| 58 | C22×C5×C8 | C23 | 1 | 6 | yes | — |
| 59 | C4×C5×Q8 | D4 | 1 | 1 | yes | characteristic |
| 60 | C4×C5×Q8 | C23 | 1 | 1 | yes | characteristic |
| 61 | C4×C5×D4 | D4 | 1 | 3 | yes | — |
| 62 | C4×C5×D4 | C23 | 1 | 3 | yes | — |
| 63 | C5×#117 | D4 | 1 | 3 | yes | — |
| 64 | C2×C42×C5 | C23 | 1 | 3 | yes | — |
| 65 | Q8×Dic5 | — | 2 | 1 | no | — |
| 66 | Q8×Dic5 | — | 2 | 2 | no | — |
| 67 | Q8×Dic5 | — | 2 | 1 | no | — |
| 68 | D4×Dic5 | — | 2 | 6 | no | — |
| 69 | D4×Dic5 | — | 2 | 3 | no | — |
| 70 | D4×Dic5 | — | 2 | 3 | no | — |
| 71 | #4072 | — | 2 | 3 | no | — |
| 72 | #4072 | — | 2 | 3 | no | — |
| 73 | C2×C4⋊Dic5 | — | 2 | 3 | no | — |
| 74 | C2×C4⋊Dic5 | C23 | 1 | 3 | yes | — |
| 75 | C2×C4⋊Dic5 | C23 | 1 | 6 | yes | — |
| 76 | #4070 | — | 2 | 3 | no | — |
| 77 | #4070 | — | 2 | 3 | no | — |
| 78 | #4070 | C23 | 1 | 6 | yes | — |
| 79 | #4070 | C23 | 1 | 6 | yes | — |
| 80 | C2×#683 | — | 2 | 3 | no | — |
| 81 | C2×C4×Dic5 | — | 2 | 3 | no | — |
| 82 | C2×Dic20 | C23 | 1 | 2 | yes | — |
| 83 | C2×Dic20 | C23 | 1 | 6 | yes | — |
| 84 | #4036 | — | 2 | 3 | no | — |
| 85 | #4036 | — | 2 | 3 | no | — |
| 86 | #4036 | — | 2 | 6 | no | — |
| 87 | #4034 | — | 2 | 3 | no | — |
| 88 | #4034 | — | 2 | 3 | no | — |
| 89 | #4034 | — | 2 | 6 | no | — |
| 90 | #4024 | — | 2 | 6 | no | — |
| 91 | #4024 | — | 2 | 6 | no | — |
| 92 | #4024 | — | 2 | 12 | no | — |
| 93 | #4016 | — | 2 | 3 | no | — |
| 94 | #4016 | — | 2 | 3 | no | — |
| 95 | #4015 | — | 2 | 3 | no | — |
| 96 | #4015 | — | 2 | 3 | no | — |
| 97 | #4015 | C23 | 1 | 1 | yes | characteristic |
| 98 | #4015 | C23 | 1 | 3 | yes | — |
| 99 | #4015 | C23 | 1 | 3 | yes | — |
| 100 | #4015 | C23 | 1 | 6 | yes | — |
| 101 | #4015 | C23 | 1 | 3 | yes | — |
| 102 | C4×Dic10 | — | 2 | 3 | no | — |
| 103 | C4×Dic10 | — | 2 | 3 | no | — |
| 104 | C4×Dic10 | — | 2 | 3 | no | — |
| 105 | C4×Dic10 | — | 2 | 3 | no | — |
| 106 | C4×Dic10 | C23 | 1 | 1 | yes | characteristic |
| 107 | C4×Dic10 | C23 | 1 | 3 | yes | — |
| 108 | C4×Dic10 | C23 | 1 | 3 | yes | — |
| 109 | C4×Dic10 | C23 | 1 | 3 | yes | — |
| 110 | C4×Dic10 | C23 | 1 | 6 | yes | — |
| 111 | C5×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 112 | C5×C4⋊C8 | C23 | 1 | 6 | yes | — |
| 113 | C5×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 114 | C5×C22⋊C8 | C23 | 1 | 6 | yes | — |
| 115 | C4×C5×C8 | C23 | 1 | 6 | yes | — |
| 116 | #3950 | C23 | 1 | 6 | yes | — |
| 117 | #3950 | C23 | 1 | 12 | yes | — |
| 118 | #3950 | C23 | 1 | 6 | yes | — |
| 119 | #3948 | C23 | 1 | 6 | yes | — |
| 120 | #3948 | C23 | 1 | 6 | yes | — |
| 121 | #3948 | C23 | 1 | 12 | yes | — |
| 122 | #3948 | C23 | 1 | 6 | yes | — |
| 123 | #3948 | C23 | 1 | 2 | yes | — |
| 124 | #3503 | — | 5 | 1 | no | — |
| 125 | Q8×#41 | — | 5 | 1 | no | — |
| 126 | Q8×Q16 | — | 5 | 2 | no | — |
| 127 | #3363 | — | 5 | 2 | no | — |
| 128 | #3338 | — | 5 | 6 | no | — |
| 129 | #3299 | — | 5 | 6 | no | — |
| 130 | #3249 | — | 5 | 3 | no | — |
| 131 | #3230 | — | 5 | 3 | no | — |
| 132 | #3104 | — | 5 | 3 | no | — |
| 133 | C2×#477 | — | 5 | 3 | no | — |
| 134 | #2988 | D5 | 1 | 1 | yes | characteristic |
| 135 | C5×#41 | Q16 | 1 | 8 | yes | complemented |
| 136 | C2×C5×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 137 | C2×C5×D4 | C2×D4 | 1 | 3 | yes | — |
| 138 | C22×C4×C5 | C2×D4 | 1 | 3 | yes | — |
| 139 | C22×C4×C5 | C2×D4 | 1 | 3 | yes | — |
| 140 | C22×C4×C5 | C24 | 1 | 3 | yes | — |
| 141 | C22×Dic5 | — | 2 | 3 | no | — |
| 142 | C22×Dic5 | — | 2 | 6 | no | — |
| 143 | C22×Dic5 | — | 2 | 3 | no | — |
| 144 | C2×Dic10 | — | 2 | 6 | no | — |
| 145 | C2×Dic10 | — | 2 | 3 | no | — |
| 146 | C2×Dic10 | — | 2 | 3 | no | — |
| 147 | C2×Dic10 | — | 2 | 6 | no | — |
| 148 | C2×Dic10 | — | 2 | 3 | no | — |
| 149 | C2×Dic10 | — | 4 | 3 | no | — |
| 150 | C2×Dic10 | — | 8 | 6 | no | — |
| 151 | C2×Dic10 | C24 | 1 | 3 | yes | — |
| 152 | C2×Dic10 | C24 | 1 | 2 | yes | — |
| 153 | C2×Dic10 | C24 | 1 | 1 | yes | characteristic |
| 154 | C2×C5×C8 | — | 4 | 6 | no | — |
| 155 | C2×C5×C8 | C24 | 1 | 6 | yes | — |
| 156 | C2×C5×C8 | C24 | 1 | 2 | yes | — |
| 157 | C5×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 158 | C5×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 159 | C5×C22⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 160 | C42×C5 | C2×D4 | 1 | 3 | yes | — |
| 161 | C42×C5 | C2×D4 | 1 | 3 | yes | — |
| 162 | C42×C5 | C24 | 1 | 1 | yes | characteristic |
| 163 | C42×C5 | C24 | 1 | 3 | yes | — |
| 164 | C22⋊Dic5 | — | 2 | 6 | no | — |
| 165 | C22⋊Dic5 | — | 2 | 6 | no | — |
| 166 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 167 | C4⋊Dic5 | — | 2 | 3 | no | — |
| 168 | C4⋊Dic5 | — | 2 | 3 | no | — |
| 169 | C4⋊Dic5 | — | 2 | 3 | no | — |
| 170 | C4⋊Dic5 | — | 2 | 6 | no | — |
| 171 | C4⋊Dic5 | — | 2 | 6 | no | — |
| 172 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 173 | C4⋊Dic5 | — | 2 | 3 | no | — |
| 174 | C4⋊Dic5 | — | 2 | 3 | no | — |
| 175 | C4⋊Dic5 | C24 | 1 | 6 | yes | — |
| 176 | C4⋊Dic5 | C24 | 1 | 1 | yes | characteristic |
| 177 | C4⋊Dic5 | C24 | 1 | 3 | yes | — |
| 178 | #683 | — | 2 | 1 | no | — |
| 179 | #683 | — | 2 | 3 | no | — |
| 180 | #683 | — | 2 | 3 | no | — |
| 181 | #683 | — | 2 | 3 | no | — |
| 182 | #683 | — | 2 | 6 | no | — |
| 183 | #683 | — | 2 | 6 | no | — |
| 184 | #683 | — | 2 | 6 | no | — |
| 185 | C4×Dic5 | — | 2 | 1 | no | — |
| 186 | C4×Dic5 | — | 2 | 3 | no | — |
| 187 | C4×Dic5 | — | 2 | 3 | no | — |
| 188 | C4×Dic5 | — | 2 | 6 | no | — |
| 189 | C4×Dic5 | — | 2 | 3 | no | — |
| 190 | Dic20 | — | 2 | 4 | no | — |
| 191 | Dic20 | — | 4 | 6 | no | — |
| 192 | Q82 | — | 5 | 2 | no | — |
| 193 | Q82 | — | 5 | 1 | no | — |
| 194 | #557 | — | 5 | 1 | no | — |
| 195 | #557 | — | 10 | 1 | no | — |
| 196 | #557 | — | 10 | 1 | no | — |
| 197 | #554 | — | 5 | 3 | no | — |
| 198 | #554 | — | 5 | 6 | no | — |
| 199 | #554 | — | 10 | 3 | no | — |
| 200 | D4×Q8 | — | 5 | 3 | no | — |
| 201 | D4×Q8 | — | 10 | 3 | no | — |
| 202 | #544 | — | 10 | 3 | no | — |
| 203 | #533 | — | 5 | 3 | no | — |
| 204 | #533 | — | 5 | 3 | no | — |
| 205 | #533 | — | 10 | 3 | no | — |
| 206 | C2×C4⋊Q8 | — | 5 | 3 | no | — |
| 207 | #520 | — | 10 | 1 | no | — |
| 208 | C4×#41 | — | 10 | 1 | no | — |
| 209 | C4×#41 | C2×D5 | 1 | 1 | yes | characteristic |
| 210 | C2×C4×Q8 | — | 5 | 3 | no | — |
| 211 | #500 | — | 5 | 6 | no | — |
| 212 | #487 | — | 5 | 6 | no | — |
| 213 | #484 | — | 5 | 6 | no | — |
| 214 | #484 | — | 5 | 12 | no | — |
| 215 | #477 | — | 5 | 3 | no | — |
| 216 | #477 | — | 5 | 6 | no | — |
| 217 | #477 | — | 5 | 6 | no | — |
| 218 | #477 | — | 5 | 6 | no | — |
| 219 | #477 | — | 5 | 6 | no | — |
| 220 | #477 | — | 5 | 3 | no | — |
| 221 | #467 | — | 5 | 12 | no | — |
| 222 | #462 | — | 5 | 1 | no | — |
| 223 | #462 | — | 5 | 3 | no | — |
| 224 | #462 | — | 5 | 6 | no | — |
| 225 | #451 | — | 5 | 6 | no | — |
| 226 | C8×Q8 | C2×D5 | 1 | 2 | yes | — |
| 227 | C4×Q16 | — | 5 | 6 | no | — |
| 228 | C4×Q16 | — | 5 | 6 | no | — |
| 229 | C8×D4 | C2×D5 | 1 | 6 | yes | — |
| 230 | #431 | C2×D5 | 1 | 3 | yes | — |
| 231 | C2×#107 | — | 5 | 6 | no | — |
| 232 | C2×C4⋊C8 | C2×D5 | 1 | 3 | yes | — |
| 233 | C2×#103 | — | 5 | 6 | no | — |
| 234 | C23×C5 | C22×D4 | 1 | 3 | yes | — |
| 235 | C5×Q8 | C2×Q16 | 1 | 4 | yes | — |
| 236 | C5×D4 | C2×Q16 | 1 | 12 | yes | — |
| 237 | C2×C4×C5 | — | 2 | 3 | no | — |
| 238 | C2×C4×C5 | — | 2 | 3 | no | — |
| 239 | C2×C4×C5 | — | 4 | 3 | no | — |
| 240 | C2×C4×C5 | C2×Q16 | 1 | 12 | yes | — |
| 241 | C2×C4×C5 | C22×D4 | 1 | 3 | yes | — |
| 242 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 243 | C2×C4×C5 | C22×D4 | 1 | 3 | yes | — |
| 244 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 245 | C2×C4×C5 | C22×D4 | 1 | 3 | yes | — |
| 246 | C2×C4×C5 | C25 | 1 | 1 | yes | characteristic |
| 247 | C2×Dic5 | — | 2 | 1 | no | — |
| 248 | C2×Dic5 | — | 2 | 1 | no | — |
| 249 | C2×Dic5 | — | 2 | 2 | no | — |
| 250 | C2×Dic5 | — | 2 | 3 | no | — |
| 251 | C2×Dic5 | — | 2 | 3 | no | — |
| 252 | C2×Dic5 | — | 2 | 6 | no | — |
| 253 | C2×Dic5 | — | 4 | 6 | no | — |
| 254 | C2×Dic5 | — | 8 | 6 | no | — |
| 255 | C2×Dic5 | — | 8 | 3 | no | — |
| 256 | Dic10 | — | 2 | 1 | no | — |
| 257 | Dic10 | — | 2 | 2 | no | — |
| 258 | Dic10 | — | 2 | 3 | no | — |
| 259 | Dic10 | — | 2 | 2 | no | — |
| 260 | Dic10 | — | 2 | 3 | no | — |
| 261 | Dic10 | — | 4 | 6 | no | — |
| 262 | Dic10 | — | 4 | 6 | no | — |
| 263 | Dic10 | — | 8 | 3 | no | — |
| 264 | Dic10 | — | 8 | 6 | no | — |
| 265 | Dic10 | 2−1+4 | 1 | 2 | yes | — |
| 266 | C5×C8 | — | 2 | 2 | no | — |
| 267 | C5×C8 | — | 2 | 6 | no | — |
| 268 | C2×#41 | D20 | 1 | 1 | yes | characteristic |
| 269 | C22×Q8 | — | 5 | 3 | no | — |
| 270 | C22×Q8 | — | 10 | 3 | no | — |
| 271 | C2×Q16 | — | 5 | 2 | no | — |
| 272 | C2×Q16 | — | 5 | 6 | no | — |
| 273 | C22×C8 | C22×D5 | 1 | 6 | yes | — |
| 274 | C4⋊Q8 | — | 5 | 3 | no | — |
| 275 | C4⋊Q8 | — | 5 | 6 | no | — |
| 276 | C4⋊Q8 | — | 5 | 3 | no | — |
| 277 | C4⋊Q8 | — | 5 | 1 | no | — |
| 278 | C4⋊Q8 | — | 5 | 3 | no | — |
| 279 | C4⋊Q8 | — | 10 | 3 | no | — |
| 280 | C4⋊Q8 | — | 10 | 3 | no | — |
| 281 | C4⋊Q8 | — | 10 | 6 | no | — |
| 282 | C4⋊Q8 | — | 10 | 3 | no | — |
| 283 | C4⋊Q8 | — | 10 | 3 | no | — |
| 284 | #125 | — | 10 | 3 | no | — |
| 285 | #125 | — | 10 | 3 | no | — |
| 286 | #125 | — | 10 | 6 | no | — |
| 287 | #125 | — | 10 | 3 | no | — |
| 288 | #125 | — | 10 | 3 | no | — |
| 289 | C22⋊Q8 | — | 5 | 6 | no | — |
| 290 | C22⋊Q8 | — | 5 | 6 | no | — |
| 291 | C22⋊Q8 | — | 10 | 3 | no | — |
| 292 | C22⋊Q8 | — | 10 | 3 | no | — |
| 293 | C22⋊Q8 | — | 10 | 6 | no | — |
| 294 | C22⋊Q8 | — | 10 | 6 | no | — |
| 295 | C22⋊Q8 | — | 10 | 12 | no | — |
| 296 | C4×Q8 | — | 5 | 1 | no | — |
| 297 | C4×Q8 | — | 5 | 3 | no | — |
| 298 | C4×Q8 | — | 5 | 3 | no | — |
| 299 | C4×Q8 | — | 5 | 3 | no | — |
| 300 | C4×Q8 | — | 5 | 6 | no | — |
| 301 | C4×Q8 | — | 10 | 1 | no | — |
| 302 | C4×Q8 | — | 10 | 1 | no | — |
| 303 | C4×Q8 | — | 10 | 2 | no | — |
| 304 | C4×Q8 | — | 10 | 3 | no | — |
| 305 | C4×Q8 | — | 10 | 3 | no | — |
| 306 | C4×Q8 | — | 10 | 3 | no | — |
| 307 | C4×Q8 | — | 10 | 3 | no | — |
| 308 | C4×Q8 | D20 | 1 | 1 | yes | characteristic |
| 309 | C4×Q8 | C22×D5 | 1 | 1 | yes | characteristic |
| 310 | C4×D4 | — | 10 | 3 | no | — |
| 311 | C4×D4 | — | 10 | 3 | no | — |
| 312 | C4×D4 | — | 10 | 6 | no | — |
| 313 | C4×D4 | D20 | 1 | 3 | yes | — |
| 314 | C4×D4 | C22×D5 | 1 | 3 | yes | — |
| 315 | #117 | — | 10 | 3 | no | — |
| 316 | #117 | — | 10 | 3 | no | — |
| 317 | #117 | D20 | 1 | 3 | yes | — |
| 318 | C2×C4⋊C4 | — | 5 | 3 | no | — |
| 319 | C2×C4⋊C4 | — | 5 | 6 | no | — |
| 320 | C2×C4⋊C4 | — | 10 | 3 | no | — |
| 321 | C2×C4⋊C4 | — | 10 | 3 | no | — |
| 322 | C2×C42 | — | 10 | 3 | no | — |
| 323 | C2×C42 | C22×D5 | 1 | 3 | yes | — |
| 324 | #107 | — | 5 | 6 | no | — |
| 325 | #107 | — | 5 | 12 | no | — |
| 326 | #107 | — | 5 | 6 | no | — |
| 327 | C4⋊C8 | C22×D5 | 1 | 3 | yes | — |
| 328 | C4⋊C8 | C22×D5 | 1 | 6 | yes | — |
| 329 | C4⋊C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 330 | #103 | — | 5 | 6 | no | — |
| 331 | #103 | — | 5 | 12 | no | — |
| 332 | #103 | — | 5 | 2 | no | — |
| 333 | #103 | — | 5 | 6 | no | — |
| 334 | #103 | — | 5 | 6 | no | — |
| 335 | C22⋊C8 | C22×D5 | 1 | 6 | yes | — |
| 336 | C4×C8 | C22×D5 | 1 | 6 | yes | — |
| 337 | C22×C5 | — | 2 | 3 | no | — |
| 338 | C22×C5 | — | 2 | 3 | no | — |
| 339 | C22×C5 | C22×Q16 | 1 | 6 | yes | — |
| 340 | C22×C5 | C23×D4 | 1 | 1 | yes | characteristic |
| 341 | C4×C5 | — | 2 | 1 | no | — |
| 342 | C4×C5 | — | 2 | 3 | no | — |
| 343 | C4×C5 | — | 2 | 3 | no | — |
| 344 | C4×C5 | C22×Q16 | 1 | 2 | yes | — |
| 345 | C4×C5 | C22×Q16 | 1 | 6 | yes | — |
| 346 | C4×C5 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 347 | C4×C5 | #585 | 1 | 1 | yes | characteristic |
| 348 | Dic5 | — | 2 | 2 | no | — |
| 349 | Dic5 | — | 4 | 6 | no | — |
| 350 | Dic5 | — | 4 | 3 | no | — |
| 351 | Dic5 | — | 4 | 1 | no | — |
| 352 | Dic5 | — | 4 | 3 | no | — |
| 353 | Dic5 | — | 4 | 2 | no | — |
| 354 | #41 | Dic20 | 1 | 8 | yes | complemented |
| 355 | C2×Q8 | — | 5 | 1 | no | — |
| 356 | C2×Q8 | — | 5 | 3 | no | — |
| 357 | C2×Q8 | — | 5 | 2 | no | — |
| 358 | C2×Q8 | — | 10 | 6 | no | — |
| 359 | C2×Q8 | — | 10 | 3 | no | — |
| 360 | C2×Q8 | — | 10 | 3 | no | — |
| 361 | C2×Q8 | — | 10 | 3 | no | — |
| 362 | C2×Q8 | — | 10 | 6 | no | — |
| 363 | C2×Q8 | — | 20 | 3 | no | — |
| 364 | C2×Q8 | — | 40 | 6 | no | — |
| 365 | C2×Q8 | C2×D20 | 1 | 1 | yes | characteristic |
| 366 | C2×D4 | C2×D20 | 1 | 3 | yes | — |
| 367 | C22×C4 | — | 10 | 3 | no | — |
| 368 | C22×C4 | — | 10 | 3 | no | — |
| 369 | C22×C4 | — | 10 | 6 | no | — |
| 370 | C22×C4 | C2×D20 | 1 | 3 | yes | — |
| 371 | C22×C4 | C2×D20 | 1 | 3 | yes | — |
| 372 | C22×C4 | C23×D5 | 1 | 3 | yes | — |
| 373 | Q16 | — | 10 | 4 | no | — |
| 374 | Q16 | — | 20 | 6 | no | — |
| 375 | C2×C8 | — | 4 | 6 | no | — |
| 376 | C2×C8 | C23×D5 | 1 | 2 | yes | — |
| 377 | C2×C8 | C23×D5 | 1 | 6 | yes | — |
| 378 | C4⋊C4 | — | 5 | 6 | no | — |
| 379 | C4⋊C4 | — | 5 | 1 | no | — |
| 380 | C4⋊C4 | — | 5 | 3 | no | — |
| 381 | C4⋊C4 | — | 10 | 3 | no | — |
| 382 | C4⋊C4 | — | 10 | 6 | no | — |
| 383 | C4⋊C4 | — | 10 | 1 | no | — |
| 384 | C4⋊C4 | — | 10 | 3 | no | — |
| 385 | C4⋊C4 | — | 10 | 6 | no | — |
| 386 | C4⋊C4 | — | 10 | 3 | no | — |
| 387 | C4⋊C4 | — | 10 | 3 | no | — |
| 388 | C4⋊C4 | — | 10 | 3 | no | — |
| 389 | C4⋊C4 | — | 10 | 1 | no | — |
| 390 | C4⋊C4 | — | 10 | 3 | no | — |
| 391 | C4⋊C4 | — | 10 | 3 | no | — |
| 392 | C4⋊C4 | — | 10 | 6 | no | — |
| 393 | C4⋊C4 | — | 10 | 1 | no | — |
| 394 | C4⋊C4 | — | 10 | 6 | no | — |
| 395 | C4⋊C4 | — | 10 | 6 | no | — |
| 396 | C4⋊C4 | — | 10 | 3 | no | — |
| 397 | C4⋊C4 | C2×D20 | 1 | 3 | yes | — |
| 398 | C4⋊C4 | C2×D20 | 1 | 3 | yes | — |
| 399 | C22⋊C4 | — | 10 | 6 | no | — |
| 400 | C22⋊C4 | — | 10 | 6 | no | — |
| 401 | C22⋊C4 | C2×D20 | 1 | 6 | yes | — |
| 402 | C42 | — | 10 | 1 | no | — |
| 403 | C42 | — | 10 | 3 | no | — |
| 404 | C42 | — | 10 | 3 | no | — |
| 405 | C42 | — | 10 | 3 | no | — |
| 406 | C42 | — | 10 | 6 | no | — |
| 407 | C42 | C2×D20 | 1 | 3 | yes | — |
| 408 | C42 | C2×D20 | 1 | 3 | yes | — |
| 409 | C42 | C23×D5 | 1 | 3 | yes | — |
| 410 | C42 | C23×D5 | 1 | 1 | yes | characteristic |
| 411 | C2×C5 | — | 2 | 6 | no | — |
| 412 | C2×C5 | #3489 | 1 | 1 | yes | characteristic |
| 413 | C2×C5 | C23×Q16 | 1 | 1 | yes | characteristic |
| 414 | C2×C5 | #3585 | 1 | 1 | yes | characteristic |
| 415 | C23 | C22×D20 | 1 | 3 | yes | — |
| 416 | Q8 | — | 5 | 2 | no | — |
| 417 | Q8 | — | 10 | 1 | no | — |
| 418 | Q8 | — | 10 | 2 | no | — |
| 419 | Q8 | — | 10 | 3 | no | — |
| 420 | Q8 | — | 10 | 2 | no | — |
| 421 | Q8 | — | 10 | 3 | no | — |
| 422 | Q8 | — | 20 | 6 | no | — |
| 423 | Q8 | — | 20 | 6 | no | — |
| 424 | Q8 | — | 40 | 6 | no | — |
| 425 | Q8 | — | 40 | 3 | no | — |
| 426 | Q8 | C2×Dic20 | 1 | 4 | yes | — |
| 427 | D4 | C2×Dic20 | 1 | 12 | yes | — |
| 428 | C2×C4 | — | 2 | 3 | no | — |
| 429 | C2×C4 | — | 2 | 3 | no | — |
| 430 | C2×C4 | — | 4 | 3 | no | — |
| 431 | C2×C4 | — | 10 | 1 | no | — |
| 432 | C2×C4 | — | 10 | 1 | no | — |
| 433 | C2×C4 | — | 10 | 2 | no | — |
| 434 | C2×C4 | — | 10 | 3 | no | — |
| 435 | C2×C4 | — | 10 | 3 | no | — |
| 436 | C2×C4 | — | 10 | 6 | no | — |
| 437 | C2×C4 | — | 20 | 6 | no | — |
| 438 | C2×C4 | — | 40 | 6 | no | — |
| 439 | C2×C4 | — | 40 | 3 | no | — |
| 440 | C2×C4 | C2×Dic20 | 1 | 12 | yes | — |
| 441 | C2×C4 | C22×D20 | 1 | 1 | yes | characteristic |
| 442 | C2×C4 | C22×D20 | 1 | 3 | yes | — |
| 443 | C2×C4 | C22×D20 | 1 | 3 | yes | — |
| 444 | C2×C4 | C22×D20 | 1 | 1 | yes | characteristic |
| 445 | C2×C4 | C22×D20 | 1 | 3 | yes | — |
| 446 | C2×C4 | C24×D5 | 1 | 1 | yes | characteristic |
| 447 | C8 | — | 2 | 6 | no | — |
| 448 | C8 | — | 2 | 2 | no | — |
| 449 | C5 | #62100 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 450 | C22 | — | 2 | 3 | no | — |
| 451 | C22 | — | 2 | 3 | no | — |
| 452 | C22 | C22×Dic20 | 1 | 6 | yes | — |
| 453 | C22 | C23×D20 | 1 | 1 | yes | characteristic |
| 454 | C4 | — | 2 | 1 | no | — |
| 455 | C4 | — | 2 | 3 | no | — |
| 456 | C4 | — | 2 | 3 | no | — |
| 457 | C4 | — | 10 | 2 | no | — |
| 458 | C4 | — | 20 | 1 | no | — |
| 459 | C4 | — | 20 | 6 | no | — |
| 460 | C4 | — | 20 | 3 | no | — |
| 461 | C4 | — | 20 | 3 | no | — |
| 462 | C4 | — | 20 | 2 | no | — |
| 463 | C4 | C22×Dic20 | 1 | 2 | yes | — |
| 464 | C4 | C22×Dic20 | 1 | 6 | yes | — |
| 465 | C4 | #66285 | 1 | 1 | yes | characteristic |
| 466 | C4 | D5×2−1+4 | 1 | 1 | yes | characteristic |
| 467 | C2 | — | 2 | 6 | no | — |
| 468 | C2 | #10617802 | 1 | 1 | yes | characteristic |
| 469 | C2 | C23×Dic20 | 1 | 1 | yes | characteristic |
| 470 | C2 | #10619068 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. Q8×Dic20 | C2 | semidirect |
| 5. #10611664 | C2 | semidirect |
| 6. #10611179 | C2 | semidirect |
| 7. #10611146 | C2 | semidirect |
| 8. #10611041 | C2 | semidirect |
| 9. #10611003 | C2 | semidirect |
| 10. #10610768 | C2 | semidirect |
| 11. C2×#65139 | C2 | semidirect |
| 135. C5×#41 | Q16 | semidirect |
| 354. #41 | Dic20 | semidirect |
| 449. C5 | #62100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617729 | 2 |
| #41×Dic10 | 2 |
| C5×#2988 | 2 |
| Q8×Dic20 | 2 |
| #10611664 | 2 |
| #10611179 | 2 |
| #10611146 | 2 |
| #10611041 | 2 |
| #10611003 | 2 |
| #10610768 | 2 |
| C2×#65139 | 2 |
| #62100 | 5 |