Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1754 conjugacy classes of subgroups.
The subgroup lattice has 584 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | D5×#541 | C2 | 1 | 2 | yes | maximal |
| 2 | C5×#3261 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10615184 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10612975 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | D5×#479 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | D5×#470 | C2 | 1 | 2 | yes | maximal |
| 7 | #10612629 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | D5×#467 | C2 | 1 | 2 | yes | maximal |
| 9 | #10612481 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #10612219 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | D5×#462 | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | #10610833 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | D5×#424 | C2 | 1 | 1 | yes | maximal, characteristic |
| 14 | C5×#541 | C22 | 1 | 2 | yes | — |
| 15 | C2×D5×Q16 | C22 | 1 | 2 | yes | — |
| 16 | C2×D5×Q16 | C22 | 1 | 2 | yes | — |
| 17 | C2×D5×M16 | C22 | 1 | 1 | yes | characteristic |
| 18 | C22×C8×D5 | C22 | 1 | 1 | yes | characteristic |
| 19 | #66065 | C22 | 1 | 2 | yes | — |
| 20 | D5×C4⋊Q8 | C22 | 1 | 2 | yes | — |
| 21 | D5×#126 | — | 2 | 4 | no | — |
| 22 | #66035 | — | 2 | 4 | no | — |
| 23 | #66031 | C22 | 1 | 2 | yes | — |
| 24 | #66030 | — | 2 | 4 | no | — |
| 25 | D5×#125 | — | 2 | 4 | no | — |
| 26 | D5×#125 | C22 | 1 | 2 | yes | — |
| 27 | D5×C22⋊Q8 | C22 | 1 | 4 | yes | — |
| 28 | #65959 | C22 | 1 | 4 | yes | — |
| 29 | #65917 | C22 | 1 | 4 | yes | — |
| 30 | C4×Q8×D5 | C22 | 1 | 4 | yes | — |
| 31 | D5×#117 | C22 | 1 | 1 | yes | characteristic |
| 32 | #65852 | C22 | 1 | 2 | yes | — |
| 33 | C5×#479 | C22 | 1 | 4 | yes | complemented |
| 34 | C5×#470 | C22 | 1 | 2 | yes | — |
| 35 | C5×#467 | C22 | 1 | 2 | yes | — |
| 36 | C5×#462 | C22 | 1 | 4 | yes | complemented |
| 37 | C5×#424 | C22 | 1 | 1 | yes | characteristic |
| 38 | #65478 | C22 | 1 | 2 | yes | — |
| 39 | #65477 | C22 | 1 | 2 | yes | — |
| 40 | #65471 | C22 | 1 | 4 | yes | complemented |
| 41 | #65471 | C22 | 1 | 4 | yes | complemented |
| 42 | #65426 | C22 | 1 | 2 | yes | — |
| 43 | #65408 | C22 | 1 | 1 | yes | characteristic |
| 44 | #65405 | C22 | 1 | 2 | yes | — |
| 45 | #65391 | C22 | 1 | 1 | yes | characteristic |
| 46 | #65379 | C22 | 1 | 4 | yes | complemented |
| 47 | #65352 | C22 | 1 | 4 | yes | complemented |
| 48 | #65341 | C22 | 1 | 4 | yes | — |
| 49 | #65340 | C22 | 1 | 4 | yes | — |
| 50 | #65320 | C22 | 1 | 4 | yes | complemented |
| 51 | #65311 | C22 | 1 | 4 | yes | complemented |
| 52 | #65288 | C22 | 1 | 1 | yes | characteristic |
| 53 | #65176 | C22 | 1 | 2 | yes | — |
| 54 | D5×#107 | C22 | 1 | 2 | yes | — |
| 55 | #65166 | C22 | 1 | 4 | yes | complemented |
| 56 | #65157 | C22 | 1 | 2 | yes | — |
| 57 | D5×#106 | C22 | 1 | 2 | yes | — |
| 58 | #65146 | C22 | 1 | 4 | yes | complemented |
| 59 | #65138 | C22 | 1 | 4 | yes | complemented |
| 60 | #65128 | C22 | 1 | 4 | yes | — |
| 61 | D5×C4⋊C8 | C22 | 1 | 4 | yes | — |
| 62 | #65118 | C22 | 1 | 4 | yes | complemented |
| 63 | #65105 | C22 | 1 | 4 | yes | — |
| 64 | #65102 | C22 | 1 | 4 | yes | — |
| 65 | D5×#103 | C22 | 1 | 4 | yes | — |
| 66 | D5×#103 | C22 | 1 | 4 | yes | — |
| 67 | #65088 | C22 | 1 | 4 | yes | complemented |
| 68 | #65085 | C22 | 1 | 4 | yes | complemented |
| 69 | #65082 | C22 | 1 | 4 | yes | complemented |
| 70 | #65082 | C22 | 1 | 4 | yes | complemented |
| 71 | C2×#3261 | — | 5 | 1 | no | maximal, Sylow |
| 72 | C2×Q8×D5 | C23 | 1 | 4 | yes | — |
| 73 | C22×C4×D5 | C23 | 1 | 1 | yes | characteristic |
| 74 | C2×C5×Q16 | C23 | 1 | 2 | yes | — |
| 75 | C2×C5×Q16 | C23 | 1 | 2 | yes | — |
| 76 | C2×C5×M16 | C23 | 1 | 1 | yes | characteristic |
| 77 | C22×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 78 | C5×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 79 | C5×#126 | — | 2 | 4 | no | — |
| 80 | C5×#125 | — | 2 | 4 | no | — |
| 81 | C5×#125 | C23 | 1 | 2 | yes | — |
| 82 | C5×C22⋊Q8 | C23 | 1 | 4 | yes | — |
| 83 | C4×C5×Q8 | C23 | 1 | 4 | yes | — |
| 84 | C5×#117 | C23 | 1 | 1 | yes | characteristic |
| 85 | #4092 | C23 | 1 | 4 | yes | — |
| 86 | Q8×Dic5 | C23 | 1 | 4 | yes | — |
| 87 | #4090 | C23 | 1 | 4 | yes | — |
| 88 | C2×#689 | C23 | 1 | 4 | yes | — |
| 89 | C2×#689 | C23 | 1 | 4 | yes | — |
| 90 | #4072 | C23 | 1 | 1 | yes | characteristic |
| 91 | #4070 | C23 | 1 | 4 | yes | — |
| 92 | C2×#681 | C23 | 1 | 1 | yes | characteristic |
| 93 | C22×#168 | C23 | 1 | 1 | yes | characteristic |
| 94 | D5×Q16 | — | 4 | 4 | no | — |
| 95 | D5×Q16 | — | 4 | 4 | no | — |
| 96 | D5×M16 | — | 4 | 2 | no | — |
| 97 | C2×Dic20 | C23 | 1 | 2 | yes | — |
| 98 | C2×Dic20 | C23 | 1 | 2 | yes | — |
| 99 | C2×#676 | C23 | 1 | 2 | yes | — |
| 100 | C2×C8×D5 | — | 4 | 2 | no | — |
| 101 | C2×C8×D5 | C23 | 1 | 2 | yes | — |
| 102 | C2×C8×D5 | C23 | 1 | 2 | yes | — |
| 103 | C2×C8×D5 | C23 | 1 | 2 | yes | — |
| 104 | #4044 | — | 2 | 4 | no | — |
| 105 | #4044 | — | 2 | 4 | no | — |
| 106 | #4044 | — | 2 | 4 | no | — |
| 107 | #4043 | C23 | 1 | 4 | yes | — |
| 108 | #4042 | — | 2 | 4 | no | — |
| 109 | #4038 | D4 | 1 | 2 | yes | — |
| 110 | D5×C4⋊C4 | — | 2 | 4 | no | — |
| 111 | D5×C4⋊C4 | — | 2 | 4 | no | — |
| 112 | D5×C4⋊C4 | — | 2 | 4 | no | — |
| 113 | D5×C4⋊C4 | — | 2 | 4 | no | — |
| 114 | D5×C4⋊C4 | D4 | 1 | 2 | yes | — |
| 115 | D5×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 116 | #4036 | — | 2 | 4 | no | — |
| 117 | #4036 | — | 2 | 4 | no | — |
| 118 | #4036 | C23 | 1 | 4 | yes | — |
| 119 | #4035 | — | 2 | 4 | no | — |
| 120 | #4035 | — | 2 | 4 | no | — |
| 121 | #4035 | — | 2 | 4 | no | — |
| 122 | #4035 | — | 2 | 4 | no | — |
| 123 | #4035 | — | 2 | 4 | no | — |
| 124 | #4034 | — | 2 | 4 | no | — |
| 125 | #4033 | — | 2 | 4 | no | — |
| 126 | #4033 | C23 | 1 | 4 | yes | — |
| 127 | D5×C22⋊C4 | — | 2 | 4 | no | — |
| 128 | D5×C22⋊C4 | D4 | 1 | 2 | yes | — |
| 129 | #4025 | — | 2 | 4 | no | — |
| 130 | #4025 | — | 2 | 4 | no | — |
| 131 | #4025 | — | 2 | 4 | no | — |
| 132 | #4024 | — | 2 | 4 | no | — |
| 133 | #4023 | D4 | 1 | 2 | yes | — |
| 134 | #4022 | — | 2 | 4 | no | — |
| 135 | #4018 | C23 | 1 | 2 | yes | — |
| 136 | C42×D5 | — | 2 | 4 | no | — |
| 137 | C42×D5 | C23 | 1 | 2 | yes | — |
| 138 | #4016 | — | 2 | 4 | no | — |
| 139 | #4016 | C23 | 1 | 2 | yes | — |
| 140 | #4015 | C23 | 1 | 2 | yes | — |
| 141 | C4×Dic10 | — | 2 | 4 | no | — |
| 142 | C4×Dic10 | C23 | 1 | 4 | yes | — |
| 143 | C5×#107 | C23 | 1 | 2 | yes | — |
| 144 | C5×#106 | C23 | 1 | 2 | yes | — |
| 145 | C5×C4⋊C8 | C23 | 1 | 4 | yes | — |
| 146 | C5×#103 | C23 | 1 | 4 | yes | — |
| 147 | C5×#103 | C23 | 1 | 4 | yes | — |
| 148 | #3967 | C23 | 1 | 4 | yes | — |
| 149 | #3967 | C23 | 1 | 4 | yes | — |
| 150 | #3950 | C23 | 1 | 2 | yes | — |
| 151 | #3949 | C23 | 1 | 2 | yes | — |
| 152 | #3948 | C23 | 1 | 4 | yes | — |
| 153 | #3948 | C23 | 1 | 4 | yes | — |
| 154 | #3946 | C23 | 1 | 4 | yes | — |
| 155 | #3946 | C23 | 1 | 4 | yes | — |
| 156 | #3942 | C23 | 1 | 4 | yes | — |
| 157 | #3942 | C23 | 1 | 4 | yes | — |
| 158 | #3940 | C23 | 1 | 4 | yes | — |
| 159 | #3939 | C23 | 1 | 4 | yes | — |
| 160 | C4⋊#168 | C23 | 1 | 4 | yes | — |
| 161 | C2×#541 | — | 5 | 2 | no | — |
| 162 | #3261 | — | 5 | 4 | no | — |
| 163 | #3261 | — | 5 | 2 | no | — |
| 164 | #3261 | — | 5 | 2 | no | — |
| 165 | #3261 | — | 5 | 4 | no | — |
| 166 | #3261 | — | 5 | 1 | no | — |
| 167 | #3261 | — | 5 | 2 | no | — |
| 168 | #3261 | D5 | 1 | 1 | yes | characteristic, direct product factor |
| 169 | C2×#479 | — | 5 | 4 | no | — |
| 170 | C2×#470 | — | 5 | 2 | no | — |
| 171 | C2×#467 | — | 5 | 2 | no | — |
| 172 | C2×#462 | — | 5 | 4 | no | — |
| 173 | C2×#424 | — | 5 | 1 | no | — |
| 174 | C23×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 175 | C2×C5×Q8 | C24 | 1 | 4 | yes | — |
| 176 | C22×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 177 | C22×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 178 | Q8×D5 | — | 2 | 8 | no | — |
| 179 | Q8×D5 | — | 2 | 8 | no | — |
| 180 | C2×C4×D5 | — | 2 | 2 | no | — |
| 181 | C2×C4×D5 | — | 2 | 2 | no | — |
| 182 | C2×C4×D5 | — | 2 | 4 | no | — |
| 183 | C2×C4×D5 | — | 2 | 4 | no | — |
| 184 | C2×C4×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 185 | C2×C4×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 186 | C2×C4×D5 | C2×D4 | 1 | 4 | yes | — |
| 187 | C2×C4×D5 | C24 | 1 | 1 | yes | characteristic |
| 188 | C2×C4×D5 | C24 | 1 | 1 | yes | characteristic |
| 189 | C2×Dic10 | — | 2 | 4 | no | — |
| 190 | C2×Dic10 | C24 | 1 | 4 | yes | — |
| 191 | C5×Q16 | — | 4 | 2 | no | — |
| 192 | C5×Q16 | — | 4 | 2 | no | — |
| 193 | C5×M16 | — | 4 | 1 | no | — |
| 194 | C2×C5×C8 | — | 4 | 1 | no | — |
| 195 | C2×C5×C8 | C24 | 1 | 2 | yes | — |
| 196 | C2×C5×C8 | C24 | 1 | 2 | yes | — |
| 197 | C5×C4⋊C4 | — | 2 | 4 | no | — |
| 198 | C5×C4⋊C4 | — | 2 | 4 | no | — |
| 199 | C5×C4⋊C4 | — | 2 | 4 | no | — |
| 200 | C5×C4⋊C4 | — | 2 | 4 | no | — |
| 201 | C5×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 202 | C5×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 203 | C5×C22⋊C4 | — | 2 | 4 | no | — |
| 204 | C5×C22⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 205 | C42×C5 | — | 2 | 4 | no | — |
| 206 | C42×C5 | C24 | 1 | 2 | yes | — |
| 207 | C22⋊Dic5 | — | 2 | 4 | no | — |
| 208 | C22⋊Dic5 | C2×D4 | 1 | 2 | yes | — |
| 209 | #689 | — | 4 | 4 | no | — |
| 210 | #689 | — | 4 | 4 | no | — |
| 211 | #685 | — | 2 | 4 | no | — |
| 212 | #685 | — | 2 | 4 | no | — |
| 213 | #685 | C2×D4 | 1 | 4 | yes | — |
| 214 | C4⋊Dic5 | — | 2 | 4 | no | — |
| 215 | C4⋊Dic5 | — | 2 | 4 | no | — |
| 216 | C4⋊Dic5 | — | 2 | 4 | no | — |
| 217 | C4⋊Dic5 | — | 2 | 4 | no | — |
| 218 | C4⋊Dic5 | C2×D4 | 1 | 2 | yes | — |
| 219 | C4⋊Dic5 | C24 | 1 | 4 | yes | — |
| 220 | #683 | — | 2 | 4 | no | — |
| 221 | #683 | — | 2 | 4 | no | — |
| 222 | #683 | — | 2 | 4 | no | — |
| 223 | #683 | — | 2 | 4 | no | — |
| 224 | #683 | — | 2 | 4 | no | — |
| 225 | #683 | — | 2 | 4 | no | — |
| 226 | #683 | — | 2 | 4 | no | — |
| 227 | #683 | — | 2 | 4 | no | — |
| 228 | #683 | — | 2 | 4 | no | — |
| 229 | #683 | C2×D4 | 1 | 4 | yes | — |
| 230 | C4×Dic5 | — | 2 | 4 | no | — |
| 231 | C4×Dic5 | — | 2 | 4 | no | — |
| 232 | C4×Dic5 | — | 2 | 4 | no | — |
| 233 | C4×Dic5 | C2×D4 | 1 | 4 | yes | — |
| 234 | C4×Dic5 | C24 | 1 | 2 | yes | — |
| 235 | #681 | — | 4 | 1 | no | — |
| 236 | C2×#168 | — | 4 | 1 | no | — |
| 237 | C2×#168 | C24 | 1 | 2 | yes | — |
| 238 | C2×#168 | C24 | 1 | 2 | yes | — |
| 239 | Dic20 | — | 4 | 2 | no | — |
| 240 | Dic20 | — | 4 | 2 | no | — |
| 241 | #676 | — | 4 | 2 | no | — |
| 242 | C8×D5 | — | 2 | 4 | no | — |
| 243 | C8×D5 | — | 2 | 4 | no | — |
| 244 | C8×D5 | — | 4 | 2 | no | — |
| 245 | C22×Q16 | — | 5 | 2 | no | — |
| 246 | C22×Q16 | — | 5 | 2 | no | — |
| 247 | C22×M16 | — | 5 | 1 | no | — |
| 248 | C23×C8 | — | 5 | 1 | no | — |
| 249 | #541 | — | 5 | 2 | no | — |
| 250 | #541 | — | 5 | 2 | no | — |
| 251 | #541 | — | 5 | 4 | no | — |
| 252 | #541 | — | 5 | 4 | no | — |
| 253 | #541 | — | 5 | 2 | no | — |
| 254 | #541 | — | 10 | 4 | no | — |
| 255 | #541 | — | 10 | 4 | no | — |
| 256 | #541 | C2×D5 | 1 | 2 | yes | — |
| 257 | C2×C4⋊Q8 | — | 5 | 2 | no | — |
| 258 | C2×#126 | — | 10 | 4 | no | — |
| 259 | C2×#125 | — | 5 | 2 | no | — |
| 260 | C2×#125 | — | 10 | 4 | no | — |
| 261 | C2×C22⋊Q8 | — | 5 | 4 | no | — |
| 262 | C2×C4×Q8 | — | 5 | 4 | no | — |
| 263 | C2×#117 | — | 5 | 1 | no | — |
| 264 | #479 | — | 5 | 4 | no | — |
| 265 | #479 | — | 5 | 4 | no | — |
| 266 | #479 | — | 5 | 4 | no | — |
| 267 | #479 | — | 5 | 4 | no | — |
| 268 | #479 | — | 5 | 4 | no | — |
| 269 | #479 | — | 5 | 4 | no | — |
| 270 | #479 | — | 5 | 4 | no | — |
| 271 | #479 | C2×D5 | 1 | 4 | yes | complemented |
| 272 | #470 | — | 5 | 2 | no | — |
| 273 | #470 | — | 5 | 2 | no | — |
| 274 | #470 | — | 5 | 4 | no | — |
| 275 | #470 | — | 5 | 2 | no | — |
| 276 | #470 | — | 5 | 4 | no | — |
| 277 | #470 | C2×D5 | 1 | 2 | yes | — |
| 278 | #467 | — | 5 | 2 | no | — |
| 279 | #467 | — | 5 | 2 | no | — |
| 280 | #467 | — | 5 | 4 | no | — |
| 281 | #467 | — | 5 | 2 | no | — |
| 282 | #467 | — | 5 | 4 | no | — |
| 283 | #467 | C2×D5 | 1 | 2 | yes | — |
| 284 | #462 | — | 5 | 4 | no | — |
| 285 | #462 | — | 5 | 4 | no | — |
| 286 | #462 | — | 5 | 4 | no | — |
| 287 | #462 | — | 5 | 4 | no | — |
| 288 | #462 | — | 5 | 4 | no | — |
| 289 | #462 | — | 5 | 4 | no | — |
| 290 | #462 | — | 5 | 4 | no | — |
| 291 | #462 | C2×D5 | 1 | 4 | yes | complemented |
| 292 | C2×#107 | — | 5 | 2 | no | — |
| 293 | C2×#106 | — | 5 | 2 | no | — |
| 294 | #424 | — | 5 | 1 | no | — |
| 295 | #424 | — | 5 | 1 | no | — |
| 296 | #424 | — | 5 | 1 | no | — |
| 297 | #424 | — | 5 | 4 | no | — |
| 298 | #424 | C2×D5 | 1 | 1 | yes | characteristic |
| 299 | C2×C4⋊C8 | — | 5 | 4 | no | — |
| 300 | C2×#103 | — | 5 | 4 | no | — |
| 301 | C2×#103 | — | 5 | 4 | no | — |
| 302 | C23×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 303 | C22×D5 | — | 2 | 2 | no | — |
| 304 | C22×D5 | — | 2 | 4 | no | — |
| 305 | C22×D5 | C22×D4 | 1 | 1 | yes | characteristic |
| 306 | C22×D5 | C22×D4 | 1 | 1 | yes | characteristic |
| 307 | C5×Q8 | — | 2 | 4 | no | — |
| 308 | C5×Q8 | — | 2 | 4 | no | — |
| 309 | C2×C4×C5 | — | 2 | 1 | no | — |
| 310 | C2×C4×C5 | — | 2 | 1 | no | — |
| 311 | C2×C4×C5 | — | 2 | 4 | no | — |
| 312 | C2×C4×C5 | — | 2 | 4 | no | — |
| 313 | C2×C4×C5 | C22×D4 | 1 | 4 | yes | — |
| 314 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 315 | C2×C4×C5 | C25 | 1 | 1 | yes | characteristic |
| 316 | C2×Dic5 | — | 2 | 2 | no | — |
| 317 | C2×Dic5 | — | 2 | 4 | no | — |
| 318 | C2×Dic5 | — | 2 | 4 | no | — |
| 319 | C2×Dic5 | C22×D4 | 1 | 4 | yes | — |
| 320 | C2×Dic5 | C22×D4 | 1 | 1 | yes | characteristic |
| 321 | C2×Dic5 | C22×D4 | 1 | 1 | yes | characteristic |
| 322 | C4×D5 | — | 2 | 2 | no | — |
| 323 | C4×D5 | — | 2 | 8 | no | — |
| 324 | C4×D5 | — | 2 | 1 | no | — |
| 325 | C4×D5 | — | 2 | 1 | no | — |
| 326 | C4×D5 | — | 2 | 2 | no | — |
| 327 | C4×D5 | — | 4 | 8 | no | — |
| 328 | C4×D5 | — | 4 | 8 | no | — |
| 329 | C4×D5 | H(5,𝔽2) | 1 | 2 | yes | — |
| 330 | C4×D5 | 2−1+4 | 1 | 2 | yes | — |
| 331 | Dic10 | — | 2 | 4 | no | — |
| 332 | Dic10 | — | 2 | 4 | no | — |
| 333 | Dic10 | — | 4 | 8 | no | — |
| 334 | C5×C8 | — | 2 | 2 | no | — |
| 335 | C5×C8 | — | 2 | 2 | no | — |
| 336 | #168 | — | 2 | 2 | no | — |
| 337 | #168 | — | 2 | 2 | no | — |
| 338 | C22×Q8 | — | 5 | 4 | no | — |
| 339 | C23×C4 | — | 5 | 1 | no | — |
| 340 | C2×Q16 | — | 5 | 4 | no | — |
| 341 | C2×Q16 | — | 5 | 4 | no | — |
| 342 | C2×Q16 | — | 5 | 2 | no | — |
| 343 | C2×Q16 | — | 5 | 2 | no | — |
| 344 | C2×Q16 | — | 20 | 4 | no | — |
| 345 | C2×Q16 | — | 20 | 4 | no | — |
| 346 | C2×Q16 | C22×D5 | 1 | 2 | yes | — |
| 347 | C2×Q16 | C22×D5 | 1 | 2 | yes | — |
| 348 | C2×M16 | — | 5 | 1 | no | — |
| 349 | C2×M16 | — | 5 | 2 | no | — |
| 350 | C2×M16 | — | 20 | 2 | no | — |
| 351 | C2×M16 | C22×D5 | 1 | 1 | yes | characteristic |
| 352 | C22×C8 | — | 5 | 1 | no | — |
| 353 | C22×C8 | — | 5 | 2 | no | — |
| 354 | C22×C8 | — | 5 | 2 | no | — |
| 355 | C22×C8 | — | 5 | 2 | no | — |
| 356 | C22×C8 | — | 20 | 2 | no | — |
| 357 | C22×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 358 | C4⋊Q8 | — | 5 | 4 | no | — |
| 359 | C4⋊Q8 | — | 5 | 2 | no | — |
| 360 | C4⋊Q8 | — | 10 | 4 | no | — |
| 361 | C4⋊Q8 | C22×D5 | 1 | 2 | yes | — |
| 362 | #126 | — | 2 | 4 | no | — |
| 363 | #126 | — | 10 | 4 | no | — |
| 364 | #126 | — | 10 | 4 | no | — |
| 365 | #126 | — | 10 | 4 | no | — |
| 366 | #126 | — | 10 | 4 | no | — |
| 367 | #126 | — | 10 | 4 | no | — |
| 368 | #126 | — | 10 | 4 | no | — |
| 369 | #126 | — | 10 | 4 | no | — |
| 370 | #125 | — | 2 | 4 | no | — |
| 371 | #125 | — | 5 | 4 | no | — |
| 372 | #125 | — | 5 | 2 | no | — |
| 373 | #125 | — | 10 | 4 | no | — |
| 374 | #125 | — | 10 | 4 | no | — |
| 375 | #125 | — | 10 | 4 | no | — |
| 376 | #125 | — | 10 | 4 | no | — |
| 377 | #125 | — | 10 | 4 | no | — |
| 378 | #125 | — | 10 | 4 | no | — |
| 379 | #125 | — | 10 | 4 | no | — |
| 380 | #125 | — | 10 | 4 | no | — |
| 381 | #125 | C22×D5 | 1 | 2 | yes | — |
| 382 | C22⋊Q8 | — | 5 | 4 | no | — |
| 383 | C22⋊Q8 | — | 5 | 4 | no | — |
| 384 | C22⋊Q8 | — | 5 | 4 | no | — |
| 385 | C22⋊Q8 | — | 10 | 4 | no | — |
| 386 | C22⋊Q8 | — | 10 | 4 | no | — |
| 387 | C22⋊Q8 | C22×D5 | 1 | 4 | yes | — |
| 388 | C4×Q8 | — | 5 | 4 | no | — |
| 389 | C4×Q8 | — | 5 | 4 | no | — |
| 390 | C4×Q8 | — | 5 | 4 | no | — |
| 391 | C4×Q8 | — | 10 | 4 | no | — |
| 392 | C4×Q8 | — | 10 | 4 | no | — |
| 393 | C4×Q8 | C22×D5 | 1 | 4 | yes | — |
| 394 | #117 | — | 5 | 1 | no | — |
| 395 | #117 | — | 5 | 2 | no | — |
| 396 | #117 | — | 5 | 2 | no | — |
| 397 | #117 | — | 5 | 2 | no | — |
| 398 | #117 | C22×D5 | 1 | 1 | yes | characteristic |
| 399 | C2×C4⋊C4 | — | 5 | 2 | no | — |
| 400 | C2×C4⋊C4 | — | 5 | 4 | no | — |
| 401 | C2×C4⋊C4 | — | 10 | 4 | no | — |
| 402 | C2×C4⋊C4 | — | 10 | 4 | no | — |
| 403 | C2×C4⋊C4 | — | 10 | 4 | no | — |
| 404 | C2×C4⋊C4 | — | 10 | 4 | no | — |
| 405 | C2×C22⋊C4 | — | 5 | 2 | no | — |
| 406 | C2×C22⋊C4 | — | 10 | 4 | no | — |
| 407 | C2×C42 | — | 5 | 2 | no | — |
| 408 | C2×C42 | — | 10 | 4 | no | — |
| 409 | #107 | — | 5 | 2 | no | — |
| 410 | #107 | — | 5 | 4 | no | — |
| 411 | #107 | C22×D5 | 1 | 2 | yes | — |
| 412 | #106 | — | 5 | 2 | no | — |
| 413 | #106 | — | 5 | 4 | no | — |
| 414 | #106 | C22×D5 | 1 | 2 | yes | — |
| 415 | C4⋊C8 | — | 5 | 4 | no | — |
| 416 | C4⋊C8 | — | 5 | 4 | no | — |
| 417 | C4⋊C8 | — | 5 | 4 | no | — |
| 418 | C4⋊C8 | C22×D5 | 1 | 4 | yes | — |
| 419 | #103 | — | 5 | 4 | no | — |
| 420 | #103 | — | 5 | 4 | no | — |
| 421 | #103 | — | 5 | 4 | no | — |
| 422 | #103 | — | 5 | 4 | no | — |
| 423 | #103 | — | 5 | 4 | no | — |
| 424 | #103 | — | 5 | 4 | no | — |
| 425 | #103 | C22×D5 | 1 | 4 | yes | — |
| 426 | #103 | C22×D5 | 1 | 4 | yes | — |
| 427 | C22×C5 | — | 2 | 1 | no | — |
| 428 | C22×C5 | — | 2 | 2 | no | — |
| 429 | C22×C5 | C23×D4 | 1 | 1 | yes | characteristic |
| 430 | C2×D5 | — | 2 | 1 | no | — |
| 431 | C2×D5 | — | 2 | 2 | no | — |
| 432 | C2×D5 | — | 4 | 4 | no | — |
| 433 | C2×D5 | #537 | 1 | 2 | yes | — |
| 434 | C2×D5 | #578 | 1 | 4 | yes | — |
| 435 | C4×C5 | — | 2 | 1 | no | — |
| 436 | C4×C5 | — | 2 | 4 | no | — |
| 437 | C4×C5 | — | 4 | 4 | no | — |
| 438 | C4×C5 | — | 4 | 4 | no | — |
| 439 | C4×C5 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 440 | C4×C5 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 441 | Dic5 | — | 2 | 1 | no | — |
| 442 | Dic5 | — | 2 | 4 | no | — |
| 443 | Dic5 | — | 4 | 4 | no | — |
| 444 | Dic5 | — | 4 | 4 | no | — |
| 445 | Dic5 | #537 | 1 | 2 | yes | — |
| 446 | C24 | — | 5 | 1 | no | — |
| 447 | C2×Q8 | — | 5 | 4 | no | — |
| 448 | C2×Q8 | — | 10 | 4 | no | — |
| 449 | C2×Q8 | — | 10 | 8 | no | — |
| 450 | C2×Q8 | — | 10 | 8 | no | — |
| 451 | C2×Q8 | C23×D5 | 1 | 4 | yes | — |
| 452 | C22×C4 | — | 5 | 1 | no | — |
| 453 | C22×C4 | — | 5 | 1 | no | — |
| 454 | C22×C4 | — | 5 | 4 | no | — |
| 455 | C22×C4 | — | 5 | 1 | no | — |
| 456 | C22×C4 | — | 5 | 1 | no | — |
| 457 | C22×C4 | — | 5 | 1 | no | — |
| 458 | C22×C4 | — | 10 | 2 | no | — |
| 459 | C22×C4 | — | 10 | 2 | no | — |
| 460 | C22×C4 | — | 10 | 4 | no | — |
| 461 | C22×C4 | — | 10 | 4 | no | — |
| 462 | C22×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 463 | Q16 | — | 4 | 2 | no | — |
| 464 | Q16 | — | 4 | 2 | no | — |
| 465 | Q16 | — | 20 | 2 | no | — |
| 466 | Q16 | — | 20 | 2 | no | — |
| 467 | Q16 | — | 20 | 4 | no | — |
| 468 | Q16 | — | 20 | 4 | no | — |
| 469 | M16 | — | 4 | 1 | no | — |
| 470 | M16 | — | 20 | 2 | no | — |
| 471 | M16 | — | 20 | 1 | no | — |
| 472 | C2×C8 | — | 4 | 1 | no | — |
| 473 | C2×C8 | — | 5 | 2 | no | — |
| 474 | C2×C8 | — | 5 | 2 | no | — |
| 475 | C2×C8 | — | 10 | 4 | no | — |
| 476 | C2×C8 | — | 10 | 4 | no | — |
| 477 | C2×C8 | — | 20 | 2 | no | — |
| 478 | C2×C8 | — | 20 | 1 | no | — |
| 479 | C2×C8 | C23×D5 | 1 | 2 | yes | — |
| 480 | C2×C8 | C23×D5 | 1 | 2 | yes | — |
| 481 | C4⋊C4 | — | 2 | 4 | no | — |
| 482 | C4⋊C4 | — | 2 | 4 | no | — |
| 483 | C4⋊C4 | — | 2 | 4 | no | — |
| 484 | C4⋊C4 | — | 2 | 4 | no | — |
| 485 | C4⋊C4 | — | 5 | 4 | no | — |
| 486 | C4⋊C4 | — | 5 | 2 | no | — |
| 487 | C4⋊C4 | — | 5 | 4 | no | — |
| 488 | C4⋊C4 | — | 10 | 4 | no | — |
| 489 | C4⋊C4 | — | 10 | 4 | no | — |
| 490 | C4⋊C4 | — | 10 | 4 | no | — |
| 491 | C4⋊C4 | — | 10 | 4 | no | — |
| 492 | C4⋊C4 | — | 10 | 4 | no | — |
| 493 | C4⋊C4 | — | 10 | 4 | no | — |
| 494 | C4⋊C4 | — | 10 | 4 | no | — |
| 495 | C4⋊C4 | — | 10 | 4 | no | — |
| 496 | C4⋊C4 | — | 10 | 4 | no | — |
| 497 | C4⋊C4 | — | 10 | 4 | no | — |
| 498 | C4⋊C4 | — | 10 | 4 | no | — |
| 499 | C4⋊C4 | — | 10 | 4 | no | — |
| 500 | C4⋊C4 | — | 10 | 4 | no | — |
| 501 | C4⋊C4 | D4×D5 | 1 | 2 | yes | — |
| 502 | C4⋊C4 | C23×D5 | 1 | 4 | yes | — |
| 503 | C22⋊C4 | — | 2 | 4 | no | — |
| 504 | C22⋊C4 | — | 5 | 2 | no | — |
| 505 | C22⋊C4 | — | 5 | 4 | no | — |
| 506 | C22⋊C4 | — | 10 | 4 | no | — |
| 507 | C22⋊C4 | — | 10 | 4 | no | — |
| 508 | C22⋊C4 | — | 10 | 4 | no | — |
| 509 | C22⋊C4 | D4×D5 | 1 | 2 | yes | — |
| 510 | C42 | — | 2 | 4 | no | — |
| 511 | C42 | — | 5 | 4 | no | — |
| 512 | C42 | — | 5 | 2 | no | — |
| 513 | C42 | — | 10 | 4 | no | — |
| 514 | C42 | — | 10 | 4 | no | — |
| 515 | C42 | — | 10 | 4 | no | — |
| 516 | C42 | C23×D5 | 1 | 2 | yes | — |
| 517 | C2×C5 | — | 4 | 1 | no | — |
| 518 | C2×C5 | C2×#537 | 1 | 1 | yes | characteristic |
| 519 | C2×C5 | C2×#578 | 1 | 2 | yes | — |
| 520 | D5 | — | 4 | 1 | no | — |
| 521 | D5 | #3261 | 1 | 4 | yes | direct product factor |
| 522 | C23 | — | 5 | 1 | no | — |
| 523 | C23 | — | 5 | 1 | no | — |
| 524 | C23 | — | 10 | 2 | no | — |
| 525 | C23 | — | 10 | 4 | no | — |
| 526 | C23 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 527 | Q8 | — | 2 | 4 | no | — |
| 528 | Q8 | — | 2 | 4 | no | — |
| 529 | Q8 | — | 10 | 4 | no | — |
| 530 | Q8 | — | 10 | 4 | no | — |
| 531 | Q8 | — | 20 | 8 | no | — |
| 532 | C2×C4 | — | 2 | 1 | no | — |
| 533 | C2×C4 | — | 2 | 1 | no | — |
| 534 | C2×C4 | — | 2 | 4 | no | — |
| 535 | C2×C4 | — | 2 | 4 | no | — |
| 536 | C2×C4 | — | 5 | 1 | no | — |
| 537 | C2×C4 | — | 5 | 2 | no | — |
| 538 | C2×C4 | — | 5 | 2 | no | — |
| 539 | C2×C4 | — | 5 | 4 | no | — |
| 540 | C2×C4 | — | 5 | 1 | no | — |
| 541 | C2×C4 | — | 10 | 2 | no | — |
| 542 | C2×C4 | — | 10 | 2 | no | — |
| 543 | C2×C4 | — | 10 | 8 | no | — |
| 544 | C2×C4 | — | 10 | 2 | no | — |
| 545 | C2×C4 | — | 10 | 1 | no | — |
| 546 | C2×C4 | — | 10 | 1 | no | — |
| 547 | C2×C4 | — | 10 | 4 | no | — |
| 548 | C2×C4 | — | 10 | 4 | no | — |
| 549 | C2×C4 | — | 20 | 8 | no | — |
| 550 | C2×C4 | — | 20 | 8 | no | — |
| 551 | C2×C4 | C2×D4×D5 | 1 | 4 | yes | — |
| 552 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 553 | C2×C4 | C24×D5 | 1 | 1 | yes | characteristic |
| 554 | C8 | — | 2 | 2 | no | — |
| 555 | C8 | — | 2 | 2 | no | — |
| 556 | C8 | — | 10 | 2 | no | — |
| 557 | C8 | — | 10 | 2 | no | — |
| 558 | C5 | C2×#3261 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 559 | C22 | — | 2 | 1 | no | — |
| 560 | C22 | — | 2 | 2 | no | — |
| 561 | C22 | — | 5 | 2 | no | — |
| 562 | C22 | — | 5 | 4 | no | — |
| 563 | C22 | — | 10 | 1 | no | — |
| 564 | C22 | — | 10 | 2 | no | — |
| 565 | C22 | — | 20 | 4 | no | — |
| 566 | C22 | C22×D4×D5 | 1 | 1 | yes | characteristic |
| 567 | C4 | — | 2 | 1 | no | — |
| 568 | C4 | — | 2 | 4 | no | — |
| 569 | C4 | — | 4 | 4 | no | — |
| 570 | C4 | — | 4 | 4 | no | — |
| 571 | C4 | — | 5 | 2 | no | — |
| 572 | C4 | — | 10 | 1 | no | — |
| 573 | C4 | — | 10 | 4 | no | — |
| 574 | C4 | — | 20 | 4 | no | — |
| 575 | C4 | — | 20 | 4 | no | — |
| 576 | C4 | D5×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 577 | C4 | D5×2−1+4 | 1 | 1 | yes | characteristic |
| 578 | C2 | — | 4 | 1 | no | — |
| 579 | C2 | — | 5 | 4 | no | — |
| 580 | C2 | — | 20 | 1 | no | — |
| 581 | C2 | D5×#537 | 1 | 1 | yes | characteristic |
| 582 | C2 | D5×#578 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#3261 | C2 | semidirect |
| 3. #10615184 | C2 | semidirect |
| 4. #10612975 | C2 | semidirect |
| 5. D5×#479 | C2 | semidirect |
| 7. #10612629 | C2 | semidirect |
| 9. #10612481 | C2 | semidirect |
| 10. #10612219 | C2 | semidirect |
| 11. D5×#462 | C2 | semidirect |
| 12. #10610833 | C2 | semidirect |
| 33. C5×#479 | C22 | semidirect |
| 36. C5×#462 | C22 | semidirect |
| 40. #65471 | C22 | semidirect |
| 41. #65471 | C22 | semidirect |
| 46. #65379 | C22 | semidirect |
| 47. #65352 | C22 | semidirect |
| 50. #65320 | C22 | semidirect |
| 51. #65311 | C22 | semidirect |
| 55. #65166 | C22 | semidirect |
| 58. #65146 | C22 | semidirect |
| 59. #65138 | C22 | semidirect |
| 62. #65118 | C22 | semidirect |
| 67. #65088 | C22 | semidirect |
| 68. #65085 | C22 | semidirect |
| 69. #65082 | C22 | semidirect |
| 70. #65082 | C22 | semidirect |
| 168. #3261 | D5 | direct (N × H) |
| 271. #479 | C2×D5 | semidirect |
| 291. #462 | C2×D5 | semidirect |
| 521. D5 | #3261 | direct (N × H) |
| 558. C5 | C2×#3261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#541 | 2 |
| C5×#3261 | 2 |
| #10615184 | 2 |
| #10612975 | 2 |
| D5×#479 | 2 |
| D5×#470 | 2 |
| #10612629 | 2 |
| D5×#467 | 2 |
| #10612481 | 2 |
| #10612219 | 2 |
| D5×#462 | 2 |
| #10610833 | 2 |
| D5×#424 | 2 |
| C2×#3261 | 5 |