Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
6338 conjugacy classes of subgroups.
The subgroup lattice has 382 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C5×#3556 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D5×#564 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #10619041 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | D5×#557 | C2 | 1 | 12 | yes | maximal, complemented |
| 5 | #10618928 | C2 | 1 | 12 | yes | maximal, complemented |
| 6 | D5×#541 | C2 | 1 | 12 | yes | maximal |
| 7 | #10618403 | C2 | 1 | 12 | yes | maximal, complemented |
| 8 | D5×#533 | C2 | 1 | 3 | yes | maximal |
| 9 | #10618171 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | C5×#564 | C22 | 1 | 4 | yes | complemented |
| 11 | C5×#557 | C22 | 1 | 12 | yes | complemented |
| 12 | C5×#541 | C22 | 1 | 12 | yes | — |
| 13 | C5×#533 | C22 | 1 | 3 | yes | — |
| 14 | #66065 | C22 | 1 | 12 | yes | — |
| 15 | #66062 | C22 | 1 | 6 | yes | — |
| 16 | D5×C4⋊Q8 | C22 | 1 | 12 | yes | — |
| 17 | D5×C4⋊Q8 | C22 | 1 | 6 | yes | — |
| 18 | #66055 | C22 | 1 | 24 | yes | complemented |
| 19 | #66055 | C22 | 1 | 12 | yes | complemented |
| 20 | D5×#126 | C22 | 1 | 16 | yes | — |
| 21 | #66035 | C22 | 1 | 48 | yes | — |
| 22 | #66031 | C22 | 1 | 12 | yes | — |
| 23 | #66030 | C22 | 1 | 48 | yes | — |
| 24 | #66022 | C22 | 1 | 6 | yes | — |
| 25 | D5×#125 | C22 | 1 | 12 | yes | — |
| 26 | D5×#125 | C22 | 1 | 48 | yes | — |
| 27 | D5×#125 | C22 | 1 | 6 | yes | — |
| 28 | C5⋊#564 | C22 | 1 | 48 | yes | complemented |
| 29 | C5⋊#564 | C22 | 1 | 12 | yes | complemented |
| 30 | #66019 | C22 | 1 | 24 | yes | complemented |
| 31 | #66019 | C22 | 1 | 48 | yes | complemented |
| 32 | D5×C22⋊Q8 | C22 | 1 | 12 | yes | — |
| 33 | #65959 | C22 | 1 | 24 | yes | — |
| 34 | #65956 | C22 | 1 | 12 | yes | — |
| 35 | #65917 | C22 | 1 | 24 | yes | — |
| 36 | #65912 | C22 | 1 | 12 | yes | — |
| 37 | C4×Q8×D5 | C22 | 1 | 24 | yes | — |
| 38 | C4×Q8×D5 | C22 | 1 | 12 | yes | — |
| 39 | #65904 | C22 | 1 | 12 | yes | complemented |
| 40 | #65903 | C22 | 1 | 24 | yes | complemented |
| 41 | #65901 | C22 | 1 | 24 | yes | complemented |
| 42 | #65901 | C22 | 1 | 12 | yes | complemented |
| 43 | D5×#117 | C22 | 1 | 6 | yes | — |
| 44 | #65852 | C22 | 1 | 12 | yes | — |
| 45 | #65851 | C22 | 1 | 6 | yes | — |
| 46 | C2×C42×D5 | C22 | 1 | 1 | yes | characteristic |
| 47 | #65804 | C22 | 1 | 3 | yes | — |
| 48 | C2×#3556 | — | 5 | 1 | no | maximal, Sylow |
| 49 | C2×Q8×D5 | C23 | 1 | 12 | yes | — |
| 50 | C22×C4×D5 | C23 | 1 | 3 | yes | — |
| 51 | C5×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 52 | C5×C4⋊Q8 | C23 | 1 | 12 | yes | — |
| 53 | C5×#126 | C23 | 1 | 16 | yes | — |
| 54 | C5×#125 | C23 | 1 | 6 | yes | — |
| 55 | C5×#125 | C23 | 1 | 12 | yes | — |
| 56 | C5×#125 | C23 | 1 | 48 | yes | — |
| 57 | C5×C22⋊Q8 | C23 | 1 | 12 | yes | — |
| 58 | C4×C5×Q8 | C23 | 1 | 24 | yes | — |
| 59 | C4×C5×Q8 | C23 | 1 | 12 | yes | — |
| 60 | C5×#117 | C23 | 1 | 6 | yes | — |
| 61 | C2×C42×C5 | C23 | 1 | 1 | yes | characteristic |
| 62 | #4092 | C23 | 1 | 12 | yes | — |
| 63 | Q8×Dic5 | C23 | 1 | 12 | yes | — |
| 64 | Q8×Dic5 | C23 | 1 | 24 | yes | — |
| 65 | #4090 | C23 | 1 | 12 | yes | — |
| 66 | #4090 | C23 | 1 | 24 | yes | — |
| 67 | #4072 | C23 | 1 | 6 | yes | — |
| 68 | #4070 | C23 | 1 | 12 | yes | — |
| 69 | C2×C4×Dic5 | C23 | 1 | 3 | yes | — |
| 70 | #4044 | C23 | 1 | 48 | yes | — |
| 71 | #4043 | C23 | 1 | 12 | yes | — |
| 72 | #4042 | C23 | 1 | 24 | yes | — |
| 73 | #4038 | C23 | 1 | 12 | yes | — |
| 74 | D5×C4⋊C4 | C23 | 1 | 12 | yes | — |
| 75 | D5×C4⋊C4 | C23 | 1 | 12 | yes | — |
| 76 | D5×C4⋊C4 | C23 | 1 | 48 | yes | — |
| 77 | D5×C4⋊C4 | C23 | 1 | 24 | yes | — |
| 78 | #4036 | C23 | 1 | 24 | yes | — |
| 79 | #4036 | C23 | 1 | 48 | yes | — |
| 80 | #4036 | C23 | 1 | 12 | yes | — |
| 81 | #4036 | C23 | 1 | 48 | yes | — |
| 82 | #4035 | C23 | 1 | 48 | yes | — |
| 83 | #4035 | C23 | 1 | 48 | yes | — |
| 84 | #4035 | C23 | 1 | 48 | yes | — |
| 85 | #4035 | C23 | 1 | 48 | yes | — |
| 86 | #4035 | C23 | 1 | 48 | yes | — |
| 87 | #4035 | C23 | 1 | 24 | yes | — |
| 88 | #4034 | C23 | 1 | 12 | yes | — |
| 89 | #4034 | C23 | 1 | 12 | yes | — |
| 90 | #4034 | C23 | 1 | 48 | yes | — |
| 91 | #4033 | C23 | 1 | 24 | yes | — |
| 92 | #4033 | C23 | 1 | 48 | yes | — |
| 93 | #4033 | C23 | 1 | 12 | yes | — |
| 94 | #4033 | C23 | 1 | 24 | yes | — |
| 95 | D5×C22⋊C4 | C23 | 1 | 12 | yes | — |
| 96 | #4025 | C23 | 1 | 48 | yes | — |
| 97 | #4024 | C23 | 1 | 24 | yes | — |
| 98 | #4023 | C23 | 1 | 12 | yes | — |
| 99 | #4022 | C23 | 1 | 16 | yes | — |
| 100 | #4018 | C23 | 1 | 12 | yes | — |
| 101 | C42×D5 | C23 | 1 | 3 | yes | — |
| 102 | C42×D5 | C23 | 1 | 12 | yes | — |
| 103 | C42×D5 | C23 | 1 | 3 | yes | — |
| 104 | C42×D5 | C23 | 1 | 1 | yes | characteristic |
| 105 | C42×D5 | C23 | 1 | 1 | yes | characteristic |
| 106 | C42×D5 | C23 | 1 | 16 | yes | — |
| 107 | #4016 | C23 | 1 | 6 | yes | — |
| 108 | #4016 | C23 | 1 | 12 | yes | — |
| 109 | #4016 | C23 | 1 | 48 | yes | — |
| 110 | #4015 | C23 | 1 | 6 | yes | — |
| 111 | #4015 | C23 | 1 | 12 | yes | — |
| 112 | C4×Dic10 | C23 | 1 | 12 | yes | — |
| 113 | C4×Dic10 | C23 | 1 | 24 | yes | — |
| 114 | C4×Dic10 | C23 | 1 | 24 | yes | — |
| 115 | C4×Dic10 | C23 | 1 | 48 | yes | — |
| 116 | #3556 | — | 5 | 4 | no | — |
| 117 | #3556 | — | 5 | 12 | no | — |
| 118 | #3556 | — | 5 | 12 | no | — |
| 119 | #3556 | — | 5 | 3 | no | — |
| 120 | #3556 | D5 | 1 | 1 | yes | characteristic, direct product factor |
| 121 | C2×#564 | — | 5 | 4 | no | — |
| 122 | C2×#557 | — | 5 | 12 | no | — |
| 123 | C2×#541 | — | 5 | 12 | no | — |
| 124 | C2×#533 | — | 5 | 3 | no | — |
| 125 | C23×D5 | C24 | 1 | 1 | yes | characteristic |
| 126 | C2×C5×Q8 | C24 | 1 | 12 | yes | — |
| 127 | C22×C4×C5 | C24 | 1 | 3 | yes | — |
| 128 | C22×Dic5 | C24 | 1 | 3 | yes | — |
| 129 | Q8×D5 | — | 2 | 48 | no | — |
| 130 | C2×C4×D5 | — | 2 | 12 | no | — |
| 131 | C2×C4×D5 | C24 | 1 | 3 | yes | — |
| 132 | C2×C4×D5 | C24 | 1 | 3 | yes | — |
| 133 | C2×C4×D5 | C24 | 1 | 3 | yes | — |
| 134 | C2×C4×D5 | C24 | 1 | 24 | yes | — |
| 135 | C2×C4×D5 | C24 | 1 | 3 | yes | — |
| 136 | C2×Dic10 | C24 | 1 | 12 | yes | — |
| 137 | C2×Dic10 | C24 | 1 | 24 | yes | — |
| 138 | C5×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 139 | C5×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 140 | C5×C4⋊C4 | C24 | 1 | 24 | yes | — |
| 141 | C5×C4⋊C4 | C24 | 1 | 48 | yes | — |
| 142 | C5×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 143 | C42×C5 | C24 | 1 | 3 | yes | — |
| 144 | C42×C5 | C24 | 1 | 1 | yes | characteristic |
| 145 | C42×C5 | C24 | 1 | 12 | yes | — |
| 146 | C42×C5 | C24 | 1 | 16 | yes | — |
| 147 | C22⋊Dic5 | C24 | 1 | 12 | yes | — |
| 148 | #685 | C24 | 1 | 24 | yes | — |
| 149 | C4⋊Dic5 | C24 | 1 | 12 | yes | — |
| 150 | C4⋊Dic5 | C24 | 1 | 48 | yes | — |
| 151 | C4⋊Dic5 | C24 | 1 | 24 | yes | — |
| 152 | C4⋊Dic5 | C24 | 1 | 12 | yes | — |
| 153 | #683 | C24 | 1 | 24 | yes | — |
| 154 | #683 | C24 | 1 | 24 | yes | — |
| 155 | #683 | C24 | 1 | 48 | yes | — |
| 156 | #683 | C24 | 1 | 48 | yes | — |
| 157 | #683 | C24 | 1 | 24 | yes | — |
| 158 | #683 | C24 | 1 | 24 | yes | — |
| 159 | C4×Dic5 | C24 | 1 | 6 | yes | — |
| 160 | C4×Dic5 | C24 | 1 | 12 | yes | — |
| 161 | C4×Dic5 | C24 | 1 | 24 | yes | — |
| 162 | C4×Dic5 | C24 | 1 | 48 | yes | — |
| 163 | C4×Dic5 | C24 | 1 | 3 | yes | — |
| 164 | C4×Dic5 | C24 | 1 | 3 | yes | — |
| 165 | #564 | — | 5 | 48 | no | — |
| 166 | #564 | — | 5 | 12 | no | — |
| 167 | #564 | C2×D5 | 1 | 4 | yes | complemented |
| 168 | #557 | — | 5 | 24 | no | — |
| 169 | #557 | — | 5 | 12 | no | — |
| 170 | #557 | — | 5 | 48 | no | — |
| 171 | #557 | — | 5 | 24 | no | — |
| 172 | #557 | — | 5 | 24 | no | — |
| 173 | #557 | — | 5 | 12 | no | — |
| 174 | #557 | — | 5 | 24 | no | — |
| 175 | #557 | — | 5 | 12 | no | — |
| 176 | #557 | C2×D5 | 1 | 12 | yes | complemented |
| 177 | #541 | — | 5 | 12 | no | — |
| 178 | #541 | — | 5 | 48 | no | — |
| 179 | #541 | — | 5 | 48 | no | — |
| 180 | #541 | — | 5 | 12 | no | — |
| 181 | #541 | — | 5 | 24 | no | — |
| 182 | #541 | — | 5 | 24 | no | — |
| 183 | #541 | — | 5 | 12 | no | — |
| 184 | #541 | C2×D5 | 1 | 12 | yes | — |
| 185 | #533 | — | 5 | 6 | no | — |
| 186 | #533 | — | 5 | 6 | no | — |
| 187 | #533 | — | 5 | 12 | no | — |
| 188 | #533 | — | 5 | 12 | no | — |
| 189 | #533 | — | 5 | 6 | no | — |
| 190 | #533 | — | 5 | 3 | no | — |
| 191 | #533 | C2×D5 | 1 | 3 | yes | — |
| 192 | C2×C4⋊Q8 | — | 5 | 6 | no | — |
| 193 | C2×C4⋊Q8 | — | 5 | 12 | no | — |
| 194 | C2×#126 | — | 5 | 16 | no | — |
| 195 | C2×#125 | — | 5 | 6 | no | — |
| 196 | C2×#125 | — | 5 | 12 | no | — |
| 197 | C2×#125 | — | 5 | 48 | no | — |
| 198 | C2×C22⋊Q8 | — | 5 | 12 | no | — |
| 199 | C2×C4×Q8 | — | 5 | 12 | no | — |
| 200 | C2×C4×Q8 | — | 5 | 24 | no | — |
| 201 | C2×#117 | — | 5 | 6 | no | — |
| 202 | C22×C42 | — | 5 | 1 | no | — |
| 203 | C23×C5 | C25 | 1 | 1 | yes | characteristic |
| 204 | C22×D5 | — | 2 | 6 | no | — |
| 205 | C22×D5 | C25 | 1 | 1 | yes | characteristic |
| 206 | C22×D5 | C25 | 1 | 1 | yes | characteristic |
| 207 | C5×Q8 | — | 2 | 24 | no | — |
| 208 | C2×C4×C5 | — | 2 | 6 | no | — |
| 209 | C2×C4×C5 | C25 | 1 | 24 | yes | — |
| 210 | C2×C4×C5 | C25 | 1 | 3 | yes | — |
| 211 | C2×C4×C5 | C25 | 1 | 3 | yes | — |
| 212 | C2×Dic5 | — | 2 | 6 | no | — |
| 213 | C2×Dic5 | C25 | 1 | 24 | yes | — |
| 214 | C2×Dic5 | C25 | 1 | 3 | yes | — |
| 215 | C2×Dic5 | C25 | 1 | 3 | yes | — |
| 216 | C4×D5 | — | 2 | 6 | no | — |
| 217 | C4×D5 | — | 2 | 48 | no | — |
| 218 | C4×D5 | — | 2 | 6 | no | — |
| 219 | C4×D5 | — | 2 | 6 | no | — |
| 220 | C4×D5 | 2−1+4 | 1 | 12 | yes | — |
| 221 | Dic10 | — | 2 | 24 | no | — |
| 222 | Dic10 | — | 2 | 48 | no | — |
| 223 | C22×Q8 | — | 5 | 12 | no | — |
| 224 | C23×C4 | — | 5 | 3 | no | — |
| 225 | C4⋊Q8 | — | 5 | 12 | no | — |
| 226 | C4⋊Q8 | — | 5 | 24 | no | — |
| 227 | C4⋊Q8 | — | 5 | 12 | no | — |
| 228 | C4⋊Q8 | — | 5 | 12 | no | — |
| 229 | C4⋊Q8 | — | 5 | 48 | no | — |
| 230 | C4⋊Q8 | — | 5 | 6 | no | — |
| 231 | C4⋊Q8 | — | 5 | 12 | no | — |
| 232 | C4⋊Q8 | C22×D5 | 1 | 6 | yes | — |
| 233 | C4⋊Q8 | C22×D5 | 1 | 12 | yes | — |
| 234 | #126 | — | 5 | 48 | no | — |
| 235 | #126 | — | 5 | 48 | no | — |
| 236 | #126 | — | 5 | 16 | no | — |
| 237 | #126 | C22×D5 | 1 | 16 | yes | — |
| 238 | #125 | — | 5 | 24 | no | — |
| 239 | #125 | — | 5 | 12 | no | — |
| 240 | #125 | — | 5 | 48 | no | — |
| 241 | #125 | — | 5 | 24 | no | — |
| 242 | #125 | — | 5 | 48 | no | — |
| 243 | #125 | — | 5 | 48 | no | — |
| 244 | #125 | — | 5 | 48 | no | — |
| 245 | #125 | — | 5 | 48 | no | — |
| 246 | #125 | — | 5 | 48 | no | — |
| 247 | #125 | — | 5 | 48 | no | — |
| 248 | #125 | — | 5 | 6 | no | — |
| 249 | #125 | — | 5 | 12 | no | — |
| 250 | #125 | — | 5 | 48 | no | — |
| 251 | #125 | C22×D5 | 1 | 6 | yes | — |
| 252 | #125 | C22×D5 | 1 | 12 | yes | — |
| 253 | #125 | C22×D5 | 1 | 48 | yes | — |
| 254 | C22⋊Q8 | — | 5 | 12 | no | — |
| 255 | C22⋊Q8 | — | 5 | 12 | no | — |
| 256 | C22⋊Q8 | — | 5 | 24 | no | — |
| 257 | C22⋊Q8 | — | 5 | 12 | no | — |
| 258 | C22⋊Q8 | — | 5 | 24 | no | — |
| 259 | C22⋊Q8 | C22×D5 | 1 | 12 | yes | — |
| 260 | C4×Q8 | — | 5 | 12 | no | — |
| 261 | C4×Q8 | — | 5 | 24 | no | — |
| 262 | C4×Q8 | — | 5 | 24 | no | — |
| 263 | C4×Q8 | — | 5 | 12 | no | — |
| 264 | C4×Q8 | — | 5 | 48 | no | — |
| 265 | C4×Q8 | — | 5 | 24 | no | — |
| 266 | C4×Q8 | — | 5 | 24 | no | — |
| 267 | C4×Q8 | — | 5 | 12 | no | — |
| 268 | C4×Q8 | — | 5 | 48 | no | — |
| 269 | C4×Q8 | — | 5 | 24 | no | — |
| 270 | C4×Q8 | C22×D5 | 1 | 12 | yes | — |
| 271 | C4×Q8 | C22×D5 | 1 | 24 | yes | — |
| 272 | #117 | — | 5 | 6 | no | — |
| 273 | #117 | — | 5 | 12 | no | — |
| 274 | #117 | — | 5 | 12 | no | — |
| 275 | #117 | — | 5 | 12 | no | — |
| 276 | #117 | C22×D5 | 1 | 6 | yes | — |
| 277 | C2×C4⋊C4 | — | 5 | 12 | no | — |
| 278 | C2×C4⋊C4 | — | 5 | 12 | no | — |
| 279 | C2×C4⋊C4 | — | 5 | 24 | no | — |
| 280 | C2×C4⋊C4 | — | 5 | 48 | no | — |
| 281 | C2×C22⋊C4 | — | 5 | 12 | no | — |
| 282 | C2×C42 | — | 5 | 3 | no | — |
| 283 | C2×C42 | — | 5 | 12 | no | — |
| 284 | C2×C42 | — | 5 | 3 | no | — |
| 285 | C2×C42 | — | 5 | 16 | no | — |
| 286 | C2×C42 | — | 5 | 1 | no | — |
| 287 | C2×C42 | — | 5 | 1 | no | — |
| 288 | C2×C42 | — | 5 | 3 | no | — |
| 289 | C2×C42 | C22×D5 | 1 | 1 | yes | characteristic |
| 290 | C22×C5 | — | 2 | 3 | no | — |
| 291 | C22×C5 | C26 | 1 | 1 | yes | characteristic |
| 292 | C2×D5 | — | 2 | 3 | no | — |
| 293 | C2×D5 | — | 4 | 4 | no | — |
| 294 | C2×D5 | C2×2−1+4 | 1 | 6 | yes | — |
| 295 | C4×C5 | — | 2 | 24 | no | — |
| 296 | C4×C5 | — | 2 | 3 | no | — |
| 297 | C4×C5 | C2×2−1+4 | 1 | 6 | yes | — |
| 298 | Dic5 | — | 2 | 24 | no | — |
| 299 | Dic5 | — | 2 | 3 | no | — |
| 300 | Dic5 | C2×2−1+4 | 1 | 6 | yes | — |
| 301 | C24 | — | 5 | 1 | no | — |
| 302 | C2×Q8 | — | 5 | 24 | no | — |
| 303 | C2×Q8 | — | 5 | 12 | no | — |
| 304 | C2×Q8 | — | 10 | 48 | no | — |
| 305 | C2×Q8 | C23×D5 | 1 | 12 | yes | — |
| 306 | C22×C4 | — | 5 | 3 | no | — |
| 307 | C22×C4 | — | 5 | 3 | no | — |
| 308 | C22×C4 | — | 5 | 24 | no | — |
| 309 | C22×C4 | — | 5 | 3 | no | — |
| 310 | C22×C4 | — | 5 | 3 | no | — |
| 311 | C22×C4 | — | 5 | 3 | no | — |
| 312 | C22×C4 | — | 10 | 12 | no | — |
| 313 | C22×C4 | C23×D5 | 1 | 3 | yes | — |
| 314 | C4⋊C4 | — | 5 | 24 | no | — |
| 315 | C4⋊C4 | — | 5 | 12 | no | — |
| 316 | C4⋊C4 | — | 5 | 24 | no | — |
| 317 | C4⋊C4 | — | 5 | 12 | no | — |
| 318 | C4⋊C4 | — | 5 | 24 | no | — |
| 319 | C4⋊C4 | — | 5 | 24 | no | — |
| 320 | C4⋊C4 | — | 5 | 24 | no | — |
| 321 | C4⋊C4 | — | 5 | 48 | no | — |
| 322 | C4⋊C4 | — | 5 | 48 | no | — |
| 323 | C4⋊C4 | — | 5 | 48 | no | — |
| 324 | C4⋊C4 | C23×D5 | 1 | 12 | yes | — |
| 325 | C4⋊C4 | C23×D5 | 1 | 12 | yes | — |
| 326 | C4⋊C4 | C23×D5 | 1 | 24 | yes | — |
| 327 | C4⋊C4 | C23×D5 | 1 | 48 | yes | — |
| 328 | C22⋊C4 | — | 5 | 12 | no | — |
| 329 | C22⋊C4 | — | 5 | 24 | no | — |
| 330 | C22⋊C4 | C23×D5 | 1 | 12 | yes | — |
| 331 | C42 | — | 5 | 3 | no | — |
| 332 | C42 | — | 5 | 6 | no | — |
| 333 | C42 | — | 5 | 3 | no | — |
| 334 | C42 | — | 5 | 24 | no | — |
| 335 | C42 | — | 5 | 12 | no | — |
| 336 | C42 | — | 5 | 48 | no | — |
| 337 | C42 | C23×D5 | 1 | 3 | yes | — |
| 338 | C42 | C23×D5 | 1 | 1 | yes | characteristic |
| 339 | C42 | C23×D5 | 1 | 12 | yes | — |
| 340 | C42 | C23×D5 | 1 | 16 | yes | — |
| 341 | C2×C5 | — | 4 | 1 | no | — |
| 342 | C2×C5 | C22×2−1+4 | 1 | 3 | yes | — |
| 343 | D5 | — | 4 | 1 | no | — |
| 344 | D5 | #3556 | 1 | 4 | yes | direct product factor |
| 345 | C23 | — | 5 | 1 | no | — |
| 346 | C23 | — | 5 | 1 | no | — |
| 347 | C23 | — | 10 | 6 | no | — |
| 348 | C23 | C24×D5 | 1 | 1 | yes | characteristic |
| 349 | Q8 | — | 2 | 24 | no | — |
| 350 | Q8 | — | 10 | 48 | no | — |
| 351 | Q8 | — | 10 | 24 | no | — |
| 352 | C2×C4 | — | 2 | 6 | no | — |
| 353 | C2×C4 | — | 5 | 3 | no | — |
| 354 | C2×C4 | — | 5 | 12 | no | — |
| 355 | C2×C4 | — | 5 | 24 | no | — |
| 356 | C2×C4 | — | 5 | 3 | no | — |
| 357 | C2×C4 | — | 10 | 6 | no | — |
| 358 | C2×C4 | — | 10 | 6 | no | — |
| 359 | C2×C4 | — | 10 | 48 | no | — |
| 360 | C2×C4 | — | 10 | 6 | no | — |
| 361 | C2×C4 | — | 10 | 6 | no | — |
| 362 | C2×C4 | C24×D5 | 1 | 24 | yes | — |
| 363 | C2×C4 | C24×D5 | 1 | 3 | yes | — |
| 364 | C2×C4 | C24×D5 | 1 | 3 | yes | — |
| 365 | C5 | C2×#3556 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 366 | C22 | — | 2 | 3 | no | — |
| 367 | C22 | — | 5 | 6 | no | — |
| 368 | C22 | — | 10 | 3 | no | — |
| 369 | C22 | — | 20 | 4 | no | — |
| 370 | C22 | C25×D5 | 1 | 1 | yes | characteristic |
| 371 | C4 | — | 2 | 3 | no | — |
| 372 | C4 | — | 2 | 24 | no | — |
| 373 | C4 | — | 5 | 6 | no | — |
| 374 | C4 | — | 10 | 3 | no | — |
| 375 | C4 | — | 10 | 24 | no | — |
| 376 | C4 | D5×2−1+4 | 1 | 6 | yes | — |
| 377 | C2 | — | 4 | 1 | no | — |
| 378 | C2 | — | 5 | 4 | no | — |
| 379 | C2 | — | 20 | 1 | no | — |
| 380 | C2 | C2×D5×2−1+4 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C25×D5 |
| commutator, socle, cosocle | C22×C5 | C26 |
| Fitting | C5×#3556 | C2 |
| prime radical | C23×D5 | C24 |
| hypercenter | #3556 | D5 |
| hypocenter | C5 | C2×#3556 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ #3556 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#3556 | C2 | semidirect |
| 2. D5×#564 | C2 | semidirect |
| 3. #10619041 | C2 | semidirect |
| 4. D5×#557 | C2 | semidirect |
| 5. #10618928 | C2 | semidirect |
| 7. #10618403 | C2 | semidirect |
| 9. #10618171 | C2 | semidirect |
| 10. C5×#564 | C22 | semidirect |
| 11. C5×#557 | C22 | semidirect |
| 18. #66055 | C22 | semidirect |
| 19. #66055 | C22 | semidirect |
| 28. C5⋊#564 | C22 | semidirect |
| 29. C5⋊#564 | C22 | semidirect |
| 30. #66019 | C22 | semidirect |
| 31. #66019 | C22 | semidirect |
| 39. #65904 | C22 | semidirect |
| 40. #65903 | C22 | semidirect |
| 41. #65901 | C22 | semidirect |
| 42. #65901 | C22 | semidirect |
| 120. #3556 | D5 | direct (N × H) |
| 167. #564 | C2×D5 | semidirect |
| 176. #557 | C2×D5 | semidirect |
| 344. D5 | #3556 | direct (N × H) |
| 365. C5 | C2×#3556 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3556 | 2 |
| D5×#564 | 2 |
| #10619041 | 2 |
| D5×#557 | 2 |
| #10618928 | 2 |
| D5×#541 | 2 |
| #10618403 | 2 |
| D5×#533 | 2 |
| #10618171 | 2 |
| C2×#3556 | 5 |