Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
6554 conjugacy classes of subgroups.
The subgroup lattice has 550 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C5×#3531 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D5×#564 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10619040 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | D5×#563 | C2 | 1 | 10 | yes | maximal, complemented |
| 5 | #10619017 | C2 | 1 | 10 | yes | maximal, complemented |
| 6 | D5×#562 | C2 | 1 | 5 | yes | maximal, complemented |
| 7 | #10618995 | C2 | 1 | 5 | yes | maximal, complemented |
| 8 | #10618187 | C2 | 1 | 5 | yes | maximal, complemented |
| 9 | D5×#533 | C2 | 1 | 5 | yes | maximal, complemented |
| 10 | D5×#529 | C2 | 1 | 10 | yes | maximal, complemented |
| 11 | #10618033 | C2 | 1 | 10 | yes | maximal, complemented |
| 12 | C5×#564 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | C5×#563 | C22 | 1 | 10 | yes | complemented |
| 14 | C5×#562 | C22 | 1 | 5 | yes | complemented |
| 15 | C5×#533 | C22 | 1 | 5 | yes | complemented |
| 16 | C5×#529 | C22 | 1 | 10 | yes | complemented |
| 17 | #66069 | C22 | 1 | 20 | yes | complemented |
| 18 | #66062 | C22 | 1 | 10 | yes | complemented |
| 19 | D5×C4⋊Q8 | C22 | 1 | 10 | yes | — |
| 20 | #66046 | C22 | 1 | 20 | yes | complemented |
| 21 | #66046 | C22 | 1 | 20 | yes | complemented |
| 22 | #66040 | C22 | 1 | 20 | yes | complemented |
| 23 | D5×#126 | C22 | 1 | 20 | yes | — |
| 24 | #66034 | C22 | 1 | 5 | yes | complemented |
| 25 | #66033 | C22 | 1 | 10 | yes | complemented |
| 26 | #66033 | C22 | 1 | 10 | yes | complemented |
| 27 | #66025 | C22 | 1 | 10 | yes | complemented |
| 28 | #66022 | C22 | 1 | 5 | yes | complemented |
| 29 | #66022 | C22 | 1 | 5 | yes | complemented |
| 30 | D5×#125 | C22 | 1 | 5 | yes | — |
| 31 | D5×#125 | C22 | 1 | 5 | yes | — |
| 32 | D5×#125 | C22 | 1 | 10 | yes | — |
| 33 | C5⋊#564 | C22 | 1 | 5 | yes | complemented |
| 34 | C5⋊#564 | C22 | 1 | 10 | yes | complemented |
| 35 | #66018 | C22 | 1 | 10 | yes | complemented |
| 36 | #66014 | C22 | 1 | 10 | yes | complemented |
| 37 | D5×#124 | C22 | 1 | 10 | yes | — |
| 38 | #66006 | C22 | 1 | 10 | yes | complemented |
| 39 | #66001 | C22 | 1 | 20 | yes | complemented |
| 40 | D5×#123 | C22 | 1 | 20 | yes | — |
| 41 | #65985 | C22 | 1 | 20 | yes | complemented |
| 42 | #65983 | C22 | 1 | 20 | yes | complemented |
| 43 | #65981 | C22 | 1 | 20 | yes | complemented |
| 44 | #65980 | C22 | 1 | 20 | yes | complemented |
| 45 | #65980 | C22 | 1 | 20 | yes | complemented |
| 46 | D5×C22⋊Q8 | C22 | 1 | 20 | yes | — |
| 47 | D5×C22⋊Q8 | C22 | 1 | 10 | yes | — |
| 48 | #65958 | C22 | 1 | 10 | yes | complemented |
| 49 | #65956 | C22 | 1 | 20 | yes | complemented |
| 50 | #65955 | C22 | 1 | 20 | yes | complemented |
| 51 | D5×#121 | C22 | 1 | 10 | yes | — |
| 52 | #65934 | C22 | 1 | 10 | yes | complemented |
| 53 | #65914 | C22 | 1 | 10 | yes | complemented |
| 54 | #65912 | C22 | 1 | 20 | yes | complemented |
| 55 | C4×Q8×D5 | C22 | 1 | 10 | yes | — |
| 56 | #65891 | C22 | 1 | 10 | yes | complemented |
| 57 | C4×D4×D5 | C22 | 1 | 10 | yes | — |
| 58 | #65872 | C22 | 1 | 20 | yes | complemented |
| 59 | #65862 | C22 | 1 | 20 | yes | complemented |
| 60 | D5×#117 | C22 | 1 | 10 | yes | — |
| 61 | #65851 | C22 | 1 | 10 | yes | complemented |
| 62 | #65813 | C22 | 1 | 10 | yes | complemented |
| 63 | C2×C42×D5 | C22 | 1 | 5 | yes | — |
| 64 | #65804 | C22 | 1 | 5 | yes | complemented |
| 65 | C2×#3531 | — | 5 | 1 | no | maximal, Sylow |
| 66 | C2×Q8×D5 | C23 | 1 | 10 | yes | — |
| 67 | C2×D4×D5 | C23 | 1 | 10 | yes | — |
| 68 | C22×C4×D5 | C23 | 1 | 5 | yes | — |
| 69 | C22×C4×D5 | C23 | 1 | 10 | yes | — |
| 70 | C5×C4⋊Q8 | C23 | 1 | 10 | yes | — |
| 71 | C5×#126 | C23 | 1 | 20 | yes | — |
| 72 | C5×#125 | C23 | 1 | 10 | yes | — |
| 73 | C5×#125 | C23 | 1 | 5 | yes | — |
| 74 | C5×#125 | C23 | 1 | 5 | yes | — |
| 75 | C5×#124 | C23 | 1 | 10 | yes | — |
| 76 | C5×#123 | C23 | 1 | 20 | yes | — |
| 77 | C5×C22⋊Q8 | C23 | 1 | 10 | yes | — |
| 78 | C5×C22⋊Q8 | C23 | 1 | 20 | yes | — |
| 79 | C5×#121 | C23 | 1 | 10 | yes | — |
| 80 | C4×C5×Q8 | C23 | 1 | 10 | yes | — |
| 81 | C4×C5×D4 | C23 | 1 | 10 | yes | — |
| 82 | C5×#117 | C23 | 1 | 10 | yes | — |
| 83 | C2×C42×C5 | C23 | 1 | 5 | yes | — |
| 84 | #4093 | C23 | 1 | 10 | yes | — |
| 85 | #4092 | C23 | 1 | 20 | yes | — |
| 86 | #4092 | C23 | 1 | 10 | yes | — |
| 87 | Q8×Dic5 | C23 | 1 | 10 | yes | — |
| 88 | #4090 | C23 | 1 | 20 | yes | — |
| 89 | #4085 | C23 | 1 | 20 | yes | — |
| 90 | #4084 | C23 | 1 | 10 | yes | — |
| 91 | #4082 | C23 | 1 | 10 | yes | — |
| 92 | #4081 | C23 | 1 | 20 | yes | — |
| 93 | D4×Dic5 | C23 | 1 | 10 | yes | — |
| 94 | #4076 | C23 | 1 | 10 | yes | — |
| 95 | #4075 | C23 | 1 | 20 | yes | — |
| 96 | C4×C22⋊D5 | C23 | 1 | 20 | yes | — |
| 97 | #4072 | C23 | 1 | 10 | yes | — |
| 98 | #4070 | C23 | 1 | 20 | yes | — |
| 99 | #4070 | C23 | 1 | 10 | yes | — |
| 100 | C2×C4×Dic5 | C23 | 1 | 5 | yes | — |
| 101 | C2×C4×Dic5 | C23 | 1 | 10 | yes | — |
| 102 | #4044 | C23 | 1 | 20 | yes | — |
| 103 | #4044 | C23 | 1 | 20 | yes | — |
| 104 | #4044 | C23 | 1 | 20 | yes | — |
| 105 | #4043 | C23 | 1 | 20 | yes | — |
| 106 | #4043 | C23 | 1 | 10 | yes | — |
| 107 | #4042 | C23 | 1 | 20 | yes | — |
| 108 | #4042 | C23 | 1 | 20 | yes | — |
| 109 | #4042 | C23 | 1 | 20 | yes | — |
| 110 | #4041 | C23 | 1 | 10 | yes | — |
| 111 | #4040 | C23 | 1 | 20 | yes | — |
| 112 | #4040 | C23 | 1 | 20 | yes | — |
| 113 | #4039 | C23 | 1 | 10 | yes | — |
| 114 | #4038 | C23 | 1 | 10 | yes | — |
| 115 | #4038 | C23 | 1 | 10 | yes | — |
| 116 | D5×C4⋊C4 | C23 | 1 | 10 | yes | — |
| 117 | D5×C4⋊C4 | C23 | 1 | 10 | yes | — |
| 118 | D5×C4⋊C4 | C23 | 1 | 20 | yes | — |
| 119 | D5×C4⋊C4 | C23 | 1 | 10 | yes | — |
| 120 | D5×C4⋊C4 | C23 | 1 | 10 | yes | — |
| 121 | #4036 | C23 | 1 | 10 | yes | — |
| 122 | #4036 | C23 | 1 | 10 | yes | — |
| 123 | #4036 | C23 | 1 | 10 | yes | — |
| 124 | #4036 | C23 | 1 | 10 | yes | — |
| 125 | #4035 | C23 | 1 | 20 | yes | — |
| 126 | #4035 | C23 | 1 | 20 | yes | — |
| 127 | #4035 | C23 | 1 | 20 | yes | — |
| 128 | #4035 | C23 | 1 | 20 | yes | — |
| 129 | #4034 | C23 | 1 | 10 | yes | — |
| 130 | #4034 | C23 | 1 | 10 | yes | — |
| 131 | #4034 | C23 | 1 | 20 | yes | — |
| 132 | #4033 | C23 | 1 | 20 | yes | — |
| 133 | #4033 | C23 | 1 | 10 | yes | — |
| 134 | #4032 | C23 | 1 | 20 | yes | — |
| 135 | #4031 | C23 | 1 | 20 | yes | — |
| 136 | #4031 | C23 | 1 | 20 | yes | — |
| 137 | #4030 | C23 | 1 | 20 | yes | — |
| 138 | #4029 | C23 | 1 | 20 | yes | — |
| 139 | #4029 | C23 | 1 | 20 | yes | — |
| 140 | #4027 | C23 | 1 | 20 | yes | — |
| 141 | D5×C22⋊C4 | C23 | 1 | 20 | yes | — |
| 142 | D5×C22⋊C4 | C23 | 1 | 20 | yes | — |
| 143 | #4025 | C23 | 1 | 20 | yes | — |
| 144 | #4025 | C23 | 1 | 20 | yes | — |
| 145 | #4025 | C23 | 1 | 20 | yes | — |
| 146 | #4024 | C23 | 1 | 20 | yes | — |
| 147 | #4024 | C23 | 1 | 20 | yes | — |
| 148 | #4024 | C23 | 1 | 20 | yes | — |
| 149 | #4023 | C23 | 1 | 20 | yes | — |
| 150 | #4022 | C23 | 1 | 20 | yes | — |
| 151 | #4021 | C23 | 1 | 10 | yes | — |
| 152 | C4×D20 | C23 | 1 | 10 | yes | — |
| 153 | #4018 | C23 | 1 | 20 | yes | — |
| 154 | C42×D5 | C23 | 1 | 5 | yes | — |
| 155 | C42×D5 | C23 | 1 | 5 | yes | — |
| 156 | C42×D5 | C23 | 1 | 10 | yes | — |
| 157 | C42×D5 | C23 | 1 | 10 | yes | — |
| 158 | C42×D5 | C23 | 1 | 5 | yes | — |
| 159 | C42×D5 | C23 | 1 | 5 | yes | — |
| 160 | #4016 | C23 | 1 | 5 | yes | — |
| 161 | #4016 | C23 | 1 | 5 | yes | — |
| 162 | #4016 | C23 | 1 | 10 | yes | — |
| 163 | #4015 | C23 | 1 | 10 | yes | — |
| 164 | C4×Dic10 | C23 | 1 | 20 | yes | — |
| 165 | C4×Dic10 | C23 | 1 | 10 | yes | — |
| 166 | #3531 | — | 5 | 1 | no | — |
| 167 | #3531 | — | 5 | 10 | no | — |
| 168 | #3531 | — | 5 | 5 | no | — |
| 169 | #3531 | — | 5 | 5 | no | — |
| 170 | #3531 | — | 5 | 10 | no | — |
| 171 | #3531 | D5 | 1 | 1 | yes | characteristic, direct product factor |
| 172 | C2×#564 | — | 5 | 1 | no | — |
| 173 | C2×#563 | — | 5 | 10 | no | — |
| 174 | C2×#562 | — | 5 | 5 | no | — |
| 175 | C2×#533 | — | 5 | 5 | no | — |
| 176 | C2×#529 | — | 5 | 10 | no | — |
| 177 | C23×D5 | C24 | 1 | 5 | yes | — |
| 178 | C2×C5×Q8 | C24 | 1 | 10 | yes | — |
| 179 | C2×C5×D4 | C24 | 1 | 10 | yes | — |
| 180 | C22×C4×C5 | C24 | 1 | 5 | yes | — |
| 181 | C22×C4×C5 | C24 | 1 | 10 | yes | — |
| 182 | C2×C22⋊D5 | C24 | 1 | 20 | yes | — |
| 183 | C22×Dic5 | C24 | 1 | 5 | yes | — |
| 184 | C22×Dic5 | C24 | 1 | 10 | yes | — |
| 185 | Q8×D5 | — | 4 | 20 | no | — |
| 186 | D4×D5 | — | 4 | 20 | no | — |
| 187 | C2×D20 | C24 | 1 | 10 | yes | — |
| 188 | C2×C4×D5 | — | 2 | 20 | no | — |
| 189 | C2×C4×D5 | — | 4 | 20 | no | — |
| 190 | C2×C4×D5 | C24 | 1 | 10 | yes | — |
| 191 | C2×C4×D5 | C24 | 1 | 10 | yes | — |
| 192 | C2×C4×D5 | C24 | 1 | 5 | yes | — |
| 193 | C2×C4×D5 | C24 | 1 | 5 | yes | — |
| 194 | C2×C4×D5 | C24 | 1 | 5 | yes | — |
| 195 | C2×C4×D5 | C24 | 1 | 10 | yes | — |
| 196 | C2×C4×D5 | C24 | 1 | 10 | yes | — |
| 197 | C2×C4×D5 | C24 | 1 | 1 | yes | characteristic |
| 198 | C2×Dic10 | C24 | 1 | 20 | yes | — |
| 199 | C2×Dic10 | C24 | 1 | 10 | yes | — |
| 200 | C5×C4⋊C4 | C24 | 1 | 10 | yes | — |
| 201 | C5×C4⋊C4 | C24 | 1 | 10 | yes | — |
| 202 | C5×C4⋊C4 | C24 | 1 | 10 | yes | — |
| 203 | C5×C4⋊C4 | C24 | 1 | 10 | yes | — |
| 204 | C5×C4⋊C4 | C24 | 1 | 20 | yes | — |
| 205 | C5×C22⋊C4 | C24 | 1 | 20 | yes | — |
| 206 | C5×C22⋊C4 | C24 | 1 | 20 | yes | — |
| 207 | C42×C5 | C24 | 1 | 10 | yes | — |
| 208 | C42×C5 | C24 | 1 | 5 | yes | — |
| 209 | C42×C5 | C24 | 1 | 5 | yes | — |
| 210 | C22⋊Dic5 | C24 | 1 | 20 | yes | — |
| 211 | C22⋊Dic5 | C24 | 1 | 20 | yes | — |
| 212 | #685 | C24 | 1 | 20 | yes | — |
| 213 | #685 | C24 | 1 | 20 | yes | — |
| 214 | #685 | C24 | 1 | 20 | yes | — |
| 215 | #685 | C24 | 1 | 20 | yes | — |
| 216 | C4⋊Dic5 | C24 | 1 | 20 | yes | — |
| 217 | C4⋊Dic5 | C24 | 1 | 10 | yes | — |
| 218 | C4⋊Dic5 | C24 | 1 | 10 | yes | — |
| 219 | C4⋊Dic5 | C24 | 1 | 10 | yes | — |
| 220 | C4⋊Dic5 | C24 | 1 | 10 | yes | — |
| 221 | #683 | C24 | 1 | 20 | yes | — |
| 222 | #683 | C24 | 1 | 20 | yes | — |
| 223 | #683 | C24 | 1 | 20 | yes | — |
| 224 | #683 | C24 | 1 | 20 | yes | — |
| 225 | #683 | C24 | 1 | 20 | yes | — |
| 226 | #683 | C24 | 1 | 20 | yes | — |
| 227 | C4×Dic5 | C24 | 1 | 10 | yes | — |
| 228 | C4×Dic5 | C24 | 1 | 10 | yes | — |
| 229 | C4×Dic5 | C24 | 1 | 10 | yes | — |
| 230 | C4×Dic5 | C24 | 1 | 5 | yes | — |
| 231 | C4×Dic5 | C24 | 1 | 10 | yes | — |
| 232 | C4×Dic5 | C24 | 1 | 5 | yes | — |
| 233 | C4×Dic5 | C24 | 1 | 10 | yes | — |
| 234 | #564 | — | 5 | 10 | no | — |
| 235 | #564 | — | 5 | 5 | no | — |
| 236 | #564 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 237 | #563 | — | 5 | 20 | no | — |
| 238 | #563 | — | 5 | 20 | no | — |
| 239 | #563 | — | 5 | 20 | no | — |
| 240 | #563 | — | 5 | 10 | no | — |
| 241 | #563 | — | 5 | 10 | no | — |
| 242 | #563 | — | 5 | 10 | no | — |
| 243 | #563 | — | 5 | 20 | no | — |
| 244 | #563 | — | 5 | 20 | no | — |
| 245 | #563 | — | 5 | 20 | no | — |
| 246 | #563 | C2×D5 | 1 | 10 | yes | complemented |
| 247 | #562 | — | 5 | 5 | no | — |
| 248 | #562 | — | 5 | 10 | no | — |
| 249 | #562 | — | 5 | 20 | no | — |
| 250 | #562 | — | 5 | 20 | no | — |
| 251 | #562 | — | 5 | 20 | no | — |
| 252 | #562 | C2×D5 | 1 | 5 | yes | complemented |
| 253 | #533 | — | 5 | 10 | no | — |
| 254 | #533 | — | 5 | 5 | no | — |
| 255 | #533 | — | 5 | 5 | no | — |
| 256 | #533 | — | 5 | 20 | no | — |
| 257 | #533 | — | 5 | 20 | no | — |
| 258 | #533 | — | 5 | 10 | no | — |
| 259 | #533 | — | 5 | 5 | no | — |
| 260 | #533 | C2×D5 | 1 | 5 | yes | complemented |
| 261 | C2×C4⋊Q8 | — | 5 | 10 | no | — |
| 262 | #529 | — | 5 | 20 | no | — |
| 263 | #529 | — | 5 | 10 | no | — |
| 264 | #529 | — | 5 | 10 | no | — |
| 265 | #529 | — | 5 | 20 | no | — |
| 266 | #529 | — | 5 | 10 | no | — |
| 267 | #529 | — | 5 | 10 | no | — |
| 268 | #529 | — | 5 | 10 | no | — |
| 269 | #529 | — | 5 | 20 | no | — |
| 270 | #529 | — | 5 | 10 | no | — |
| 271 | #529 | — | 5 | 20 | no | — |
| 272 | #529 | — | 5 | 10 | no | — |
| 273 | #529 | C2×D5 | 1 | 10 | yes | complemented |
| 274 | C2×#126 | — | 5 | 20 | no | — |
| 275 | C2×#125 | — | 5 | 10 | no | — |
| 276 | C2×#125 | — | 5 | 5 | no | — |
| 277 | C2×#125 | — | 5 | 5 | no | — |
| 278 | C2×#124 | — | 5 | 10 | no | — |
| 279 | C2×#123 | — | 5 | 20 | no | — |
| 280 | C2×C22⋊Q8 | — | 5 | 10 | no | — |
| 281 | C2×C22⋊Q8 | — | 5 | 20 | no | — |
| 282 | C2×#121 | — | 5 | 10 | no | — |
| 283 | C2×C4×Q8 | — | 5 | 10 | no | — |
| 284 | C2×C4×D4 | — | 5 | 10 | no | — |
| 285 | C2×#117 | — | 5 | 10 | no | — |
| 286 | C22×C42 | — | 5 | 5 | no | — |
| 287 | C23×C5 | C25 | 1 | 5 | yes | — |
| 288 | C22×D5 | — | 2 | 10 | no | — |
| 289 | C22×D5 | — | 2 | 20 | no | — |
| 290 | C22×D5 | C25 | 1 | 5 | yes | — |
| 291 | C22×D5 | C25 | 1 | 1 | yes | characteristic |
| 292 | C5×Q8 | — | 4 | 10 | no | — |
| 293 | C5×D4 | — | 4 | 10 | no | — |
| 294 | C2×C4×C5 | — | 2 | 10 | no | — |
| 295 | C2×C4×C5 | — | 4 | 10 | no | — |
| 296 | C2×C4×C5 | C25 | 1 | 10 | yes | — |
| 297 | C2×C4×C5 | C25 | 1 | 5 | yes | — |
| 298 | C2×C4×C5 | C25 | 1 | 10 | yes | — |
| 299 | C2×C4×C5 | C25 | 1 | 1 | yes | characteristic |
| 300 | C22⋊D5 | — | 4 | 20 | no | — |
| 301 | C2×Dic5 | — | 2 | 10 | no | — |
| 302 | C2×Dic5 | — | 4 | 10 | no | — |
| 303 | C2×Dic5 | C25 | 1 | 5 | yes | — |
| 304 | C2×Dic5 | C25 | 1 | 10 | yes | — |
| 305 | C2×Dic5 | C25 | 1 | 10 | yes | — |
| 306 | C2×Dic5 | C25 | 1 | 1 | yes | characteristic |
| 307 | D20 | — | 4 | 10 | no | — |
| 308 | C4×D5 | — | 2 | 10 | no | — |
| 309 | C4×D5 | — | 2 | 20 | no | — |
| 310 | C4×D5 | — | 2 | 20 | no | — |
| 311 | C4×D5 | — | 2 | 10 | no | — |
| 312 | C4×D5 | — | 2 | 10 | no | — |
| 313 | C4×D5 | — | 4 | 10 | no | — |
| 314 | C4×D5 | — | 4 | 10 | no | — |
| 315 | C4×D5 | 2−1+4 | 1 | 4 | yes | — |
| 316 | Dic10 | — | 4 | 10 | no | — |
| 317 | Dic10 | — | 4 | 20 | no | — |
| 318 | C22×Q8 | — | 5 | 10 | no | — |
| 319 | C22×D4 | — | 5 | 10 | no | — |
| 320 | C23×C4 | — | 5 | 5 | no | — |
| 321 | C23×C4 | — | 5 | 10 | no | — |
| 322 | C4⋊Q8 | — | 5 | 20 | no | — |
| 323 | C4⋊Q8 | — | 5 | 20 | no | — |
| 324 | C4⋊Q8 | — | 5 | 10 | no | — |
| 325 | C4⋊Q8 | — | 5 | 10 | no | — |
| 326 | C4⋊Q8 | — | 5 | 10 | no | — |
| 327 | C4⋊Q8 | C22×D5 | 1 | 10 | yes | — |
| 328 | #126 | — | 5 | 20 | no | — |
| 329 | #126 | — | 5 | 20 | no | — |
| 330 | #126 | — | 5 | 20 | no | — |
| 331 | #126 | — | 5 | 20 | no | — |
| 332 | #126 | — | 5 | 20 | no | — |
| 333 | #126 | — | 5 | 20 | no | — |
| 334 | #126 | — | 5 | 20 | no | — |
| 335 | #126 | C22×D5 | 1 | 20 | yes | — |
| 336 | #125 | — | 5 | 20 | no | — |
| 337 | #125 | — | 5 | 20 | no | — |
| 338 | #125 | — | 5 | 10 | no | — |
| 339 | #125 | — | 5 | 10 | no | — |
| 340 | #125 | — | 5 | 20 | no | — |
| 341 | #125 | — | 5 | 10 | no | — |
| 342 | #125 | — | 5 | 20 | no | — |
| 343 | #125 | — | 5 | 10 | no | — |
| 344 | #125 | — | 5 | 10 | no | — |
| 345 | #125 | — | 5 | 5 | no | — |
| 346 | #125 | — | 5 | 5 | no | — |
| 347 | #125 | C22×D5 | 1 | 10 | yes | — |
| 348 | #125 | C22×D5 | 1 | 5 | yes | — |
| 349 | #125 | C22×D5 | 1 | 5 | yes | — |
| 350 | #124 | — | 5 | 10 | no | — |
| 351 | #124 | — | 5 | 10 | no | — |
| 352 | #124 | — | 5 | 20 | no | — |
| 353 | #124 | — | 5 | 20 | no | — |
| 354 | #124 | — | 5 | 10 | no | — |
| 355 | #124 | C22×D5 | 1 | 10 | yes | — |
| 356 | #123 | — | 5 | 20 | no | — |
| 357 | #123 | — | 5 | 20 | no | — |
| 358 | #123 | — | 5 | 20 | no | — |
| 359 | #123 | — | 5 | 20 | no | — |
| 360 | #123 | — | 5 | 20 | no | — |
| 361 | #123 | — | 5 | 20 | no | — |
| 362 | #123 | — | 5 | 20 | no | — |
| 363 | #123 | C22×D5 | 1 | 20 | yes | — |
| 364 | C22⋊Q8 | — | 5 | 10 | no | — |
| 365 | C22⋊Q8 | — | 5 | 20 | no | — |
| 366 | C22⋊Q8 | — | 5 | 10 | no | — |
| 367 | C22⋊Q8 | — | 5 | 20 | no | — |
| 368 | C22⋊Q8 | — | 5 | 20 | no | — |
| 369 | C22⋊Q8 | — | 5 | 10 | no | — |
| 370 | C22⋊Q8 | — | 5 | 20 | no | — |
| 371 | C22⋊Q8 | — | 5 | 20 | no | — |
| 372 | C22⋊Q8 | — | 5 | 20 | no | — |
| 373 | C22⋊Q8 | — | 5 | 20 | no | — |
| 374 | C22⋊Q8 | — | 5 | 20 | no | — |
| 375 | C22⋊Q8 | — | 5 | 20 | no | — |
| 376 | C22⋊Q8 | C22×D5 | 1 | 10 | yes | — |
| 377 | C22⋊Q8 | C22×D5 | 1 | 20 | yes | — |
| 378 | #121 | — | 5 | 10 | no | — |
| 379 | #121 | — | 5 | 20 | no | — |
| 380 | #121 | — | 5 | 10 | no | — |
| 381 | #121 | — | 5 | 10 | no | — |
| 382 | #121 | — | 5 | 20 | no | — |
| 383 | #121 | C22×D5 | 1 | 10 | yes | — |
| 384 | C4×Q8 | — | 5 | 10 | no | — |
| 385 | C4×Q8 | — | 5 | 20 | no | — |
| 386 | C4×Q8 | — | 5 | 10 | no | — |
| 387 | C4×Q8 | — | 5 | 20 | no | — |
| 388 | C4×Q8 | — | 5 | 10 | no | — |
| 389 | C4×Q8 | C22×D5 | 1 | 10 | yes | — |
| 390 | C4×D4 | — | 5 | 10 | no | — |
| 391 | C4×D4 | — | 5 | 20 | no | — |
| 392 | C4×D4 | — | 5 | 10 | no | — |
| 393 | C4×D4 | — | 5 | 20 | no | — |
| 394 | C4×D4 | — | 5 | 10 | no | — |
| 395 | C4×D4 | C22×D5 | 1 | 10 | yes | — |
| 396 | #117 | — | 5 | 10 | no | — |
| 397 | #117 | — | 5 | 10 | no | — |
| 398 | #117 | — | 5 | 10 | no | — |
| 399 | #117 | — | 5 | 20 | no | — |
| 400 | #117 | — | 5 | 20 | no | — |
| 401 | #117 | C22×D5 | 1 | 10 | yes | — |
| 402 | C2×C4⋊C4 | — | 5 | 10 | no | — |
| 403 | C2×C4⋊C4 | — | 5 | 10 | no | — |
| 404 | C2×C4⋊C4 | — | 5 | 10 | no | — |
| 405 | C2×C4⋊C4 | — | 5 | 10 | no | — |
| 406 | C2×C4⋊C4 | — | 5 | 20 | no | — |
| 407 | C2×C22⋊C4 | — | 5 | 20 | no | — |
| 408 | C2×C22⋊C4 | — | 5 | 20 | no | — |
| 409 | C2×C42 | — | 5 | 10 | no | — |
| 410 | C2×C42 | — | 5 | 5 | no | — |
| 411 | C2×C42 | — | 5 | 10 | no | — |
| 412 | C2×C42 | — | 5 | 5 | no | — |
| 413 | C2×C42 | — | 5 | 5 | no | — |
| 414 | C2×C42 | — | 5 | 5 | no | — |
| 415 | C2×C42 | — | 5 | 5 | no | — |
| 416 | C2×C42 | — | 5 | 10 | no | — |
| 417 | C2×C42 | C22×D5 | 1 | 5 | yes | — |
| 418 | C22×C5 | — | 2 | 5 | no | — |
| 419 | C22×C5 | — | 2 | 10 | no | — |
| 420 | C22×C5 | C26 | 1 | 1 | yes | characteristic |
| 421 | C2×D5 | — | 2 | 5 | no | — |
| 422 | C2×D5 | — | 2 | 10 | no | — |
| 423 | C2×D5 | — | 4 | 20 | no | — |
| 424 | C2×D5 | C2×2−1+4 | 1 | 2 | yes | — |
| 425 | C2×D5 | #585 | 1 | 4 | yes | — |
| 426 | C4×C5 | — | 2 | 5 | no | — |
| 427 | C4×C5 | — | 2 | 10 | no | — |
| 428 | C4×C5 | — | 2 | 10 | no | — |
| 429 | C4×C5 | C2×2−1+4 | 1 | 2 | yes | — |
| 430 | Dic5 | — | 2 | 5 | no | — |
| 431 | Dic5 | — | 2 | 10 | no | — |
| 432 | Dic5 | — | 2 | 10 | no | — |
| 433 | Dic5 | C2×2−1+4 | 1 | 2 | yes | — |
| 434 | C24 | — | 5 | 5 | no | — |
| 435 | C2×Q8 | — | 5 | 10 | no | — |
| 436 | C2×Q8 | — | 5 | 20 | no | — |
| 437 | C2×Q8 | — | 20 | 20 | no | — |
| 438 | C2×Q8 | C23×D5 | 1 | 10 | yes | — |
| 439 | C2×D4 | — | 5 | 20 | no | — |
| 440 | C2×D4 | — | 5 | 10 | no | — |
| 441 | C2×D4 | — | 20 | 20 | no | — |
| 442 | C2×D4 | C23×D5 | 1 | 10 | yes | — |
| 443 | C22×C4 | — | 5 | 1 | no | — |
| 444 | C22×C4 | — | 5 | 5 | no | — |
| 445 | C22×C4 | — | 5 | 10 | no | — |
| 446 | C22×C4 | — | 5 | 5 | no | — |
| 447 | C22×C4 | — | 5 | 10 | no | — |
| 448 | C22×C4 | — | 5 | 10 | no | — |
| 449 | C22×C4 | — | 5 | 5 | no | — |
| 450 | C22×C4 | — | 5 | 5 | no | — |
| 451 | C22×C4 | — | 5 | 10 | no | — |
| 452 | C22×C4 | — | 5 | 10 | no | — |
| 453 | C22×C4 | — | 10 | 20 | no | — |
| 454 | C22×C4 | — | 20 | 20 | no | — |
| 455 | C22×C4 | C23×D5 | 1 | 5 | yes | — |
| 456 | C22×C4 | C23×D5 | 1 | 10 | yes | — |
| 457 | C4⋊C4 | — | 5 | 20 | no | — |
| 458 | C4⋊C4 | — | 5 | 10 | no | — |
| 459 | C4⋊C4 | — | 5 | 20 | no | — |
| 460 | C4⋊C4 | — | 5 | 10 | no | — |
| 461 | C4⋊C4 | — | 5 | 20 | no | — |
| 462 | C4⋊C4 | — | 5 | 10 | no | — |
| 463 | C4⋊C4 | — | 5 | 20 | no | — |
| 464 | C4⋊C4 | — | 5 | 10 | no | — |
| 465 | C4⋊C4 | — | 5 | 20 | no | — |
| 466 | C4⋊C4 | — | 5 | 20 | no | — |
| 467 | C4⋊C4 | — | 5 | 20 | no | — |
| 468 | C4⋊C4 | C23×D5 | 1 | 10 | yes | — |
| 469 | C4⋊C4 | C23×D5 | 1 | 10 | yes | — |
| 470 | C4⋊C4 | C23×D5 | 1 | 10 | yes | — |
| 471 | C4⋊C4 | C23×D5 | 1 | 10 | yes | — |
| 472 | C4⋊C4 | C23×D5 | 1 | 20 | yes | — |
| 473 | C22⋊C4 | — | 5 | 20 | no | — |
| 474 | C22⋊C4 | — | 5 | 20 | no | — |
| 475 | C22⋊C4 | — | 5 | 20 | no | — |
| 476 | C22⋊C4 | — | 5 | 20 | no | — |
| 477 | C22⋊C4 | — | 5 | 20 | no | — |
| 478 | C22⋊C4 | — | 5 | 20 | no | — |
| 479 | C22⋊C4 | C23×D5 | 1 | 20 | yes | — |
| 480 | C22⋊C4 | C23×D5 | 1 | 20 | yes | — |
| 481 | C42 | — | 5 | 10 | no | — |
| 482 | C42 | — | 5 | 10 | no | — |
| 483 | C42 | — | 5 | 10 | no | — |
| 484 | C42 | — | 5 | 5 | no | — |
| 485 | C42 | — | 5 | 10 | no | — |
| 486 | C42 | — | 5 | 5 | no | — |
| 487 | C42 | — | 5 | 10 | no | — |
| 488 | C42 | C23×D5 | 1 | 5 | yes | — |
| 489 | C42 | C23×D5 | 1 | 5 | yes | — |
| 490 | C42 | C23×D5 | 1 | 10 | yes | — |
| 491 | C2×C5 | — | 4 | 5 | no | — |
| 492 | C2×C5 | C22×2−1+4 | 1 | 1 | yes | characteristic |
| 493 | C2×C5 | C2×#585 | 1 | 2 | yes | — |
| 494 | D5 | — | 4 | 5 | no | — |
| 495 | D5 | #3531 | 1 | 4 | yes | direct product factor |
| 496 | C23 | — | 5 | 1 | no | — |
| 497 | C23 | — | 5 | 5 | no | — |
| 498 | C23 | — | 10 | 10 | no | — |
| 499 | C23 | — | 10 | 20 | no | — |
| 500 | C23 | C24×D5 | 1 | 5 | yes | — |
| 501 | Q8 | — | 4 | 10 | no | — |
| 502 | Q8 | — | 20 | 10 | no | — |
| 503 | Q8 | — | 20 | 20 | no | — |
| 504 | D4 | — | 4 | 10 | no | — |
| 505 | D4 | — | 20 | 10 | no | — |
| 506 | D4 | — | 20 | 20 | no | — |
| 507 | C2×C4 | — | 2 | 10 | no | — |
| 508 | C2×C4 | — | 4 | 10 | no | — |
| 509 | C2×C4 | — | 5 | 1 | no | — |
| 510 | C2×C4 | — | 5 | 4 | no | — |
| 511 | C2×C4 | — | 5 | 5 | no | — |
| 512 | C2×C4 | — | 5 | 10 | no | — |
| 513 | C2×C4 | — | 5 | 10 | no | — |
| 514 | C2×C4 | — | 10 | 10 | no | — |
| 515 | C2×C4 | — | 10 | 10 | no | — |
| 516 | C2×C4 | — | 10 | 20 | no | — |
| 517 | C2×C4 | — | 10 | 20 | no | — |
| 518 | C2×C4 | — | 10 | 10 | no | — |
| 519 | C2×C4 | — | 10 | 10 | no | — |
| 520 | C2×C4 | — | 20 | 10 | no | — |
| 521 | C2×C4 | — | 20 | 10 | no | — |
| 522 | C2×C4 | — | 20 | 10 | no | — |
| 523 | C2×C4 | C24×D5 | 1 | 5 | yes | — |
| 524 | C2×C4 | C24×D5 | 1 | 10 | yes | — |
| 525 | C2×C4 | C24×D5 | 1 | 10 | yes | — |
| 526 | C2×C4 | C24×D5 | 1 | 1 | yes | characteristic |
| 527 | C5 | C2×#3531 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 528 | C22 | — | 2 | 5 | no | — |
| 529 | C22 | — | 2 | 10 | no | — |
| 530 | C22 | — | 5 | 2 | no | — |
| 531 | C22 | — | 5 | 4 | no | — |
| 532 | C22 | — | 10 | 5 | no | — |
| 533 | C22 | — | 10 | 10 | no | — |
| 534 | C22 | — | 20 | 20 | no | — |
| 535 | C22 | C25×D5 | 1 | 1 | yes | characteristic |
| 536 | C4 | — | 2 | 5 | no | — |
| 537 | C4 | — | 2 | 10 | no | — |
| 538 | C4 | — | 2 | 10 | no | — |
| 539 | C4 | — | 5 | 2 | no | — |
| 540 | C4 | — | 10 | 5 | no | — |
| 541 | C4 | — | 10 | 10 | no | — |
| 542 | C4 | — | 10 | 10 | no | — |
| 543 | C4 | D5×2−1+4 | 1 | 2 | yes | — |
| 544 | C2 | — | 4 | 5 | no | — |
| 545 | C2 | — | 5 | 4 | no | — |
| 546 | C2 | — | 20 | 5 | no | — |
| 547 | C2 | C2×D5×2−1+4 | 1 | 1 | yes | characteristic |
| 548 | C2 | D5×#585 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C24×D5 |
| commutator, socle, cosocle | C22×C5 | C26 |
| Frattini | C22 | C25×D5 |
| Fitting | C5×#3531 | C2 |
| hypercenter | #3531 | D5 |
| hypocenter | C5 | C2×#3531 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C2×C4 ◁ #3531 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#3531 | C2 | semidirect |
| 2. D5×#564 | C2 | semidirect |
| 3. #10619040 | C2 | semidirect |
| 4. D5×#563 | C2 | semidirect |
| 5. #10619017 | C2 | semidirect |
| 6. D5×#562 | C2 | semidirect |
| 7. #10618995 | C2 | semidirect |
| 8. #10618187 | C2 | semidirect |
| 9. D5×#533 | C2 | semidirect |
| 10. D5×#529 | C2 | semidirect |
| 11. #10618033 | C2 | semidirect |
| 12. C5×#564 | C22 | semidirect |
| 13. C5×#563 | C22 | semidirect |
| 14. C5×#562 | C22 | semidirect |
| 15. C5×#533 | C22 | semidirect |
| 16. C5×#529 | C22 | semidirect |
| 17. #66069 | C22 | semidirect |
| 18. #66062 | C22 | semidirect |
| 20. #66046 | C22 | semidirect |
| 21. #66046 | C22 | semidirect |
| 22. #66040 | C22 | semidirect |
| 24. #66034 | C22 | semidirect |
| 25. #66033 | C22 | semidirect |
| 26. #66033 | C22 | semidirect |
| 27. #66025 | C22 | semidirect |
| 28. #66022 | C22 | semidirect |
| 29. #66022 | C22 | semidirect |
| 33. C5⋊#564 | C22 | semidirect |
| 34. C5⋊#564 | C22 | semidirect |
| 35. #66018 | C22 | semidirect |
| 36. #66014 | C22 | semidirect |
| 38. #66006 | C22 | semidirect |
| 39. #66001 | C22 | semidirect |
| 41. #65985 | C22 | semidirect |
| 42. #65983 | C22 | semidirect |
| 43. #65981 | C22 | semidirect |
| 44. #65980 | C22 | semidirect |
| 45. #65980 | C22 | semidirect |
| 48. #65958 | C22 | semidirect |
| 49. #65956 | C22 | semidirect |
| 50. #65955 | C22 | semidirect |
| 52. #65934 | C22 | semidirect |
| 53. #65914 | C22 | semidirect |
| 54. #65912 | C22 | semidirect |
| 56. #65891 | C22 | semidirect |
| 58. #65872 | C22 | semidirect |
| 59. #65862 | C22 | semidirect |
| 61. #65851 | C22 | semidirect |
| 62. #65813 | C22 | semidirect |
| 64. #65804 | C22 | semidirect |
| 171. #3531 | D5 | direct (N × H) |
| 236. #564 | C2×D5 | semidirect |
| 246. #563 | C2×D5 | semidirect |
| 252. #562 | C2×D5 | semidirect |
| 260. #533 | C2×D5 | semidirect |
| 273. #529 | C2×D5 | semidirect |
| 495. D5 | #3531 | direct (N × H) |
| 527. C5 | C2×#3531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3531 | 2 |
| D5×#564 | 2 |
| #10619040 | 2 |
| D5×#563 | 2 |
| #10619017 | 2 |
| D5×#562 | 2 |
| #10618995 | 2 |
| #10618187 | 2 |
| D5×#533 | 2 |
| D5×#529 | 2 |
| #10618033 | 2 |
| C2×#3531 | 5 |