Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
6640 conjugacy classes of subgroups.
The subgroup lattice has 480 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C5×#3444 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10618187 | C2 | 1 | 6 | yes | maximal, complemented |
| 3 | #10618149 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | #10618072 | C2 | 1 | 12 | yes | maximal, complemented |
| 5 | #10618033 | C2 | 1 | 12 | yes | maximal, complemented |
| 6 | #10617949 | C2 | 1 | 12 | yes | maximal, complemented |
| 7 | #10617737 | C2 | 1 | 12 | yes | maximal, complemented |
| 8 | #10617581 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C5×#533 | C22 | 1 | 3 | yes | complemented |
| 10 | C5×#532 | C22 | 1 | 3 | yes | — |
| 11 | C5×#529 | C22 | 1 | 12 | yes | complemented |
| 12 | C5×#525 | C22 | 1 | 6 | yes | complemented |
| 13 | C4×C5×#41 | C22 | 1 | 6 | yes | complemented |
| 14 | C22×C42×C5 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | #66166 | C22 | 1 | 12 | yes | — |
| 16 | #66162 | C22 | 1 | 12 | yes | complemented |
| 17 | #66125 | C22 | 1 | 12 | yes | complemented |
| 18 | #66069 | C22 | 1 | 12 | yes | complemented |
| 19 | #66054 | C22 | 1 | 4 | yes | complemented |
| 20 | #66046 | C22 | 1 | 24 | yes | complemented |
| 21 | #66045 | C22 | 1 | 8 | yes | complemented |
| 22 | #66034 | C22 | 1 | 6 | yes | complemented |
| 23 | #66033 | C22 | 1 | 12 | yes | complemented |
| 24 | C5⋊#564 | C22 | 1 | 6 | yes | complemented |
| 25 | #66018 | C22 | 1 | 12 | yes | complemented |
| 26 | #66017 | C22 | 1 | 6 | yes | complemented |
| 27 | #66006 | C22 | 1 | 6 | yes | complemented |
| 28 | #66001 | C22 | 1 | 24 | yes | complemented |
| 29 | #66000 | C22 | 1 | 12 | yes | complemented |
| 30 | #65985 | C22 | 1 | 12 | yes | complemented |
| 31 | #65981 | C22 | 1 | 24 | yes | complemented |
| 32 | #65980 | C22 | 1 | 24 | yes | complemented |
| 33 | #65955 | C22 | 1 | 24 | yes | complemented |
| 34 | #65954 | C22 | 1 | 24 | yes | complemented |
| 35 | #65929 | C22 | 1 | 12 | yes | complemented |
| 36 | #65928 | C22 | 1 | 4 | yes | complemented |
| 37 | #65914 | C22 | 1 | 24 | yes | complemented |
| 38 | #65912 | C22 | 1 | 24 | yes | complemented |
| 39 | #65891 | C22 | 1 | 24 | yes | complemented |
| 40 | #65882 | C22 | 1 | 24 | yes | — |
| 41 | #65881 | C22 | 1 | 24 | yes | complemented |
| 42 | #65881 | C22 | 1 | 24 | yes | complemented |
| 43 | #65872 | C22 | 1 | 24 | yes | complemented |
| 44 | #65872 | C22 | 1 | 24 | yes | complemented |
| 45 | #65862 | C22 | 1 | 24 | yes | complemented |
| 46 | #65862 | C22 | 1 | 24 | yes | complemented |
| 47 | #65858 | C22 | 1 | 12 | yes | complemented |
| 48 | #65851 | C22 | 1 | 12 | yes | complemented |
| 49 | #65813 | C22 | 1 | 12 | yes | complemented |
| 50 | #65813 | C22 | 1 | 12 | yes | complemented |
| 51 | #65811 | C22 | 1 | 6 | yes | — |
| 52 | C4×#709 | C22 | 1 | 12 | yes | complemented |
| 53 | C4×#709 | C22 | 1 | 12 | yes | complemented |
| 54 | C2×C42×D5 | C22 | 1 | 4 | yes | complemented |
| 55 | #65804 | C22 | 1 | 6 | yes | complemented |
| 56 | #62694 | — | 5 | 1 | no | maximal, Sylow |
| 57 | C2×C5×#41 | C23 | 1 | 6 | yes | — |
| 58 | C23×C4×C5 | C23 | 1 | 3 | yes | — |
| 59 | C2×#709 | C23 | 1 | 12 | yes | — |
| 60 | C2×#709 | C23 | 1 | 12 | yes | — |
| 61 | C22×C4×D5 | C23 | 1 | 12 | yes | — |
| 62 | C5×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 63 | C5×#127 | C23 | 1 | 1 | yes | characteristic |
| 64 | C5×#126 | C23 | 1 | 8 | yes | — |
| 65 | C5×#125 | C23 | 1 | 6 | yes | — |
| 66 | C5×#124 | C23 | 1 | 6 | yes | — |
| 67 | C5×#123 | C23 | 1 | 12 | yes | — |
| 68 | C5×C22⋊Q8 | C23 | 1 | 12 | yes | — |
| 69 | C5×#121 | C23 | 1 | 12 | yes | — |
| 70 | C5×#120 | C23 | 1 | 4 | yes | — |
| 71 | C4×C5×Q8 | C23 | 1 | 12 | yes | — |
| 72 | C4×C5×D4 | C23 | 1 | 12 | yes | — |
| 73 | C4×C5×D4 | C23 | 1 | 24 | yes | — |
| 74 | C5×#117 | C23 | 1 | 12 | yes | — |
| 75 | C5×#117 | C23 | 1 | 6 | yes | — |
| 76 | C2×C42×C5 | C23 | 1 | 6 | yes | — |
| 77 | C2×C42×C5 | C23 | 1 | 4 | yes | — |
| 78 | C2×C42×C5 | C23 | 1 | 3 | yes | — |
| 79 | C2×C42×C5 | C23 | 1 | 3 | yes | — |
| 80 | #4099 | C23 | 1 | 8 | yes | — |
| 81 | #4093 | C23 | 1 | 12 | yes | — |
| 82 | #4092 | C23 | 1 | 24 | yes | — |
| 83 | #4090 | C23 | 1 | 12 | yes | — |
| 84 | #4086 | C23 | 1 | 12 | yes | — |
| 85 | #4085 | C23 | 1 | 24 | yes | — |
| 86 | #4085 | C23 | 1 | 24 | yes | — |
| 87 | #4084 | C23 | 1 | 24 | yes | — |
| 88 | #4083 | C23 | 1 | 12 | yes | — |
| 89 | #4083 | C23 | 1 | 12 | yes | — |
| 90 | #4082 | C23 | 1 | 12 | yes | — |
| 91 | #4081 | C23 | 1 | 12 | yes | — |
| 92 | #4081 | C23 | 1 | 12 | yes | — |
| 93 | #4076 | C23 | 1 | 12 | yes | — |
| 94 | #4076 | C23 | 1 | 12 | yes | — |
| 95 | #4075 | C23 | 1 | 24 | yes | — |
| 96 | C4×C22⋊D5 | C23 | 1 | 24 | yes | — |
| 97 | C4×C22⋊D5 | C23 | 1 | 24 | yes | — |
| 98 | C4×C22⋊D5 | C23 | 1 | 24 | yes | — |
| 99 | C4×C22⋊D5 | C23 | 1 | 24 | yes | — |
| 100 | #4072 | C23 | 1 | 12 | yes | — |
| 101 | #4072 | C23 | 1 | 12 | yes | — |
| 102 | #4070 | C23 | 1 | 12 | yes | — |
| 103 | #4070 | C23 | 1 | 12 | yes | — |
| 104 | C2×C4×Dic5 | C23 | 1 | 12 | yes | — |
| 105 | #4044 | C23 | 1 | 24 | yes | — |
| 106 | #4044 | C23 | 1 | 24 | yes | — |
| 107 | #4043 | C23 | 1 | 24 | yes | — |
| 108 | #4042 | C23 | 1 | 24 | yes | — |
| 109 | #4042 | C23 | 1 | 24 | yes | — |
| 110 | #4041 | C23 | 1 | 24 | yes | — |
| 111 | #4040 | C23 | 1 | 24 | yes | — |
| 112 | #4040 | C23 | 1 | 24 | yes | — |
| 113 | #4036 | C23 | 1 | 24 | yes | — |
| 114 | #4035 | C23 | 1 | 24 | yes | — |
| 115 | #4035 | C23 | 1 | 24 | yes | — |
| 116 | #4034 | C23 | 1 | 24 | yes | — |
| 117 | #4032 | C23 | 1 | 24 | yes | — |
| 118 | #4031 | C23 | 1 | 24 | yes | — |
| 119 | #4031 | C23 | 1 | 24 | yes | — |
| 120 | #4030 | C23 | 1 | 24 | yes | — |
| 121 | #4030 | C23 | 1 | 24 | yes | — |
| 122 | #4029 | C23 | 1 | 24 | yes | — |
| 123 | #4029 | C23 | 1 | 24 | yes | — |
| 124 | #4028 | C23 | 1 | 24 | yes | — |
| 125 | #4025 | C23 | 1 | 24 | yes | — |
| 126 | #4025 | C23 | 1 | 24 | yes | — |
| 127 | #4024 | C23 | 1 | 24 | yes | — |
| 128 | #4024 | C23 | 1 | 24 | yes | — |
| 129 | #4022 | C23 | 1 | 8 | yes | — |
| 130 | #4022 | C23 | 1 | 8 | yes | — |
| 131 | #4021 | C23 | 1 | 12 | yes | — |
| 132 | #4020 | C23 | 1 | 2 | yes | — |
| 133 | C4×D20 | C23 | 1 | 12 | yes | — |
| 134 | C4×D20 | C23 | 1 | 12 | yes | — |
| 135 | C4×D20 | C23 | 1 | 24 | yes | — |
| 136 | #4018 | C23 | 1 | 24 | yes | — |
| 137 | #4018 | C23 | 1 | 24 | yes | — |
| 138 | C42×D5 | C23 | 1 | 8 | yes | — |
| 139 | C42×D5 | C23 | 1 | 24 | yes | — |
| 140 | #4016 | C23 | 1 | 12 | yes | — |
| 141 | #4015 | C23 | 1 | 6 | yes | — |
| 142 | C4×Dic10 | C23 | 1 | 12 | yes | — |
| 143 | C4×Dic10 | C23 | 1 | 12 | yes | — |
| 144 | C4×Dic10 | C23 | 1 | 24 | yes | — |
| 145 | #3531 | — | 5 | 6 | no | — |
| 146 | #3531 | — | 5 | 12 | no | — |
| 147 | #3529 | — | 5 | 6 | no | — |
| 148 | #3529 | — | 5 | 12 | no | — |
| 149 | #3529 | — | 5 | 12 | no | — |
| 150 | #3444 | — | 5 | 2 | no | — |
| 151 | #3444 | — | 5 | 12 | no | — |
| 152 | #3444 | D5 | 1 | 1 | yes | characteristic, complemented |
| 153 | C24×C5 | C24 | 1 | 1 | yes | characteristic |
| 154 | C23×D5 | C24 | 1 | 4 | yes | — |
| 155 | C5×#41 | — | 4 | 12 | no | — |
| 156 | C2×C5×Q8 | C24 | 1 | 6 | yes | — |
| 157 | C2×C5×D4 | C24 | 1 | 12 | yes | — |
| 158 | C2×C5×D4 | C24 | 1 | 6 | yes | — |
| 159 | C22×C4×C5 | — | 4 | 6 | no | — |
| 160 | C22×C4×C5 | C24 | 1 | 3 | yes | — |
| 161 | C22×C4×C5 | C24 | 1 | 6 | yes | — |
| 162 | C22×C4×C5 | C24 | 1 | 12 | yes | — |
| 163 | C22×C4×C5 | C24 | 1 | 6 | yes | — |
| 164 | C22×C4×C5 | C24 | 1 | 3 | yes | — |
| 165 | C2×C22⋊D5 | C24 | 1 | 24 | yes | — |
| 166 | C2×C22⋊D5 | C24 | 1 | 24 | yes | — |
| 167 | C22×Dic5 | C24 | 1 | 12 | yes | — |
| 168 | #709 | — | 4 | 24 | no | — |
| 169 | #709 | — | 4 | 24 | no | — |
| 170 | C2×D20 | C24 | 1 | 12 | yes | — |
| 171 | C2×D20 | C24 | 1 | 12 | yes | — |
| 172 | C2×C4×D5 | — | 4 | 24 | no | — |
| 173 | C2×C4×D5 | C24 | 1 | 24 | yes | — |
| 174 | C2×C4×D5 | C24 | 1 | 24 | yes | — |
| 175 | C2×Dic10 | C24 | 1 | 12 | yes | — |
| 176 | C2×Dic10 | C24 | 1 | 12 | yes | — |
| 177 | C5×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 178 | C5×C4⋊C4 | C24 | 1 | 24 | yes | — |
| 179 | C5×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 180 | C5×C22⋊C4 | C24 | 1 | 24 | yes | — |
| 181 | C42×C5 | C24 | 1 | 3 | yes | — |
| 182 | C42×C5 | C24 | 1 | 6 | yes | — |
| 183 | C42×C5 | C24 | 1 | 3 | yes | — |
| 184 | C42×C5 | C24 | 1 | 2 | yes | — |
| 185 | C42×C5 | C24 | 1 | 1 | yes | characteristic |
| 186 | C42×C5 | C24 | 1 | 12 | yes | — |
| 187 | C42×C5 | C24 | 1 | 1 | yes | characteristic |
| 188 | C22⋊Dic5 | C24 | 1 | 24 | yes | — |
| 189 | C22⋊Dic5 | C24 | 1 | 12 | yes | — |
| 190 | C22⋊Dic5 | C24 | 1 | 12 | yes | — |
| 191 | #685 | C24 | 1 | 24 | yes | — |
| 192 | #685 | C24 | 1 | 24 | yes | — |
| 193 | #685 | C24 | 1 | 24 | yes | — |
| 194 | #685 | C24 | 1 | 24 | yes | — |
| 195 | C4⋊Dic5 | C24 | 1 | 12 | yes | — |
| 196 | C4⋊Dic5 | C24 | 1 | 12 | yes | — |
| 197 | C4⋊Dic5 | C24 | 1 | 24 | yes | — |
| 198 | #683 | C24 | 1 | 24 | yes | — |
| 199 | #683 | C24 | 1 | 24 | yes | — |
| 200 | #683 | C24 | 1 | 24 | yes | — |
| 201 | #683 | C24 | 1 | 24 | yes | — |
| 202 | C4×Dic5 | C24 | 1 | 24 | yes | — |
| 203 | C4×Dic5 | C24 | 1 | 12 | yes | — |
| 204 | C4×Dic5 | C24 | 1 | 12 | yes | — |
| 205 | #564 | — | 5 | 6 | no | — |
| 206 | #563 | — | 5 | 12 | no | — |
| 207 | #563 | — | 5 | 24 | no | — |
| 208 | #563 | — | 5 | 12 | no | — |
| 209 | #563 | — | 5 | 6 | no | — |
| 210 | #563 | — | 5 | 12 | no | — |
| 211 | #563 | — | 5 | 24 | no | — |
| 212 | #562 | — | 5 | 6 | no | — |
| 213 | #562 | — | 5 | 12 | no | — |
| 214 | #562 | — | 5 | 24 | no | — |
| 215 | #562 | — | 5 | 24 | no | — |
| 216 | #562 | — | 5 | 24 | no | — |
| 217 | H(3,𝔽4) | — | 5 | 6 | no | — |
| 218 | H(3,𝔽4) | — | 5 | 4 | no | — |
| 219 | #560 | — | 5 | 4 | no | — |
| 220 | #560 | — | 5 | 8 | no | — |
| 221 | #560 | — | 5 | 12 | no | — |
| 222 | #560 | — | 5 | 24 | no | — |
| 223 | #560 | — | 5 | 12 | no | — |
| 224 | #533 | — | 5 | 24 | no | — |
| 225 | #533 | — | 5 | 12 | no | — |
| 226 | #533 | — | 5 | 6 | no | — |
| 227 | #533 | C2×D5 | 1 | 3 | yes | complemented |
| 228 | #532 | — | 5 | 12 | no | — |
| 229 | #532 | — | 5 | 24 | no | — |
| 230 | #532 | — | 5 | 6 | no | — |
| 231 | #532 | C2×D5 | 1 | 3 | yes | — |
| 232 | #529 | — | 5 | 24 | no | — |
| 233 | #529 | — | 5 | 24 | no | — |
| 234 | #529 | — | 5 | 24 | no | — |
| 235 | #529 | — | 5 | 24 | no | — |
| 236 | #529 | — | 5 | 24 | no | — |
| 237 | #529 | — | 5 | 24 | no | — |
| 238 | #529 | — | 5 | 12 | no | — |
| 239 | #529 | — | 5 | 12 | no | — |
| 240 | #529 | C2×D5 | 1 | 12 | yes | complemented |
| 241 | #525 | — | 5 | 12 | no | — |
| 242 | #525 | — | 5 | 12 | no | — |
| 243 | #525 | — | 5 | 24 | no | — |
| 244 | #525 | — | 5 | 24 | no | — |
| 245 | #525 | — | 5 | 12 | no | — |
| 246 | #525 | C2×D5 | 1 | 6 | yes | complemented |
| 247 | C4×#41 | — | 5 | 12 | no | — |
| 248 | C4×#41 | — | 5 | 12 | no | — |
| 249 | C4×#41 | C2×D5 | 1 | 6 | yes | complemented |
| 250 | C22×C42 | — | 5 | 4 | no | — |
| 251 | C22×C42 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 252 | C23×C5 | — | 4 | 3 | no | — |
| 253 | C23×C5 | C25 | 1 | 3 | yes | — |
| 254 | C23×C5 | C25 | 1 | 4 | yes | — |
| 255 | C22×D5 | — | 4 | 12 | no | — |
| 256 | C22×D5 | C25 | 1 | 8 | yes | — |
| 257 | C5×Q8 | — | 4 | 6 | no | — |
| 258 | C5×D4 | — | 4 | 12 | no | — |
| 259 | C5×D4 | — | 4 | 6 | no | — |
| 260 | C2×C4×C5 | — | 2 | 24 | no | — |
| 261 | C2×C4×C5 | — | 2 | 12 | no | — |
| 262 | C2×C4×C5 | — | 2 | 6 | no | — |
| 263 | C2×C4×C5 | — | 4 | 3 | no | — |
| 264 | C2×C4×C5 | — | 4 | 6 | no | — |
| 265 | C2×C4×C5 | C25 | 1 | 12 | yes | — |
| 266 | C2×C4×C5 | C25 | 1 | 3 | yes | — |
| 267 | C2×C4×C5 | C25 | 1 | 6 | yes | — |
| 268 | C2×C4×C5 | C25 | 1 | 3 | yes | — |
| 269 | C22⋊D5 | — | 4 | 24 | no | — |
| 270 | C22⋊D5 | — | 4 | 24 | no | — |
| 271 | C2×Dic5 | — | 4 | 12 | no | — |
| 272 | C2×Dic5 | C25 | 1 | 24 | yes | — |
| 273 | D20 | — | 4 | 12 | no | — |
| 274 | D20 | — | 4 | 12 | no | — |
| 275 | C4×D5 | — | 2 | 48 | no | — |
| 276 | C4×D5 | — | 4 | 24 | no | — |
| 277 | Dic10 | — | 4 | 12 | no | — |
| 278 | Dic10 | — | 4 | 12 | no | — |
| 279 | C2×#41 | — | 5 | 12 | no | — |
| 280 | C2×#41 | — | 5 | 12 | no | — |
| 281 | C2×#41 | C22×D5 | 1 | 6 | yes | — |
| 282 | C23×C4 | — | 5 | 12 | no | — |
| 283 | C23×C4 | C22×D5 | 1 | 3 | yes | — |
| 284 | C4⋊Q8 | — | 5 | 12 | no | — |
| 285 | C4⋊Q8 | — | 5 | 24 | no | — |
| 286 | C4⋊Q8 | — | 5 | 6 | no | — |
| 287 | C4⋊Q8 | C22×D5 | 1 | 3 | yes | — |
| 288 | #127 | — | 5 | 12 | no | — |
| 289 | #127 | — | 5 | 2 | no | — |
| 290 | #127 | C22×D5 | 1 | 1 | yes | characteristic |
| 291 | #126 | — | 5 | 24 | no | — |
| 292 | #126 | — | 5 | 24 | no | — |
| 293 | #126 | — | 5 | 24 | no | — |
| 294 | #126 | — | 5 | 24 | no | — |
| 295 | #126 | — | 5 | 8 | no | — |
| 296 | #126 | — | 5 | 8 | no | — |
| 297 | #126 | C22×D5 | 1 | 8 | yes | — |
| 298 | #125 | — | 5 | 24 | no | — |
| 299 | #125 | — | 5 | 24 | no | — |
| 300 | #125 | — | 5 | 24 | no | — |
| 301 | #125 | — | 5 | 12 | no | — |
| 302 | #125 | C22×D5 | 1 | 6 | yes | — |
| 303 | #124 | — | 5 | 12 | no | — |
| 304 | #124 | — | 5 | 12 | no | — |
| 305 | #124 | — | 5 | 24 | no | — |
| 306 | #124 | — | 5 | 24 | no | — |
| 307 | #124 | — | 5 | 12 | no | — |
| 308 | #124 | C22×D5 | 1 | 6 | yes | — |
| 309 | #123 | — | 5 | 12 | no | — |
| 310 | #123 | — | 5 | 12 | no | — |
| 311 | #123 | — | 5 | 24 | no | — |
| 312 | #123 | — | 5 | 24 | no | — |
| 313 | #123 | — | 5 | 24 | no | — |
| 314 | #123 | — | 5 | 24 | no | — |
| 315 | #123 | — | 5 | 24 | no | — |
| 316 | #123 | — | 5 | 24 | no | — |
| 317 | #123 | C22×D5 | 1 | 12 | yes | — |
| 318 | C22⋊Q8 | — | 5 | 24 | no | — |
| 319 | C22⋊Q8 | — | 5 | 12 | no | — |
| 320 | C22⋊Q8 | — | 5 | 12 | no | — |
| 321 | C22⋊Q8 | — | 5 | 24 | no | — |
| 322 | C22⋊Q8 | — | 5 | 24 | no | — |
| 323 | C22⋊Q8 | — | 5 | 24 | no | — |
| 324 | C22⋊Q8 | — | 5 | 24 | no | — |
| 325 | C22⋊Q8 | — | 5 | 24 | no | — |
| 326 | C22⋊Q8 | C22×D5 | 1 | 12 | yes | — |
| 327 | #121 | — | 5 | 24 | no | — |
| 328 | #121 | — | 5 | 24 | no | — |
| 329 | #121 | — | 5 | 24 | no | — |
| 330 | #121 | — | 5 | 12 | no | — |
| 331 | #121 | — | 5 | 12 | no | — |
| 332 | #121 | — | 5 | 24 | no | — |
| 333 | #121 | — | 5 | 24 | no | — |
| 334 | #121 | — | 5 | 24 | no | — |
| 335 | #121 | C22×D5 | 1 | 12 | yes | — |
| 336 | #120 | — | 5 | 8 | no | — |
| 337 | #120 | — | 5 | 12 | no | — |
| 338 | #120 | — | 5 | 12 | no | — |
| 339 | #120 | — | 5 | 24 | no | — |
| 340 | #120 | C22×D5 | 1 | 4 | yes | — |
| 341 | C4×Q8 | — | 5 | 24 | no | — |
| 342 | C4×Q8 | — | 5 | 12 | no | — |
| 343 | C4×Q8 | — | 5 | 12 | no | — |
| 344 | C4×Q8 | C22×D5 | 1 | 12 | yes | — |
| 345 | C4×D4 | — | 5 | 24 | no | — |
| 346 | C4×D4 | — | 5 | 24 | no | — |
| 347 | C4×D4 | — | 5 | 24 | no | — |
| 348 | C4×D4 | — | 5 | 24 | no | — |
| 349 | C4×D4 | — | 5 | 24 | no | — |
| 350 | C4×D4 | — | 5 | 12 | no | — |
| 351 | C4×D4 | — | 5 | 12 | no | — |
| 352 | C4×D4 | C22×D5 | 1 | 12 | yes | — |
| 353 | C4×D4 | C22×D5 | 1 | 24 | yes | — |
| 354 | #117 | — | 5 | 12 | no | — |
| 355 | #117 | — | 5 | 12 | no | — |
| 356 | #117 | — | 5 | 24 | no | — |
| 357 | #117 | — | 5 | 24 | no | — |
| 358 | #117 | C22×D5 | 1 | 12 | yes | — |
| 359 | #117 | C22×D5 | 1 | 6 | yes | — |
| 360 | C2×C42 | — | 5 | 12 | no | — |
| 361 | C2×C42 | — | 5 | 24 | no | — |
| 362 | C2×C42 | — | 5 | 8 | no | — |
| 363 | C2×C42 | C22×D5 | 1 | 3 | yes | — |
| 364 | C2×C42 | C22×D5 | 1 | 6 | yes | — |
| 365 | C2×C42 | C22×D5 | 1 | 3 | yes | — |
| 366 | C2×C42 | C22×D5 | 1 | 4 | yes | — |
| 367 | C22×C5 | — | 2 | 12 | no | — |
| 368 | C22×C5 | — | 2 | 6 | no | — |
| 369 | C22×C5 | — | 2 | 3 | no | — |
| 370 | C22×C5 | — | 4 | 4 | no | — |
| 371 | C22×C5 | C26 | 1 | 1 | yes | characteristic |
| 372 | C2×D5 | — | 2 | 24 | no | — |
| 373 | C2×D5 | — | 4 | 16 | no | — |
| 374 | C4×C5 | — | 2 | 6 | no | — |
| 375 | C4×C5 | — | 2 | 12 | no | — |
| 376 | C4×C5 | — | 2 | 3 | no | — |
| 377 | C4×C5 | #585 | 1 | 6 | yes | — |
| 378 | Dic5 | — | 2 | 24 | no | — |
| 379 | C24 | — | 5 | 4 | no | — |
| 380 | C24 | C23×D5 | 1 | 1 | yes | characteristic |
| 381 | #41 | — | 4 | 12 | no | — |
| 382 | #41 | — | 20 | 24 | no | — |
| 383 | #41 | — | 20 | 24 | no | — |
| 384 | C2×Q8 | — | 5 | 12 | no | — |
| 385 | C2×Q8 | — | 5 | 12 | no | — |
| 386 | C2×Q8 | C23×D5 | 1 | 6 | yes | — |
| 387 | C2×D4 | — | 5 | 24 | no | — |
| 388 | C2×D4 | — | 5 | 24 | no | — |
| 389 | C2×D4 | — | 5 | 12 | no | — |
| 390 | C2×D4 | — | 5 | 12 | no | — |
| 391 | C2×D4 | C23×D5 | 1 | 6 | yes | — |
| 392 | C2×D4 | C23×D5 | 1 | 12 | yes | — |
| 393 | C22×C4 | — | 4 | 6 | no | — |
| 394 | C22×C4 | — | 5 | 12 | no | — |
| 395 | C22×C4 | — | 5 | 24 | no | — |
| 396 | C22×C4 | — | 5 | 24 | no | — |
| 397 | C22×C4 | — | 20 | 24 | no | — |
| 398 | C22×C4 | C23×D5 | 1 | 12 | yes | — |
| 399 | C22×C4 | C23×D5 | 1 | 6 | yes | — |
| 400 | C22×C4 | C23×D5 | 1 | 3 | yes | — |
| 401 | C22×C4 | C23×D5 | 1 | 3 | yes | — |
| 402 | C22×C4 | C23×D5 | 1 | 6 | yes | — |
| 403 | C4⋊C4 | — | 5 | 24 | no | — |
| 404 | C4⋊C4 | — | 5 | 24 | no | — |
| 405 | C4⋊C4 | — | 5 | 24 | no | — |
| 406 | C4⋊C4 | — | 5 | 24 | no | — |
| 407 | C4⋊C4 | — | 5 | 24 | no | — |
| 408 | C4⋊C4 | — | 5 | 12 | no | — |
| 409 | C4⋊C4 | — | 5 | 12 | no | — |
| 410 | C4⋊C4 | C23×D5 | 1 | 24 | yes | — |
| 411 | C4⋊C4 | C23×D5 | 1 | 12 | yes | — |
| 412 | C22⋊C4 | — | 5 | 24 | no | — |
| 413 | C22⋊C4 | — | 5 | 12 | no | — |
| 414 | C22⋊C4 | — | 5 | 12 | no | — |
| 415 | C22⋊C4 | — | 5 | 24 | no | — |
| 416 | C22⋊C4 | — | 5 | 24 | no | — |
| 417 | C22⋊C4 | — | 5 | 24 | no | — |
| 418 | C22⋊C4 | — | 5 | 24 | no | — |
| 419 | C22⋊C4 | C23×D5 | 1 | 24 | yes | — |
| 420 | C22⋊C4 | C23×D5 | 1 | 12 | yes | — |
| 421 | C42 | — | 5 | 24 | no | — |
| 422 | C42 | — | 5 | 12 | no | — |
| 423 | C42 | — | 5 | 12 | no | — |
| 424 | C42 | C23×D5 | 1 | 12 | yes | — |
| 425 | C42 | C23×D5 | 1 | 6 | yes | — |
| 426 | C42 | C23×D5 | 1 | 3 | yes | — |
| 427 | C42 | C23×D5 | 1 | 3 | yes | — |
| 428 | C42 | C23×D5 | 1 | 1 | yes | characteristic |
| 429 | C42 | C23×D5 | 1 | 2 | yes | — |
| 430 | C42 | C23×D5 | 1 | 1 | yes | characteristic |
| 431 | C2×C5 | — | 4 | 4 | no | — |
| 432 | C2×C5 | — | 4 | 3 | no | — |
| 433 | C2×C5 | C2×#585 | 1 | 3 | yes | — |
| 434 | D5 | — | 4 | 8 | no | — |
| 435 | C23 | — | 4 | 3 | no | — |
| 436 | C23 | — | 5 | 8 | no | — |
| 437 | C23 | — | 20 | 12 | no | — |
| 438 | C23 | C24×D5 | 1 | 3 | yes | — |
| 439 | C23 | C24×D5 | 1 | 4 | yes | — |
| 440 | Q8 | — | 4 | 6 | no | — |
| 441 | Q8 | — | 20 | 12 | no | — |
| 442 | Q8 | — | 20 | 12 | no | — |
| 443 | D4 | — | 4 | 6 | no | — |
| 444 | D4 | — | 4 | 12 | no | — |
| 445 | D4 | — | 20 | 12 | no | — |
| 446 | D4 | — | 20 | 12 | no | — |
| 447 | D4 | — | 20 | 24 | no | — |
| 448 | D4 | — | 20 | 24 | no | — |
| 449 | C2×C4 | — | 2 | 6 | no | — |
| 450 | C2×C4 | — | 2 | 12 | no | — |
| 451 | C2×C4 | — | 2 | 24 | no | — |
| 452 | C2×C4 | — | 4 | 6 | no | — |
| 453 | C2×C4 | — | 4 | 3 | no | — |
| 454 | C2×C4 | — | 5 | 24 | no | — |
| 455 | C2×C4 | — | 10 | 48 | no | — |
| 456 | C2×C4 | — | 20 | 24 | no | — |
| 457 | C2×C4 | — | 20 | 12 | no | — |
| 458 | C2×C4 | C24×D5 | 1 | 12 | yes | — |
| 459 | C2×C4 | C24×D5 | 1 | 3 | yes | — |
| 460 | C2×C4 | C24×D5 | 1 | 6 | yes | — |
| 461 | C2×C4 | C24×D5 | 1 | 3 | yes | — |
| 462 | C5 | #62694 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 463 | C22 | — | 2 | 3 | no | — |
| 464 | C22 | — | 2 | 6 | no | — |
| 465 | C22 | — | 2 | 12 | no | — |
| 466 | C22 | — | 4 | 4 | no | — |
| 467 | C22 | — | 10 | 24 | no | — |
| 468 | C22 | — | 20 | 16 | no | — |
| 469 | C22 | C25×D5 | 1 | 1 | yes | characteristic |
| 470 | C4 | — | 2 | 3 | no | — |
| 471 | C4 | — | 2 | 6 | no | — |
| 472 | C4 | — | 2 | 12 | no | — |
| 473 | C4 | — | 10 | 24 | no | — |
| 474 | C4 | #66283 | 1 | 6 | yes | — |
| 475 | C2 | — | 4 | 3 | no | — |
| 476 | C2 | — | 4 | 4 | no | — |
| 477 | C2 | — | 20 | 8 | no | — |
| 478 | C2 | C2×#66283 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center | C42 | C23×D5 |
| commutator, socle, cosocle | C22×C5 | C26 |
| Frattini | C22 | C25×D5 |
| Fitting | C5×#3444 | C2 |
| hypercenter | #3444 | D5 |
| hypocenter | C5 | #62694 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C42 ◁ #3444 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#3444 | C2 | semidirect |
| 2. #10618187 | C2 | semidirect |
| 3. #10618149 | C2 | semidirect |
| 4. #10618072 | C2 | semidirect |
| 5. #10618033 | C2 | semidirect |
| 6. #10617949 | C2 | semidirect |
| 7. #10617737 | C2 | semidirect |
| 8. #10617581 | C2 | semidirect |
| 9. C5×#533 | C22 | semidirect |
| 11. C5×#529 | C22 | semidirect |
| 12. C5×#525 | C22 | semidirect |
| 13. C4×C5×#41 | C22 | semidirect |
| 14. C22×C42×C5 | C22 | semidirect |
| 16. #66162 | C22 | semidirect |
| 17. #66125 | C22 | semidirect |
| 18. #66069 | C22 | semidirect |
| 19. #66054 | C22 | semidirect |
| 20. #66046 | C22 | semidirect |
| 21. #66045 | C22 | semidirect |
| 22. #66034 | C22 | semidirect |
| 23. #66033 | C22 | semidirect |
| 24. C5⋊#564 | C22 | semidirect |
| 25. #66018 | C22 | semidirect |
| 26. #66017 | C22 | semidirect |
| 27. #66006 | C22 | semidirect |
| 28. #66001 | C22 | semidirect |
| 29. #66000 | C22 | semidirect |
| 30. #65985 | C22 | semidirect |
| 31. #65981 | C22 | semidirect |
| 32. #65980 | C22 | semidirect |
| 33. #65955 | C22 | semidirect |
| 34. #65954 | C22 | semidirect |
| 35. #65929 | C22 | semidirect |
| 36. #65928 | C22 | semidirect |
| 37. #65914 | C22 | semidirect |
| 38. #65912 | C22 | semidirect |
| 39. #65891 | C22 | semidirect |
| 41. #65881 | C22 | semidirect |
| 42. #65881 | C22 | semidirect |
| 43. #65872 | C22 | semidirect |
| 44. #65872 | C22 | semidirect |
| 45. #65862 | C22 | semidirect |
| 46. #65862 | C22 | semidirect |
| 47. #65858 | C22 | semidirect |
| 48. #65851 | C22 | semidirect |
| 49. #65813 | C22 | semidirect |
| 50. #65813 | C22 | semidirect |
| 52. C4×#709 | C22 | semidirect |
| 53. C4×#709 | C22 | semidirect |
| 54. C2×C42×D5 | C22 | semidirect |
| 55. #65804 | C22 | semidirect |
| 152. #3444 | D5 | semidirect |
| 227. #533 | C2×D5 | semidirect |
| 240. #529 | C2×D5 | semidirect |
| 246. #525 | C2×D5 | semidirect |
| 249. C4×#41 | C2×D5 | semidirect |
| 251. C22×C42 | C2×D5 | semidirect |
| 462. C5 | #62694 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3444 | 2 |
| #10618187 | 2 |
| #10618149 | 2 |
| #10618072 | 2 |
| #10618033 | 2 |
| #10617949 | 2 |
| #10617737 | 2 |
| #10617581 | 2 |
| #62694 | 5 |