Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1860 conjugacy classes of subgroups.
The subgroup lattice has 576 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11756459 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C5×#5688 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×C5⋊#564 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11753824 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #11753600 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #11753551 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #11753467 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #11753392 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #11753374 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #11752701 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #11752474 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #10618187 | — | 3 | 1 | no | maximal, Hall |
| 13 | C3×C5×#125 | C22 | 1 | 1 | yes | characteristic |
| 14 | #91785 | C22 | 1 | 4 | yes | — |
| 15 | #91784 | C22 | 1 | 4 | yes | — |
| 16 | #91783 | C22 | 1 | 4 | yes | — |
| 17 | #91764 | C22 | 1 | 2 | yes | — |
| 18 | C5×#896 | C22 | 1 | 4 | yes | — |
| 19 | C5×#892 | C22 | 1 | 2 | yes | — |
| 20 | C5×#888 | C22 | 1 | 2 | yes | — |
| 21 | C5×#887 | C22 | 1 | 4 | yes | — |
| 22 | C42×C5×D3 | C22 | 1 | 1 | yes | characteristic |
| 23 | C5×#870 | C22 | 1 | 1 | yes | characteristic |
| 24 | C3×#4036 | C22 | 1 | 4 | yes | — |
| 25 | C3×#4035 | C22 | 1 | 4 | yes | — |
| 26 | C3×#4035 | C22 | 1 | 4 | yes | — |
| 27 | C3×#4016 | C22 | 1 | 2 | yes | — |
| 28 | #91460 | C22 | 1 | 2 | yes | — |
| 29 | #91446 | C22 | 1 | 4 | yes | — |
| 30 | #91433 | C22 | 1 | 4 | yes | — |
| 31 | #91433 | C22 | 1 | 4 | yes | — |
| 32 | #91429 | C22 | 1 | 4 | yes | — |
| 33 | #91428 | C22 | 1 | 4 | yes | — |
| 34 | #91428 | C22 | 1 | 2 | yes | — |
| 35 | #91424 | C22 | 1 | 4 | yes | — |
| 36 | #91420 | C22 | 1 | 4 | yes | — |
| 37 | #91419 | C22 | 1 | 4 | yes | — |
| 38 | #91403 | C22 | 1 | 4 | yes | — |
| 39 | #91403 | C22 | 1 | 4 | yes | — |
| 40 | C4×#1200 | C22 | 1 | 4 | yes | — |
| 41 | #91383 | C22 | 1 | 4 | yes | — |
| 42 | #91380 | C22 | 1 | 4 | yes | — |
| 43 | #91378 | C22 | 1 | 4 | yes | — |
| 44 | #91377 | C22 | 1 | 4 | yes | — |
| 45 | #91375 | C22 | 1 | 4 | yes | — |
| 46 | #91365 | C22 | 1 | 2 | yes | — |
| 47 | #91355 | C22 | 1 | 4 | yes | — |
| 48 | #91351 | C22 | 1 | 4 | yes | — |
| 49 | #91350 | C22 | 1 | 4 | yes | — |
| 50 | #91345 | C22 | 1 | 4 | yes | — |
| 51 | #91345 | C22 | 1 | 4 | yes | — |
| 52 | #91341 | C22 | 1 | 4 | yes | — |
| 53 | #91340 | C22 | 1 | 2 | yes | — |
| 54 | #91337 | C22 | 1 | 4 | yes | — |
| 55 | #91329 | C22 | 1 | 4 | yes | — |
| 56 | #91328 | C22 | 1 | 4 | yes | — |
| 57 | #91324 | C22 | 1 | 4 | yes | — |
| 58 | #87139 | — | 5 | 1 | no | maximal, Hall |
| 59 | C5×#533 | — | 3 | 1 | no | — |
| 60 | #66069 | — | 3 | 4 | no | — |
| 61 | #66034 | — | 3 | 1 | no | — |
| 62 | #66033 | — | 3 | 2 | no | — |
| 63 | C5⋊#564 | D3 | 1 | 1 | yes | characteristic, complemented |
| 64 | #65981 | — | 3 | 4 | no | — |
| 65 | #65980 | — | 3 | 4 | no | — |
| 66 | #65914 | — | 3 | 4 | no | — |
| 67 | #65912 | — | 3 | 4 | no | — |
| 68 | #65862 | — | 3 | 4 | no | — |
| 69 | #65813 | — | 3 | 2 | no | — |
| 70 | C2×D60 | C23 | 1 | 4 | yes | — |
| 71 | C2×D60 | C23 | 1 | 2 | yes | — |
| 72 | C2×C4×D15 | C23 | 1 | 4 | yes | — |
| 73 | C2×Dic30 | C23 | 1 | 2 | yes | — |
| 74 | C2×C4×C5×D3 | C23 | 1 | 1 | yes | characteristic |
| 75 | C2×C4×C5×D3 | C23 | 1 | 2 | yes | — |
| 76 | C2×C5×Dic6 | C23 | 1 | 4 | yes | — |
| 77 | C2×#1204 | C23 | 1 | 4 | yes | — |
| 78 | C2×#1203 | C23 | 1 | 4 | yes | — |
| 79 | C2×#1200 | C23 | 1 | 4 | yes | — |
| 80 | C2×#1200 | C23 | 1 | 4 | yes | — |
| 81 | C3×C5×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 82 | C3×C5×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 83 | C3×C42×C5 | C23 | 1 | 1 | yes | characteristic |
| 84 | #6714 | C23 | 1 | 4 | yes | — |
| 85 | #6714 | C23 | 1 | 4 | yes | — |
| 86 | #6714 | C23 | 1 | 4 | yes | — |
| 87 | #6712 | C23 | 1 | 4 | yes | — |
| 88 | C5×(C2×D3)⋊C4 | C23 | 1 | 4 | yes | — |
| 89 | C5×C4⋊Dic3 | C23 | 1 | 2 | yes | — |
| 90 | C5×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 91 | C5×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 92 | C4×C5×Dic3 | C23 | 1 | 4 | yes | — |
| 93 | C4×C5×Dic3 | C23 | 1 | 2 | yes | — |
| 94 | C4×C5×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 95 | C3×C4⋊Dic5 | C23 | 1 | 2 | yes | — |
| 96 | C3×C4⋊Dic5 | C23 | 1 | 4 | yes | — |
| 97 | C3×C4⋊Dic5 | C23 | 1 | 2 | yes | — |
| 98 | C3×#683 | C23 | 1 | 4 | yes | — |
| 99 | C3×#683 | C23 | 1 | 4 | yes | — |
| 100 | C3×#683 | C23 | 1 | 4 | yes | — |
| 101 | C3×#683 | C23 | 1 | 4 | yes | — |
| 102 | C3×C4×Dic5 | C23 | 1 | 4 | yes | — |
| 103 | Dic3⋊Dic5 | C23 | 1 | 4 | yes | — |
| 104 | #6669 | C23 | 1 | 4 | yes | — |
| 105 | #6668 | C23 | 1 | 4 | yes | — |
| 106 | #6668 | C23 | 1 | 4 | yes | — |
| 107 | #6667 | C23 | 1 | 4 | yes | — |
| 108 | #6667 | C23 | 1 | 4 | yes | — |
| 109 | #6667 | C23 | 1 | 4 | yes | — |
| 110 | #6667 | C23 | 1 | 4 | yes | — |
| 111 | #6667 | C23 | 1 | 4 | yes | — |
| 112 | (C2×D3)⋊Dic5 | C23 | 1 | 4 | yes | — |
| 113 | Dic3×Dic5 | C23 | 1 | 4 | yes | — |
| 114 | Dic3×Dic5 | C23 | 1 | 4 | yes | — |
| 115 | C3×#564 | — | 5 | 1 | no | — |
| 116 | #5700 | — | 5 | 1 | no | — |
| 117 | #5700 | — | 5 | 4 | no | — |
| 118 | #5699 | — | 5 | 4 | no | — |
| 119 | #5699 | — | 5 | 4 | no | — |
| 120 | #5699 | — | 5 | 2 | no | — |
| 121 | #5691 | — | 5 | 4 | no | — |
| 122 | #5691 | — | 5 | 4 | no | — |
| 123 | #5691 | — | 5 | 2 | no | — |
| 124 | #5688 | — | 5 | 4 | no | — |
| 125 | #5688 | D5 | 1 | 1 | yes | characteristic, complemented |
| 126 | C5×C4⋊Q8 | — | 3 | 2 | no | — |
| 127 | C5×#125 | — | 3 | 1 | no | — |
| 128 | C5×#125 | C2×D3 | 1 | 1 | yes | characteristic |
| 129 | C5×C22⋊Q8 | — | 3 | 4 | no | — |
| 130 | C4×C5×Q8 | — | 3 | 4 | no | — |
| 131 | C5×#117 | — | 3 | 2 | no | — |
| 132 | C2×C42×C5 | — | 3 | 1 | no | — |
| 133 | #4093 | — | 3 | 4 | no | — |
| 134 | #4092 | — | 3 | 4 | no | — |
| 135 | #4092 | — | 3 | 4 | no | — |
| 136 | #4090 | — | 3 | 4 | no | — |
| 137 | #4076 | — | 3 | 2 | no | — |
| 138 | #4075 | — | 3 | 4 | no | — |
| 139 | C4×C22⋊D5 | — | 3 | 4 | no | — |
| 140 | #4070 | — | 3 | 2 | no | — |
| 141 | #4044 | — | 3 | 4 | no | — |
| 142 | #4044 | — | 3 | 4 | no | — |
| 143 | #4044 | — | 3 | 4 | no | — |
| 144 | #4043 | — | 3 | 4 | no | — |
| 145 | #4042 | — | 3 | 4 | no | — |
| 146 | #4042 | — | 3 | 4 | no | — |
| 147 | #4042 | — | 3 | 4 | no | — |
| 148 | #4041 | — | 3 | 4 | no | — |
| 149 | #4040 | — | 3 | 4 | no | — |
| 150 | #4040 | — | 3 | 4 | no | — |
| 151 | #4040 | — | 3 | 4 | no | — |
| 152 | #4036 | C2×D3 | 1 | 4 | yes | — |
| 153 | #4035 | — | 3 | 4 | no | — |
| 154 | #4035 | C2×D3 | 1 | 4 | yes | — |
| 155 | #4035 | C2×D3 | 1 | 4 | yes | — |
| 156 | #4034 | — | 3 | 4 | no | — |
| 157 | #4031 | — | 3 | 4 | no | — |
| 158 | #4030 | — | 3 | 4 | no | — |
| 159 | #4029 | — | 3 | 4 | no | — |
| 160 | #4025 | — | 3 | 4 | no | — |
| 161 | #4022 | — | 3 | 4 | no | — |
| 162 | #4021 | — | 3 | 2 | no | — |
| 163 | C4×D20 | — | 3 | 2 | no | — |
| 164 | C4×D20 | — | 3 | 4 | no | — |
| 165 | #4018 | — | 3 | 4 | no | — |
| 166 | #4018 | — | 3 | 4 | no | — |
| 167 | C42×D5 | — | 3 | 4 | no | — |
| 168 | #4016 | C2×D3 | 1 | 2 | yes | — |
| 169 | C4×Dic10 | — | 3 | 2 | no | — |
| 170 | C4×Dic10 | — | 3 | 4 | no | — |
| 171 | #3531 | — | 15 | 1 | no | Sylow |
| 172 | C22×D15 | C24 | 1 | 4 | yes | — |
| 173 | C22×C5×D3 | C24 | 1 | 1 | yes | characteristic |
| 174 | C2×C3×C4×C5 | C24 | 1 | 4 | yes | — |
| 175 | C2×C3×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 176 | C2×C3×C4×C5 | C24 | 1 | 2 | yes | — |
| 177 | C2×Dic15 | C24 | 1 | 4 | yes | — |
| 178 | D60 | — | 4 | 4 | no | — |
| 179 | D60 | — | 4 | 2 | no | — |
| 180 | C4×D15 | — | 4 | 4 | no | — |
| 181 | Dic30 | — | 4 | 2 | no | — |
| 182 | C2×C5×Dic3 | C24 | 1 | 4 | yes | — |
| 183 | C2×C5×Dic3 | C24 | 1 | 2 | yes | — |
| 184 | C2×C5×Dic3 | C24 | 1 | 1 | yes | characteristic |
| 185 | C4×C5×D3 | — | 2 | 2 | no | — |
| 186 | C4×C5×D3 | — | 4 | 2 | no | — |
| 187 | C5×Dic6 | — | 4 | 4 | no | — |
| 188 | C2×C3×Dic5 | C24 | 1 | 4 | yes | — |
| 189 | C2×C3×Dic5 | C24 | 1 | 4 | yes | — |
| 190 | #1204 | — | 4 | 4 | no | — |
| 191 | #1203 | — | 4 | 4 | no | — |
| 192 | #1200 | — | 2 | 8 | no | — |
| 193 | #1200 | — | 4 | 4 | no | — |
| 194 | C3×#125 | — | 5 | 4 | no | — |
| 195 | C3×#125 | — | 5 | 4 | no | — |
| 196 | C3×#125 | — | 5 | 4 | no | — |
| 197 | C3×#125 | — | 5 | 2 | no | — |
| 198 | C3×#125 | C2×D5 | 1 | 1 | yes | characteristic |
| 199 | #898 | — | 5 | 4 | no | — |
| 200 | #898 | — | 5 | 4 | no | — |
| 201 | #898 | — | 5 | 4 | no | — |
| 202 | #898 | — | 5 | 4 | no | — |
| 203 | #898 | — | 5 | 4 | no | — |
| 204 | #897 | — | 5 | 2 | no | — |
| 205 | #897 | — | 5 | 4 | no | — |
| 206 | #897 | — | 5 | 4 | no | — |
| 207 | #896 | — | 5 | 4 | no | — |
| 208 | #896 | — | 5 | 4 | no | — |
| 209 | #896 | — | 5 | 4 | no | — |
| 210 | #896 | — | 5 | 4 | no | — |
| 211 | #896 | C2×D5 | 1 | 4 | yes | — |
| 212 | #895 | — | 5 | 2 | no | — |
| 213 | #895 | — | 5 | 4 | no | — |
| 214 | #895 | — | 5 | 4 | no | — |
| 215 | #894 | — | 5 | 4 | no | — |
| 216 | #894 | — | 5 | 4 | no | — |
| 217 | #894 | — | 5 | 4 | no | — |
| 218 | #894 | — | 5 | 4 | no | — |
| 219 | #894 | — | 5 | 4 | no | — |
| 220 | #893 | — | 5 | 4 | no | — |
| 221 | #893 | — | 5 | 4 | no | — |
| 222 | #893 | — | 5 | 2 | no | — |
| 223 | #892 | — | 5 | 4 | no | — |
| 224 | #892 | — | 5 | 4 | no | — |
| 225 | #892 | C2×D5 | 1 | 2 | yes | — |
| 226 | #888 | — | 5 | 4 | no | — |
| 227 | #888 | — | 5 | 4 | no | — |
| 228 | #888 | C2×D5 | 1 | 2 | yes | — |
| 229 | #887 | — | 5 | 4 | no | — |
| 230 | #887 | — | 5 | 2 | no | — |
| 231 | #887 | C2×D5 | 1 | 4 | yes | — |
| 232 | #875 | — | 5 | 4 | no | — |
| 233 | #875 | — | 5 | 2 | no | — |
| 234 | #875 | — | 5 | 4 | no | — |
| 235 | C42×D3 | — | 5 | 4 | no | — |
| 236 | C42×D3 | C2×D5 | 1 | 1 | yes | characteristic |
| 237 | #870 | — | 5 | 4 | no | — |
| 238 | #870 | C2×D5 | 1 | 1 | yes | characteristic |
| 239 | C2×C5×Q8 | — | 3 | 4 | no | — |
| 240 | C22×C4×C5 | — | 3 | 1 | no | — |
| 241 | C22×C4×C5 | — | 3 | 2 | no | — |
| 242 | C2×C22⋊D5 | — | 3 | 4 | no | — |
| 243 | C2×D20 | — | 3 | 2 | no | — |
| 244 | C2×D20 | — | 3 | 4 | no | — |
| 245 | C2×C4×D5 | — | 3 | 4 | no | — |
| 246 | C2×C4×D5 | — | 3 | 4 | no | — |
| 247 | C2×C4×D5 | — | 3 | 4 | no | — |
| 248 | C2×Dic10 | — | 3 | 2 | no | — |
| 249 | C2×Dic10 | — | 3 | 4 | no | — |
| 250 | C5×C4⋊C4 | — | 3 | 2 | no | — |
| 251 | C5×C4⋊C4 | — | 3 | 4 | no | — |
| 252 | C5×C4⋊C4 | — | 3 | 4 | no | — |
| 253 | C5×C4⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 254 | C5×C4⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 255 | C5×C22⋊C4 | — | 3 | 4 | no | — |
| 256 | C42×C5 | — | 3 | 2 | no | — |
| 257 | C42×C5 | — | 3 | 1 | no | — |
| 258 | C42×C5 | — | 3 | 4 | no | — |
| 259 | C42×C5 | C22×D3 | 1 | 1 | yes | characteristic |
| 260 | C22⋊Dic5 | — | 3 | 4 | no | — |
| 261 | #685 | — | 3 | 4 | no | — |
| 262 | #685 | — | 3 | 4 | no | — |
| 263 | #685 | — | 3 | 4 | no | — |
| 264 | #685 | — | 3 | 4 | no | — |
| 265 | #685 | — | 3 | 4 | no | — |
| 266 | #685 | — | 3 | 4 | no | — |
| 267 | #685 | — | 3 | 4 | no | — |
| 268 | #685 | — | 3 | 4 | no | — |
| 269 | C4⋊Dic5 | — | 3 | 4 | no | — |
| 270 | C4⋊Dic5 | C22×D3 | 1 | 2 | yes | — |
| 271 | C4⋊Dic5 | C22×D3 | 1 | 2 | yes | — |
| 272 | C4⋊Dic5 | C22×D3 | 1 | 4 | yes | — |
| 273 | #683 | — | 3 | 4 | no | — |
| 274 | #683 | — | 3 | 4 | no | — |
| 275 | #683 | — | 3 | 4 | no | — |
| 276 | #683 | — | 3 | 4 | no | — |
| 277 | #683 | C22×D3 | 1 | 4 | yes | — |
| 278 | #683 | C22×D3 | 1 | 4 | yes | — |
| 279 | #683 | C22×D3 | 1 | 4 | yes | — |
| 280 | #683 | C22×D3 | 1 | 4 | yes | — |
| 281 | C4×Dic5 | — | 3 | 4 | no | — |
| 282 | C4×Dic5 | — | 3 | 4 | no | — |
| 283 | C4×Dic5 | C22×D3 | 1 | 4 | yes | — |
| 284 | #564 | — | 5 | 1 | no | — |
| 285 | #563 | — | 15 | 4 | no | — |
| 286 | #563 | — | 15 | 2 | no | — |
| 287 | #563 | — | 15 | 4 | no | — |
| 288 | #562 | — | 15 | 4 | no | — |
| 289 | #562 | — | 15 | 1 | no | — |
| 290 | #533 | — | 3 | 1 | no | — |
| 291 | #533 | — | 15 | 4 | no | — |
| 292 | #529 | — | 15 | 2 | no | — |
| 293 | #529 | — | 15 | 4 | no | — |
| 294 | #529 | — | 15 | 4 | no | — |
| 295 | C22×C3×C5 | C25 | 1 | 1 | yes | characteristic |
| 296 | C2×D15 | — | 2 | 4 | no | — |
| 297 | C2×D15 | — | 2 | 4 | no | — |
| 298 | C2×D15 | — | 2 | 4 | no | — |
| 299 | C2×C5×D3 | — | 2 | 1 | no | — |
| 300 | C2×C5×D3 | — | 2 | 2 | no | — |
| 301 | C3×C4×C5 | — | 2 | 1 | no | — |
| 302 | C3×C4×C5 | — | 2 | 4 | no | — |
| 303 | C3×C4×C5 | — | 2 | 2 | no | — |
| 304 | Dic15 | — | 2 | 4 | no | — |
| 305 | C3×Dic5 | — | 2 | 4 | no | — |
| 306 | C3×Dic5 | — | 2 | 4 | no | — |
| 307 | C5×Dic3 | — | 2 | 4 | no | — |
| 308 | C5×Dic3 | — | 2 | 2 | no | — |
| 309 | C5×Dic3 | 2−1+4 | 1 | 2 | yes | — |
| 310 | C2×D12 | — | 5 | 4 | no | — |
| 311 | C2×D12 | — | 5 | 4 | no | — |
| 312 | C2×D12 | — | 5 | 2 | no | — |
| 313 | C2×C4×D3 | — | 5 | 4 | no | — |
| 314 | C2×C4×D3 | — | 5 | 4 | no | — |
| 315 | C2×C4×D3 | — | 5 | 4 | no | — |
| 316 | C2×C4×D3 | C22×D5 | 1 | 1 | yes | characteristic |
| 317 | C2×C4×D3 | C22×D5 | 1 | 2 | yes | — |
| 318 | C2×Dic6 | — | 5 | 2 | no | — |
| 319 | C2×Dic6 | — | 5 | 4 | no | — |
| 320 | C2×Dic6 | C22×D5 | 1 | 4 | yes | — |
| 321 | C3×C4⋊C4 | — | 5 | 4 | no | — |
| 322 | C3×C4⋊C4 | — | 5 | 4 | no | — |
| 323 | C3×C4⋊C4 | — | 5 | 4 | no | — |
| 324 | C3×C4⋊C4 | — | 5 | 4 | no | — |
| 325 | C3×C4⋊C4 | — | 5 | 2 | no | — |
| 326 | C3×C4⋊C4 | — | 5 | 4 | no | — |
| 327 | C3×C4⋊C4 | — | 5 | 2 | no | — |
| 328 | C3×C4⋊C4 | C22×D5 | 1 | 4 | yes | — |
| 329 | C3×C4⋊C4 | C22×D5 | 1 | 2 | yes | — |
| 330 | C3×C42 | — | 5 | 4 | no | — |
| 331 | C3×C42 | C22×D5 | 1 | 1 | yes | characteristic |
| 332 | (C2×D3)⋊C4 | — | 5 | 4 | no | — |
| 333 | (C2×D3)⋊C4 | — | 5 | 4 | no | — |
| 334 | (C2×D3)⋊C4 | — | 5 | 4 | no | — |
| 335 | (C2×D3)⋊C4 | — | 5 | 4 | no | — |
| 336 | (C2×D3)⋊C4 | — | 5 | 4 | no | — |
| 337 | (C2×D3)⋊C4 | — | 5 | 4 | no | — |
| 338 | (C2×D3)⋊C4 | — | 5 | 4 | no | — |
| 339 | (C2×D3)⋊C4 | — | 5 | 4 | no | — |
| 340 | (C2×D3)⋊C4 | — | 5 | 4 | no | — |
| 341 | (C2×D3)⋊C4 | C22×D5 | 1 | 4 | yes | — |
| 342 | C4⋊Dic3 | — | 5 | 4 | no | — |
| 343 | C4⋊Dic3 | — | 5 | 4 | no | — |
| 344 | C4⋊Dic3 | C22×D5 | 1 | 2 | yes | — |
| 345 | Dic3⋊C4 | — | 5 | 4 | no | — |
| 346 | Dic3⋊C4 | — | 5 | 4 | no | — |
| 347 | Dic3⋊C4 | — | 5 | 4 | no | — |
| 348 | Dic3⋊C4 | C22×D5 | 1 | 4 | yes | — |
| 349 | Dic3⋊C4 | C22×D5 | 1 | 4 | yes | — |
| 350 | C4×Dic3 | — | 5 | 4 | no | — |
| 351 | C4×Dic3 | — | 5 | 4 | no | — |
| 352 | C4×Dic3 | C22×D5 | 1 | 4 | yes | — |
| 353 | C4×Dic3 | C22×D5 | 1 | 2 | yes | — |
| 354 | C4×Dic3 | C22×D5 | 1 | 1 | yes | characteristic |
| 355 | C23×C5 | — | 3 | 1 | no | — |
| 356 | C22×D5 | — | 3 | 4 | no | — |
| 357 | C5×Q8 | — | 12 | 4 | no | — |
| 358 | C2×C4×C5 | — | 3 | 1 | no | — |
| 359 | C2×C4×C5 | — | 3 | 4 | no | — |
| 360 | C2×C4×C5 | — | 3 | 2 | no | — |
| 361 | C2×C4×C5 | — | 6 | 2 | no | — |
| 362 | C2×C4×C5 | — | 12 | 2 | no | — |
| 363 | C2×C4×C5 | C23×D3 | 1 | 4 | yes | — |
| 364 | C2×C4×C5 | C23×D3 | 1 | 1 | yes | characteristic |
| 365 | C2×C4×C5 | C23×D3 | 1 | 2 | yes | — |
| 366 | C22⋊D5 | — | 12 | 4 | no | — |
| 367 | C2×Dic5 | — | 3 | 4 | no | — |
| 368 | C2×Dic5 | C23×D3 | 1 | 4 | yes | — |
| 369 | C2×Dic5 | C23×D3 | 1 | 4 | yes | — |
| 370 | D20 | — | 12 | 2 | no | — |
| 371 | D20 | — | 12 | 4 | no | — |
| 372 | C4×D5 | — | 6 | 8 | no | — |
| 373 | C4×D5 | — | 12 | 4 | no | — |
| 374 | C4×D5 | — | 12 | 4 | no | — |
| 375 | Dic10 | — | 12 | 4 | no | — |
| 376 | Dic10 | — | 12 | 2 | no | — |
| 377 | C4⋊Q8 | — | 3 | 2 | no | — |
| 378 | C4⋊Q8 | — | 15 | 4 | no | — |
| 379 | C4⋊Q8 | — | 15 | 4 | no | — |
| 380 | #126 | — | 15 | 4 | no | — |
| 381 | #126 | — | 15 | 4 | no | — |
| 382 | #126 | — | 15 | 4 | no | — |
| 383 | #126 | — | 15 | 4 | no | — |
| 384 | #126 | — | 15 | 4 | no | — |
| 385 | #125 | — | 3 | 1 | no | — |
| 386 | #125 | — | 5 | 4 | no | — |
| 387 | #125 | — | 5 | 4 | no | — |
| 388 | #125 | — | 5 | 4 | no | — |
| 389 | #125 | — | 5 | 2 | no | — |
| 390 | #125 | — | 15 | 4 | no | — |
| 391 | #125 | D3×D5 | 1 | 1 | yes | characteristic |
| 392 | #124 | — | 15 | 4 | no | — |
| 393 | #124 | — | 15 | 4 | no | — |
| 394 | #124 | — | 15 | 2 | no | — |
| 395 | #123 | — | 15 | 4 | no | — |
| 396 | #123 | — | 15 | 4 | no | — |
| 397 | #123 | — | 15 | 4 | no | — |
| 398 | #123 | — | 15 | 4 | no | — |
| 399 | #123 | — | 15 | 4 | no | — |
| 400 | C22⋊Q8 | — | 3 | 4 | no | — |
| 401 | C22⋊Q8 | — | 15 | 4 | no | — |
| 402 | C22⋊Q8 | — | 15 | 4 | no | — |
| 403 | C22⋊Q8 | — | 15 | 4 | no | — |
| 404 | C22⋊Q8 | — | 15 | 2 | no | — |
| 405 | C22⋊Q8 | — | 15 | 4 | no | — |
| 406 | C22⋊Q8 | — | 15 | 4 | no | — |
| 407 | C22⋊Q8 | — | 15 | 4 | no | — |
| 408 | #121 | — | 15 | 4 | no | — |
| 409 | #121 | — | 15 | 2 | no | — |
| 410 | #121 | — | 15 | 4 | no | — |
| 411 | C4×Q8 | — | 3 | 4 | no | — |
| 412 | C4×Q8 | — | 15 | 2 | no | — |
| 413 | C4×Q8 | — | 15 | 4 | no | — |
| 414 | C4×D4 | — | 15 | 2 | no | — |
| 415 | C4×D4 | — | 15 | 4 | no | — |
| 416 | C4×D4 | — | 15 | 4 | no | — |
| 417 | #117 | — | 3 | 2 | no | — |
| 418 | #117 | — | 15 | 4 | no | — |
| 419 | #117 | — | 15 | 4 | no | — |
| 420 | C2×C42 | — | 3 | 1 | no | — |
| 421 | C2×C42 | — | 15 | 4 | no | — |
| 422 | C2×C3×C5 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 423 | C2×C3×C5 | #585 | 1 | 2 | yes | — |
| 424 | D15 | — | 4 | 4 | no | — |
| 425 | C5×D3 | — | 4 | 1 | no | — |
| 426 | C22×D3 | — | 5 | 4 | no | — |
| 427 | C22×D3 | C23×D5 | 1 | 1 | yes | characteristic |
| 428 | C2×C3×C4 | — | 5 | 4 | no | — |
| 429 | C2×C3×C4 | — | 5 | 4 | no | — |
| 430 | C2×C3×C4 | C23×D5 | 1 | 4 | yes | — |
| 431 | C2×C3×C4 | C23×D5 | 1 | 2 | yes | — |
| 432 | C2×C3×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 433 | C2×Dic3 | — | 5 | 4 | no | — |
| 434 | C2×Dic3 | C23×D5 | 1 | 4 | yes | — |
| 435 | C2×Dic3 | C23×D5 | 1 | 2 | yes | — |
| 436 | C2×Dic3 | C23×D5 | 1 | 1 | yes | characteristic |
| 437 | D12 | — | 20 | 4 | no | — |
| 438 | D12 | — | 20 | 2 | no | — |
| 439 | D12 | — | 20 | 4 | no | — |
| 440 | C4×D3 | — | 2 | 2 | no | — |
| 441 | C4×D3 | — | 4 | 2 | no | — |
| 442 | C4×D3 | — | 10 | 8 | no | — |
| 443 | C4×D3 | — | 20 | 4 | no | — |
| 444 | C4×D3 | — | 20 | 4 | no | — |
| 445 | Dic6 | — | 4 | 4 | no | — |
| 446 | Dic6 | — | 20 | 4 | no | — |
| 447 | Dic6 | — | 20 | 2 | no | — |
| 448 | C22×C5 | — | 6 | 1 | no | — |
| 449 | C22×C5 | — | 6 | 2 | no | — |
| 450 | C22×C5 | C24×D3 | 1 | 1 | yes | characteristic |
| 451 | C2×D5 | — | 6 | 4 | no | — |
| 452 | C2×D5 | — | 6 | 4 | no | — |
| 453 | C2×D5 | — | 6 | 4 | no | — |
| 454 | C4×C5 | — | 2 | 1 | no | — |
| 455 | C4×C5 | — | 2 | 2 | no | — |
| 456 | C4×C5 | — | 2 | 4 | no | — |
| 457 | C4×C5 | — | 3 | 2 | no | — |
| 458 | C4×C5 | — | 6 | 4 | no | — |
| 459 | C4×C5 | — | 6 | 2 | no | — |
| 460 | Dic5 | — | 2 | 4 | no | — |
| 461 | Dic5 | — | 2 | 4 | no | — |
| 462 | Dic5 | — | 6 | 4 | no | — |
| 463 | C2×Q8 | — | 3 | 4 | no | — |
| 464 | C2×Q8 | — | 15 | 4 | no | — |
| 465 | C2×Q8 | — | 15 | 2 | no | — |
| 466 | C2×D4 | — | 15 | 4 | no | — |
| 467 | C2×D4 | — | 15 | 4 | no | — |
| 468 | C2×D4 | — | 15 | 2 | no | — |
| 469 | C22×C4 | — | 3 | 1 | no | — |
| 470 | C22×C4 | — | 3 | 2 | no | — |
| 471 | C22×C4 | — | 15 | 4 | no | — |
| 472 | C22×C4 | — | 15 | 4 | no | — |
| 473 | C22×C4 | — | 15 | 4 | no | — |
| 474 | C4⋊C4 | — | 3 | 2 | no | — |
| 475 | C4⋊C4 | — | 3 | 4 | no | — |
| 476 | C4⋊C4 | — | 3 | 4 | no | — |
| 477 | C4⋊C4 | — | 5 | 4 | no | — |
| 478 | C4⋊C4 | — | 5 | 4 | no | — |
| 479 | C4⋊C4 | — | 5 | 4 | no | — |
| 480 | C4⋊C4 | — | 5 | 4 | no | — |
| 481 | C4⋊C4 | — | 5 | 2 | no | — |
| 482 | C4⋊C4 | — | 5 | 4 | no | — |
| 483 | C4⋊C4 | — | 5 | 2 | no | — |
| 484 | C4⋊C4 | — | 15 | 4 | no | — |
| 485 | C4⋊C4 | — | 15 | 4 | no | — |
| 486 | C4⋊C4 | — | 15 | 4 | no | — |
| 487 | C4⋊C4 | — | 15 | 4 | no | — |
| 488 | C4⋊C4 | — | 15 | 4 | no | — |
| 489 | C4⋊C4 | C2×D3×D5 | 1 | 2 | yes | — |
| 490 | C4⋊C4 | C2×D3×D5 | 1 | 4 | yes | — |
| 491 | C22⋊C4 | — | 3 | 4 | no | — |
| 492 | C22⋊C4 | — | 15 | 4 | no | — |
| 493 | C22⋊C4 | — | 15 | 4 | no | — |
| 494 | C22⋊C4 | — | 15 | 4 | no | — |
| 495 | C22⋊C4 | — | 15 | 4 | no | — |
| 496 | C22⋊C4 | — | 15 | 4 | no | — |
| 497 | C22⋊C4 | — | 15 | 4 | no | — |
| 498 | C22⋊C4 | — | 15 | 4 | no | — |
| 499 | C22⋊C4 | — | 15 | 4 | no | — |
| 500 | C22⋊C4 | — | 15 | 4 | no | — |
| 501 | C42 | — | 3 | 2 | no | — |
| 502 | C42 | — | 3 | 1 | no | — |
| 503 | C42 | — | 3 | 4 | no | — |
| 504 | C42 | — | 5 | 4 | no | — |
| 505 | C42 | — | 15 | 4 | no | — |
| 506 | C42 | — | 15 | 4 | no | — |
| 507 | C42 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 508 | C3×C5 | #3531 | 1 | 1 | yes | characteristic, complemented, Hall |
| 509 | C22×C3 | C24×D5 | 1 | 1 | yes | characteristic |
| 510 | C2×D3 | — | 2 | 1 | no | — |
| 511 | C2×D3 | — | 2 | 2 | no | — |
| 512 | C2×D3 | — | 10 | 4 | no | — |
| 513 | C2×D3 | — | 10 | 4 | no | — |
| 514 | C2×D3 | — | 10 | 4 | no | — |
| 515 | C3×C4 | — | 2 | 1 | no | — |
| 516 | C3×C4 | — | 2 | 4 | no | — |
| 517 | C3×C4 | — | 2 | 2 | no | — |
| 518 | C3×C4 | — | 10 | 4 | no | — |
| 519 | C3×C4 | — | 10 | 4 | no | — |
| 520 | Dic3 | — | 2 | 2 | no | — |
| 521 | Dic3 | — | 2 | 4 | no | — |
| 522 | Dic3 | — | 10 | 4 | no | — |
| 523 | Dic3 | #4147 | 1 | 2 | yes | — |
| 524 | C2×C5 | — | 12 | 1 | no | — |
| 525 | C2×C5 | D3×2−1+4 | 1 | 1 | yes | characteristic |
| 526 | C2×C5 | #5968 | 1 | 2 | yes | — |
| 527 | D5 | — | 12 | 4 | no | — |
| 528 | C23 | — | 3 | 1 | no | — |
| 529 | C23 | — | 15 | 4 | no | — |
| 530 | Q8 | — | 12 | 4 | no | — |
| 531 | Q8 | — | 60 | 2 | no | — |
| 532 | Q8 | — | 60 | 4 | no | — |
| 533 | D4 | — | 60 | 2 | no | — |
| 534 | D4 | — | 60 | 4 | no | — |
| 535 | D4 | — | 60 | 4 | no | — |
| 536 | C2×C4 | — | 3 | 1 | no | — |
| 537 | C2×C4 | — | 3 | 2 | no | — |
| 538 | C2×C4 | — | 3 | 4 | no | — |
| 539 | C2×C4 | — | 5 | 4 | no | — |
| 540 | C2×C4 | — | 5 | 4 | no | — |
| 541 | C2×C4 | — | 6 | 2 | no | — |
| 542 | C2×C4 | — | 12 | 2 | no | — |
| 543 | C2×C4 | — | 15 | 4 | no | — |
| 544 | C2×C4 | — | 30 | 8 | no | — |
| 545 | C2×C4 | — | 60 | 4 | no | — |
| 546 | C2×C4 | — | 60 | 4 | no | — |
| 547 | C2×C4 | C22×D3×D5 | 1 | 4 | yes | — |
| 548 | C2×C4 | C22×D3×D5 | 1 | 1 | yes | characteristic |
| 549 | C2×C4 | C22×D3×D5 | 1 | 2 | yes | — |
| 550 | C2×C3 | C2×#4147 | 1 | 1 | yes | characteristic |
| 551 | C2×C3 | #66283 | 1 | 2 | yes | — |
| 552 | D3 | — | 4 | 1 | no | — |
| 553 | D3 | — | 20 | 4 | no | — |
| 554 | C5 | #87139 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 555 | C22 | — | 6 | 2 | no | — |
| 556 | C22 | — | 6 | 1 | no | — |
| 557 | C22 | — | 30 | 4 | no | — |
| 558 | C22 | — | 30 | 4 | no | — |
| 559 | C22 | — | 30 | 4 | no | — |
| 560 | C22 | C23×D3×D5 | 1 | 1 | yes | characteristic |
| 561 | C4 | — | 2 | 2 | no | — |
| 562 | C4 | — | 2 | 4 | no | — |
| 563 | C4 | — | 2 | 1 | no | — |
| 564 | C4 | — | 3 | 2 | no | — |
| 565 | C4 | — | 6 | 2 | no | — |
| 566 | C4 | — | 6 | 4 | no | — |
| 567 | C4 | — | 10 | 4 | no | — |
| 568 | C4 | — | 10 | 4 | no | — |
| 569 | C4 | — | 30 | 4 | no | — |
| 570 | C3 | #10618187 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 571 | C2 | — | 12 | 1 | no | — |
| 572 | C2 | — | 60 | 4 | no | — |
| 573 | C2 | D3×#4147 | 1 | 1 | yes | characteristic |
| 574 | C2 | #11757063 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D3×D5 |
| commutator, socle, cosocle | C22×C3×C5 | C25 |
| Fitting | C3×C5×#125 | C22 |
| hypercenter | #125 | D3×D5 |
| hypocenter | C3×C5 | #3531 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ #125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11756459 | C2 | semidirect |
| 2. C5×#5688 | C2 | semidirect |
| 3. C3×C5⋊#564 | C2 | semidirect |
| 4. #11753824 | C2 | semidirect |
| 5. #11753600 | C2 | semidirect |
| 6. #11753551 | C2 | semidirect |
| 7. #11753467 | C2 | semidirect |
| 8. #11753392 | C2 | semidirect |
| 9. #11753374 | C2 | semidirect |
| 10. #11752701 | C2 | semidirect |
| 11. #11752474 | C2 | semidirect |
| 63. C5⋊#564 | D3 | semidirect |
| 125. #5688 | D5 | semidirect |
| 508. C3×C5 | #3531 | semidirect |
| 554. C5 | #87139 | semidirect |
| 570. C3 | #10618187 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756459 | 2 |
| C5×#5688 | 2 |
| C3×C5⋊#564 | 2 |
| #11753824 | 2 |
| #11753600 | 2 |
| #11753551 | 2 |
| #11753467 | 2 |
| #11753392 | 2 |
| #11753374 | 2 |
| #11752701 | 2 |
| #11752474 | 2 |
| #10618187 | 3 |
| #87139 | 5 |