Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1128 conjugacy classes of subgroups.
The subgroup lattice has 536 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11756427 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#91521 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C2×#91497 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #11752556 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C5×#5060 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C3×#65347 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11749320 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11749073 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11747097 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11747073 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11746983 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #10613600 | — | 3 | 1 | no | maximal, Hall |
| 13 | C2×#6821 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×#6819 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×#6766 | C22 | 1 | 2 | yes | — |
| 16 | C3×C5×#124 | C22 | 1 | 1 | yes | characteristic |
| 17 | #91833 | C22 | 1 | 1 | yes | characteristic |
| 18 | #91829 | C22 | 1 | 1 | yes | characteristic |
| 19 | #91773 | — | 2 | 2 | no | — |
| 20 | #91770 | — | 2 | 2 | no | — |
| 21 | #91764 | C22 | 1 | 1 | yes | characteristic |
| 22 | C42×D15 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×C5×#216 | C22 | 1 | 2 | yes | — |
| 24 | C2×C5×#214 | C22 | 1 | 2 | yes | — |
| 25 | C5×#869 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×C3×#688 | C22 | 1 | 2 | yes | — |
| 27 | C2×C3×#686 | C22 | 1 | 2 | yes | — |
| 28 | C3×#4020 | C22 | 1 | 1 | yes | characteristic |
| 29 | #91521 | — | 2 | 8 | no | — |
| 30 | #91497 | — | 2 | 8 | no | — |
| 31 | #91465 | — | 2 | 2 | no | — |
| 32 | #91434 | — | 2 | 2 | no | — |
| 33 | #91368 | C22 | 1 | 2 | yes | — |
| 34 | C2×#6663 | C22 | 1 | 2 | yes | — |
| 35 | C2×#6660 | C22 | 1 | 2 | yes | — |
| 36 | C2×#6657 | C22 | 1 | 2 | yes | — |
| 37 | C2×#6653 | C22 | 1 | 2 | yes | — |
| 38 | C2×#6648 | C22 | 1 | 2 | yes | — |
| 39 | C5×#803 | C22 | 1 | 1 | yes | characteristic |
| 40 | C3×#3935 | C22 | 1 | 1 | yes | characteristic |
| 41 | #90954 | C22 | 1 | 2 | yes | — |
| 42 | #81844 | — | 5 | 1 | no | maximal, Hall |
| 43 | C2×#4065 | — | 3 | 2 | no | — |
| 44 | C2×#4062 | — | 3 | 2 | no | — |
| 45 | #66059 | — | 3 | 1 | no | — |
| 46 | #66002 | — | 3 | 1 | no | — |
| 47 | C5×#497 | — | 3 | 1 | no | — |
| 48 | #65479 | — | 3 | 2 | no | — |
| 49 | #65465 | — | 3 | 2 | no | — |
| 50 | #65375 | — | 3 | 1 | no | — |
| 51 | #65347 | D3 | 1 | 1 | yes | characteristic, complemented |
| 52 | #65001 | — | 3 | 1 | no | — |
| 53 | D5×#97 | — | 3 | 1 | no | — |
| 54 | C2×C3×C5×Q8 | C23 | 1 | 1 | yes | characteristic |
| 55 | C2×C3×C5×D4 | C23 | 1 | 1 | yes | characteristic |
| 56 | C2×#1220 | — | 2 | 1 | no | — |
| 57 | C2×#1220 | — | 2 | 2 | no | — |
| 58 | C22×Dic15 | — | 2 | 1 | no | — |
| 59 | #6821 | — | 2 | 4 | no | — |
| 60 | #6819 | — | 2 | 4 | no | — |
| 61 | C2×D60 | — | 2 | 1 | no | — |
| 62 | C2×D60 | C23 | 1 | 1 | yes | characteristic |
| 63 | C2×C4×D15 | — | 2 | 1 | no | — |
| 64 | C2×C4×D15 | D4 | 1 | 2 | yes | — |
| 65 | C2×C4×D15 | C23 | 1 | 1 | yes | characteristic |
| 66 | C2×Dic30 | C23 | 1 | 1 | yes | characteristic |
| 67 | C2×C5×Dic6 | C23 | 1 | 2 | yes | — |
| 68 | C2×C3×D20 | — | 2 | 2 | no | — |
| 69 | C2×C3×D20 | C23 | 1 | 2 | yes | — |
| 70 | C2×#1202 | — | 2 | 2 | no | — |
| 71 | C2×D5×Dic3 | — | 2 | 2 | no | — |
| 72 | #6766 | — | 2 | 4 | no | — |
| 73 | #6766 | — | 2 | 4 | no | — |
| 74 | C3×C5×C22⋊C4 | — | 2 | 2 | no | — |
| 75 | C3×C42×C5 | C23 | 1 | 1 | yes | characteristic |
| 76 | #6714 | — | 2 | 2 | no | — |
| 77 | #6712 | — | 2 | 2 | no | — |
| 78 | C4×Dic15 | D4 | 1 | 2 | yes | — |
| 79 | C4×Dic15 | C23 | 1 | 1 | yes | characteristic |
| 80 | C5×#216 | — | 2 | 4 | no | — |
| 81 | C5×#214 | — | 2 | 4 | no | — |
| 82 | C5×C4⋊Dic3 | — | 2 | 2 | no | — |
| 83 | C2×C5×C3⋊C8 | C23 | 1 | 2 | yes | — |
| 84 | C3×#688 | — | 2 | 4 | no | — |
| 85 | C3×#686 | — | 2 | 4 | no | — |
| 86 | C2×C3×#168 | C23 | 1 | 2 | yes | — |
| 87 | #6665 | — | 2 | 4 | no | — |
| 88 | #6663 | — | 2 | 4 | no | — |
| 89 | #6660 | — | 2 | 4 | no | — |
| 90 | #6657 | — | 2 | 4 | no | — |
| 91 | #6653 | — | 2 | 4 | no | — |
| 92 | #6648 | D4 | 1 | 8 | yes | complemented |
| 93 | C2×#916 | — | 5 | 2 | no | — |
| 94 | C2×#912 | — | 5 | 2 | no | — |
| 95 | #5716 | — | 5 | 1 | no | — |
| 96 | #5668 | — | 5 | 1 | no | — |
| 97 | C3×#496 | — | 5 | 1 | no | — |
| 98 | #5167 | — | 5 | 2 | no | — |
| 99 | #5154 | — | 5 | 2 | no | — |
| 100 | #5074 | — | 5 | 1 | no | — |
| 101 | #5060 | D5 | 1 | 1 | yes | characteristic, complemented |
| 102 | #4715 | — | 5 | 1 | no | — |
| 103 | D3×#97 | — | 5 | 1 | no | — |
| 104 | C2×#713 | — | 3 | 1 | no | — |
| 105 | C2×#713 | — | 3 | 2 | no | — |
| 106 | C2×#711 | — | 3 | 1 | no | — |
| 107 | C2×C5×Q16 | — | 3 | 2 | no | — |
| 108 | C2×C5×SD16 | — | 3 | 2 | no | — |
| 109 | C5×C4⋊Q8 | — | 3 | 1 | no | — |
| 110 | C5×#124 | C2×D3 | 1 | 1 | yes | characteristic |
| 111 | #4093 | — | 3 | 2 | no | — |
| 112 | #4090 | — | 3 | 1 | no | — |
| 113 | C2×#689 | — | 3 | 2 | no | — |
| 114 | C2×#688 | — | 3 | 2 | no | — |
| 115 | C2×#688 | C2×D3 | 1 | 2 | yes | — |
| 116 | #4086 | — | 3 | 1 | no | — |
| 117 | C2×#686 | C2×D3 | 1 | 2 | yes | — |
| 118 | #4065 | — | 6 | 8 | no | — |
| 119 | #4062 | — | 6 | 8 | no | — |
| 120 | C2×D40 | — | 3 | 2 | no | — |
| 121 | C2×#677 | — | 3 | 2 | no | — |
| 122 | C2×C8×D5 | — | 3 | 2 | no | — |
| 123 | #4041 | — | 6 | 2 | no | — |
| 124 | #4039 | — | 6 | 2 | no | — |
| 125 | #4030 | — | 6 | 2 | no | — |
| 126 | #4027 | — | 6 | 2 | no | — |
| 127 | #4021 | — | 3 | 1 | no | — |
| 128 | #4020 | C2×D3 | 1 | 1 | yes | characteristic |
| 129 | C42×D5 | — | 3 | 1 | no | — |
| 130 | C5×#97 | — | 3 | 1 | no | — |
| 131 | #3947 | — | 3 | 2 | no | — |
| 132 | #3935 | C2×D3 | 1 | 1 | yes | characteristic |
| 133 | #3150 | — | 15 | 1 | no | Sylow |
| 134 | C23×C3×C5 | — | 2 | 1 | no | — |
| 135 | C22×D15 | — | 2 | 1 | no | — |
| 136 | C22×D15 | C2×D4 | 1 | 1 | yes | characteristic |
| 137 | C22×C3×D5 | — | 2 | 2 | no | — |
| 138 | C3×C5×Q8 | — | 2 | 2 | no | — |
| 139 | C3×C5×D4 | — | 2 | 2 | no | — |
| 140 | C2×C3×C4×C5 | — | 2 | 1 | no | — |
| 141 | C2×C3×C4×C5 | C2×D4 | 1 | 2 | yes | — |
| 142 | C2×C3×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 143 | #1220 | — | 4 | 4 | no | — |
| 144 | #1220 | — | 4 | 2 | no | — |
| 145 | C2×Dic15 | — | 2 | 1 | no | — |
| 146 | C2×Dic15 | — | 4 | 2 | no | — |
| 147 | C2×Dic15 | C2×D4 | 1 | 2 | yes | — |
| 148 | C2×Dic15 | C2×D4 | 1 | 1 | yes | characteristic |
| 149 | D60 | — | 2 | 2 | no | — |
| 150 | D60 | — | 4 | 2 | no | — |
| 151 | C4×D15 | — | 4 | 2 | no | — |
| 152 | C4×D15 | — | 4 | 2 | no | — |
| 153 | C4×D15 | C2×D4 | 1 | 4 | yes | — |
| 154 | Dic30 | — | 2 | 2 | no | — |
| 155 | C2×C5×Dic3 | — | 2 | 2 | no | — |
| 156 | C5×Dic6 | — | 2 | 2 | no | — |
| 157 | C5×Dic6 | — | 2 | 2 | no | — |
| 158 | C3×D20 | — | 2 | 2 | no | — |
| 159 | C3×D20 | — | 2 | 2 | no | — |
| 160 | C3×D20 | — | 4 | 4 | no | — |
| 161 | #1202 | — | 4 | 4 | no | — |
| 162 | D5×Dic3 | — | 4 | 4 | no | — |
| 163 | C3×#168 | C2×D4 | 1 | 4 | yes | — |
| 164 | C5×C3⋊C8 | C2×D4 | 1 | 4 | yes | — |
| 165 | C2×#239 | — | 5 | 1 | no | — |
| 166 | C2×#237 | — | 5 | 1 | no | — |
| 167 | C2×#237 | — | 5 | 2 | no | — |
| 168 | C2×C3×SD16 | — | 5 | 2 | no | — |
| 169 | C2×C3×D8 | — | 5 | 2 | no | — |
| 170 | C3×#127 | — | 5 | 1 | no | — |
| 171 | C3×#124 | C2×D5 | 1 | 1 | yes | characteristic |
| 172 | #944 | — | 5 | 1 | no | — |
| 173 | C2×#216 | C2×D5 | 1 | 2 | yes | — |
| 174 | #940 | — | 5 | 1 | no | — |
| 175 | #938 | — | 10 | 2 | no | — |
| 176 | #936 | — | 5 | 2 | no | — |
| 177 | D4×Dic3 | — | 10 | 2 | no | — |
| 178 | C2×#214 | — | 5 | 2 | no | — |
| 179 | C2×#214 | C2×D5 | 1 | 2 | yes | — |
| 180 | C2×#213 | — | 5 | 2 | no | — |
| 181 | #916 | — | 10 | 8 | no | — |
| 182 | #912 | — | 10 | 8 | no | — |
| 183 | C2×Dic12 | — | 5 | 2 | no | — |
| 184 | C2×#204 | — | 5 | 2 | no | — |
| 185 | C2×D3×C8 | — | 5 | 2 | no | — |
| 186 | #884 | — | 10 | 2 | no | — |
| 187 | #67⋊C4 | — | 10 | 2 | no | — |
| 188 | #875 | — | 5 | 1 | no | — |
| 189 | C42×D3 | — | 5 | 1 | no | — |
| 190 | #869 | C2×D5 | 1 | 1 | yes | characteristic |
| 191 | C3×#97 | — | 5 | 1 | no | — |
| 192 | #815 | — | 5 | 2 | no | — |
| 193 | #803 | C2×D5 | 1 | 1 | yes | characteristic |
| 194 | C2×C5×Q8 | — | 3 | 2 | no | — |
| 195 | C2×C5×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 196 | C2×C5×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 197 | C2×C22⋊D5 | — | 6 | 2 | no | — |
| 198 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 199 | C22×Dic5 | — | 6 | 1 | no | — |
| 200 | #713 | — | 6 | 4 | no | — |
| 201 | #713 | — | 6 | 4 | no | — |
| 202 | #713 | — | 6 | 4 | no | — |
| 203 | #711 | — | 6 | 4 | no | — |
| 204 | C2×D20 | — | 2 | 2 | no | — |
| 205 | C2×D20 | — | 3 | 1 | no | — |
| 206 | C2×D20 | — | 6 | 1 | no | — |
| 207 | C2×D20 | — | 6 | 2 | no | — |
| 208 | C2×D20 | C22×D3 | 1 | 2 | yes | — |
| 209 | C2×C4×D5 | — | 3 | 1 | no | — |
| 210 | C2×C4×D5 | — | 3 | 2 | no | — |
| 211 | C2×C4×D5 | — | 6 | 1 | no | — |
| 212 | C2×C4×D5 | — | 6 | 2 | no | — |
| 213 | C2×Dic10 | — | 3 | 1 | no | — |
| 214 | C5×Q16 | — | 6 | 4 | no | — |
| 215 | C5×SD16 | — | 6 | 4 | no | — |
| 216 | C2×C5×C8 | — | 3 | 2 | no | — |
| 217 | C5×C4⋊C4 | — | 6 | 2 | no | — |
| 218 | C5×C22⋊C4 | — | 2 | 2 | no | — |
| 219 | C42×C5 | C22×D3 | 1 | 1 | yes | characteristic |
| 220 | #689 | — | 6 | 4 | no | — |
| 221 | #688 | — | 2 | 4 | no | — |
| 222 | #688 | — | 6 | 4 | no | — |
| 223 | #686 | — | 2 | 4 | no | — |
| 224 | #685 | — | 6 | 4 | no | — |
| 225 | #685 | — | 6 | 2 | no | — |
| 226 | #683 | — | 6 | 2 | no | — |
| 227 | C4×Dic5 | — | 3 | 2 | no | — |
| 228 | C4×Dic5 | — | 3 | 1 | no | — |
| 229 | C2×#168 | C22×D3 | 1 | 2 | yes | — |
| 230 | D40 | — | 6 | 4 | no | — |
| 231 | #677 | — | 6 | 4 | no | — |
| 232 | C8×D5 | — | 3 | 8 | no | — |
| 233 | C2×#135 | — | 15 | 2 | no | — |
| 234 | C2×#135 | — | 15 | 2 | no | — |
| 235 | #532 | — | 15 | 1 | no | — |
| 236 | #532 | — | 15 | 1 | no | — |
| 237 | #497 | — | 3 | 1 | no | — |
| 238 | #497 | — | 15 | 1 | no | — |
| 239 | #497 | — | 15 | 2 | no | — |
| 240 | #496 | — | 5 | 1 | no | — |
| 241 | #496 | — | 15 | 1 | no | — |
| 242 | #496 | — | 15 | 2 | no | — |
| 243 | C2×#97 | — | 15 | 1 | no | — |
| 244 | C22×C3×C5 | — | 4 | 1 | no | — |
| 245 | C22×C3×C5 | — | 4 | 2 | no | — |
| 246 | C22×C3×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 247 | C2×D15 | — | 2 | 2 | no | — |
| 248 | C2×D15 | — | 4 | 1 | no | — |
| 249 | C2×D15 | — | 4 | 2 | no | — |
| 250 | C2×D15 | #127 | 1 | 2 | yes | — |
| 251 | C2×C3×D5 | — | 4 | 2 | no | — |
| 252 | C2×C3×D5 | — | 4 | 4 | no | — |
| 253 | C3×C4×C5 | — | 2 | 2 | no | — |
| 254 | C3×C4×C5 | — | 4 | 1 | no | — |
| 255 | C3×C4×C5 | C22×D4 | 1 | 2 | yes | — |
| 256 | Dic15 | — | 2 | 2 | no | — |
| 257 | Dic15 | — | 4 | 1 | no | — |
| 258 | Dic15 | #127 | 1 | 2 | yes | — |
| 259 | C5×Dic3 | — | 4 | 2 | no | — |
| 260 | C2×C3×Q8 | C22×D5 | 1 | 1 | yes | characteristic |
| 261 | C2×C3×D4 | — | 5 | 2 | no | — |
| 262 | C2×C3×D4 | — | 10 | 2 | no | — |
| 263 | C2×C3×D4 | C22×D5 | 1 | 1 | yes | characteristic |
| 264 | C2×#67 | — | 10 | 2 | no | — |
| 265 | C2×#67 | — | 10 | 2 | no | — |
| 266 | C2×#67 | — | 10 | 1 | no | — |
| 267 | C22×Dic3 | — | 10 | 2 | no | — |
| 268 | C22×Dic3 | — | 10 | 1 | no | — |
| 269 | #239 | — | 10 | 4 | no | — |
| 270 | #237 | — | 10 | 4 | no | — |
| 271 | #237 | — | 10 | 4 | no | — |
| 272 | #237 | — | 10 | 4 | no | — |
| 273 | C2×D12 | — | 5 | 1 | no | — |
| 274 | C2×D12 | — | 10 | 1 | no | — |
| 275 | C2×C4×D3 | — | 5 | 1 | no | — |
| 276 | C2×C4×D3 | — | 5 | 2 | no | — |
| 277 | C2×C4×D3 | — | 10 | 1 | no | — |
| 278 | C2×Dic6 | — | 5 | 1 | no | — |
| 279 | C2×Dic6 | C22×D5 | 1 | 2 | yes | — |
| 280 | C3×SD16 | — | 10 | 4 | no | — |
| 281 | C3×D8 | — | 10 | 4 | no | — |
| 282 | C2×C3×C8 | — | 5 | 2 | no | — |
| 283 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 284 | C3×C42 | C22×D5 | 1 | 1 | yes | characteristic |
| 285 | #217 | — | 10 | 4 | no | — |
| 286 | #216 | — | 2 | 4 | no | — |
| 287 | #214 | — | 2 | 4 | no | — |
| 288 | #214 | — | 10 | 4 | no | — |
| 289 | #213 | — | 10 | 4 | no | — |
| 290 | (C2×D3)⋊C4 | — | 10 | 2 | no | — |
| 291 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 292 | Dic3⋊C4 | — | 10 | 2 | no | — |
| 293 | C4×Dic3 | — | 5 | 2 | no | — |
| 294 | C4×Dic3 | — | 5 | 1 | no | — |
| 295 | C2×C3⋊C8 | C22×D5 | 1 | 2 | yes | — |
| 296 | Dic12 | — | 10 | 4 | no | — |
| 297 | #204 | — | 10 | 4 | no | — |
| 298 | D3×C8 | — | 5 | 8 | no | — |
| 299 | C23×C5 | — | 2 | 1 | no | — |
| 300 | C22×D5 | — | 2 | 2 | no | — |
| 301 | C22×D5 | — | 3 | 1 | no | — |
| 302 | C22×D5 | — | 6 | 1 | no | — |
| 303 | C5×Q8 | — | 2 | 2 | no | — |
| 304 | C5×Q8 | — | 6 | 2 | no | — |
| 305 | C5×Q8 | — | 6 | 2 | no | — |
| 306 | C5×D4 | — | 2 | 2 | no | — |
| 307 | C2×C4×C5 | — | 2 | 1 | no | — |
| 308 | C2×C4×C5 | — | 6 | 2 | no | — |
| 309 | C2×C4×C5 | D3×D4 | 1 | 2 | yes | — |
| 310 | C2×C4×C5 | C23×D3 | 1 | 1 | yes | characteristic |
| 311 | C22⋊D5 | — | 12 | 4 | no | — |
| 312 | C22⋊D5 | — | 12 | 2 | no | — |
| 313 | C2×Dic5 | — | 3 | 1 | no | — |
| 314 | C2×Dic5 | — | 3 | 2 | no | — |
| 315 | C2×Dic5 | — | 6 | 1 | no | — |
| 316 | C2×Dic5 | — | 12 | 2 | no | — |
| 317 | D20 | — | 2 | 2 | no | — |
| 318 | D20 | — | 2 | 2 | no | — |
| 319 | D20 | — | 4 | 4 | no | — |
| 320 | D20 | — | 6 | 2 | no | — |
| 321 | D20 | — | 12 | 2 | no | — |
| 322 | D20 | — | 12 | 4 | no | — |
| 323 | C4×D5 | — | 3 | 4 | no | — |
| 324 | C4×D5 | — | 12 | 2 | no | — |
| 325 | C4×D5 | — | 12 | 4 | no | — |
| 326 | C4×D5 | — | 12 | 2 | no | — |
| 327 | Dic10 | — | 6 | 2 | no | — |
| 328 | C5×C8 | — | 3 | 4 | no | — |
| 329 | #168 | D3×D4 | 1 | 4 | yes | — |
| 330 | C2×#41 | — | 15 | 2 | no | — |
| 331 | C2×#41 | — | 15 | 1 | no | — |
| 332 | C2×#41 | — | 15 | 1 | no | — |
| 333 | #135 | — | 30 | 8 | no | — |
| 334 | #135 | — | 30 | 8 | no | — |
| 335 | C2×Q16 | — | 3 | 2 | no | — |
| 336 | C2×Q16 | — | 15 | 2 | no | — |
| 337 | C2×SD16 | — | 3 | 2 | no | — |
| 338 | C2×SD16 | — | 5 | 2 | no | — |
| 339 | C2×SD16 | — | 15 | 2 | no | — |
| 340 | C2×SD16 | — | 15 | 2 | no | — |
| 341 | C2×D8 | — | 5 | 2 | no | — |
| 342 | C2×D8 | — | 15 | 2 | no | — |
| 343 | C22×C8 | — | 15 | 2 | no | — |
| 344 | C4⋊Q8 | — | 3 | 1 | no | — |
| 345 | C4⋊Q8 | — | 15 | 1 | no | — |
| 346 | #127 | — | 5 | 1 | no | — |
| 347 | #127 | — | 15 | 1 | no | — |
| 348 | #124 | — | 15 | 2 | no | — |
| 349 | #124 | — | 15 | 1 | no | — |
| 350 | #124 | D3×D5 | 1 | 1 | yes | characteristic |
| 351 | #121 | — | 30 | 2 | no | — |
| 352 | #121 | — | 30 | 2 | no | — |
| 353 | C4×D4 | — | 30 | 2 | no | — |
| 354 | C4×D4 | — | 30 | 2 | no | — |
| 355 | C2×C42 | — | 15 | 1 | no | — |
| 356 | #97 | — | 3 | 1 | no | — |
| 357 | #97 | — | 5 | 1 | no | — |
| 358 | #97 | — | 15 | 2 | no | — |
| 359 | C2×C3×C5 | — | 8 | 1 | no | — |
| 360 | C2×C3×C5 | C2×#127 | 1 | 1 | yes | characteristic |
| 361 | C2×C3×C5 | #575 | 1 | 2 | yes | — |
| 362 | D15 | — | 2 | 2 | no | — |
| 363 | D15 | — | 8 | 1 | no | — |
| 364 | C3×D5 | — | 8 | 2 | no | — |
| 365 | C23×C3 | — | 2 | 1 | no | — |
| 366 | C23×C3 | — | 10 | 2 | no | — |
| 367 | C22×D3 | — | 5 | 1 | no | — |
| 368 | C22×D3 | — | 10 | 1 | no | — |
| 369 | C3×Q8 | — | 2 | 2 | no | — |
| 370 | C3×D4 | — | 2 | 2 | no | — |
| 371 | C3×D4 | — | 10 | 2 | no | — |
| 372 | C3×D4 | — | 10 | 2 | no | — |
| 373 | C3×D4 | — | 20 | 4 | no | — |
| 374 | C2×C3×C4 | — | 2 | 1 | no | — |
| 375 | C2×C3×C4 | D4×D5 | 1 | 2 | yes | — |
| 376 | C2×C3×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 377 | #67 | — | 20 | 4 | no | — |
| 378 | #67 | — | 20 | 4 | no | — |
| 379 | #67 | — | 20 | 2 | no | — |
| 380 | C2×Dic3 | — | 2 | 2 | no | — |
| 381 | C2×Dic3 | — | 5 | 1 | no | — |
| 382 | C2×Dic3 | — | 5 | 2 | no | — |
| 383 | C2×Dic3 | — | 10 | 1 | no | — |
| 384 | C2×Dic3 | — | 20 | 4 | no | — |
| 385 | C2×Dic3 | — | 20 | 2 | no | — |
| 386 | D12 | — | 10 | 2 | no | — |
| 387 | D12 | — | 20 | 2 | no | — |
| 388 | C4×D3 | — | 5 | 4 | no | — |
| 389 | C4×D3 | — | 20 | 2 | no | — |
| 390 | C4×D3 | — | 20 | 2 | no | — |
| 391 | Dic6 | — | 2 | 2 | no | — |
| 392 | Dic6 | — | 2 | 2 | no | — |
| 393 | Dic6 | — | 10 | 2 | no | — |
| 394 | C3×C8 | — | 5 | 4 | no | — |
| 395 | C3⋊C8 | D4×D5 | 1 | 4 | yes | — |
| 396 | C22×C5 | — | 4 | 1 | no | — |
| 397 | C22×C5 | — | 4 | 2 | no | — |
| 398 | C22×C5 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 399 | C2×D5 | — | 3 | 2 | no | — |
| 400 | C2×D5 | — | 4 | 2 | no | — |
| 401 | C2×D5 | — | 4 | 4 | no | — |
| 402 | C2×D5 | — | 6 | 2 | no | — |
| 403 | C2×D5 | — | 12 | 1 | no | — |
| 404 | C2×D5 | — | 12 | 2 | no | — |
| 405 | C4×C5 | — | 2 | 2 | no | — |
| 406 | C4×C5 | — | 4 | 1 | no | — |
| 407 | C4×C5 | — | 12 | 2 | no | — |
| 408 | C4×C5 | C2×D3×D4 | 1 | 2 | yes | — |
| 409 | Dic5 | — | 3 | 2 | no | — |
| 410 | Dic5 | — | 6 | 2 | no | — |
| 411 | Dic5 | — | 12 | 1 | no | — |
| 412 | #41 | — | 30 | 4 | no | — |
| 413 | #41 | — | 30 | 4 | no | — |
| 414 | #41 | — | 30 | 4 | no | — |
| 415 | #41 | — | 30 | 4 | no | — |
| 416 | C2×Q8 | — | 3 | 2 | no | — |
| 417 | C2×Q8 | — | 15 | 1 | no | — |
| 418 | C2×Q8 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 419 | C2×D4 | — | 5 | 2 | no | — |
| 420 | C2×D4 | — | 10 | 2 | no | — |
| 421 | C2×D4 | — | 15 | 1 | no | — |
| 422 | C2×D4 | — | 30 | 1 | no | — |
| 423 | C2×D4 | — | 30 | 2 | no | — |
| 424 | C2×D4 | — | 30 | 2 | no | — |
| 425 | C2×D4 | — | 30 | 1 | no | — |
| 426 | C2×D4 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 427 | C22×C4 | — | 15 | 1 | no | — |
| 428 | C22×C4 | — | 15 | 2 | no | — |
| 429 | C22×C4 | — | 30 | 1 | no | — |
| 430 | C22×C4 | — | 30 | 2 | no | — |
| 431 | C22×C4 | — | 30 | 1 | no | — |
| 432 | Q16 | — | 6 | 4 | no | — |
| 433 | Q16 | — | 30 | 4 | no | — |
| 434 | SD16 | — | 6 | 4 | no | — |
| 435 | SD16 | — | 10 | 4 | no | — |
| 436 | SD16 | — | 30 | 4 | no | — |
| 437 | SD16 | — | 30 | 4 | no | — |
| 438 | D8 | — | 10 | 4 | no | — |
| 439 | D8 | — | 30 | 4 | no | — |
| 440 | C2×C8 | — | 3 | 2 | no | — |
| 441 | C2×C8 | — | 5 | 2 | no | — |
| 442 | C2×C8 | — | 15 | 8 | no | — |
| 443 | C4⋊C4 | — | 6 | 2 | no | — |
| 444 | C4⋊C4 | — | 30 | 2 | no | — |
| 445 | C22⋊C4 | — | 2 | 2 | no | — |
| 446 | C22⋊C4 | — | 30 | 4 | no | — |
| 447 | C22⋊C4 | — | 30 | 2 | no | — |
| 448 | C42 | — | 15 | 2 | no | — |
| 449 | C42 | — | 15 | 1 | no | — |
| 450 | C42 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 451 | C3×C5 | #3150 | 1 | 1 | yes | characteristic, complemented, Hall |
| 452 | C22×C3 | — | 4 | 1 | no | — |
| 453 | C22×C3 | — | 4 | 2 | no | — |
| 454 | C22×C3 | — | 20 | 2 | no | — |
| 455 | C22×C3 | — | 20 | 4 | no | — |
| 456 | C22×C3 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 457 | C2×D3 | — | 5 | 2 | no | — |
| 458 | C2×D3 | — | 10 | 2 | no | — |
| 459 | C2×D3 | — | 20 | 1 | no | — |
| 460 | C2×D3 | — | 20 | 2 | no | — |
| 461 | C3×C4 | — | 2 | 2 | no | — |
| 462 | C3×C4 | — | 4 | 1 | no | — |
| 463 | C3×C4 | C2×D4×D5 | 1 | 2 | yes | — |
| 464 | Dic3 | — | 4 | 2 | no | — |
| 465 | Dic3 | — | 5 | 2 | no | — |
| 466 | Dic3 | — | 10 | 2 | no | — |
| 467 | Dic3 | — | 20 | 1 | no | — |
| 468 | C2×C5 | — | 8 | 1 | no | — |
| 469 | C2×C5 | D3×#127 | 1 | 1 | yes | characteristic |
| 470 | C2×C5 | #5773 | 1 | 2 | yes | — |
| 471 | D5 | — | 6 | 2 | no | — |
| 472 | D5 | — | 8 | 2 | no | — |
| 473 | D5 | — | 24 | 1 | no | — |
| 474 | C23 | — | 2 | 1 | no | — |
| 475 | C23 | — | 10 | 2 | no | — |
| 476 | C23 | — | 15 | 1 | no | — |
| 477 | C23 | — | 30 | 1 | no | — |
| 478 | Q8 | — | 2 | 2 | no | — |
| 479 | Q8 | — | 6 | 2 | no | — |
| 480 | Q8 | — | 6 | 2 | no | — |
| 481 | Q8 | — | 30 | 2 | no | — |
| 482 | D4 | — | 2 | 2 | no | — |
| 483 | D4 | — | 10 | 2 | no | — |
| 484 | D4 | — | 10 | 2 | no | — |
| 485 | D4 | — | 20 | 4 | no | — |
| 486 | D4 | — | 30 | 2 | no | — |
| 487 | D4 | — | 60 | 2 | no | — |
| 488 | D4 | — | 60 | 4 | no | — |
| 489 | D4 | — | 60 | 4 | no | — |
| 490 | D4 | — | 60 | 2 | no | — |
| 491 | C2×C4 | — | 2 | 1 | no | — |
| 492 | C2×C4 | — | 6 | 2 | no | — |
| 493 | C2×C4 | — | 15 | 1 | no | — |
| 494 | C2×C4 | — | 15 | 4 | no | — |
| 495 | C2×C4 | — | 15 | 2 | no | — |
| 496 | C2×C4 | — | 30 | 1 | no | — |
| 497 | C2×C4 | — | 60 | 2 | no | — |
| 498 | C2×C4 | — | 60 | 2 | no | — |
| 499 | C2×C4 | — | 60 | 4 | no | — |
| 500 | C2×C4 | — | 60 | 2 | no | — |
| 501 | C2×C4 | #6790 | 1 | 2 | yes | — |
| 502 | C2×C4 | C22×D3×D5 | 1 | 1 | yes | characteristic |
| 503 | C8 | — | 3 | 4 | no | — |
| 504 | C8 | — | 5 | 4 | no | — |
| 505 | C2×C3 | — | 8 | 1 | no | — |
| 506 | C2×C3 | — | 40 | 2 | no | — |
| 507 | C2×C3 | D5×#127 | 1 | 1 | yes | characteristic |
| 508 | C2×C3 | #66111 | 1 | 2 | yes | — |
| 509 | D3 | — | 10 | 2 | no | — |
| 510 | D3 | — | 40 | 1 | no | — |
| 511 | C5 | #81844 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 512 | C22 | — | 4 | 1 | no | — |
| 513 | C22 | — | 4 | 2 | no | — |
| 514 | C22 | — | 15 | 2 | no | — |
| 515 | C22 | — | 20 | 2 | no | — |
| 516 | C22 | — | 20 | 4 | no | — |
| 517 | C22 | — | 30 | 2 | no | — |
| 518 | C22 | — | 60 | 1 | no | — |
| 519 | C22 | — | 60 | 2 | no | — |
| 520 | C22 | C2×#6790 | 1 | 1 | yes | characteristic |
| 521 | C4 | — | 2 | 2 | no | — |
| 522 | C4 | — | 4 | 1 | no | — |
| 523 | C4 | — | 12 | 2 | no | — |
| 524 | C4 | — | 15 | 2 | no | — |
| 525 | C4 | — | 30 | 2 | no | — |
| 526 | C4 | — | 60 | 1 | no | — |
| 527 | C4 | D3×D4×D5 | 1 | 2 | yes | — |
| 528 | C3 | #10613600 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 529 | C2 | — | 8 | 1 | no | — |
| 530 | C2 | — | 30 | 2 | no | — |
| 531 | C2 | — | 40 | 2 | no | — |
| 532 | C2 | — | 120 | 1 | no | — |
| 533 | C2 | #11755052 | 1 | 1 | yes | characteristic |
| 534 | C2 | #11755349 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11756427 | C2 | semidirect |
| 2. C2×#91521 | C2 | semidirect |
| 3. C2×#91497 | C2 | semidirect |
| 4. #11752556 | C2 | semidirect |
| 5. C5×#5060 | C2 | semidirect |
| 6. C3×#65347 | C2 | semidirect |
| 7. #11749320 | C2 | semidirect |
| 8. #11749073 | C2 | semidirect |
| 9. #11747097 | C2 | semidirect |
| 10. #11747073 | C2 | semidirect |
| 11. #11746983 | C2 | semidirect |
| 51. #65347 | D3 | semidirect |
| 92. #6648 | D4 | semidirect |
| 101. #5060 | D5 | semidirect |
| 451. C3×C5 | #3150 | semidirect |
| 511. C5 | #81844 | semidirect |
| 528. C3 | #10613600 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756427 | 2 |
| C2×#91521 | 2 |
| C2×#91497 | 2 |
| #11752556 | 2 |
| C5×#5060 | 2 |
| C3×#65347 | 2 |
| #11749320 | 2 |
| #11749073 | 2 |
| #11747097 | 2 |
| #11747073 | 2 |
| #11746983 | 2 |
| #10613600 | 3 |
| #81844 | 5 |