Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
460 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11752656 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11750813 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11747032 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11746911 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C5×#4464 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C3×#64685 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11745848 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10599144 | — | 3 | 1 | no | maximal, Hall |
| 9 | C2×D120 | — | 2 | 1 | no | — |
| 10 | C2×#6706 | — | 2 | 1 | no | — |
| 11 | #91764 | C22 | 1 | 1 | yes | characteristic |
| 12 | #91763 | C22 | 1 | 1 | yes | characteristic |
| 13 | C5×#875 | C22 | 1 | 1 | yes | characteristic |
| 14 | C3×#4016 | C22 | 1 | 1 | yes | characteristic |
| 15 | #91438 | — | 2 | 1 | no | — |
| 16 | #91432 | — | 2 | 1 | no | — |
| 17 | #91427 | — | 2 | 1 | no | — |
| 18 | #91424 | — | 2 | 1 | no | — |
| 19 | #91420 | — | 2 | 1 | no | — |
| 20 | #91416 | — | 2 | 1 | no | — |
| 21 | C2×#6660 | — | 2 | 1 | no | — |
| 22 | C2×#6654 | — | 2 | 1 | no | — |
| 23 | C3×C5×#97 | C22 | 1 | 1 | yes | characteristic |
| 24 | C5×#803 | C22 | 1 | 1 | yes | characteristic |
| 25 | C3×#3935 | C22 | 1 | 1 | yes | characteristic |
| 26 | #90968 | — | 2 | 1 | no | — |
| 27 | #90968 | — | 2 | 1 | no | — |
| 28 | #68370 | — | 5 | 1 | no | maximal, Hall |
| 29 | #66018 | — | 3 | 1 | no | — |
| 30 | #65347 | — | 3 | 1 | no | — |
| 31 | #65002 | — | 3 | 1 | no | — |
| 32 | #65001 | — | 3 | 1 | no | — |
| 33 | C5×#329 | — | 3 | 1 | no | — |
| 34 | #64685 | D3 | 1 | 1 | yes | characteristic, complemented |
| 35 | #64684 | — | 3 | 1 | no | — |
| 36 | C2×D60 | — | 2 | 1 | no | — |
| 37 | C2×D60 | — | 2 | 1 | no | — |
| 38 | C2×D60 | — | 2 | 1 | no | — |
| 39 | C2×D60 | D4 | 1 | 1 | yes | characteristic |
| 40 | C2×Dic30 | D4 | 1 | 1 | yes | characteristic |
| 41 | C2×C5×D12 | D4 | 1 | 1 | yes | characteristic |
| 42 | C2×C5×Dic6 | D4 | 1 | 1 | yes | characteristic |
| 43 | C2×#1203 | — | 2 | 1 | no | — |
| 44 | C2×#1203 | — | 2 | 1 | no | — |
| 45 | C2×#1200 | — | 2 | 1 | no | — |
| 46 | C2×D3×Dic5 | — | 2 | 1 | no | — |
| 47 | C2×C3×C5×C8 | — | 2 | 1 | no | — |
| 48 | C3×C42×C5 | C23 | 1 | 1 | yes | characteristic |
| 49 | #6714 | — | 2 | 1 | no | — |
| 50 | #6714 | — | 2 | 1 | no | — |
| 51 | D120 | — | 4 | 2 | no | — |
| 52 | #6706 | — | 4 | 2 | no | — |
| 53 | C5×(C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 54 | C5×(C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 55 | C2×C5×C3⋊C8 | — | 2 | 1 | no | — |
| 56 | C3×C4⋊Dic5 | D4 | 1 | 1 | yes | characteristic |
| 57 | C3×C4⋊Dic5 | D4 | 1 | 1 | yes | characteristic |
| 58 | C3×#683 | — | 2 | 1 | no | — |
| 59 | C3×#683 | — | 2 | 1 | no | — |
| 60 | C2×C3×#168 | — | 2 | 1 | no | — |
| 61 | Dic3⋊Dic5 | — | 2 | 1 | no | — |
| 62 | #6669 | — | 2 | 1 | no | — |
| 63 | #6667 | — | 2 | 1 | no | — |
| 64 | (C2×D3)⋊Dic5 | — | 2 | 1 | no | — |
| 65 | #6660 | — | 4 | 2 | no | — |
| 66 | #6654 | — | 4 | 2 | no | — |
| 67 | #5700 | — | 5 | 1 | no | — |
| 68 | #5067 | — | 5 | 1 | no | — |
| 69 | #4712 | — | 5 | 1 | no | — |
| 70 | #4712 | — | 5 | 1 | no | — |
| 71 | C3×#330 | — | 5 | 1 | no | — |
| 72 | #4464 | — | 5 | 1 | no | — |
| 73 | #4464 | D5 | 1 | 1 | yes | characteristic, complemented |
| 74 | C5×#124 | — | 3 | 1 | no | — |
| 75 | #4092 | — | 6 | 1 | no | — |
| 76 | C2×#688 | — | 6 | 1 | no | — |
| 77 | #4085 | — | 6 | 1 | no | — |
| 78 | C2×#686 | — | 6 | 1 | no | — |
| 79 | C2×D40 | — | 6 | 1 | no | — |
| 80 | C2×#677 | — | 6 | 1 | no | — |
| 81 | #4032 | — | 6 | 1 | no | — |
| 82 | #4030 | — | 6 | 1 | no | — |
| 83 | #4029 | — | 6 | 1 | no | — |
| 84 | #4024 | — | 6 | 1 | no | — |
| 85 | #4021 | — | 3 | 1 | no | — |
| 86 | #4020 | — | 3 | 1 | no | — |
| 87 | #4016 | C2×D3 | 1 | 1 | yes | characteristic |
| 88 | C5×#97 | — | 3 | 1 | no | — |
| 89 | C5×#97 | C2×D3 | 1 | 1 | yes | characteristic |
| 90 | #3953 | — | 6 | 1 | no | — |
| 91 | #3953 | — | 6 | 1 | no | — |
| 92 | #3935 | C2×D3 | 1 | 1 | yes | characteristic |
| 93 | #1656 | — | 15 | 1 | no | Sylow |
| 94 | C22×D15 | — | 2 | 1 | no | — |
| 95 | C22×D15 | — | 4 | 1 | no | — |
| 96 | C22×C5×D3 | — | 2 | 1 | no | — |
| 97 | C2×C3×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 98 | C2×C3×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 99 | C2×C3×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 100 | C2×Dic15 | — | 2 | 1 | no | — |
| 101 | D60 | — | 4 | 1 | no | — |
| 102 | D60 | — | 4 | 1 | no | — |
| 103 | D60 | — | 4 | 1 | no | — |
| 104 | D60 | — | 4 | 1 | no | — |
| 105 | D60 | — | 4 | 2 | no | — |
| 106 | D60 | — | 4 | 1 | no | — |
| 107 | Dic30 | — | 4 | 1 | no | — |
| 108 | C2×C5×Dic3 | — | 2 | 1 | no | — |
| 109 | C5×D12 | — | 4 | 1 | no | — |
| 110 | C5×Dic6 | — | 4 | 1 | no | — |
| 111 | C2×C3×Dic5 | — | 2 | 1 | no | — |
| 112 | C2×C3×Dic5 | — | 2 | 1 | no | — |
| 113 | #1203 | — | 8 | 1 | no | — |
| 114 | #1203 | — | 8 | 1 | no | — |
| 115 | #1200 | — | 8 | 1 | no | — |
| 116 | D3×Dic5 | — | 8 | 1 | no | — |
| 117 | C3×C5×C8 | — | 2 | 2 | no | — |
| 118 | C3×#168 | — | 2 | 2 | no | — |
| 119 | C5×C3⋊C8 | — | 4 | 1 | no | — |
| 120 | C3×#125 | — | 5 | 1 | no | — |
| 121 | C2×D24 | — | 10 | 1 | no | — |
| 122 | C2×D24 | — | 10 | 1 | no | — |
| 123 | C2×#204 | — | 10 | 1 | no | — |
| 124 | C2×#204 | — | 10 | 1 | no | — |
| 125 | #896 | — | 10 | 1 | no | — |
| 126 | #896 | — | 10 | 1 | no | — |
| 127 | #895 | — | 10 | 1 | no | — |
| 128 | #895 | — | 10 | 1 | no | — |
| 129 | #894 | — | 10 | 1 | no | — |
| 130 | #894 | — | 10 | 1 | no | — |
| 131 | #875 | — | 5 | 1 | no | — |
| 132 | #875 | C2×D5 | 1 | 1 | yes | characteristic |
| 133 | #874 | — | 5 | 1 | no | — |
| 134 | C3×#97 | — | 5 | 1 | no | — |
| 135 | C3×#97 | C2×D5 | 1 | 1 | yes | characteristic |
| 136 | #809 | — | 10 | 1 | no | — |
| 137 | #809 | — | 10 | 1 | no | — |
| 138 | #803 | C2×D5 | 1 | 1 | yes | characteristic |
| 139 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 140 | C2×C5×D4 | — | 3 | 1 | no | — |
| 141 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 142 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 143 | C22×Dic5 | — | 6 | 1 | no | — |
| 144 | C2×D20 | — | 3 | 1 | no | — |
| 145 | C2×D20 | — | 6 | 1 | no | — |
| 146 | C2×D20 | — | 6 | 1 | no | — |
| 147 | C2×D20 | — | 6 | 1 | no | — |
| 148 | C2×C4×D5 | — | 6 | 1 | no | — |
| 149 | C2×Dic10 | — | 3 | 1 | no | — |
| 150 | C2×C5×C8 | — | 2 | 1 | no | — |
| 151 | C2×C5×C8 | — | 6 | 1 | no | — |
| 152 | C5×C22⋊C4 | — | 6 | 1 | no | — |
| 153 | C5×C22⋊C4 | — | 6 | 1 | no | — |
| 154 | C42×C5 | C22×D3 | 1 | 1 | yes | characteristic |
| 155 | C22⋊Dic5 | — | 6 | 1 | no | — |
| 156 | #688 | — | 12 | 2 | no | — |
| 157 | #686 | — | 12 | 2 | no | — |
| 158 | #685 | — | 6 | 1 | no | — |
| 159 | #685 | — | 6 | 1 | no | — |
| 160 | #685 | — | 6 | 1 | no | — |
| 161 | C4⋊Dic5 | — | 6 | 1 | no | — |
| 162 | C4⋊Dic5 | D12 | 1 | 1 | yes | characteristic |
| 163 | C4⋊Dic5 | D12 | 1 | 1 | yes | characteristic |
| 164 | #683 | — | 2 | 1 | no | — |
| 165 | #683 | — | 2 | 1 | no | — |
| 166 | #683 | — | 6 | 1 | no | — |
| 167 | C2×#168 | — | 2 | 1 | no | — |
| 168 | D40 | — | 12 | 2 | no | — |
| 169 | #677 | — | 12 | 2 | no | — |
| 170 | #562 | — | 15 | 1 | no | — |
| 171 | #496 | — | 15 | 1 | no | — |
| 172 | #496 | — | 15 | 1 | no | — |
| 173 | #490 | — | 15 | 1 | no | — |
| 174 | #330 | — | 5 | 1 | no | — |
| 175 | #329 | — | 3 | 1 | no | — |
| 176 | #329 | — | 15 | 1 | no | — |
| 177 | C22×C3×C5 | #120 | 1 | 1 | yes | characteristic |
| 178 | C2×D15 | — | 4 | 1 | no | — |
| 179 | C2×D15 | — | 4 | 1 | no | — |
| 180 | C2×D15 | — | 4 | 1 | no | — |
| 181 | C2×D15 | — | 8 | 1 | no | — |
| 182 | C2×D15 | — | 8 | 1 | no | — |
| 183 | C2×D15 | — | 8 | 1 | no | — |
| 184 | C2×C5×D3 | — | 4 | 1 | no | — |
| 185 | C2×C5×D3 | — | 4 | 1 | no | — |
| 186 | C2×C5×D3 | — | 4 | 1 | no | — |
| 187 | C3×C4×C5 | — | 2 | 1 | no | — |
| 188 | C3×C4×C5 | — | 2 | 1 | no | — |
| 189 | C3×C4×C5 | — | 2 | 1 | no | — |
| 190 | Dic15 | — | 4 | 1 | no | — |
| 191 | C3×Dic5 | — | 4 | 1 | no | — |
| 192 | C3×Dic5 | — | 4 | 1 | no | — |
| 193 | C5×Dic3 | — | 4 | 1 | no | — |
| 194 | C2×D12 | — | 5 | 1 | no | — |
| 195 | C2×D12 | — | 10 | 1 | no | — |
| 196 | C2×D12 | — | 10 | 1 | no | — |
| 197 | C2×D12 | — | 10 | 1 | no | — |
| 198 | C2×D12 | — | 10 | 1 | no | — |
| 199 | C2×D12 | — | 10 | 1 | no | — |
| 200 | C2×D12 | D20 | 1 | 1 | yes | characteristic |
| 201 | C2×C4×D3 | — | 10 | 1 | no | — |
| 202 | C2×C4×D3 | — | 10 | 1 | no | — |
| 203 | C2×Dic6 | — | 5 | 1 | no | — |
| 204 | C2×Dic6 | D20 | 1 | 1 | yes | characteristic |
| 205 | C2×C3×C8 | — | 2 | 1 | no | — |
| 206 | C2×C3×C8 | — | 10 | 1 | no | — |
| 207 | C3×C4⋊C4 | — | 5 | 1 | no | — |
| 208 | C3×C4⋊C4 | — | 5 | 1 | no | — |
| 209 | C3×C4⋊C4 | — | 10 | 1 | no | — |
| 210 | C3×C4⋊C4 | — | 10 | 1 | no | — |
| 211 | C3×C42 | C22×D5 | 1 | 1 | yes | characteristic |
| 212 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 213 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 214 | (C2×D3)⋊C4 | — | 10 | 1 | no | — |
| 215 | (C2×D3)⋊C4 | — | 10 | 1 | no | — |
| 216 | (C2×D3)⋊C4 | — | 10 | 1 | no | — |
| 217 | (C2×D3)⋊C4 | — | 10 | 1 | no | — |
| 218 | Dic3⋊C4 | — | 10 | 1 | no | — |
| 219 | Dic3⋊C4 | — | 10 | 1 | no | — |
| 220 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 221 | D24 | — | 20 | 2 | no | — |
| 222 | D24 | — | 20 | 2 | no | — |
| 223 | #204 | — | 20 | 2 | no | — |
| 224 | #204 | — | 20 | 2 | no | — |
| 225 | C23×C5 | — | 6 | 1 | no | — |
| 226 | C22×D5 | — | 6 | 1 | no | — |
| 227 | C22×D5 | — | 12 | 1 | no | — |
| 228 | C5×Q8 | — | 12 | 1 | no | — |
| 229 | C5×D4 | — | 12 | 1 | no | — |
| 230 | C2×C4×C5 | — | 6 | 1 | no | — |
| 231 | C2×C4×C5 | C2×D12 | 1 | 1 | yes | characteristic |
| 232 | C2×C4×C5 | D3×D4 | 1 | 1 | yes | characteristic |
| 233 | C2×C4×C5 | D3×D4 | 1 | 1 | yes | characteristic |
| 234 | C22⋊D5 | — | 24 | 1 | no | — |
| 235 | C22⋊D5 | — | 24 | 1 | no | — |
| 236 | C2×Dic5 | — | 2 | 1 | no | — |
| 237 | C2×Dic5 | — | 2 | 1 | no | — |
| 238 | C2×Dic5 | — | 6 | 1 | no | — |
| 239 | C2×Dic5 | — | 24 | 1 | no | — |
| 240 | D20 | — | 12 | 1 | no | — |
| 241 | D20 | — | 12 | 1 | no | — |
| 242 | D20 | — | 12 | 1 | no | — |
| 243 | D20 | — | 12 | 1 | no | — |
| 244 | D20 | — | 12 | 1 | no | — |
| 245 | D20 | — | 12 | 2 | no | — |
| 246 | C4×D5 | — | 24 | 1 | no | — |
| 247 | Dic10 | — | 12 | 1 | no | — |
| 248 | C5×C8 | — | 2 | 2 | no | — |
| 249 | C5×C8 | — | 12 | 1 | no | — |
| 250 | #168 | — | 2 | 2 | no | — |
| 251 | C2×SD16 | — | 30 | 1 | no | — |
| 252 | C2×SD16 | — | 30 | 1 | no | — |
| 253 | C2×D8 | — | 30 | 1 | no | — |
| 254 | C2×D8 | — | 30 | 1 | no | — |
| 255 | #127 | — | 15 | 1 | no | — |
| 256 | #125 | — | 5 | 1 | no | — |
| 257 | #124 | — | 3 | 1 | no | — |
| 258 | #124 | — | 15 | 1 | no | — |
| 259 | #123 | — | 30 | 1 | no | — |
| 260 | #123 | — | 30 | 1 | no | — |
| 261 | C22⋊Q8 | — | 30 | 1 | no | — |
| 262 | C22⋊Q8 | — | 30 | 1 | no | — |
| 263 | #121 | — | 30 | 1 | no | — |
| 264 | #121 | — | 30 | 1 | no | — |
| 265 | #102 | — | 30 | 1 | no | — |
| 266 | #102 | — | 30 | 1 | no | — |
| 267 | #97 | — | 3 | 1 | no | — |
| 268 | #97 | — | 5 | 1 | no | — |
| 269 | #97 | D3×D5 | 1 | 1 | yes | characteristic |
| 270 | C2×C3×C5 | #453 | 1 | 1 | yes | characteristic |
| 271 | C2×C3×C5 | #453 | 1 | 1 | yes | characteristic |
| 272 | C2×C3×C5 | #454 | 1 | 1 | yes | characteristic |
| 273 | D15 | — | 8 | 1 | no | — |
| 274 | D15 | — | 16 | 1 | no | — |
| 275 | C5×D3 | — | 8 | 1 | no | — |
| 276 | C22×D3 | — | 2 | 1 | no | — |
| 277 | C22×D3 | — | 10 | 1 | no | — |
| 278 | C22×D3 | — | 20 | 1 | no | — |
| 279 | C2×C3×C4 | — | 10 | 1 | no | — |
| 280 | C2×C3×C4 | — | 10 | 1 | no | — |
| 281 | C2×C3×C4 | C2×D20 | 1 | 1 | yes | characteristic |
| 282 | C2×C3×C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 283 | C2×C3×C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 284 | C2×Dic3 | — | 2 | 1 | no | — |
| 285 | C2×Dic3 | — | 10 | 1 | no | — |
| 286 | D12 | — | 4 | 1 | no | — |
| 287 | D12 | — | 20 | 1 | no | — |
| 288 | D12 | — | 20 | 1 | no | — |
| 289 | D12 | — | 20 | 1 | no | — |
| 290 | D12 | — | 20 | 1 | no | — |
| 291 | D12 | — | 20 | 1 | no | — |
| 292 | D12 | — | 20 | 2 | no | — |
| 293 | D12 | — | 40 | 1 | no | — |
| 294 | D12 | — | 40 | 1 | no | — |
| 295 | C4×D3 | — | 40 | 1 | no | — |
| 296 | C4×D3 | — | 40 | 1 | no | — |
| 297 | Dic6 | — | 4 | 1 | no | — |
| 298 | Dic6 | — | 20 | 1 | no | — |
| 299 | C3×C8 | — | 2 | 2 | no | — |
| 300 | C3×C8 | — | 10 | 2 | no | — |
| 301 | C3⋊C8 | — | 4 | 1 | no | — |
| 302 | C22×C5 | — | 12 | 1 | no | — |
| 303 | C22×C5 | — | 12 | 1 | no | — |
| 304 | C22×C5 | — | 12 | 1 | no | — |
| 305 | C22×C5 | #882 | 1 | 1 | yes | characteristic |
| 306 | C2×D5 | — | 12 | 1 | no | — |
| 307 | C2×D5 | — | 12 | 1 | no | — |
| 308 | C2×D5 | — | 12 | 1 | no | — |
| 309 | C2×D5 | — | 24 | 1 | no | — |
| 310 | C2×D5 | — | 24 | 1 | no | — |
| 311 | C2×D5 | — | 24 | 1 | no | — |
| 312 | C4×C5 | — | 2 | 1 | no | — |
| 313 | C4×C5 | — | 2 | 1 | no | — |
| 314 | C4×C5 | — | 2 | 1 | no | — |
| 315 | C4×C5 | — | 12 | 1 | no | — |
| 316 | Dic5 | — | 4 | 1 | no | — |
| 317 | Dic5 | — | 4 | 1 | no | — |
| 318 | Dic5 | — | 12 | 1 | no | — |
| 319 | C2×Q8 | — | 3 | 1 | no | — |
| 320 | C2×Q8 | — | 15 | 1 | no | — |
| 321 | C2×D4 | — | 3 | 1 | no | — |
| 322 | C2×D4 | — | 15 | 1 | no | — |
| 323 | C2×D4 | — | 30 | 1 | no | — |
| 324 | C2×D4 | — | 30 | 1 | no | — |
| 325 | C2×D4 | — | 30 | 1 | no | — |
| 326 | C2×D4 | — | 30 | 1 | no | — |
| 327 | C2×D4 | — | 30 | 1 | no | — |
| 328 | C22×C4 | — | 30 | 1 | no | — |
| 329 | C22×C4 | — | 30 | 1 | no | — |
| 330 | SD16 | — | 60 | 2 | no | — |
| 331 | SD16 | — | 60 | 2 | no | — |
| 332 | D8 | — | 60 | 2 | no | — |
| 333 | D8 | — | 60 | 2 | no | — |
| 334 | C2×C8 | — | 2 | 1 | no | — |
| 335 | C2×C8 | — | 6 | 1 | no | — |
| 336 | C2×C8 | — | 10 | 1 | no | — |
| 337 | C4⋊C4 | — | 5 | 1 | no | — |
| 338 | C4⋊C4 | — | 5 | 1 | no | — |
| 339 | C4⋊C4 | — | 10 | 1 | no | — |
| 340 | C4⋊C4 | — | 10 | 1 | no | — |
| 341 | C4⋊C4 | — | 30 | 1 | no | — |
| 342 | C4⋊C4 | — | 30 | 1 | no | — |
| 343 | C22⋊C4 | — | 6 | 1 | no | — |
| 344 | C22⋊C4 | — | 6 | 1 | no | — |
| 345 | C22⋊C4 | — | 30 | 1 | no | — |
| 346 | C22⋊C4 | — | 30 | 1 | no | — |
| 347 | C22⋊C4 | — | 30 | 1 | no | — |
| 348 | C22⋊C4 | — | 30 | 1 | no | — |
| 349 | C42 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 350 | C3×C5 | #1656 | 1 | 1 | yes | characteristic, complemented, Hall |
| 351 | C22×C3 | #4028 | 1 | 1 | yes | characteristic |
| 352 | C2×D3 | — | 4 | 1 | no | — |
| 353 | C2×D3 | — | 4 | 1 | no | — |
| 354 | C2×D3 | — | 4 | 1 | no | — |
| 355 | C2×D3 | — | 20 | 1 | no | — |
| 356 | C2×D3 | — | 20 | 1 | no | — |
| 357 | C2×D3 | — | 20 | 1 | no | — |
| 358 | C2×D3 | — | 40 | 1 | no | — |
| 359 | C2×D3 | — | 40 | 1 | no | — |
| 360 | C2×D3 | — | 40 | 1 | no | — |
| 361 | C3×C4 | — | 2 | 1 | no | — |
| 362 | C3×C4 | — | 2 | 1 | no | — |
| 363 | C3×C4 | — | 2 | 1 | no | — |
| 364 | C3×C4 | — | 20 | 1 | no | — |
| 365 | C3×C4 | — | 20 | 1 | no | — |
| 366 | Dic3 | — | 4 | 1 | no | — |
| 367 | Dic3 | — | 20 | 1 | no | — |
| 368 | C2×C5 | — | 24 | 1 | no | — |
| 369 | C2×C5 | #4753 | 1 | 1 | yes | characteristic |
| 370 | C2×C5 | #4822 | 1 | 1 | yes | characteristic |
| 371 | C2×C5 | #4822 | 1 | 1 | yes | characteristic |
| 372 | D5 | — | 24 | 1 | no | — |
| 373 | D5 | — | 48 | 1 | no | — |
| 374 | C23 | — | 6 | 1 | no | — |
| 375 | C23 | — | 30 | 1 | no | — |
| 376 | C23 | — | 60 | 1 | no | — |
| 377 | Q8 | — | 12 | 1 | no | — |
| 378 | Q8 | — | 60 | 1 | no | — |
| 379 | D4 | — | 12 | 1 | no | — |
| 380 | D4 | — | 60 | 1 | no | — |
| 381 | D4 | — | 60 | 1 | no | — |
| 382 | D4 | — | 60 | 1 | no | — |
| 383 | D4 | — | 60 | 1 | no | — |
| 384 | D4 | — | 60 | 1 | no | — |
| 385 | D4 | — | 60 | 2 | no | — |
| 386 | D4 | — | 120 | 1 | no | — |
| 387 | D4 | — | 120 | 1 | no | — |
| 388 | C2×C4 | — | 6 | 1 | no | — |
| 389 | C2×C4 | — | 10 | 1 | no | — |
| 390 | C2×C4 | — | 10 | 1 | no | — |
| 391 | C2×C4 | — | 30 | 1 | no | — |
| 392 | C2×C4 | — | 120 | 1 | no | — |
| 393 | C2×C4 | — | 120 | 1 | no | — |
| 394 | C2×C4 | D5×D12 | 1 | 1 | yes | characteristic |
| 395 | C2×C4 | D3×D20 | 1 | 1 | yes | characteristic |
| 396 | C2×C4 | #6790 | 1 | 1 | yes | characteristic |
| 397 | C8 | — | 2 | 2 | no | — |
| 398 | C8 | — | 10 | 2 | no | — |
| 399 | C8 | — | 12 | 1 | no | — |
| 400 | C2×C3 | #65036 | 1 | 1 | yes | characteristic |
| 401 | C2×C3 | #65111 | 1 | 1 | yes | characteristic |
| 402 | C2×C3 | #65116 | 1 | 1 | yes | characteristic |
| 403 | D3 | — | 8 | 1 | no | — |
| 404 | D3 | — | 40 | 1 | no | — |
| 405 | D3 | — | 80 | 1 | no | — |
| 406 | C5 | #68370 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 407 | C22 | — | 12 | 1 | no | — |
| 408 | C22 | — | 12 | 1 | no | — |
| 409 | C22 | — | 12 | 1 | no | — |
| 410 | C22 | — | 60 | 1 | no | — |
| 411 | C22 | — | 60 | 1 | no | — |
| 412 | C22 | — | 60 | 1 | no | — |
| 413 | C22 | — | 120 | 1 | no | — |
| 414 | C22 | — | 120 | 1 | no | — |
| 415 | C22 | — | 120 | 1 | no | — |
| 416 | C22 | #91476 | 1 | 1 | yes | characteristic |
| 417 | C4 | — | 2 | 1 | no | — |
| 418 | C4 | — | 2 | 1 | no | — |
| 419 | C4 | — | 2 | 1 | no | — |
| 420 | C4 | — | 12 | 1 | no | — |
| 421 | C4 | — | 20 | 1 | no | — |
| 422 | C4 | — | 20 | 1 | no | — |
| 423 | C4 | — | 60 | 1 | no | — |
| 424 | C3 | #10599144 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 425 | C2 | — | 24 | 1 | no | — |
| 426 | C2 | — | 120 | 1 | no | — |
| 427 | C2 | — | 240 | 1 | no | — |
| 428 | C2 | #11747118 | 1 | 1 | yes | characteristic |
| 429 | C2 | #11748249 | 1 | 1 | yes | characteristic |
| 430 | C2 | #11748263 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11752656 | C2 | semidirect |
| 2. #11750813 | C2 | semidirect |
| 3. #11747032 | C2 | semidirect |
| 4. #11746911 | C2 | semidirect |
| 5. C5×#4464 | C2 | semidirect |
| 6. C3×#64685 | C2 | semidirect |
| 7. #11745848 | C2 | semidirect |
| 34. #64685 | D3 | semidirect |
| 73. #4464 | D5 | semidirect |
| 350. C3×C5 | #1656 | semidirect |
| 406. C5 | #68370 | semidirect |
| 424. C3 | #10599144 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752656 | 2 |
| #11750813 | 2 |
| #11747032 | 2 |
| #11746911 | 2 |
| C5×#4464 | 2 |
| C3×#64685 | 2 |
| #11745848 | 2 |
| #10599144 | 3 |
| #68370 | 5 |