Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
524 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 524 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 | #11752772 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C5×#4712 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11747042 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11747031 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11746285 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C3×#64684 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11745847 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10602119 | — | 3 | 1 | no | maximal, Hall |
| 9 | #91764 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×C5×D24 | — | 2 | 1 | no | — |
| 11 | C2×C5×#204 | — | 2 | 1 | no | — |
| 12 | C5×#875 | C22 | 1 | 1 | yes | characteristic |
| 13 | C5×#874 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | C3×#4021 | C22 | 1 | 1 | yes | characteristic |
| 15 | #91476 | — | 2 | 1 | no | — |
| 16 | #91475 | — | 2 | 1 | no | — |
| 17 | #91474 | — | 2 | 1 | no | — |
| 18 | #91462 | — | 2 | 1 | no | — |
| 19 | #91455 | — | 2 | 1 | no | — |
| 20 | #91326 | — | 2 | 1 | no | — |
| 21 | C2×#6659 | — | 2 | 1 | no | — |
| 22 | C2×#6656 | — | 2 | 1 | no | — |
| 23 | C2×#6654 | — | 2 | 1 | no | — |
| 24 | C2×#6652 | — | 2 | 1 | no | — |
| 25 | C3×C5×#97 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | #91087 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | C3×#3935 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | #68350 | — | 5 | 1 | no | maximal, Hall |
| 29 | #66017 | — | 3 | 1 | no | — |
| 30 | C5×#496 | — | 3 | 1 | no | — |
| 31 | #65363 | — | 3 | 1 | no | — |
| 32 | #65363 | — | 3 | 1 | no | — |
| 33 | #64760 | — | 3 | 1 | no | — |
| 34 | #64684 | — | 3 | 1 | no | — |
| 35 | #64684 | D3 | 1 | 1 | yes | characteristic, complemented |
| 36 | C22×D3×D5 | — | 2 | 1 | no | — |
| 37 | C2×D60 | D4 | 1 | 1 | yes | characteristic |
| 38 | C2×Dic30 | D4 | 1 | 1 | yes | characteristic |
| 39 | C2×C5×D12 | — | 2 | 1 | no | — |
| 40 | C2×C5×D12 | — | 2 | 1 | no | — |
| 41 | C2×C5×D12 | — | 2 | 1 | no | — |
| 42 | C2×C5×D12 | D4 | 1 | 1 | yes | characteristic |
| 43 | C2×C5×Dic6 | D4 | 1 | 1 | yes | characteristic |
| 44 | C2×C3×D20 | D4 | 1 | 1 | yes | characteristic |
| 45 | C2×C3×Dic10 | D4 | 1 | 1 | yes | characteristic |
| 46 | C2×#1203 | — | 2 | 1 | no | — |
| 47 | C2×#1202 | — | 2 | 1 | no | — |
| 48 | C2×#1201 | — | 2 | 1 | no | — |
| 49 | C2×C3×C5×C8 | — | 2 | 1 | no | — |
| 50 | C3×C42×C5 | C23 | 1 | 1 | yes | characteristic |
| 51 | #6714 | — | 2 | 1 | no | — |
| 52 | #6714 | — | 2 | 1 | no | — |
| 53 | C2×C3⋊#168 | — | 2 | 1 | no | — |
| 54 | C5×(C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 55 | C5×(C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 56 | C5×D24 | — | 4 | 2 | no | — |
| 57 | C5×#204 | — | 4 | 2 | no | — |
| 58 | C3×#685 | — | 2 | 1 | no | — |
| 59 | C3×#685 | — | 2 | 1 | no | — |
| 60 | C2×C3×#168 | — | 2 | 1 | no | — |
| 61 | #6667 | — | 2 | 1 | no | — |
| 62 | (C2×D3)⋊Dic5 | — | 2 | 1 | no | — |
| 63 | #6665 | — | 2 | 1 | no | — |
| 64 | Dic3×Dic5 | — | 2 | 1 | no | — |
| 65 | #6659 | — | 4 | 2 | no | — |
| 66 | #6656 | — | 4 | 2 | no | — |
| 67 | #6654 | — | 4 | 2 | no | — |
| 68 | #6652 | — | 4 | 2 | no | — |
| 69 | #5683 | — | 5 | 1 | no | — |
| 70 | #5058 | — | 5 | 1 | no | — |
| 71 | #4712 | — | 5 | 1 | no | — |
| 72 | #4712 | D5 | 1 | 1 | yes | characteristic, complemented |
| 73 | C3×#329 | — | 5 | 1 | no | — |
| 74 | #4464 | — | 5 | 1 | no | — |
| 75 | #4464 | — | 5 | 1 | no | — |
| 76 | C2×C5×SD16 | — | 6 | 1 | no | — |
| 77 | C2×C5×D8 | — | 6 | 1 | no | — |
| 78 | C5×#127 | — | 3 | 1 | no | — |
| 79 | C5×#124 | — | 3 | 1 | no | — |
| 80 | #4093 | — | 6 | 1 | no | — |
| 81 | #4083 | — | 6 | 1 | no | — |
| 82 | C2×#687 | — | 6 | 1 | no | — |
| 83 | C2×#687 | — | 6 | 1 | no | — |
| 84 | C2×#686 | — | 6 | 1 | no | — |
| 85 | C2×#686 | — | 6 | 1 | no | — |
| 86 | #4031 | — | 6 | 1 | no | — |
| 87 | #4031 | — | 6 | 1 | no | — |
| 88 | #4028 | — | 6 | 1 | no | — |
| 89 | #4028 | — | 6 | 1 | no | — |
| 90 | #4021 | — | 3 | 1 | no | — |
| 91 | #4021 | C2×D3 | 1 | 1 | yes | characteristic |
| 92 | C5×#97 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 93 | #3935 | — | 3 | 1 | no | — |
| 94 | #3935 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 95 | #1655 | — | 15 | 1 | no | Sylow |
| 96 | C22×D15 | — | 2 | 1 | no | — |
| 97 | C22×C5×D3 | — | 2 | 1 | no | — |
| 98 | C22×C5×D3 | — | 4 | 1 | no | — |
| 99 | C22×C3×D5 | — | 2 | 1 | no | — |
| 100 | C2×D3×D5 | — | 8 | 1 | no | — |
| 101 | C2×D3×D5 | — | 8 | 1 | no | — |
| 102 | C2×D3×D5 | — | 8 | 1 | no | — |
| 103 | C2×C3×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 104 | C2×C3×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 105 | C2×C3×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 106 | C2×Dic15 | — | 2 | 1 | no | — |
| 107 | D60 | — | 4 | 1 | no | — |
| 108 | Dic30 | — | 4 | 1 | no | — |
| 109 | C2×C5×Dic3 | — | 2 | 1 | no | — |
| 110 | C5×D12 | — | 4 | 1 | no | — |
| 111 | C5×D12 | — | 4 | 1 | no | — |
| 112 | C5×D12 | — | 4 | 1 | no | — |
| 113 | C5×D12 | — | 4 | 1 | no | — |
| 114 | C5×D12 | — | 4 | 1 | no | — |
| 115 | C5×D12 | — | 4 | 1 | no | — |
| 116 | C5×D12 | — | 4 | 1 | no | — |
| 117 | C5×Dic6 | — | 4 | 1 | no | — |
| 118 | C2×C3×Dic5 | — | 2 | 1 | no | — |
| 119 | C3×D20 | — | 4 | 1 | no | — |
| 120 | C3×Dic10 | — | 4 | 1 | no | — |
| 121 | #1203 | — | 8 | 1 | no | — |
| 122 | #1202 | — | 8 | 1 | no | — |
| 123 | #1201 | — | 8 | 1 | no | — |
| 124 | C3×C5×C8 | — | 2 | 2 | no | — |
| 125 | C3⋊#168 | — | 2 | 2 | no | — |
| 126 | C3×#168 | — | 2 | 2 | no | — |
| 127 | C3×#124 | — | 5 | 1 | no | — |
| 128 | #947 | — | 10 | 1 | no | — |
| 129 | C2×#215 | — | 10 | 1 | no | — |
| 130 | #937 | — | 10 | 1 | no | — |
| 131 | C2×#213 | — | 10 | 1 | no | — |
| 132 | C2×D24 | — | 2 | 1 | no | — |
| 133 | C2×D24 | — | 10 | 1 | no | — |
| 134 | C2×#204 | — | 2 | 1 | no | — |
| 135 | C2×#204 | — | 10 | 1 | no | — |
| 136 | #885 | — | 10 | 1 | no | — |
| 137 | #885 | — | 10 | 1 | no | — |
| 138 | #882 | — | 10 | 1 | no | — |
| 139 | #882 | — | 10 | 1 | no | — |
| 140 | #875 | — | 5 | 1 | no | — |
| 141 | #875 | C2×D5 | 1 | 1 | yes | characteristic |
| 142 | #874 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 143 | C3×#97 | — | 5 | 1 | no | — |
| 144 | C3×#97 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 145 | #803 | — | 5 | 1 | no | — |
| 146 | C23×D5 | — | 6 | 1 | no | — |
| 147 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 148 | C2×C5×D4 | — | 3 | 1 | no | — |
| 149 | C2×C5×D4 | — | 6 | 1 | no | — |
| 150 | C2×C5×D4 | — | 6 | 1 | no | — |
| 151 | C2×C5×D4 | — | 6 | 1 | no | — |
| 152 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 153 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 154 | C2×D20 | — | 3 | 1 | no | — |
| 155 | C2×D20 | — | 6 | 1 | no | — |
| 156 | C2×D20 | D12 | 1 | 1 | yes | characteristic |
| 157 | C2×Dic10 | — | 3 | 1 | no | — |
| 158 | C2×Dic10 | D12 | 1 | 1 | yes | characteristic |
| 159 | C5×SD16 | — | 12 | 2 | no | — |
| 160 | C5×D8 | — | 12 | 2 | no | — |
| 161 | C2×C5×C8 | — | 2 | 1 | no | — |
| 162 | C5×C22⋊C4 | — | 6 | 1 | no | — |
| 163 | C5×C22⋊C4 | — | 6 | 1 | no | — |
| 164 | C42×C5 | C22×D3 | 1 | 1 | yes | characteristic |
| 165 | C22⋊Dic5 | — | 6 | 1 | no | — |
| 166 | #687 | — | 12 | 2 | no | — |
| 167 | #687 | — | 12 | 2 | no | — |
| 168 | #686 | — | 12 | 2 | no | — |
| 169 | #686 | — | 12 | 2 | no | — |
| 170 | #685 | — | 2 | 1 | no | — |
| 171 | #685 | — | 2 | 1 | no | — |
| 172 | #685 | — | 6 | 1 | no | — |
| 173 | #685 | — | 6 | 1 | no | — |
| 174 | #685 | — | 6 | 1 | no | — |
| 175 | #685 | — | 6 | 1 | no | — |
| 176 | C4×Dic5 | — | 6 | 1 | no | — |
| 177 | C2×#168 | — | 2 | 1 | no | — |
| 178 | C2×#168 | — | 6 | 1 | no | — |
| 179 | H(3,𝔽4) | — | 15 | 1 | no | — |
| 180 | #496 | — | 3 | 1 | no | — |
| 181 | #496 | — | 15 | 1 | no | — |
| 182 | #496 | — | 15 | 1 | no | — |
| 183 | #329 | — | 5 | 1 | no | — |
| 184 | #329 | — | 15 | 1 | no | — |
| 185 | #329 | — | 15 | 1 | no | — |
| 186 | C22×C3×C5 | #120 | 1 | 1 | yes | characteristic |
| 187 | C2×D15 | — | 4 | 1 | no | — |
| 188 | C2×D15 | — | 4 | 1 | no | — |
| 189 | C2×D15 | — | 4 | 1 | no | — |
| 190 | C2×C5×D3 | — | 4 | 1 | no | — |
| 191 | C2×C5×D3 | — | 4 | 1 | no | — |
| 192 | C2×C5×D3 | — | 4 | 1 | no | — |
| 193 | C2×C5×D3 | — | 8 | 1 | no | — |
| 194 | C2×C5×D3 | — | 8 | 1 | no | — |
| 195 | C2×C5×D3 | — | 8 | 1 | no | — |
| 196 | C2×C3×D5 | — | 4 | 1 | no | — |
| 197 | C2×C3×D5 | — | 4 | 1 | no | — |
| 198 | C2×C3×D5 | — | 4 | 1 | no | — |
| 199 | D3×D5 | — | 8 | 4 | no | — |
| 200 | C3×C4×C5 | — | 2 | 1 | no | — |
| 201 | C3×C4×C5 | — | 2 | 1 | no | — |
| 202 | C3×C4×C5 | — | 2 | 1 | no | — |
| 203 | Dic15 | — | 4 | 1 | no | — |
| 204 | C3×Dic5 | — | 4 | 1 | no | — |
| 205 | C5×Dic3 | — | 4 | 1 | no | — |
| 206 | C23×D3 | — | 10 | 1 | no | — |
| 207 | C2×C3×Q8 | — | 5 | 1 | no | — |
| 208 | C2×C3×D4 | — | 5 | 1 | no | — |
| 209 | C2×#67 | — | 10 | 1 | no | — |
| 210 | C2×#67 | — | 10 | 1 | no | — |
| 211 | C2×D12 | — | 2 | 1 | no | — |
| 212 | C2×D12 | — | 2 | 1 | no | — |
| 213 | C2×D12 | — | 2 | 1 | no | — |
| 214 | C2×D12 | — | 5 | 1 | no | — |
| 215 | C2×D12 | — | 10 | 1 | no | — |
| 216 | C2×D12 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 217 | C2×Dic6 | — | 5 | 1 | no | — |
| 218 | C2×Dic6 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 219 | C2×C3×C8 | — | 2 | 1 | no | — |
| 220 | C2×C3×C8 | — | 10 | 1 | no | — |
| 221 | C3×C22⋊C4 | — | 10 | 1 | no | — |
| 222 | C3×C22⋊C4 | — | 10 | 1 | no | — |
| 223 | C3×C42 | C22×D5 | 1 | 1 | yes | characteristic |
| 224 | #217 | — | 10 | 1 | no | — |
| 225 | #215 | — | 20 | 2 | no | — |
| 226 | #213 | — | 20 | 2 | no | — |
| 227 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 228 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 229 | (C2×D3)⋊C4 | — | 10 | 1 | no | — |
| 230 | (C2×D3)⋊C4 | — | 10 | 1 | no | — |
| 231 | (C2×D3)⋊C4 | — | 10 | 1 | no | — |
| 232 | (C2×D3)⋊C4 | — | 10 | 1 | no | — |
| 233 | C4×Dic3 | — | 10 | 1 | no | — |
| 234 | C2×C3⋊C8 | — | 10 | 1 | no | — |
| 235 | D24 | — | 4 | 2 | no | — |
| 236 | D24 | — | 20 | 2 | no | — |
| 237 | #204 | — | 4 | 2 | no | — |
| 238 | #204 | — | 20 | 2 | no | — |
| 239 | C23×C5 | — | 6 | 1 | no | — |
| 240 | C23×C5 | — | 12 | 1 | no | — |
| 241 | C22×D5 | — | 2 | 1 | no | — |
| 242 | C22×D5 | — | 6 | 1 | no | — |
| 243 | C22×D5 | — | 24 | 1 | no | — |
| 244 | C22×D5 | — | 24 | 1 | no | — |
| 245 | C22×D5 | — | 24 | 1 | no | — |
| 246 | C5×Q8 | — | 12 | 1 | no | — |
| 247 | C5×D4 | — | 12 | 1 | no | — |
| 248 | C5×D4 | — | 12 | 1 | no | — |
| 249 | C5×D4 | — | 12 | 1 | no | — |
| 250 | C5×D4 | — | 12 | 1 | no | — |
| 251 | C5×D4 | — | 12 | 1 | no | — |
| 252 | C5×D4 | — | 12 | 1 | no | — |
| 253 | C5×D4 | — | 12 | 1 | no | — |
| 254 | C2×C4×C5 | — | 6 | 1 | no | — |
| 255 | C2×C4×C5 | C2×D12 | 1 | 1 | yes | characteristic |
| 256 | C2×C4×C5 | D3×D4 | 1 | 1 | yes | characteristic |
| 257 | C2×C4×C5 | D3×D4 | 1 | 1 | yes | characteristic |
| 258 | C22⋊D5 | — | 24 | 1 | no | — |
| 259 | C22⋊D5 | — | 24 | 1 | no | — |
| 260 | C2×Dic5 | — | 2 | 1 | no | — |
| 261 | C2×Dic5 | — | 6 | 1 | no | — |
| 262 | D20 | — | 4 | 1 | no | — |
| 263 | D20 | — | 12 | 1 | no | — |
| 264 | D20 | — | 24 | 1 | no | — |
| 265 | Dic10 | — | 4 | 1 | no | — |
| 266 | Dic10 | — | 12 | 1 | no | — |
| 267 | C5×C8 | — | 2 | 2 | no | — |
| 268 | #168 | — | 2 | 2 | no | — |
| 269 | #168 | — | 6 | 2 | no | — |
| 270 | C2×SD16 | — | 6 | 1 | no | — |
| 271 | C2×SD16 | — | 30 | 1 | no | — |
| 272 | C2×SD16 | — | 30 | 1 | no | — |
| 273 | C2×D8 | — | 6 | 1 | no | — |
| 274 | C2×D8 | — | 30 | 1 | no | — |
| 275 | C2×D8 | — | 30 | 1 | no | — |
| 276 | #127 | — | 3 | 1 | no | — |
| 277 | #124 | — | 3 | 1 | no | — |
| 278 | #124 | — | 5 | 1 | no | — |
| 279 | #124 | — | 15 | 1 | no | — |
| 280 | #124 | — | 30 | 1 | no | — |
| 281 | #124 | — | 30 | 1 | no | — |
| 282 | #124 | — | 30 | 1 | no | — |
| 283 | #120 | — | 30 | 1 | no | — |
| 284 | #120 | — | 30 | 1 | no | — |
| 285 | #120 | — | 30 | 1 | no | — |
| 286 | #97 | — | 5 | 1 | no | — |
| 287 | #97 | — | 15 | 1 | no | — |
| 288 | #97 | D3×D5 | 1 | 1 | yes | characteristic, complemented |
| 289 | C2×C3×C5 | #453 | 1 | 1 | yes | characteristic |
| 290 | C2×C3×C5 | #453 | 1 | 1 | yes | characteristic |
| 291 | C2×C3×C5 | #453 | 1 | 1 | yes | characteristic |
| 292 | D15 | — | 8 | 1 | no | — |
| 293 | C3×D5 | — | 8 | 1 | no | — |
| 294 | C5×D3 | — | 8 | 1 | no | — |
| 295 | C5×D3 | — | 16 | 1 | no | — |
| 296 | C23×C3 | — | 10 | 1 | no | — |
| 297 | C22×D3 | — | 2 | 1 | no | — |
| 298 | C22×D3 | — | 4 | 1 | no | — |
| 299 | C22×D3 | — | 10 | 1 | no | — |
| 300 | C22×D3 | — | 40 | 1 | no | — |
| 301 | C22×D3 | — | 40 | 1 | no | — |
| 302 | C22×D3 | — | 40 | 1 | no | — |
| 303 | C3×Q8 | — | 20 | 1 | no | — |
| 304 | C3×D4 | — | 20 | 1 | no | — |
| 305 | C2×C3×C4 | — | 10 | 1 | no | — |
| 306 | C2×C3×C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 307 | C2×C3×C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 308 | C2×C3×C4 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 309 | #67 | — | 40 | 1 | no | — |
| 310 | #67 | — | 40 | 1 | no | — |
| 311 | C2×Dic3 | — | 2 | 1 | no | — |
| 312 | C2×Dic3 | — | 10 | 1 | no | — |
| 313 | D12 | — | 4 | 1 | no | — |
| 314 | D12 | — | 4 | 1 | no | — |
| 315 | D12 | — | 4 | 1 | no | — |
| 316 | D12 | — | 4 | 1 | no | — |
| 317 | D12 | — | 4 | 1 | no | — |
| 318 | D12 | — | 4 | 1 | no | — |
| 319 | D12 | — | 4 | 1 | no | — |
| 320 | D12 | — | 20 | 1 | no | — |
| 321 | D12 | — | 40 | 1 | no | — |
| 322 | Dic6 | — | 4 | 1 | no | — |
| 323 | Dic6 | — | 20 | 1 | no | — |
| 324 | C3×C8 | — | 2 | 2 | no | — |
| 325 | C3×C8 | — | 10 | 2 | no | — |
| 326 | C3⋊C8 | — | 10 | 2 | no | — |
| 327 | C22×C5 | — | 12 | 1 | no | — |
| 328 | C22×C5 | — | 12 | 1 | no | — |
| 329 | C22×C5 | — | 12 | 1 | no | — |
| 330 | C22×C5 | — | 24 | 1 | no | — |
| 331 | C22×C5 | — | 24 | 1 | no | — |
| 332 | C22×C5 | — | 24 | 1 | no | — |
| 333 | C22×C5 | #882 | 1 | 1 | yes | characteristic |
| 334 | C2×D5 | — | 4 | 1 | no | — |
| 335 | C2×D5 | — | 4 | 1 | no | — |
| 336 | C2×D5 | — | 4 | 1 | no | — |
| 337 | C2×D5 | — | 12 | 1 | no | — |
| 338 | C2×D5 | — | 12 | 1 | no | — |
| 339 | C2×D5 | — | 12 | 1 | no | — |
| 340 | C2×D5 | — | 24 | 4 | no | — |
| 341 | C4×C5 | — | 2 | 1 | no | — |
| 342 | C4×C5 | — | 2 | 1 | no | — |
| 343 | C4×C5 | — | 2 | 1 | no | — |
| 344 | C4×C5 | — | 12 | 1 | no | — |
| 345 | Dic5 | — | 4 | 1 | no | — |
| 346 | Dic5 | — | 12 | 1 | no | — |
| 347 | C24 | — | 30 | 1 | no | — |
| 348 | C2×Q8 | — | 3 | 1 | no | — |
| 349 | C2×Q8 | — | 5 | 1 | no | — |
| 350 | C2×Q8 | — | 15 | 1 | no | — |
| 351 | C2×D4 | — | 3 | 1 | no | — |
| 352 | C2×D4 | — | 5 | 1 | no | — |
| 353 | C2×D4 | — | 6 | 1 | no | — |
| 354 | C2×D4 | — | 6 | 1 | no | — |
| 355 | C2×D4 | — | 6 | 1 | no | — |
| 356 | C2×D4 | — | 15 | 1 | no | — |
| 357 | C2×D4 | — | 30 | 1 | no | — |
| 358 | C2×D4 | — | 30 | 1 | no | — |
| 359 | C2×D4 | — | 30 | 1 | no | — |
| 360 | SD16 | — | 12 | 2 | no | — |
| 361 | SD16 | — | 60 | 2 | no | — |
| 362 | SD16 | — | 60 | 2 | no | — |
| 363 | D8 | — | 12 | 2 | no | — |
| 364 | D8 | — | 60 | 2 | no | — |
| 365 | D8 | — | 60 | 2 | no | — |
| 366 | C2×C8 | — | 2 | 1 | no | — |
| 367 | C2×C8 | — | 10 | 1 | no | — |
| 368 | C2×C8 | — | 30 | 1 | no | — |
| 369 | C22⋊C4 | — | 6 | 1 | no | — |
| 370 | C22⋊C4 | — | 6 | 1 | no | — |
| 371 | C22⋊C4 | — | 10 | 1 | no | — |
| 372 | C22⋊C4 | — | 10 | 1 | no | — |
| 373 | C22⋊C4 | — | 30 | 1 | no | — |
| 374 | C22⋊C4 | — | 30 | 1 | no | — |
| 375 | C22⋊C4 | — | 30 | 1 | no | — |
| 376 | C22⋊C4 | — | 30 | 1 | no | — |
| 377 | C22⋊C4 | — | 30 | 1 | no | — |
| 378 | C42 | — | 30 | 1 | no | — |
| 379 | C42 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 380 | C3×C5 | #1655 | 1 | 1 | yes | characteristic, complemented, Hall |
| 381 | C22×C3 | — | 20 | 1 | no | — |
| 382 | C22×C3 | — | 20 | 1 | no | — |
| 383 | C22×C3 | — | 20 | 1 | no | — |
| 384 | C22×C3 | #4083 | 1 | 1 | yes | characteristic |
| 385 | C2×D3 | — | 4 | 1 | no | — |
| 386 | C2×D3 | — | 4 | 1 | no | — |
| 387 | C2×D3 | — | 4 | 1 | no | — |
| 388 | C2×D3 | — | 8 | 1 | no | — |
| 389 | C2×D3 | — | 8 | 1 | no | — |
| 390 | C2×D3 | — | 8 | 1 | no | — |
| 391 | C2×D3 | — | 20 | 1 | no | — |
| 392 | C2×D3 | — | 20 | 1 | no | — |
| 393 | C2×D3 | — | 20 | 1 | no | — |
| 394 | C2×D3 | — | 40 | 4 | no | — |
| 395 | C3×C4 | — | 2 | 1 | no | — |
| 396 | C3×C4 | — | 2 | 1 | no | — |
| 397 | C3×C4 | — | 2 | 1 | no | — |
| 398 | C3×C4 | — | 20 | 1 | no | — |
| 399 | Dic3 | — | 4 | 1 | no | — |
| 400 | Dic3 | — | 20 | 1 | no | — |
| 401 | C2×C5 | — | 24 | 1 | no | — |
| 402 | C2×C5 | — | 48 | 1 | no | — |
| 403 | C2×C5 | #4747 | 1 | 1 | yes | characteristic |
| 404 | C2×C5 | #4822 | 1 | 1 | yes | characteristic |
| 405 | C2×C5 | #4822 | 1 | 1 | yes | characteristic |
| 406 | D5 | — | 8 | 1 | no | — |
| 407 | D5 | — | 24 | 1 | no | — |
| 408 | C23 | — | 6 | 1 | no | — |
| 409 | C23 | — | 10 | 1 | no | — |
| 410 | C23 | — | 12 | 1 | no | — |
| 411 | C23 | — | 30 | 1 | no | — |
| 412 | C23 | — | 120 | 1 | no | — |
| 413 | C23 | — | 120 | 1 | no | — |
| 414 | C23 | — | 120 | 1 | no | — |
| 415 | Q8 | — | 12 | 1 | no | — |
| 416 | Q8 | — | 20 | 1 | no | — |
| 417 | Q8 | — | 60 | 1 | no | — |
| 418 | D4 | — | 12 | 1 | no | — |
| 419 | D4 | — | 12 | 1 | no | — |
| 420 | D4 | — | 12 | 1 | no | — |
| 421 | D4 | — | 12 | 1 | no | — |
| 422 | D4 | — | 12 | 1 | no | — |
| 423 | D4 | — | 12 | 1 | no | — |
| 424 | D4 | — | 12 | 1 | no | — |
| 425 | D4 | — | 20 | 1 | no | — |
| 426 | D4 | — | 60 | 1 | no | — |
| 427 | D4 | — | 120 | 1 | no | — |
| 428 | D4 | — | 120 | 1 | no | — |
| 429 | D4 | — | 120 | 1 | no | — |
| 430 | C2×C4 | — | 6 | 1 | no | — |
| 431 | C2×C4 | — | 10 | 1 | no | — |
| 432 | C2×C4 | — | 30 | 1 | no | — |
| 433 | C2×C4 | D5×D12 | 1 | 1 | yes | characteristic |
| 434 | C2×C4 | #6777 | 1 | 1 | yes | characteristic |
| 435 | C2×C4 | D3×C22⋊D5 | 1 | 1 | yes | characteristic |
| 436 | C8 | — | 2 | 2 | no | — |
| 437 | C8 | — | 10 | 2 | no | — |
| 438 | C8 | — | 30 | 2 | no | — |
| 439 | C2×C3 | — | 40 | 1 | no | — |
| 440 | C2×C3 | #65366 | 1 | 1 | yes | characteristic |
| 441 | C2×C3 | #65487 | 1 | 1 | yes | characteristic |
| 442 | C2×C3 | #65487 | 1 | 1 | yes | characteristic |
| 443 | D3 | — | 8 | 1 | no | — |
| 444 | D3 | — | 16 | 1 | no | — |
| 445 | D3 | — | 40 | 1 | no | — |
| 446 | C5 | #68350 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 447 | C22 | — | 12 | 1 | no | — |
| 448 | C22 | — | 12 | 1 | no | — |
| 449 | C22 | — | 12 | 1 | no | — |
| 450 | C22 | — | 20 | 1 | no | — |
| 451 | C22 | — | 20 | 1 | no | — |
| 452 | C22 | — | 20 | 1 | no | — |
| 453 | C22 | — | 24 | 1 | no | — |
| 454 | C22 | — | 24 | 1 | no | — |
| 455 | C22 | — | 24 | 1 | no | — |
| 456 | C22 | — | 60 | 1 | no | — |
| 457 | C22 | — | 60 | 1 | no | — |
| 458 | C22 | — | 60 | 1 | no | — |
| 459 | C22 | — | 120 | 4 | no | — |
| 460 | C22 | #91475 | 1 | 1 | yes | characteristic |
| 461 | C4 | — | 2 | 1 | no | — |
| 462 | C4 | — | 2 | 1 | no | — |
| 463 | C4 | — | 2 | 1 | no | — |
| 464 | C4 | — | 12 | 1 | no | — |
| 465 | C4 | — | 20 | 1 | no | — |
| 466 | C4 | — | 60 | 1 | no | — |
| 467 | C3 | #10602119 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 468 | C2 | — | 24 | 1 | no | — |
| 469 | C2 | — | 40 | 1 | no | — |
| 470 | C2 | — | 48 | 1 | no | — |
| 471 | C2 | — | 120 | 1 | no | — |
| 472 | C2 | #11747116 | 1 | 1 | yes | characteristic |
| 473 | C2 | #11748246 | 1 | 1 | yes | characteristic |
| 474 | C2 | #11748247 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11752772 | C2 | semidirect |
| 2. C5×#4712 | C2 | semidirect |
| 3. #11747042 | C2 | semidirect |
| 4. #11747031 | C2 | semidirect |
| 5. #11746285 | C2 | semidirect |
| 6. C3×#64684 | C2 | semidirect |
| 7. #11745847 | C2 | semidirect |
| 13. C5×#874 | C22 | semidirect |
| 25. C3×C5×#97 | C22 | semidirect |
| 26. #91087 | C22 | semidirect |
| 27. C3×#3935 | C22 | semidirect |
| 35. #64684 | D3 | semidirect |
| 72. #4712 | D5 | semidirect |
| 92. C5×#97 | C2×D3 | semidirect |
| 94. #3935 | C2×D3 | semidirect |
| 142. #874 | C2×D5 | semidirect |
| 144. C3×#97 | C2×D5 | semidirect |
| 288. #97 | D3×D5 | semidirect |
| 380. C3×C5 | #1655 | semidirect |
| 446. C5 | #68350 | semidirect |
| 467. C3 | #10602119 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752772 | 2 |
| C5×#4712 | 2 |
| #11747042 | 2 |
| #11747031 | 2 |
| #11746285 | 2 |
| C3×#64684 | 2 |
| #11745847 | 2 |
| #10602119 | 3 |
| #68350 | 5 |