Finite Group DatabasebetaFinite Group DatabasebetaOrder 2880.
467 conjugacy classes of subgroups; only the 13 normal subgroups are shown.
This group has 467 conjugacy classes of subgroups — too many to draw. Only its 13 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 | S4×A5 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | A4⋊S5 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | A4×S5 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | D4×S5 | — | 3 | 1 | no | maximal |
| 5 | A4×A5 | C22 | 1 | 1 | yes | characteristic, complemented |
| 6 | D3×S5 | — | 4 | 1 | no | maximal |
| 7 | S42 | — | 5 | 1 | no | maximal, Hall |
| 8 | AGL(1,𝔽5)×S4 | — | 6 | 1 | no | maximal |
| 9 | C22×S5 | — | 3 | 1 | no | — |
| 10 | C22×S5 | D3 | 1 | 1 | yes | characteristic, complemented |
| 11 | D4×A5 | — | 3 | 1 | no | — |
| 12 | C22⋊S5 | — | 3 | 1 | no | — |
| 13 | C22⋊S5 | — | 3 | 1 | no | — |
| 14 | C4⋊S5 | — | 3 | 1 | no | — |
| 15 | C4×S5 | — | 3 | 1 | no | — |
| 16 | D3×A5 | — | 4 | 1 | no | — |
| 17 | ΓL(2,𝔽4) | — | 4 | 1 | no | — |
| 18 | C3×S5 | — | 4 | 1 | no | — |
| 19 | C2×D3×S4 | — | 10 | 1 | no | maximal |
| 20 | A4⋊S4 | — | 5 | 1 | no | — |
| 21 | A4×S4 | — | 5 | 1 | no | — |
| 22 | A4×S4 | — | 5 | 1 | no | — |
| 23 | D5×S4 | — | 6 | 1 | no | — |
| 24 | A4×AGL(1,𝔽5) | — | 6 | 1 | no | — |
| 25 | A4⋊AGL(1,𝔽5) | — | 6 | 1 | no | — |
| 26 | C22×A5 | — | 3 | 1 | no | — |
| 27 | C22×A5 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 28 | C2×S5 | — | 3 | 1 | no | — |
| 29 | C2×S5 | — | 3 | 1 | no | — |
| 30 | C2×S5 | — | 3 | 1 | no | — |
| 31 | C2×S5 | — | 6 | 1 | no | — |
| 32 | C2×S5 | — | 6 | 1 | no | — |
| 33 | C4×A5 | — | 3 | 1 | no | — |
| 34 | A5⋊C4 | — | 3 | 1 | no | — |
| 35 | D4×S4 | — | 15 | 1 | no | — |
| 36 | D4×S4 | — | 15 | 1 | no | — |
| 37 | C3×A5 | — | 4 | 1 | no | — |
| 38 | D4×AGL(1,𝔽5) | — | 18 | 1 | no | — |
| 39 | C2×D3×A4 | — | 10 | 1 | no | — |
| 40 | C2×C3⋊S4 | — | 10 | 1 | no | — |
| 41 | C2×C3×S4 | — | 10 | 1 | no | — |
| 42 | A42 | — | 5 | 1 | no | — |
| 43 | D3×S4 | — | 10 | 1 | no | — |
| 44 | D3×S4 | — | 10 | 1 | no | — |
| 45 | D3×S4 | — | 10 | 1 | no | — |
| 46 | D3×S4 | — | 10 | 1 | no | — |
| 47 | D3×S4 | — | 20 | 1 | no | — |
| 48 | D5×A4 | — | 6 | 1 | no | — |
| 49 | C5⋊S4 | — | 6 | 1 | no | — |
| 50 | C5×S4 | — | 6 | 1 | no | — |
| 51 | D3×AGL(1,𝔽5) | — | 24 | 1 | no | — |
| 52 | C2×A5 | — | 3 | 1 | no | — |
| 53 | C2×A5 | — | 6 | 1 | no | — |
| 54 | S5 | — | 3 | 1 | no | — |
| 55 | S5 | — | 6 | 1 | no | — |
| 56 | S5 | S4 | 1 | 1 | yes | characteristic, direct product factor |
| 57 | #1020 | — | 30 | 1 | no | — |
| 58 | C22×S4 | — | 5 | 1 | no | — |
| 59 | C22×S4 | — | 5 | 1 | no | — |
| 60 | C22×S4 | — | 15 | 1 | no | — |
| 61 | C22×S4 | — | 15 | 1 | no | — |
| 62 | C2×D3×D4 | — | 30 | 1 | no | — |
| 63 | D4×A4 | — | 15 | 1 | no | — |
| 64 | D4×A4 | — | 15 | 1 | no | — |
| 65 | GL(2,ℤ/4) | — | 15 | 1 | no | — |
| 66 | GL(2,ℤ/4) | — | 15 | 1 | no | — |
| 67 | GL(2,ℤ/4) | — | 15 | 1 | no | — |
| 68 | GL(2,ℤ/4) | — | 15 | 1 | no | — |
| 69 | C4⋊S4 | — | 15 | 1 | no | — |
| 70 | C4⋊S4 | — | 15 | 1 | no | — |
| 71 | C4×S4 | — | 15 | 1 | no | — |
| 72 | C4×S4 | — | 15 | 1 | no | — |
| 73 | C22×AGL(1,𝔽5) | — | 6 | 1 | no | — |
| 74 | C22×AGL(1,𝔽5) | — | 18 | 1 | no | — |
| 75 | D4×D5 | — | 18 | 1 | no | — |
| 76 | C22⋊AGL(1,𝔽5) | — | 18 | 1 | no | — |
| 77 | C22⋊AGL(1,𝔽5) | — | 18 | 1 | no | — |
| 78 | C4⋊AGL(1,𝔽5) | — | 18 | 1 | no | — |
| 79 | C4×AGL(1,𝔽5) | — | 18 | 1 | no | — |
| 80 | C2×C3×A4 | — | 10 | 1 | no | — |
| 81 | C2×D32 | — | 40 | 1 | no | — |
| 82 | D3×A4 | — | 10 | 1 | no | — |
| 83 | D3×A4 | — | 10 | 1 | no | — |
| 84 | D3×A4 | — | 20 | 1 | no | — |
| 85 | C3⋊S4 | — | 10 | 1 | no | — |
| 86 | C3⋊S4 | — | 10 | 1 | no | — |
| 87 | C3⋊S4 | — | 20 | 1 | no | — |
| 88 | C3×S4 | — | 10 | 1 | no | — |
| 89 | C3×S4 | — | 10 | 1 | no | — |
| 90 | C3×S4 | — | 20 | 1 | no | — |
| 91 | D42 | — | 45 | 1 | no | Sylow |
| 92 | C5×A4 | — | 6 | 1 | no | — |
| 93 | D3×D5 | — | 24 | 1 | no | — |
| 94 | ΓL(1,𝔽16) | — | 24 | 1 | no | — |
| 95 | C3×AGL(1,𝔽5) | — | 24 | 1 | no | — |
| 96 | A5 | C2×S4 | 1 | 1 | yes | characteristic, complemented |
| 97 | C23×D3 | — | 10 | 1 | no | — |
| 98 | C23×D3 | — | 30 | 1 | no | — |
| 99 | C22⋊A4 | — | 10 | 1 | no | — |
| 100 | C22×A4 | — | 5 | 1 | no | — |
| 101 | C22×A4 | — | 5 | 1 | no | — |
| 102 | C22×A4 | — | 15 | 1 | no | — |
| 103 | C22×A4 | — | 15 | 1 | no | — |
| 104 | C2×S4 | — | 10 | 1 | no | — |
| 105 | C2×S4 | — | 15 | 1 | no | — |
| 106 | C2×S4 | — | 15 | 1 | no | — |
| 107 | C2×S4 | — | 15 | 1 | no | — |
| 108 | C2×S4 | — | 15 | 1 | no | — |
| 109 | C2×S4 | — | 15 | 1 | no | — |
| 110 | C2×S4 | — | 15 | 1 | no | — |
| 111 | C2×S4 | — | 30 | 1 | no | — |
| 112 | C2×S4 | — | 30 | 1 | no | — |
| 113 | C2×S4 | — | 30 | 1 | no | — |
| 114 | C2×S4 | — | 60 | 1 | no | — |
| 115 | C2×C3×D4 | — | 30 | 1 | no | — |
| 116 | C2×#67 | — | 30 | 1 | no | — |
| 117 | C2×#67 | — | 30 | 1 | no | — |
| 118 | D3×D4 | — | 30 | 1 | no | — |
| 119 | D3×D4 | — | 30 | 1 | no | — |
| 120 | D3×D4 | — | 30 | 1 | no | — |
| 121 | D3×D4 | — | 30 | 1 | no | — |
| 122 | D3×D4 | — | 30 | 1 | no | — |
| 123 | D3×D4 | — | 30 | 1 | no | — |
| 124 | D3×D4 | — | 30 | 1 | no | — |
| 125 | D3×D4 | — | 30 | 1 | no | — |
| 126 | D3×D4 | — | 60 | 1 | no | — |
| 127 | C2×D12 | — | 30 | 1 | no | — |
| 128 | C2×C4×D3 | — | 30 | 1 | no | — |
| 129 | C4×A4 | — | 15 | 1 | no | — |
| 130 | C4×A4 | — | 15 | 1 | no | — |
| 131 | SL(2,ℤ/4) | — | 15 | 1 | no | — |
| 132 | SL(2,ℤ/4) | — | 15 | 1 | no | — |
| 133 | C22×D5 | — | 6 | 1 | no | — |
| 134 | C22×D5 | — | 18 | 1 | no | — |
| 135 | C2×AGL(1,𝔽5) | — | 18 | 1 | no | — |
| 136 | C2×AGL(1,𝔽5) | — | 18 | 1 | no | — |
| 137 | C2×AGL(1,𝔽5) | — | 18 | 1 | no | — |
| 138 | C2×AGL(1,𝔽5) | — | 18 | 1 | no | — |
| 139 | C2×AGL(1,𝔽5) | — | 36 | 1 | no | — |
| 140 | C2×AGL(1,𝔽5) | — | 36 | 1 | no | — |
| 141 | C5×D4 | — | 18 | 1 | no | — |
| 142 | C22⋊D5 | — | 18 | 1 | no | — |
| 143 | C22⋊D5 | — | 18 | 1 | no | — |
| 144 | D20 | — | 18 | 1 | no | — |
| 145 | C4×D5 | — | 18 | 1 | no | — |
| 146 | C2×C3⋊D3 | — | 40 | 1 | no | — |
| 147 | C2×C3×D3 | — | 40 | 1 | no | — |
| 148 | C2×C3×D3 | — | 40 | 1 | no | — |
| 149 | C3×A4 | — | 10 | 1 | no | — |
| 150 | C3×A4 | — | 20 | 1 | no | — |
| 151 | D32 | — | 40 | 1 | no | — |
| 152 | D32 | — | 40 | 1 | no | — |
| 153 | D32 | — | 40 | 1 | no | — |
| 154 | D32 | — | 40 | 1 | no | — |
| 155 | C22×D4 | — | 15 | 1 | no | — |
| 156 | C22×D4 | — | 15 | 1 | no | — |
| 157 | C22×D4 | — | 45 | 1 | no | — |
| 158 | C22×D4 | — | 45 | 1 | no | — |
| 159 | #127 | — | 45 | 1 | no | — |
| 160 | #121 | — | 45 | 1 | no | — |
| 161 | #121 | — | 45 | 1 | no | — |
| 162 | #121 | — | 45 | 1 | no | — |
| 163 | #121 | — | 45 | 1 | no | — |
| 164 | #120 | — | 45 | 1 | no | — |
| 165 | #120 | — | 45 | 1 | no | — |
| 166 | #120 | — | 45 | 1 | no | — |
| 167 | #120 | — | 45 | 1 | no | — |
| 168 | C4×D4 | — | 45 | 1 | no | — |
| 169 | C4×D4 | — | 45 | 1 | no | — |
| 170 | D15 | — | 24 | 1 | no | — |
| 171 | C3×D5 | — | 24 | 1 | no | — |
| 172 | C5×D3 | — | 24 | 1 | no | — |
| 173 | C23×C3 | — | 10 | 1 | no | — |
| 174 | C23×C3 | — | 30 | 1 | no | — |
| 175 | C22×D3 | — | 10 | 1 | no | — |
| 176 | C22×D3 | — | 10 | 1 | no | — |
| 177 | C22×D3 | — | 20 | 1 | no | — |
| 178 | C22×D3 | — | 30 | 1 | no | — |
| 179 | C22×D3 | — | 30 | 1 | no | — |
| 180 | C22×D3 | — | 30 | 1 | no | — |
| 181 | C22×D3 | — | 30 | 1 | no | — |
| 182 | C22×D3 | — | 30 | 1 | no | — |
| 183 | C22×D3 | — | 30 | 1 | no | — |
| 184 | C22×D3 | — | 30 | 1 | no | — |
| 185 | C22×D3 | — | 30 | 1 | no | — |
| 186 | C22×D3 | — | 30 | 1 | no | — |
| 187 | C22×D3 | — | 60 | 1 | no | — |
| 188 | C22×D3 | — | 60 | 1 | no | — |
| 189 | C22×D3 | — | 60 | 1 | no | — |
| 190 | C22×D3 | — | 60 | 1 | no | — |
| 191 | C22×D3 | — | 60 | 1 | no | — |
| 192 | C2×A4 | — | 10 | 1 | no | — |
| 193 | C2×A4 | — | 15 | 1 | no | — |
| 194 | C2×A4 | — | 15 | 1 | no | — |
| 195 | C2×A4 | — | 20 | 1 | no | — |
| 196 | C2×A4 | — | 30 | 1 | no | — |
| 197 | S4 | — | 5 | 1 | no | — |
| 198 | S4 | — | 10 | 1 | no | — |
| 199 | S4 | — | 15 | 1 | no | — |
| 200 | S4 | — | 15 | 1 | no | — |
| 201 | S4 | — | 30 | 1 | no | — |
| 202 | S4 | — | 60 | 1 | no | — |
| 203 | S4 | — | 60 | 1 | no | — |
| 204 | S4 | — | 120 | 1 | no | — |
| 205 | S4 | — | 120 | 1 | no | — |
| 206 | S4 | S5 | 1 | 1 | yes | characteristic, direct product factor |
| 207 | C3×D4 | — | 30 | 1 | no | — |
| 208 | C3×D4 | — | 30 | 1 | no | — |
| 209 | C3×D4 | — | 30 | 1 | no | — |
| 210 | C3×D4 | — | 30 | 1 | no | — |
| 211 | C3×D4 | — | 60 | 1 | no | — |
| 212 | C2×C3×C4 | — | 30 | 1 | no | — |
| 213 | #67 | — | 30 | 1 | no | — |
| 214 | #67 | — | 30 | 1 | no | — |
| 215 | #67 | — | 30 | 1 | no | — |
| 216 | #67 | — | 30 | 1 | no | — |
| 217 | #67 | — | 30 | 1 | no | — |
| 218 | #67 | — | 30 | 1 | no | — |
| 219 | #67 | — | 30 | 1 | no | — |
| 220 | #67 | — | 30 | 1 | no | — |
| 221 | #67 | — | 60 | 1 | no | — |
| 222 | #67 | — | 60 | 1 | no | — |
| 223 | C2×Dic3 | — | 30 | 1 | no | — |
| 224 | D12 | — | 30 | 1 | no | — |
| 225 | D12 | — | 30 | 1 | no | — |
| 226 | D12 | — | 30 | 1 | no | — |
| 227 | D12 | — | 30 | 1 | no | — |
| 228 | D12 | — | 60 | 1 | no | — |
| 229 | C4×D3 | — | 30 | 1 | no | — |
| 230 | C4×D3 | — | 30 | 1 | no | — |
| 231 | C4×D3 | — | 30 | 1 | no | — |
| 232 | C4×D3 | — | 30 | 1 | no | — |
| 233 | C4×D3 | — | 60 | 1 | no | — |
| 234 | C22×C5 | — | 6 | 1 | no | — |
| 235 | C22×C5 | — | 18 | 1 | no | — |
| 236 | C2×D5 | — | 18 | 1 | no | — |
| 237 | C2×D5 | — | 18 | 1 | no | — |
| 238 | C2×D5 | — | 18 | 1 | no | — |
| 239 | C2×D5 | — | 36 | 1 | no | — |
| 240 | C2×D5 | — | 36 | 1 | no | — |
| 241 | AGL(1,𝔽5) | — | 6 | 1 | no | — |
| 242 | AGL(1,𝔽5) | — | 18 | 1 | no | — |
| 243 | AGL(1,𝔽5) | — | 36 | 1 | no | — |
| 244 | AGL(1,𝔽5) | — | 36 | 1 | no | — |
| 245 | C4×C5 | — | 18 | 1 | no | — |
| 246 | Dic5 | — | 18 | 1 | no | — |
| 247 | C2×C32 | — | 40 | 1 | no | — |
| 248 | C3⋊D3 | — | 40 | 1 | no | — |
| 249 | C3⋊D3 | — | 40 | 1 | no | — |
| 250 | C3×D3 | — | 40 | 1 | no | — |
| 251 | C3×D3 | — | 40 | 1 | no | — |
| 252 | C3×D3 | — | 40 | 1 | no | — |
| 253 | C3×D3 | — | 40 | 1 | no | — |
| 254 | C24 | — | 5 | 1 | no | — |
| 255 | C24 | — | 15 | 1 | no | — |
| 256 | C24 | — | 15 | 1 | no | — |
| 257 | C24 | — | 45 | 1 | no | — |
| 258 | C2×D4 | — | 30 | 1 | no | — |
| 259 | C2×D4 | — | 45 | 1 | no | — |
| 260 | C2×D4 | — | 45 | 1 | no | — |
| 261 | C2×D4 | — | 45 | 1 | no | — |
| 262 | C2×D4 | — | 45 | 1 | no | — |
| 263 | C2×D4 | — | 45 | 1 | no | — |
| 264 | C2×D4 | — | 45 | 1 | no | — |
| 265 | C2×D4 | — | 45 | 1 | no | — |
| 266 | C2×D4 | — | 45 | 1 | no | — |
| 267 | C2×D4 | — | 45 | 1 | no | — |
| 268 | C2×D4 | — | 45 | 1 | no | — |
| 269 | C2×D4 | — | 45 | 1 | no | — |
| 270 | C2×D4 | — | 45 | 1 | no | — |
| 271 | C2×D4 | — | 45 | 1 | no | — |
| 272 | C2×D4 | — | 45 | 1 | no | — |
| 273 | C2×D4 | — | 45 | 1 | no | — |
| 274 | C2×D4 | — | 45 | 1 | no | — |
| 275 | C2×D4 | — | 90 | 1 | no | — |
| 276 | C2×D4 | — | 90 | 1 | no | — |
| 277 | C2×D4 | — | 90 | 1 | no | — |
| 278 | C2×D4 | — | 90 | 1 | no | — |
| 279 | C2×D4 | — | 90 | 1 | no | — |
| 280 | C2×D4 | — | 90 | 1 | no | — |
| 281 | C2×D4 | — | 90 | 1 | no | — |
| 282 | C22×C4 | — | 15 | 1 | no | — |
| 283 | C22×C4 | — | 15 | 1 | no | — |
| 284 | C22×C4 | — | 45 | 1 | no | — |
| 285 | C22×C4 | — | 45 | 1 | no | — |
| 286 | C4⋊C4 | — | 45 | 1 | no | — |
| 287 | C4⋊C4 | — | 45 | 1 | no | — |
| 288 | C22⋊C4 | — | 45 | 1 | no | — |
| 289 | C22⋊C4 | — | 45 | 1 | no | — |
| 290 | C22⋊C4 | — | 45 | 1 | no | — |
| 291 | C22⋊C4 | — | 45 | 1 | no | — |
| 292 | C22⋊C4 | — | 45 | 1 | no | — |
| 293 | C22⋊C4 | — | 45 | 1 | no | — |
| 294 | C22⋊C4 | — | 45 | 1 | no | — |
| 295 | C22⋊C4 | — | 45 | 1 | no | — |
| 296 | C42 | — | 45 | 1 | no | — |
| 297 | C3×C5 | — | 24 | 1 | no | — |
| 298 | C22×C3 | — | 10 | 1 | no | — |
| 299 | C22×C3 | — | 20 | 1 | no | — |
| 300 | C22×C3 | — | 30 | 1 | no | — |
| 301 | C22×C3 | — | 30 | 1 | no | — |
| 302 | C22×C3 | — | 30 | 1 | no | — |
| 303 | C22×C3 | — | 30 | 1 | no | — |
| 304 | C22×C3 | — | 60 | 1 | no | — |
| 305 | C22×C3 | — | 60 | 1 | no | — |
| 306 | C22×C3 | — | 60 | 1 | no | — |
| 307 | C2×D3 | — | 10 | 1 | no | — |
| 308 | C2×D3 | — | 30 | 1 | no | — |
| 309 | C2×D3 | — | 30 | 1 | no | — |
| 310 | C2×D3 | — | 30 | 1 | no | — |
| 311 | C2×D3 | — | 30 | 1 | no | — |
| 312 | C2×D3 | — | 30 | 1 | no | — |
| 313 | C2×D3 | — | 30 | 1 | no | — |
| 314 | C2×D3 | — | 30 | 1 | no | — |
| 315 | C2×D3 | — | 30 | 1 | no | — |
| 316 | C2×D3 | — | 30 | 1 | no | — |
| 317 | C2×D3 | — | 40 | 1 | no | — |
| 318 | C2×D3 | — | 60 | 1 | no | — |
| 319 | C2×D3 | — | 60 | 1 | no | — |
| 320 | C2×D3 | — | 60 | 1 | no | — |
| 321 | C2×D3 | — | 60 | 1 | no | — |
| 322 | C2×D3 | — | 60 | 1 | no | — |
| 323 | C2×D3 | — | 60 | 1 | no | — |
| 324 | C2×D3 | — | 60 | 1 | no | — |
| 325 | C2×D3 | — | 60 | 1 | no | — |
| 326 | C2×D3 | — | 60 | 1 | no | — |
| 327 | C2×D3 | — | 60 | 1 | no | — |
| 328 | C2×D3 | — | 60 | 1 | no | — |
| 329 | C2×D3 | — | 60 | 1 | no | — |
| 330 | C2×D3 | — | 60 | 1 | no | — |
| 331 | C2×D3 | — | 60 | 1 | no | — |
| 332 | C2×D3 | — | 120 | 1 | no | — |
| 333 | C2×D3 | — | 240 | 1 | no | — |
| 334 | A4 | — | 5 | 1 | no | — |
| 335 | A4 | — | 20 | 1 | no | — |
| 336 | A4 | — | 40 | 1 | no | — |
| 337 | A4 | — | 120 | 1 | no | — |
| 338 | A4 | C2×S5 | 1 | 1 | yes | characteristic, complemented |
| 339 | C3×C4 | — | 30 | 1 | no | — |
| 340 | C3×C4 | — | 30 | 1 | no | — |
| 341 | C3×C4 | — | 60 | 1 | no | — |
| 342 | Dic3 | — | 30 | 1 | no | — |
| 343 | Dic3 | — | 30 | 1 | no | — |
| 344 | Dic3 | — | 60 | 1 | no | — |
| 345 | C2×C5 | — | 18 | 1 | no | — |
| 346 | C2×C5 | — | 36 | 1 | no | — |
| 347 | D5 | — | 6 | 1 | no | — |
| 348 | D5 | — | 18 | 1 | no | — |
| 349 | D5 | — | 36 | 1 | no | — |
| 350 | C32 | — | 40 | 1 | no | Sylow |
| 351 | C23 | — | 10 | 1 | no | — |
| 352 | C23 | — | 15 | 1 | no | — |
| 353 | C23 | — | 15 | 1 | no | — |
| 354 | C23 | — | 30 | 1 | no | — |
| 355 | C23 | — | 30 | 1 | no | — |
| 356 | C23 | — | 45 | 1 | no | — |
| 357 | C23 | — | 45 | 1 | no | — |
| 358 | C23 | — | 45 | 1 | no | — |
| 359 | C23 | — | 45 | 1 | no | — |
| 360 | C23 | — | 45 | 1 | no | — |
| 361 | C23 | — | 45 | 1 | no | — |
| 362 | C23 | — | 90 | 1 | no | — |
| 363 | C23 | — | 90 | 1 | no | — |
| 364 | C23 | — | 90 | 1 | no | — |
| 365 | C23 | — | 90 | 1 | no | — |
| 366 | C23 | — | 90 | 1 | no | — |
| 367 | C23 | — | 180 | 1 | no | — |
| 368 | D4 | — | 3 | 1 | no | — |
| 369 | D4 | — | 15 | 1 | no | — |
| 370 | D4 | — | 30 | 1 | no | — |
| 371 | D4 | — | 30 | 1 | no | — |
| 372 | D4 | — | 30 | 1 | no | — |
| 373 | D4 | — | 45 | 1 | no | — |
| 374 | D4 | — | 45 | 1 | no | — |
| 375 | D4 | — | 45 | 1 | no | — |
| 376 | D4 | — | 45 | 1 | no | — |
| 377 | D4 | — | 45 | 1 | no | — |
| 378 | D4 | — | 45 | 1 | no | — |
| 379 | D4 | — | 90 | 1 | no | — |
| 380 | D4 | — | 90 | 1 | no | — |
| 381 | D4 | — | 90 | 1 | no | — |
| 382 | D4 | — | 90 | 1 | no | — |
| 383 | D4 | — | 90 | 1 | no | — |
| 384 | D4 | — | 90 | 1 | no | — |
| 385 | D4 | — | 90 | 1 | no | — |
| 386 | D4 | — | 90 | 1 | no | — |
| 387 | D4 | — | 90 | 1 | no | — |
| 388 | D4 | — | 90 | 1 | no | — |
| 389 | D4 | — | 90 | 1 | no | — |
| 390 | D4 | — | 180 | 1 | no | — |
| 391 | D4 | — | 180 | 1 | no | — |
| 392 | C2×C4 | — | 30 | 1 | no | — |
| 393 | C2×C4 | — | 45 | 1 | no | — |
| 394 | C2×C4 | — | 45 | 1 | no | — |
| 395 | C2×C4 | — | 45 | 1 | no | — |
| 396 | C2×C4 | — | 45 | 1 | no | — |
| 397 | C2×C4 | — | 45 | 1 | no | — |
| 398 | C2×C4 | — | 45 | 1 | no | — |
| 399 | C2×C4 | — | 45 | 1 | no | — |
| 400 | C2×C4 | — | 90 | 1 | no | — |
| 401 | C2×C4 | — | 90 | 1 | no | — |
| 402 | C2×C4 | — | 90 | 1 | no | — |
| 403 | C2×C3 | — | 10 | 1 | no | — |
| 404 | C2×C3 | — | 30 | 1 | no | — |
| 405 | C2×C3 | — | 30 | 1 | no | — |
| 406 | C2×C3 | — | 40 | 1 | no | — |
| 407 | C2×C3 | — | 60 | 1 | no | — |
| 408 | C2×C3 | — | 60 | 1 | no | — |
| 409 | C2×C3 | — | 60 | 1 | no | — |
| 410 | C2×C3 | — | 80 | 1 | no | — |
| 411 | D3 | — | 4 | 1 | no | — |
| 412 | D3 | — | 10 | 1 | no | — |
| 413 | D3 | — | 10 | 1 | no | — |
| 414 | D3 | — | 30 | 1 | no | — |
| 415 | D3 | — | 30 | 1 | no | — |
| 416 | D3 | — | 40 | 1 | no | — |
| 417 | D3 | — | 60 | 1 | no | — |
| 418 | D3 | — | 60 | 1 | no | — |
| 419 | D3 | — | 60 | 1 | no | — |
| 420 | D3 | — | 240 | 1 | no | — |
| 421 | D3 | — | 240 | 1 | no | — |
| 422 | C5 | — | 6 | 1 | no | Sylow |
| 423 | C22 | — | 3 | 1 | no | — |
| 424 | C22 | — | 5 | 1 | no | — |
| 425 | C22 | — | 15 | 1 | no | — |
| 426 | C22 | — | 30 | 1 | no | — |
| 427 | C22 | — | 30 | 1 | no | — |
| 428 | C22 | — | 30 | 1 | no | — |
| 429 | C22 | — | 30 | 1 | no | — |
| 430 | C22 | — | 45 | 1 | no | — |
| 431 | C22 | — | 45 | 1 | no | — |
| 432 | C22 | — | 45 | 1 | no | — |
| 433 | C22 | — | 45 | 1 | no | — |
| 434 | C22 | — | 45 | 1 | no | — |
| 435 | C22 | — | 60 | 1 | no | — |
| 436 | C22 | — | 60 | 1 | no | — |
| 437 | C22 | — | 90 | 1 | no | — |
| 438 | C22 | — | 90 | 1 | no | — |
| 439 | C22 | — | 90 | 1 | no | — |
| 440 | C22 | — | 90 | 1 | no | — |
| 441 | C22 | — | 90 | 1 | no | — |
| 442 | C22 | — | 90 | 1 | no | — |
| 443 | C22 | — | 90 | 1 | no | — |
| 444 | C22 | — | 90 | 1 | no | — |
| 445 | C22 | — | 180 | 1 | no | — |
| 446 | C22 | — | 180 | 1 | no | — |
| 447 | C22 | D3×S5 | 1 | 1 | yes | characteristic, complemented |
| 448 | C4 | — | 3 | 1 | no | — |
| 449 | C4 | — | 15 | 1 | no | — |
| 450 | C4 | — | 30 | 1 | no | — |
| 451 | C4 | — | 45 | 1 | no | — |
| 452 | C4 | — | 45 | 1 | no | — |
| 453 | C4 | — | 90 | 1 | no | — |
| 454 | C4 | — | 90 | 1 | no | — |
| 455 | C3 | — | 4 | 1 | no | — |
| 456 | C3 | — | 10 | 1 | no | — |
| 457 | C3 | — | 80 | 1 | no | — |
| 458 | C2 | — | 3 | 1 | no | — |
| 459 | C2 | — | 6 | 1 | no | — |
| 460 | C2 | — | 10 | 1 | no | — |
| 461 | C2 | — | 15 | 1 | no | — |
| 462 | C2 | — | 30 | 1 | no | — |
| 463 | C2 | — | 45 | 1 | no | — |
| 464 | C2 | — | 60 | 1 | no | — |
| 465 | C2 | — | 90 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | A4×A5 | C22 |
| Fitting | C22 | D3×S5 |
| socle | C22×A5 | C2×D3 |
| LCS | G ▷ A4×A5 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. S4×A5 | C2 | semidirect |
| 2. A4⋊S5 | C2 | semidirect |
| 3. A4×S5 | C2 | semidirect |
| 5. A4×A5 | C22 | semidirect |
| 10. C22×S5 | D3 | semidirect |
| 27. C22×A5 | C2×D3 | semidirect |
| 56. S5 | S4 | direct (N × H) |
| 96. A5 | C2×S4 | semidirect |
| 206. S4 | S5 | direct (N × H) |
| 338. A4 | C2×S5 | semidirect |
| 447. C22 | D3×S5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| S4×A5 | 2 |
| A4⋊S5 | 2 |
| A4×S5 | 2 |
| D4×S5 | 3 |
| D3×S5 | 4 |
| S42 | 5 |
| AGL(1,𝔽5)×S4 | 6 |
| C2×D3×S4 | 10 |