Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
736 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 82 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 | #11754660 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11750833 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11748932 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11748524 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C5×#4468 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C3×#64690 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11745958 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10598899 | — | 3 | 1 | no | maximal, Hall |
| 9 | C22×D60 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | C2×D3×C22⋊D5 | — | 2 | 1 | no | — |
| 11 | C22×#1203 | — | 2 | 1 | no | — |
| 12 | #91819 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×D120 | — | 2 | 1 | no | — |
| 14 | C2×C5×(C2×D3)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 15 | C3×#4076 | C22 | 1 | 1 | yes | characteristic |
| 16 | #91569 | — | 2 | 1 | no | — |
| 17 | C2×#6667 | — | 2 | 1 | no | — |
| 18 | #91476 | — | 2 | 1 | no | — |
| 19 | #91474 | — | 2 | 1 | no | — |
| 20 | #91457 | — | 2 | 1 | no | — |
| 21 | #91427 | — | 2 | 1 | no | — |
| 22 | C2×#6653 | — | 2 | 1 | no | — |
| 23 | C3×C5×C22⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | #91105 | — | 2 | 1 | no | — |
| 25 | C5×#830 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | C3×#3963 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | #90968 | — | 2 | 1 | no | — |
| 28 | #68284 | — | 5 | 1 | no | maximal, Hall |
| 29 | #65827 | — | 3 | 1 | no | — |
| 30 | #65249 | — | 3 | 1 | no | — |
| 31 | #65021 | — | 3 | 1 | no | — |
| 32 | #65021 | — | 3 | 1 | no | — |
| 33 | C5×#323 | — | 3 | 1 | no | — |
| 34 | #64690 | — | 3 | 1 | no | — |
| 35 | #64690 | D3 | 1 | 1 | yes | characteristic, complemented |
| 36 | C23×D15 | — | 2 | 1 | no | — |
| 37 | C23×C5×D3 | D4 | 1 | 1 | yes | characteristic |
| 38 | C22×D3×D5 | — | 2 | 1 | no | — |
| 39 | C22×C3×C4×C5 | C23 | 1 | 1 | yes | characteristic |
| 40 | C2×#1220 | — | 2 | 1 | no | — |
| 41 | C2×D60 | — | 2 | 1 | no | — |
| 42 | C2×D60 | — | 2 | 1 | no | — |
| 43 | C2×D60 | — | 4 | 2 | no | — |
| 44 | C2×D60 | D4 | 1 | 1 | yes | characteristic, complemented |
| 45 | C22×C5×Dic3 | D4 | 1 | 1 | yes | characteristic |
| 46 | C2×C3×C22⋊D5 | — | 2 | 1 | no | — |
| 47 | C22×C3×Dic5 | — | 2 | 1 | no | — |
| 48 | C2×C3×D20 | D4 | 1 | 1 | yes | characteristic, complemented |
| 49 | D3×C22⋊D5 | — | 4 | 2 | no | — |
| 50 | D3×C22⋊D5 | — | 4 | 2 | no | — |
| 51 | C2×#1203 | — | 2 | 1 | no | — |
| 52 | C2×#1203 | — | 4 | 2 | no | — |
| 53 | C2×#1203 | — | 4 | 2 | no | — |
| 54 | C2×#1203 | — | 4 | 2 | no | — |
| 55 | C2×#1202 | — | 2 | 1 | no | — |
| 56 | C2×#1201 | — | 2 | 1 | no | — |
| 57 | C2×D3×Dic5 | — | 2 | 1 | no | — |
| 58 | C2×C3×C5×C8 | — | 2 | 1 | no | — |
| 59 | #6714 | — | 2 | 1 | no | — |
| 60 | C4⋊Dic15 | D4 | 1 | 1 | yes | characteristic, complemented |
| 61 | D120 | — | 4 | 2 | no | — |
| 62 | C5×(C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 63 | C5×(C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 64 | C2×C5×C3⋊C8 | — | 2 | 1 | no | — |
| 65 | C3×#685 | — | 2 | 1 | no | — |
| 66 | C3×C4⋊Dic5 | D4 | 1 | 1 | yes | characteristic, complemented |
| 67 | Dic3⋊Dic5 | — | 2 | 1 | no | — |
| 68 | #6667 | — | 2 | 1 | no | — |
| 69 | #6667 | — | 4 | 2 | no | — |
| 70 | #6665 | — | 2 | 1 | no | — |
| 71 | #6653 | — | 4 | 2 | no | — |
| 72 | #5605 | — | 5 | 1 | no | — |
| 73 | #5036 | — | 5 | 1 | no | — |
| 74 | #4732 | — | 5 | 1 | no | — |
| 75 | #4671 | — | 5 | 1 | no | — |
| 76 | C3×#327 | — | 5 | 1 | no | — |
| 77 | #4468 | D5 | 1 | 1 | yes | characteristic, complemented |
| 78 | #4451 | — | 5 | 1 | no | — |
| 79 | C22×C22⋊D5 | — | 6 | 1 | no | — |
| 80 | C22×C22⋊D5 | — | 6 | 1 | no | — |
| 81 | C22×D20 | — | 3 | 1 | no | — |
| 82 | C2×C5×C22⋊C4 | — | 3 | 1 | no | — |
| 83 | #4076 | — | 3 | 1 | no | — |
| 84 | #4076 | — | 6 | 1 | no | — |
| 85 | #4076 | C2×D3 | 1 | 1 | yes | characteristic |
| 86 | C2×#685 | — | 6 | 1 | no | — |
| 87 | C2×D40 | — | 6 | 1 | no | — |
| 88 | C2×D40 | — | 6 | 1 | no | — |
| 89 | #4032 | — | 6 | 1 | no | — |
| 90 | #4032 | — | 6 | 1 | no | — |
| 91 | #4028 | — | 6 | 1 | no | — |
| 92 | #4028 | — | 6 | 1 | no | — |
| 93 | C5×C22⋊C8 | — | 3 | 1 | no | — |
| 94 | C5×C22⋊C8 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 95 | #3963 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 96 | #3953 | — | 6 | 1 | no | — |
| 97 | #3953 | — | 6 | 1 | no | — |
| 98 | #1595 | — | 15 | 1 | no | Sylow |
| 99 | C23×C3×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 100 | C22×D15 | — | 2 | 2 | no | — |
| 101 | C22×D15 | — | 2 | 1 | no | — |
| 102 | C22×D15 | — | 4 | 1 | no | — |
| 103 | C22×D15 | — | 4 | 1 | no | — |
| 104 | C22×D15 | — | 4 | 1 | no | — |
| 105 | C22×D15 | — | 4 | 1 | no | — |
| 106 | C22×D15 | — | 4 | 1 | no | — |
| 107 | C22×D15 | — | 4 | 1 | no | — |
| 108 | C22×C5×D3 | — | 2 | 1 | no | — |
| 109 | C22×C5×D3 | — | 2 | 1 | no | — |
| 110 | C22×C5×D3 | — | 4 | 1 | no | — |
| 111 | C22×C5×D3 | — | 4 | 1 | no | — |
| 112 | C22×C5×D3 | D8 | 1 | 2 | yes | complemented |
| 113 | C22×C3×D5 | — | 2 | 1 | no | — |
| 114 | C2×D3×D5 | — | 4 | 2 | no | — |
| 115 | C2×D3×D5 | — | 8 | 1 | no | — |
| 116 | C2×D3×D5 | — | 8 | 1 | no | — |
| 117 | C2×C3×C4×C5 | — | 4 | 1 | no | — |
| 118 | C2×C3×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 119 | C2×C3×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 120 | #1220 | — | 4 | 1 | no | — |
| 121 | #1220 | — | 4 | 1 | no | — |
| 122 | C2×Dic15 | — | 2 | 1 | no | — |
| 123 | D60 | — | 2 | 2 | no | — |
| 124 | D60 | — | 2 | 2 | no | — |
| 125 | D60 | — | 4 | 1 | no | — |
| 126 | D60 | — | 4 | 1 | no | — |
| 127 | D60 | — | 4 | 1 | no | — |
| 128 | C2×C5×Dic3 | — | 2 | 1 | no | — |
| 129 | C2×C5×Dic3 | — | 4 | 1 | no | — |
| 130 | C3×C22⋊D5 | — | 4 | 1 | no | — |
| 131 | C3×C22⋊D5 | — | 4 | 1 | no | — |
| 132 | C2×C3×Dic5 | — | 2 | 2 | no | — |
| 133 | C2×C3×Dic5 | — | 2 | 1 | no | — |
| 134 | C2×C3×Dic5 | — | 4 | 1 | no | — |
| 135 | C2×C3×Dic5 | — | 4 | 1 | no | — |
| 136 | C3×D20 | — | 4 | 1 | no | — |
| 137 | #1203 | — | 4 | 2 | no | — |
| 138 | #1203 | — | 4 | 8 | no | — |
| 139 | #1202 | — | 8 | 1 | no | — |
| 140 | #1201 | — | 4 | 2 | no | — |
| 141 | D3×Dic5 | — | 4 | 2 | no | — |
| 142 | C3×C5×C8 | — | 4 | 1 | no | — |
| 143 | C5×C3⋊C8 | — | 4 | 1 | no | — |
| 144 | C2×D3×D4 | — | 10 | 1 | no | — |
| 145 | C22×D12 | — | 5 | 1 | no | — |
| 146 | C22×D12 | — | 10 | 1 | no | — |
| 147 | C3×#121 | — | 5 | 1 | no | — |
| 148 | #939 | — | 10 | 1 | no | — |
| 149 | #937 | — | 10 | 1 | no | — |
| 150 | C2×#213 | — | 10 | 1 | no | — |
| 151 | #930 | — | 5 | 1 | no | — |
| 152 | C2×(C2×D3)⋊C4 | — | 10 | 1 | no | — |
| 153 | C2×(C2×D3)⋊C4 | C2×D5 | 1 | 1 | yes | characteristic |
| 154 | C2×D24 | — | 10 | 1 | no | — |
| 155 | #894 | — | 10 | 1 | no | — |
| 156 | #883 | — | 10 | 1 | no | — |
| 157 | #882 | — | 10 | 1 | no | — |
| 158 | C3×C22⋊C8 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 159 | C3×#95 | — | 5 | 1 | no | — |
| 160 | #830 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 161 | #821 | — | 10 | 1 | no | — |
| 162 | #809 | — | 10 | 1 | no | — |
| 163 | C24×C5 | — | 3 | 1 | no | — |
| 164 | C23×D5 | — | 6 | 1 | no | — |
| 165 | C23×D5 | — | 6 | 1 | no | — |
| 166 | C22×C4×C5 | — | 3 | 1 | no | — |
| 167 | C22×C4×C5 | C22×D3 | 1 | 1 | yes | characteristic |
| 168 | C2×C22⋊D5 | — | 2 | 1 | no | — |
| 169 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 170 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 171 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 172 | C2×C22⋊D5 | — | 12 | 2 | no | — |
| 173 | C2×C22⋊D5 | — | 12 | 2 | no | — |
| 174 | C2×C22⋊D5 | — | 12 | 2 | no | — |
| 175 | C2×C22⋊D5 | — | 12 | 2 | no | — |
| 176 | C2×C22⋊D5 | — | 12 | 2 | no | — |
| 177 | C22×Dic5 | — | 2 | 1 | no | — |
| 178 | C22×Dic5 | — | 6 | 1 | no | — |
| 179 | C2×D20 | — | 3 | 1 | no | — |
| 180 | C2×D20 | — | 6 | 1 | no | — |
| 181 | C2×D20 | — | 6 | 1 | no | — |
| 182 | C2×D20 | — | 6 | 1 | no | — |
| 183 | C2×D20 | — | 12 | 2 | no | — |
| 184 | C2×D20 | D12 | 1 | 1 | yes | characteristic, complemented |
| 185 | C2×C5×C8 | — | 2 | 1 | no | — |
| 186 | C2×C5×C8 | — | 6 | 1 | no | — |
| 187 | C5×C22⋊C4 | — | 6 | 1 | no | — |
| 188 | C5×C22⋊C4 | — | 6 | 1 | no | — |
| 189 | #685 | — | 2 | 1 | no | — |
| 190 | #685 | — | 6 | 1 | no | — |
| 191 | #685 | — | 6 | 1 | no | — |
| 192 | #685 | — | 6 | 1 | no | — |
| 193 | #685 | — | 12 | 2 | no | — |
| 194 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 195 | C4⋊Dic5 | — | 6 | 1 | no | — |
| 196 | C4⋊Dic5 | D12 | 1 | 1 | yes | characteristic, complemented |
| 197 | D40 | — | 12 | 2 | no | — |
| 198 | D40 | — | 12 | 2 | no | — |
| 199 | #534 | — | 15 | 1 | no | — |
| 200 | #447 | — | 15 | 1 | no | — |
| 201 | #447 | — | 15 | 1 | no | — |
| 202 | #392 | — | 15 | 1 | no | — |
| 203 | #327 | — | 5 | 1 | no | — |
| 204 | #327 | — | 15 | 1 | no | — |
| 205 | #323 | — | 3 | 1 | no | — |
| 206 | C22×C3×C5 | — | 2 | 1 | no | — |
| 207 | C22×C3×C5 | — | 2 | 1 | no | — |
| 208 | C22×C3×C5 | #120 | 1 | 1 | yes | characteristic |
| 209 | C22×C3×C5 | C2×D8 | 1 | 1 | yes | characteristic |
| 210 | C22×C3×C5 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 211 | C2×D15 | — | 4 | 2 | no | — |
| 212 | C2×D15 | — | 4 | 2 | no | — |
| 213 | C2×D15 | — | 4 | 1 | no | — |
| 214 | C2×D15 | — | 4 | 1 | no | — |
| 215 | C2×D15 | — | 4 | 2 | no | — |
| 216 | C2×D15 | — | 4 | 1 | no | — |
| 217 | C2×D15 | — | 8 | 1 | no | — |
| 218 | C2×D15 | — | 8 | 1 | no | — |
| 219 | C2×D15 | — | 8 | 1 | no | — |
| 220 | C2×D15 | — | 8 | 1 | no | — |
| 221 | C2×C5×D3 | — | 2 | 2 | no | — |
| 222 | C2×C5×D3 | — | 4 | 1 | no | — |
| 223 | C2×C5×D3 | — | 4 | 1 | no | — |
| 224 | C2×C5×D3 | — | 4 | 2 | no | — |
| 225 | C2×C5×D3 | — | 8 | 1 | no | — |
| 226 | C2×C3×D5 | — | 4 | 1 | no | — |
| 227 | C2×C3×D5 | — | 4 | 1 | no | — |
| 228 | C2×C3×D5 | — | 4 | 1 | no | — |
| 229 | D3×D5 | — | 8 | 4 | no | — |
| 230 | C3×C4×C5 | — | 2 | 1 | no | — |
| 231 | C3×C4×C5 | — | 2 | 1 | no | — |
| 232 | Dic15 | — | 4 | 1 | no | — |
| 233 | C3×Dic5 | — | 4 | 2 | no | — |
| 234 | C3×Dic5 | — | 4 | 1 | no | — |
| 235 | C5×Dic3 | — | 4 | 1 | no | — |
| 236 | C23×D3 | — | 10 | 1 | no | — |
| 237 | C23×D3 | — | 10 | 1 | no | — |
| 238 | C23×D3 | D20 | 1 | 1 | yes | characteristic |
| 239 | C2×C3×D4 | — | 5 | 1 | no | — |
| 240 | C2×C3×D4 | — | 10 | 1 | no | — |
| 241 | C22×C3×C4 | — | 10 | 1 | no | — |
| 242 | C22×C3×C4 | C22×D5 | 1 | 1 | yes | characteristic |
| 243 | C2×#67 | — | 10 | 1 | no | — |
| 244 | C2×#67 | — | 10 | 1 | no | — |
| 245 | C2×#67 | — | 10 | 1 | no | — |
| 246 | C22×Dic3 | D20 | 1 | 1 | yes | characteristic |
| 247 | D3×D4 | — | 20 | 2 | no | — |
| 248 | D3×D4 | — | 20 | 2 | no | — |
| 249 | C2×D12 | — | 5 | 1 | no | — |
| 250 | C2×D12 | — | 10 | 1 | no | — |
| 251 | C2×D12 | — | 10 | 1 | no | — |
| 252 | C2×D12 | — | 10 | 1 | no | — |
| 253 | C2×D12 | — | 20 | 2 | no | — |
| 254 | C2×D12 | — | 20 | 2 | no | — |
| 255 | C2×D12 | — | 20 | 2 | no | — |
| 256 | C2×D12 | — | 20 | 2 | no | — |
| 257 | C2×C4×D3 | — | 10 | 1 | no | — |
| 258 | C2×C3×C8 | — | 2 | 1 | no | — |
| 259 | C3×C4⋊C4 | — | 5 | 1 | no | — |
| 260 | C3×C22⋊C4 | — | 10 | 1 | no | — |
| 261 | #217 | — | 10 | 1 | no | — |
| 262 | #213 | — | 20 | 2 | no | — |
| 263 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 264 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 265 | (C2×D3)⋊C4 | — | 10 | 1 | no | — |
| 266 | (C2×D3)⋊C4 | — | 10 | 1 | no | — |
| 267 | (C2×D3)⋊C4 | — | 20 | 2 | no | — |
| 268 | C4⋊Dic3 | — | 5 | 1 | no | — |
| 269 | Dic3⋊C4 | — | 10 | 1 | no | — |
| 270 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 271 | D24 | — | 20 | 2 | no | — |
| 272 | C23×C5 | — | 3 | 2 | no | — |
| 273 | C23×C5 | — | 6 | 1 | no | — |
| 274 | C23×C5 | — | 6 | 1 | no | — |
| 275 | C23×C5 | — | 12 | 1 | no | — |
| 276 | C23×C5 | — | 12 | 1 | no | — |
| 277 | C23×C5 | D3×D4 | 1 | 1 | yes | characteristic |
| 278 | C22×D5 | — | 2 | 1 | no | — |
| 279 | C22×D5 | — | 6 | 2 | no | — |
| 280 | C22×D5 | — | 6 | 1 | no | — |
| 281 | C22×D5 | — | 12 | 2 | no | — |
| 282 | C22×D5 | — | 12 | 1 | no | — |
| 283 | C22×D5 | — | 12 | 1 | no | — |
| 284 | C22×D5 | — | 12 | 1 | no | — |
| 285 | C22×D5 | — | 12 | 1 | no | — |
| 286 | C22×D5 | — | 12 | 1 | no | — |
| 287 | C22×D5 | — | 12 | 1 | no | — |
| 288 | C22×D5 | — | 24 | 1 | no | — |
| 289 | C22×D5 | — | 24 | 1 | no | — |
| 290 | C2×C4×C5 | — | 4 | 1 | no | — |
| 291 | C2×C4×C5 | — | 6 | 1 | no | — |
| 292 | C2×C4×C5 | — | 12 | 1 | no | — |
| 293 | C2×C4×C5 | C2×D12 | 1 | 1 | yes | characteristic |
| 294 | C2×C4×C5 | D3×D4 | 1 | 1 | yes | characteristic |
| 295 | C22⋊D5 | — | 4 | 1 | no | — |
| 296 | C22⋊D5 | — | 4 | 1 | no | — |
| 297 | C22⋊D5 | — | 12 | 2 | no | — |
| 298 | C22⋊D5 | — | 12 | 8 | no | — |
| 299 | C22⋊D5 | — | 12 | 2 | no | — |
| 300 | C22⋊D5 | — | 12 | 1 | no | — |
| 301 | C22⋊D5 | — | 12 | 1 | no | — |
| 302 | C2×Dic5 | — | 2 | 2 | no | — |
| 303 | C2×Dic5 | — | 2 | 1 | no | — |
| 304 | C2×Dic5 | — | 4 | 1 | no | — |
| 305 | C2×Dic5 | — | 4 | 1 | no | — |
| 306 | C2×Dic5 | — | 6 | 1 | no | — |
| 307 | C2×Dic5 | — | 12 | 2 | no | — |
| 308 | D20 | — | 4 | 1 | no | — |
| 309 | D20 | — | 6 | 2 | no | — |
| 310 | D20 | — | 6 | 2 | no | — |
| 311 | D20 | — | 12 | 1 | no | — |
| 312 | D20 | — | 12 | 1 | no | — |
| 313 | D20 | — | 12 | 1 | no | — |
| 314 | D20 | — | 24 | 1 | no | — |
| 315 | C5×C8 | — | 4 | 1 | no | — |
| 316 | C5×C8 | — | 12 | 1 | no | — |
| 317 | C22×D4 | — | 15 | 1 | no | — |
| 318 | C22×D4 | — | 30 | 1 | no | — |
| 319 | C22×D4 | — | 30 | 1 | no | — |
| 320 | C2×D8 | — | 30 | 1 | no | — |
| 321 | C2×D8 | — | 30 | 1 | no | — |
| 322 | #123 | — | 30 | 1 | no | — |
| 323 | #123 | — | 30 | 1 | no | — |
| 324 | #121 | — | 5 | 1 | no | — |
| 325 | #121 | — | 15 | 1 | no | — |
| 326 | #121 | — | 30 | 1 | no | — |
| 327 | #120 | — | 30 | 1 | no | — |
| 328 | #120 | — | 30 | 1 | no | — |
| 329 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 330 | C2×C22⋊C4 | — | 30 | 1 | no | — |
| 331 | #102 | — | 30 | 1 | no | — |
| 332 | #102 | — | 30 | 1 | no | — |
| 333 | C22⋊C8 | — | 3 | 1 | no | — |
| 334 | C22⋊C8 | D3×D5 | 1 | 1 | yes | characteristic, complemented |
| 335 | #95 | — | 5 | 1 | no | — |
| 336 | C2×C3×C5 | — | 2 | 1 | no | — |
| 337 | C2×C3×C5 | — | 2 | 1 | no | — |
| 338 | C2×C3×C5 | #447 | 1 | 1 | yes | characteristic |
| 339 | C2×C3×C5 | #453 | 1 | 1 | yes | characteristic |
| 340 | C2×C3×C5 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 341 | D15 | — | 8 | 1 | no | — |
| 342 | D15 | — | 8 | 2 | no | — |
| 343 | C3×D5 | — | 8 | 1 | no | — |
| 344 | C5×D3 | — | 4 | 2 | no | — |
| 345 | C23×C3 | — | 10 | 1 | no | — |
| 346 | C23×C3 | C2×D20 | 1 | 1 | yes | characteristic |
| 347 | C22×D3 | — | 2 | 1 | no | — |
| 348 | C22×D3 | — | 2 | 1 | no | — |
| 349 | C22×D3 | — | 4 | 1 | no | — |
| 350 | C22×D3 | — | 4 | 1 | no | — |
| 351 | C22×D3 | — | 10 | 2 | no | — |
| 352 | C22×D3 | — | 10 | 1 | no | — |
| 353 | C22×D3 | — | 20 | 2 | no | — |
| 354 | C22×D3 | — | 20 | 1 | no | — |
| 355 | C22×D3 | — | 20 | 1 | no | — |
| 356 | C22×D3 | — | 20 | 1 | no | — |
| 357 | C22×D3 | — | 20 | 1 | no | — |
| 358 | C22×D3 | — | 20 | 1 | no | — |
| 359 | C22×D3 | — | 20 | 1 | no | — |
| 360 | C22×D3 | — | 40 | 1 | no | — |
| 361 | C22×D3 | — | 40 | 1 | no | — |
| 362 | C22×D3 | D40 | 1 | 2 | yes | complemented |
| 363 | C3×D4 | — | 20 | 1 | no | — |
| 364 | C3×D4 | — | 20 | 1 | no | — |
| 365 | C3×D4 | — | 20 | 1 | no | — |
| 366 | C2×C3×C4 | — | 4 | 1 | no | — |
| 367 | C2×C3×C4 | — | 10 | 2 | no | — |
| 368 | C2×C3×C4 | — | 10 | 1 | no | — |
| 369 | C2×C3×C4 | — | 20 | 1 | no | — |
| 370 | C2×C3×C4 | — | 20 | 1 | no | — |
| 371 | C2×C3×C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 372 | C2×C3×C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 373 | #67 | — | 20 | 2 | no | — |
| 374 | #67 | — | 20 | 1 | no | — |
| 375 | #67 | — | 20 | 1 | no | — |
| 376 | #67 | — | 40 | 1 | no | — |
| 377 | C2×Dic3 | — | 2 | 1 | no | — |
| 378 | C2×Dic3 | — | 4 | 1 | no | — |
| 379 | C2×Dic3 | — | 10 | 1 | no | — |
| 380 | D12 | — | 10 | 2 | no | — |
| 381 | D12 | — | 10 | 2 | no | — |
| 382 | D12 | — | 20 | 1 | no | — |
| 383 | D12 | — | 20 | 1 | no | — |
| 384 | D12 | — | 20 | 1 | no | — |
| 385 | D12 | — | 20 | 2 | no | — |
| 386 | D12 | — | 20 | 8 | no | — |
| 387 | C4×D3 | — | 20 | 2 | no | — |
| 388 | C3×C8 | — | 4 | 1 | no | — |
| 389 | C3⋊C8 | — | 4 | 1 | no | — |
| 390 | C22×C5 | — | 2 | 1 | no | — |
| 391 | C22×C5 | — | 2 | 1 | no | — |
| 392 | C22×C5 | — | 6 | 2 | no | — |
| 393 | C22×C5 | — | 12 | 2 | no | — |
| 394 | C22×C5 | — | 12 | 1 | no | — |
| 395 | C22×C5 | — | 12 | 1 | no | — |
| 396 | C22×C5 | — | 24 | 1 | no | — |
| 397 | C22×C5 | #882 | 1 | 1 | yes | characteristic |
| 398 | C22×C5 | D3×D8 | 1 | 1 | yes | characteristic |
| 399 | C22×C5 | #914 | 1 | 1 | yes | characteristic |
| 400 | C2×D5 | — | 4 | 1 | no | — |
| 401 | C2×D5 | — | 4 | 1 | no | — |
| 402 | C2×D5 | — | 4 | 1 | no | — |
| 403 | C2×D5 | — | 12 | 2 | no | — |
| 404 | C2×D5 | — | 12 | 2 | no | — |
| 405 | C2×D5 | — | 12 | 2 | no | — |
| 406 | C2×D5 | — | 12 | 1 | no | — |
| 407 | C2×D5 | — | 12 | 1 | no | — |
| 408 | C2×D5 | — | 12 | 1 | no | — |
| 409 | C2×D5 | — | 24 | 4 | no | — |
| 410 | C2×D5 | — | 24 | 1 | no | — |
| 411 | C2×D5 | — | 24 | 1 | no | — |
| 412 | C2×D5 | — | 24 | 1 | no | — |
| 413 | C2×D5 | — | 24 | 1 | no | — |
| 414 | C4×C5 | — | 2 | 1 | no | — |
| 415 | C4×C5 | — | 2 | 1 | no | — |
| 416 | C4×C5 | — | 12 | 1 | no | — |
| 417 | Dic5 | — | 4 | 2 | no | — |
| 418 | Dic5 | — | 4 | 1 | no | — |
| 419 | Dic5 | — | 12 | 1 | no | — |
| 420 | C24 | — | 3 | 1 | no | — |
| 421 | C24 | — | 30 | 1 | no | — |
| 422 | C24 | — | 30 | 1 | no | — |
| 423 | C2×D4 | — | 5 | 1 | no | — |
| 424 | C2×D4 | — | 10 | 1 | no | — |
| 425 | C2×D4 | — | 15 | 1 | no | — |
| 426 | C2×D4 | — | 30 | 1 | no | — |
| 427 | C2×D4 | — | 30 | 1 | no | — |
| 428 | C2×D4 | — | 30 | 1 | no | — |
| 429 | C2×D4 | — | 30 | 1 | no | — |
| 430 | C2×D4 | — | 30 | 1 | no | — |
| 431 | C2×D4 | — | 30 | 1 | no | — |
| 432 | C2×D4 | — | 60 | 2 | no | — |
| 433 | C2×D4 | — | 60 | 2 | no | — |
| 434 | C2×D4 | — | 60 | 2 | no | — |
| 435 | C2×D4 | — | 60 | 2 | no | — |
| 436 | C2×D4 | — | 60 | 2 | no | — |
| 437 | C2×D4 | — | 60 | 2 | no | — |
| 438 | C22×C4 | — | 3 | 1 | no | — |
| 439 | C22×C4 | — | 10 | 1 | no | — |
| 440 | C22×C4 | — | 30 | 1 | no | — |
| 441 | C22×C4 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 442 | D8 | — | 60 | 2 | no | — |
| 443 | D8 | — | 60 | 2 | no | — |
| 444 | C2×C8 | — | 2 | 1 | no | — |
| 445 | C2×C8 | — | 6 | 1 | no | — |
| 446 | C4⋊C4 | — | 5 | 1 | no | — |
| 447 | C4⋊C4 | — | 15 | 1 | no | — |
| 448 | C4⋊C4 | — | 30 | 1 | no | — |
| 449 | C22⋊C4 | — | 6 | 1 | no | — |
| 450 | C22⋊C4 | — | 6 | 1 | no | — |
| 451 | C22⋊C4 | — | 10 | 1 | no | — |
| 452 | C22⋊C4 | — | 30 | 1 | no | — |
| 453 | C22⋊C4 | — | 30 | 1 | no | — |
| 454 | C22⋊C4 | — | 30 | 1 | no | — |
| 455 | C22⋊C4 | — | 60 | 2 | no | — |
| 456 | C3×C5 | #1595 | 1 | 1 | yes | characteristic, complemented, Hall |
| 457 | C22×C3 | — | 2 | 1 | no | — |
| 458 | C22×C3 | — | 2 | 1 | no | — |
| 459 | C22×C3 | — | 20 | 1 | no | — |
| 460 | C22×C3 | — | 20 | 1 | no | — |
| 461 | C22×C3 | — | 20 | 1 | no | — |
| 462 | C22×C3 | #4028 | 1 | 1 | yes | characteristic |
| 463 | C22×C3 | C2×D40 | 1 | 1 | yes | characteristic |
| 464 | C22×C3 | #4054 | 1 | 1 | yes | characteristic |
| 465 | C2×D3 | — | 2 | 2 | no | — |
| 466 | C2×D3 | — | 4 | 1 | no | — |
| 467 | C2×D3 | — | 4 | 1 | no | — |
| 468 | C2×D3 | — | 4 | 2 | no | — |
| 469 | C2×D3 | — | 8 | 1 | no | — |
| 470 | C2×D3 | — | 20 | 2 | no | — |
| 471 | C2×D3 | — | 20 | 2 | no | — |
| 472 | C2×D3 | — | 20 | 2 | no | — |
| 473 | C2×D3 | — | 20 | 1 | no | — |
| 474 | C2×D3 | — | 20 | 1 | no | — |
| 475 | C2×D3 | — | 20 | 1 | no | — |
| 476 | C2×D3 | — | 40 | 4 | no | — |
| 477 | C2×D3 | — | 40 | 1 | no | — |
| 478 | C2×D3 | — | 40 | 1 | no | — |
| 479 | C2×D3 | — | 40 | 1 | no | — |
| 480 | C2×D3 | — | 40 | 1 | no | — |
| 481 | C3×C4 | — | 2 | 1 | no | — |
| 482 | C3×C4 | — | 2 | 1 | no | — |
| 483 | C3×C4 | — | 20 | 2 | no | — |
| 484 | C3×C4 | — | 20 | 1 | no | — |
| 485 | Dic3 | — | 4 | 1 | no | — |
| 486 | Dic3 | — | 20 | 1 | no | — |
| 487 | C2×C5 | — | 2 | 1 | no | — |
| 488 | C2×C5 | — | 2 | 1 | no | — |
| 489 | C2×C5 | — | 12 | 2 | no | — |
| 490 | C2×C5 | #4741 | 1 | 1 | yes | characteristic |
| 491 | C2×C5 | #4773 | 1 | 1 | yes | characteristic |
| 492 | C2×C5 | #4822 | 1 | 1 | yes | characteristic |
| 493 | D5 | — | 8 | 1 | no | — |
| 494 | D5 | — | 24 | 2 | no | — |
| 495 | D5 | — | 24 | 1 | no | — |
| 496 | C23 | — | 3 | 2 | no | — |
| 497 | C23 | — | 6 | 1 | no | — |
| 498 | C23 | — | 6 | 1 | no | — |
| 499 | C23 | — | 10 | 1 | no | — |
| 500 | C23 | — | 12 | 1 | no | — |
| 501 | C23 | — | 12 | 1 | no | — |
| 502 | C23 | — | 30 | 2 | no | — |
| 503 | C23 | — | 30 | 1 | no | — |
| 504 | C23 | — | 60 | 1 | no | — |
| 505 | C23 | — | 60 | 1 | no | — |
| 506 | C23 | — | 60 | 1 | no | — |
| 507 | C23 | — | 60 | 2 | no | — |
| 508 | C23 | — | 60 | 1 | no | — |
| 509 | C23 | — | 60 | 1 | no | — |
| 510 | C23 | — | 60 | 1 | no | — |
| 511 | C23 | — | 120 | 1 | no | — |
| 512 | C23 | — | 120 | 1 | no | — |
| 513 | C23 | D3×D20 | 1 | 1 | yes | characteristic |
| 514 | D4 | — | 20 | 1 | no | — |
| 515 | D4 | — | 20 | 1 | no | — |
| 516 | D4 | — | 20 | 1 | no | — |
| 517 | D4 | — | 30 | 2 | no | — |
| 518 | D4 | — | 30 | 2 | no | — |
| 519 | D4 | — | 60 | 1 | no | — |
| 520 | D4 | — | 60 | 1 | no | — |
| 521 | D4 | — | 60 | 1 | no | — |
| 522 | D4 | — | 60 | 2 | no | — |
| 523 | D4 | — | 60 | 8 | no | — |
| 524 | D4 | — | 60 | 2 | no | — |
| 525 | D4 | — | 60 | 1 | no | — |
| 526 | D4 | — | 60 | 1 | no | — |
| 527 | D4 | — | 120 | 1 | no | — |
| 528 | C2×C4 | — | 4 | 1 | no | — |
| 529 | C2×C4 | — | 6 | 1 | no | — |
| 530 | C2×C4 | — | 10 | 2 | no | — |
| 531 | C2×C4 | — | 10 | 1 | no | — |
| 532 | C2×C4 | — | 12 | 1 | no | — |
| 533 | C2×C4 | — | 20 | 1 | no | — |
| 534 | C2×C4 | — | 20 | 1 | no | — |
| 535 | C2×C4 | — | 30 | 1 | no | — |
| 536 | C2×C4 | — | 60 | 2 | no | — |
| 537 | C2×C4 | D5×D12 | 1 | 1 | yes | characteristic |
| 538 | C2×C4 | #6790 | 1 | 1 | yes | characteristic |
| 539 | C8 | — | 4 | 1 | no | — |
| 540 | C8 | — | 12 | 1 | no | — |
| 541 | C2×C3 | — | 2 | 1 | no | — |
| 542 | C2×C3 | — | 2 | 1 | no | — |
| 543 | C2×C3 | — | 40 | 1 | no | — |
| 544 | C2×C3 | #65021 | 1 | 1 | yes | characteristic |
| 545 | C2×C3 | #65030 | 1 | 1 | yes | characteristic |
| 546 | C2×C3 | #65036 | 1 | 1 | yes | characteristic |
| 547 | D3 | — | 4 | 2 | no | — |
| 548 | D3 | — | 40 | 2 | no | — |
| 549 | D3 | — | 40 | 1 | no | — |
| 550 | C5 | #68284 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 551 | C22 | — | 2 | 1 | no | — |
| 552 | C22 | — | 2 | 1 | no | — |
| 553 | C22 | — | 6 | 2 | no | — |
| 554 | C22 | — | 12 | 2 | no | — |
| 555 | C22 | — | 12 | 1 | no | — |
| 556 | C22 | — | 12 | 1 | no | — |
| 557 | C22 | — | 20 | 1 | no | — |
| 558 | C22 | — | 20 | 1 | no | — |
| 559 | C22 | — | 20 | 1 | no | — |
| 560 | C22 | — | 24 | 1 | no | — |
| 561 | C22 | — | 60 | 2 | no | — |
| 562 | C22 | — | 60 | 2 | no | — |
| 563 | C22 | — | 60 | 1 | no | — |
| 564 | C22 | — | 60 | 2 | no | — |
| 565 | C22 | — | 60 | 1 | no | — |
| 566 | C22 | — | 60 | 1 | no | — |
| 567 | C22 | — | 120 | 1 | no | — |
| 568 | C22 | — | 120 | 1 | no | — |
| 569 | C22 | — | 120 | 4 | no | — |
| 570 | C22 | — | 120 | 1 | no | — |
| 571 | C22 | — | 120 | 1 | no | — |
| 572 | C22 | D3×D40 | 1 | 1 | yes | characteristic |
| 573 | C22 | #91253 | 1 | 1 | yes | characteristic |
| 574 | C22 | #91476 | 1 | 1 | yes | characteristic |
| 575 | C4 | — | 2 | 1 | no | — |
| 576 | C4 | — | 2 | 1 | no | — |
| 577 | C4 | — | 12 | 1 | no | — |
| 578 | C4 | — | 20 | 2 | no | — |
| 579 | C4 | — | 20 | 1 | no | — |
| 580 | C4 | — | 60 | 1 | no | — |
| 581 | C3 | #10598899 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 582 | C2 | — | 2 | 1 | no | — |
| 583 | C2 | — | 2 | 1 | no | — |
| 584 | C2 | — | 12 | 2 | no | — |
| 585 | C2 | — | 40 | 1 | no | — |
| 586 | C2 | — | 120 | 2 | no | — |
| 587 | C2 | — | 120 | 1 | no | — |
| 588 | C2 | #11747137 | 1 | 1 | yes | characteristic |
| 589 | C2 | #11748121 | 1 | 1 | yes | characteristic |
| 590 | C2 | #11748249 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11754660 | C2 | semidirect |
| 2. #11750833 | C2 | semidirect |
| 3. #11748932 | C2 | semidirect |
| 4. #11748524 | C2 | semidirect |
| 5. C5×#4468 | C2 | semidirect |
| 6. C3×#64690 | C2 | semidirect |
| 7. #11745958 | C2 | semidirect |
| 9. C22×D60 | C22 | semidirect |
| 23. C3×C5×C22⋊C8 | C22 | semidirect |
| 25. C5×#830 | C22 | semidirect |
| 26. C3×#3963 | C22 | semidirect |
| 35. #64690 | D3 | semidirect |
| 44. C2×D60 | D4 | semidirect |
| 48. C2×C3×D20 | D4 | semidirect |
| 60. C4⋊Dic15 | D4 | semidirect |
| 66. C3×C4⋊Dic5 | D4 | semidirect |
| 77. #4468 | D5 | semidirect |
| 94. C5×C22⋊C8 | C2×D3 | semidirect |
| 95. #3963 | C2×D3 | semidirect |
| 112. C22×C5×D3 | D8 | semidirect |
| 158. C3×C22⋊C8 | C2×D5 | semidirect |
| 160. #830 | C2×D5 | semidirect |
| 184. C2×D20 | D12 | semidirect |
| 196. C4⋊Dic5 | D12 | semidirect |
| 334. C22⋊C8 | D3×D5 | semidirect |
| 362. C22×D3 | D40 | semidirect |
| 456. C3×C5 | #1595 | semidirect |
| 550. C5 | #68284 | semidirect |
| 581. C3 | #10598899 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11754660 | 2 |
| #11750833 | 2 |
| #11748932 | 2 |
| #11748524 | 2 |
| C5×#4468 | 2 |
| C3×#64690 | 2 |
| #11745958 | 2 |
| #10598899 | 3 |
| #68284 | 5 |