Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
952 conjugacy classes of subgroups.
The subgroup lattice has 552 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11754703 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #11754697 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #11751178 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C5×#5077 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#65362 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11749139 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11748947 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11747114 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11747018 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #10612013 | — | 3 | 1 | no | maximal, Hall |
| 11 | #92095 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | C5×#1004 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | #92017 | C22 | 1 | 2 | yes | complemented |
| 14 | C3×C5×#127 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | #91821 | C22 | 1 | 2 | yes | complemented |
| 16 | C5×#932 | C22 | 1 | 2 | yes | complemented |
| 17 | C2×C3×#686 | C22 | 1 | 2 | yes | complemented |
| 18 | C2×C3×#686 | C22 | 1 | 2 | yes | complemented |
| 19 | C3×#4020 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | #91498 | — | 2 | 2 | no | — |
| 21 | #91497 | — | 2 | 2 | no | — |
| 22 | #91494 | — | 2 | 2 | no | — |
| 23 | #91493 | — | 2 | 2 | no | — |
| 24 | #91482 | — | 2 | 2 | no | — |
| 25 | #91481 | — | 2 | 2 | no | — |
| 26 | #91480 | — | 2 | 2 | no | — |
| 27 | D3×#686 | — | 2 | 2 | no | — |
| 28 | #91312 | C22 | 1 | 2 | yes | complemented |
| 29 | #91303 | C22 | 1 | 2 | yes | — |
| 30 | #91298 | C22 | 1 | 2 | yes | complemented |
| 31 | #91290 | C22 | 1 | 2 | yes | complemented |
| 32 | #91286 | C22 | 1 | 2 | yes | complemented |
| 33 | #91117 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | #91089 | C22 | 1 | 2 | yes | complemented |
| 35 | C5×#833 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | C5×#805 | C22 | 1 | 2 | yes | complemented |
| 37 | C3×C4×#168 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | #90991 | C22 | 1 | 2 | yes | complemented |
| 39 | #90958 | C22 | 1 | 2 | yes | complemented |
| 40 | #81791 | — | 5 | 1 | no | maximal, Hall |
| 41 | #66169 | — | 3 | 2 | no | — |
| 42 | #66108 | — | 3 | 2 | no | — |
| 43 | C5×#453 | — | 3 | 1 | no | — |
| 44 | #65488 | — | 3 | 2 | no | — |
| 45 | #65366 | — | 3 | 1 | no | — |
| 46 | #65362 | D3 | 1 | 1 | yes | characteristic, complemented |
| 47 | #65113 | — | 3 | 2 | no | — |
| 48 | #65111 | — | 3 | 2 | no | — |
| 49 | #65038 | — | 3 | 2 | no | — |
| 50 | C2×C3×C5×D4 | — | 4 | 1 | no | — |
| 51 | C2×C3×C5×D4 | C23 | 1 | 1 | yes | characteristic |
| 52 | C2×C3×C5×D4 | C23 | 1 | 1 | yes | characteristic |
| 53 | C2×#1220 | — | 4 | 1 | no | — |
| 54 | #6819 | — | 2 | 2 | no | — |
| 55 | D4×D15 | — | 2 | 2 | no | — |
| 56 | #6817 | C23 | 1 | 2 | yes | — |
| 57 | C2×C5×#67 | — | 4 | 1 | no | — |
| 58 | C5×#237 | — | 2 | 2 | no | — |
| 59 | C5×D3×D4 | — | 2 | 2 | no | — |
| 60 | C5×#235 | C23 | 1 | 2 | yes | — |
| 61 | C2×C3×D20 | — | 4 | 1 | no | — |
| 62 | C2×C3×D20 | C23 | 1 | 2 | yes | — |
| 63 | D5×#67 | — | 4 | 2 | no | — |
| 64 | #6777 | — | 2 | 2 | no | — |
| 65 | D3×D20 | — | 2 | 2 | no | — |
| 66 | #6766 | — | 2 | 2 | no | — |
| 67 | #6765 | — | 2 | 2 | no | — |
| 68 | C3×C42×C5 | C23 | 1 | 1 | yes | characteristic |
| 69 | #6716 | — | 2 | 2 | no | — |
| 70 | #6715 | — | 2 | 2 | no | — |
| 71 | #6710 | C23 | 1 | 2 | yes | — |
| 72 | C5×#214 | — | 2 | 2 | no | — |
| 73 | C5×#213 | — | 2 | 2 | no | — |
| 74 | C5×#208 | C23 | 1 | 2 | yes | — |
| 75 | C3×#686 | — | 2 | 2 | no | — |
| 76 | C3×#686 | — | 2 | 2 | no | — |
| 77 | C3×#686 | — | 2 | 2 | no | — |
| 78 | C3×#686 | — | 2 | 2 | no | — |
| 79 | C2×C3×#168 | C23 | 1 | 2 | yes | — |
| 80 | #6663 | D4 | 1 | 2 | yes | complemented |
| 81 | #6660 | D4 | 1 | 2 | yes | complemented |
| 82 | #6659 | D4 | 1 | 2 | yes | complemented |
| 83 | #6657 | — | 2 | 2 | no | — |
| 84 | #6655 | — | 2 | 2 | no | — |
| 85 | #6654 | D4 | 1 | 2 | yes | complemented |
| 86 | #6653 | — | 2 | 2 | no | — |
| 87 | #6652 | — | 2 | 2 | no | — |
| 88 | #6651 | — | 2 | 2 | no | — |
| 89 | #6650 | — | 2 | 2 | no | — |
| 90 | #6648 | — | 2 | 2 | no | — |
| 91 | D3×#168 | — | 2 | 2 | no | — |
| 92 | #5757 | — | 5 | 2 | no | — |
| 93 | #5757 | — | 5 | 2 | no | — |
| 94 | C3×#493 | — | 5 | 1 | no | — |
| 95 | #5160 | — | 5 | 2 | no | — |
| 96 | #5160 | — | 5 | 2 | no | — |
| 97 | #5077 | — | 5 | 1 | no | — |
| 98 | #5077 | — | 5 | 2 | no | — |
| 99 | #5077 | D5 | 1 | 1 | yes | characteristic, complemented |
| 100 | #4700 | — | 5 | 2 | no | — |
| 101 | C5×H(5,𝔽2) | — | 3 | 1 | no | — |
| 102 | #4149 | — | 3 | 2 | no | — |
| 103 | #4144 | — | 3 | 1 | no | — |
| 104 | C5×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 105 | C5×#127 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 106 | #4096 | — | 3 | 2 | no | — |
| 107 | #4096 | — | 6 | 2 | no | — |
| 108 | #4095 | — | 3 | 2 | no | — |
| 109 | #4095 | — | 6 | 2 | no | — |
| 110 | #4094 | — | 3 | 2 | no | — |
| 111 | #4078 | — | 3 | 2 | no | — |
| 112 | #4078 | — | 6 | 2 | no | — |
| 113 | C2×#686 | — | 6 | 2 | no | — |
| 114 | C2×#686 | C2×D3 | 1 | 2 | yes | complemented |
| 115 | C2×#686 | C2×D3 | 1 | 2 | yes | complemented |
| 116 | #4062 | — | 6 | 2 | no | — |
| 117 | #4060 | — | 6 | 2 | no | — |
| 118 | #4057 | — | 6 | 2 | no | — |
| 119 | D5×D8 | — | 6 | 2 | no | — |
| 120 | #4054 | — | 3 | 2 | no | — |
| 121 | #4053 | — | 3 | 2 | no | — |
| 122 | #4020 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 123 | C5×#104 | — | 3 | 2 | no | — |
| 124 | C5×#100 | — | 3 | 1 | no | — |
| 125 | #3965 | — | 3 | 1 | no | — |
| 126 | #3955 | — | 3 | 2 | no | — |
| 127 | #3954 | — | 3 | 2 | no | — |
| 128 | #3937 | — | 3 | 2 | no | — |
| 129 | C4×#168 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 130 | #3292 | — | 15 | 1 | no | Sylow |
| 131 | C23×C3×C5 | — | 2 | 1 | no | — |
| 132 | C23×C3×C5 | — | 2 | 1 | no | — |
| 133 | C22×D15 | — | 4 | 1 | no | — |
| 134 | C22×C5×D3 | — | 4 | 1 | no | — |
| 135 | C22×C3×D5 | — | 2 | 2 | no | — |
| 136 | C2×D3×D5 | — | 4 | 2 | no | — |
| 137 | C3×C5×D4 | — | 2 | 2 | no | — |
| 138 | C3×C5×D4 | — | 2 | 2 | no | — |
| 139 | C3×C5×D4 | — | 8 | 2 | no | — |
| 140 | C2×C3×C4×C5 | — | 2 | 1 | no | — |
| 141 | C2×C3×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 142 | #1220 | — | 2 | 2 | no | — |
| 143 | #1220 | — | 4 | 2 | no | — |
| 144 | C2×Dic15 | — | 4 | 1 | no | — |
| 145 | D60 | C2×D4 | 1 | 2 | yes | — |
| 146 | C4×D15 | — | 2 | 2 | no | — |
| 147 | Dic30 | C2×D4 | 1 | 2 | yes | — |
| 148 | C5×#67 | — | 2 | 2 | no | — |
| 149 | C5×#67 | — | 4 | 2 | no | — |
| 150 | C2×C5×Dic3 | — | 4 | 1 | no | — |
| 151 | C5×D12 | C2×D4 | 1 | 2 | yes | — |
| 152 | C4×C5×D3 | — | 2 | 2 | no | — |
| 153 | C5×Dic6 | C2×D4 | 1 | 2 | yes | — |
| 154 | C3×D20 | — | 2 | 2 | no | — |
| 155 | C3×D20 | — | 2 | 2 | no | — |
| 156 | C3×D20 | — | 8 | 2 | no | — |
| 157 | #1202 | — | 4 | 2 | no | — |
| 158 | #1201 | — | 4 | 2 | no | — |
| 159 | D5×Dic3 | — | 4 | 2 | no | — |
| 160 | C3⋊#168 | — | 2 | 2 | no | — |
| 161 | C3×#168 | C2×D4 | 1 | 2 | yes | — |
| 162 | C3×#168 | C2×D4 | 1 | 2 | yes | — |
| 163 | C5×C3⋊C8 | — | 2 | 2 | no | — |
| 164 | #1004 | — | 5 | 1 | no | — |
| 165 | #1004 | — | 5 | 2 | no | — |
| 166 | #1004 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 167 | C2×C3×D8 | — | 5 | 2 | no | — |
| 168 | C2×C3×D8 | — | 5 | 2 | no | — |
| 169 | C3×#127 | — | 5 | 1 | no | — |
| 170 | C3×#127 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 171 | #932 | — | 5 | 2 | no | — |
| 172 | #932 | — | 5 | 2 | no | — |
| 173 | #932 | — | 5 | 2 | no | — |
| 174 | #932 | C2×D5 | 1 | 2 | yes | complemented |
| 175 | #912 | — | 10 | 2 | no | — |
| 176 | #912 | — | 10 | 2 | no | — |
| 177 | #911 | — | 10 | 2 | no | — |
| 178 | #911 | — | 10 | 2 | no | — |
| 179 | #911 | — | 10 | 2 | no | — |
| 180 | #911 | — | 10 | 2 | no | — |
| 181 | D3×D8 | — | 10 | 2 | no | — |
| 182 | D3×D8 | — | 10 | 2 | no | — |
| 183 | #904 | — | 5 | 2 | no | — |
| 184 | #901 | — | 5 | 2 | no | — |
| 185 | #901 | — | 5 | 2 | no | — |
| 186 | C3×C4×C8 | — | 5 | 1 | no | — |
| 187 | #833 | — | 5 | 1 | no | — |
| 188 | #833 | — | 5 | 2 | no | — |
| 189 | #833 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 190 | #819 | — | 5 | 2 | no | — |
| 191 | #805 | — | 5 | 2 | no | — |
| 192 | #805 | C2×D5 | 1 | 2 | yes | complemented |
| 193 | C5×#41 | — | 3 | 2 | no | — |
| 194 | C5×#41 | — | 6 | 2 | no | — |
| 195 | C2×C5×D4 | — | 4 | 1 | no | — |
| 196 | C2×C5×D4 | — | 6 | 2 | no | — |
| 197 | C2×C5×D4 | — | 12 | 1 | no | — |
| 198 | C2×C5×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 199 | C2×C5×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 200 | C2×C22⋊D5 | — | 12 | 1 | no | — |
| 201 | #713 | — | 6 | 2 | no | — |
| 202 | #711 | — | 6 | 2 | no | — |
| 203 | D4×D5 | — | 6 | 2 | no | — |
| 204 | D4×D5 | — | 6 | 2 | no | — |
| 205 | D4×D5 | — | 12 | 2 | no | — |
| 206 | #709 | — | 3 | 2 | no | — |
| 207 | #709 | — | 6 | 2 | no | — |
| 208 | C2×D20 | — | 4 | 1 | no | — |
| 209 | C2×D20 | — | 6 | 2 | no | — |
| 210 | C2×D20 | C22×D3 | 1 | 2 | yes | — |
| 211 | C5×SD16 | — | 6 | 2 | no | — |
| 212 | C5×D8 | — | 6 | 2 | no | — |
| 213 | C5×M16 | — | 3 | 2 | no | — |
| 214 | C42×C5 | C22×D3 | 1 | 1 | yes | characteristic |
| 215 | #689 | — | 3 | 2 | no | — |
| 216 | #688 | — | 3 | 2 | no | — |
| 217 | #688 | — | 6 | 2 | no | — |
| 218 | #687 | — | 3 | 2 | no | — |
| 219 | #687 | — | 6 | 2 | no | — |
| 220 | #686 | — | 2 | 2 | no | — |
| 221 | #686 | — | 2 | 2 | no | — |
| 222 | #686 | — | 2 | 2 | no | — |
| 223 | #686 | — | 2 | 2 | no | — |
| 224 | #686 | — | 3 | 2 | no | — |
| 225 | #686 | — | 6 | 2 | no | — |
| 226 | #686 | — | 6 | 2 | no | — |
| 227 | #681 | — | 3 | 2 | no | — |
| 228 | #681 | — | 6 | 2 | no | — |
| 229 | C2×#168 | — | 6 | 2 | no | — |
| 230 | C2×#168 | C22×D3 | 1 | 2 | yes | — |
| 231 | D40 | — | 6 | 2 | no | — |
| 232 | #677 | — | 6 | 2 | no | — |
| 233 | #676 | — | 6 | 2 | no | — |
| 234 | C8×D5 | — | 6 | 2 | no | — |
| 235 | #576 | — | 15 | 2 | no | — |
| 236 | #576 | — | 15 | 2 | no | — |
| 237 | #493 | — | 5 | 1 | no | — |
| 238 | #472 | — | 15 | 2 | no | — |
| 239 | #472 | — | 15 | 2 | no | — |
| 240 | #453 | — | 3 | 1 | no | — |
| 241 | #453 | — | 15 | 2 | no | — |
| 242 | #453 | — | 15 | 1 | no | — |
| 243 | #443 | — | 15 | 2 | no | — |
| 244 | C22×C3×C5 | — | 4 | 1 | no | — |
| 245 | C22×C3×C5 | — | 4 | 1 | no | — |
| 246 | C22×C3×C5 | — | 8 | 1 | no | — |
| 247 | C22×C3×C5 | — | 8 | 1 | no | — |
| 248 | C22×C3×C5 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 249 | C2×D15 | — | 2 | 2 | no | — |
| 250 | C2×D15 | — | 16 | 1 | no | — |
| 251 | C2×C5×D3 | — | 2 | 2 | no | — |
| 252 | C2×C5×D3 | — | 16 | 1 | no | — |
| 253 | C2×C3×D5 | — | 4 | 2 | no | — |
| 254 | C2×C3×D5 | — | 8 | 2 | no | — |
| 255 | D3×D5 | — | 16 | 2 | no | — |
| 256 | C3×C4×C5 | — | 2 | 2 | no | — |
| 257 | C3×C4×C5 | C22×D4 | 1 | 2 | yes | — |
| 258 | Dic15 | — | 2 | 2 | no | — |
| 259 | C5×Dic3 | — | 2 | 2 | no | — |
| 260 | C2×C3×D4 | — | 4 | 1 | no | — |
| 261 | C2×C3×D4 | — | 5 | 2 | no | — |
| 262 | C2×C3×D4 | — | 20 | 1 | no | — |
| 263 | C2×C3×D4 | C22×D5 | 1 | 1 | yes | characteristic |
| 264 | C2×C3×D4 | C22×D5 | 1 | 1 | yes | characteristic |
| 265 | C2×#67 | — | 4 | 1 | no | — |
| 266 | C2×#67 | — | 20 | 2 | no | — |
| 267 | C2×#67 | — | 20 | 1 | no | — |
| 268 | #237 | — | 2 | 2 | no | — |
| 269 | #237 | — | 10 | 2 | no | — |
| 270 | #237 | — | 10 | 2 | no | — |
| 271 | #237 | — | 10 | 2 | no | — |
| 272 | D3×D4 | — | 2 | 2 | no | — |
| 273 | D3×D4 | — | 10 | 2 | no | — |
| 274 | D3×D4 | — | 10 | 2 | no | — |
| 275 | D3×D4 | — | 10 | 2 | no | — |
| 276 | #235 | — | 5 | 2 | no | — |
| 277 | #235 | C22×D5 | 1 | 2 | yes | — |
| 278 | C3×D8 | — | 10 | 2 | no | — |
| 279 | C3×D8 | — | 10 | 2 | no | — |
| 280 | C3×D8 | — | 10 | 2 | no | — |
| 281 | C3×D8 | — | 10 | 2 | no | — |
| 282 | C2×C3×C8 | — | 5 | 2 | no | — |
| 283 | C3×C42 | C22×D5 | 1 | 1 | yes | characteristic |
| 284 | #214 | — | 2 | 2 | no | — |
| 285 | #214 | — | 10 | 2 | no | — |
| 286 | #214 | — | 10 | 2 | no | — |
| 287 | #214 | — | 10 | 2 | no | — |
| 288 | #213 | — | 2 | 2 | no | — |
| 289 | #213 | — | 10 | 2 | no | — |
| 290 | #213 | — | 10 | 2 | no | — |
| 291 | #213 | — | 10 | 2 | no | — |
| 292 | #208 | — | 5 | 2 | no | — |
| 293 | #208 | C22×D5 | 1 | 2 | yes | — |
| 294 | Dic12 | — | 5 | 2 | no | — |
| 295 | D24 | — | 5 | 2 | no | — |
| 296 | #204 | — | 5 | 2 | no | — |
| 297 | #204 | — | 5 | 2 | no | — |
| 298 | ΓL(1,𝔽25) | — | 10 | 2 | no | — |
| 299 | ΓL(1,𝔽25) | — | 10 | 2 | no | — |
| 300 | D3×C8 | — | 10 | 2 | no | — |
| 301 | D3×C8 | — | 10 | 2 | no | — |
| 302 | C23×C5 | — | 2 | 1 | no | — |
| 303 | C23×C5 | — | 2 | 1 | no | — |
| 304 | C23×C5 | — | 12 | 1 | no | — |
| 305 | C22×D5 | — | 2 | 2 | no | — |
| 306 | C22×D5 | — | 12 | 2 | no | — |
| 307 | C22×D5 | — | 12 | 1 | no | — |
| 308 | C5×Q8 | — | 3 | 2 | no | — |
| 309 | C5×D4 | — | 2 | 2 | no | — |
| 310 | C5×D4 | — | 2 | 2 | no | — |
| 311 | C5×D4 | — | 3 | 2 | no | — |
| 312 | C5×D4 | — | 6 | 2 | no | — |
| 313 | C5×D4 | — | 8 | 2 | no | — |
| 314 | C5×D4 | — | 12 | 2 | no | — |
| 315 | C2×C4×C5 | — | 2 | 1 | no | — |
| 316 | C2×C4×C5 | — | 6 | 2 | no | — |
| 317 | C2×C4×C5 | — | 12 | 1 | no | — |
| 318 | C2×C4×C5 | C23×D3 | 1 | 1 | yes | characteristic |
| 319 | C22⋊D5 | — | 6 | 2 | no | — |
| 320 | C22⋊D5 | — | 12 | 2 | no | — |
| 321 | C22⋊D5 | — | 12 | 2 | no | — |
| 322 | C2×Dic5 | — | 12 | 1 | no | — |
| 323 | D20 | — | 2 | 2 | no | — |
| 324 | D20 | — | 2 | 2 | no | — |
| 325 | D20 | — | 3 | 2 | no | — |
| 326 | D20 | — | 8 | 2 | no | — |
| 327 | D20 | — | 12 | 2 | no | — |
| 328 | C4×D5 | — | 6 | 2 | no | — |
| 329 | C4×D5 | — | 12 | 2 | no | — |
| 330 | Dic10 | — | 3 | 2 | no | — |
| 331 | C5×C8 | — | 6 | 2 | no | — |
| 332 | #168 | — | 6 | 2 | no | — |
| 333 | #168 | D3×D4 | 1 | 2 | yes | — |
| 334 | #168 | D3×D4 | 1 | 2 | yes | — |
| 335 | H(5,𝔽2) | — | 3 | 1 | no | — |
| 336 | H(5,𝔽2) | — | 15 | 2 | no | — |
| 337 | H(5,𝔽2) | — | 15 | 1 | no | — |
| 338 | AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 339 | AGL(1,ℤ/8) | — | 15 | 2 | no | — |
| 340 | AGL(1,ℤ/8) | — | 15 | 2 | no | — |
| 341 | AGL(1,ℤ/8) | — | 15 | 2 | no | — |
| 342 | AGL(1,ℤ/8) | — | 30 | 2 | no | — |
| 343 | AGL(1,ℤ/8) | — | 30 | 2 | no | — |
| 344 | AGL(1,ℤ/8) | — | 30 | 2 | no | — |
| 345 | AGL(1,ℤ/8) | — | 30 | 2 | no | — |
| 346 | #135 | — | 15 | 2 | no | — |
| 347 | #135 | — | 30 | 2 | no | — |
| 348 | #135 | — | 30 | 2 | no | — |
| 349 | C2×D8 | — | 5 | 2 | no | — |
| 350 | C2×D8 | — | 5 | 2 | no | — |
| 351 | C2×D8 | — | 30 | 2 | no | — |
| 352 | C2×D8 | — | 30 | 2 | no | — |
| 353 | #131 | — | 15 | 2 | no | — |
| 354 | #131 | — | 15 | 2 | no | — |
| 355 | #127 | — | 5 | 1 | no | — |
| 356 | #127 | D3×D5 | 1 | 1 | yes | characteristic, complemented |
| 357 | #108 | — | 15 | 2 | no | — |
| 358 | #104 | — | 3 | 2 | no | — |
| 359 | #104 | — | 15 | 2 | no | — |
| 360 | #100 | — | 3 | 1 | no | — |
| 361 | #100 | — | 15 | 2 | no | — |
| 362 | #100 | — | 15 | 1 | no | — |
| 363 | C4×C8 | — | 5 | 1 | no | — |
| 364 | C2×C3×C5 | — | 2 | 1 | no | — |
| 365 | C2×C3×C5 | — | 8 | 1 | no | — |
| 366 | C2×C3×C5 | — | 8 | 1 | no | — |
| 367 | C2×C3×C5 | D42 | 1 | 1 | yes | characteristic |
| 368 | D15 | — | 4 | 2 | no | — |
| 369 | C3×D5 | — | 8 | 2 | no | — |
| 370 | C5×D3 | — | 4 | 2 | no | — |
| 371 | C23×C3 | — | 2 | 1 | no | — |
| 372 | C23×C3 | — | 2 | 1 | no | — |
| 373 | C23×C3 | — | 10 | 2 | no | — |
| 374 | C22×D3 | — | 4 | 1 | no | — |
| 375 | C22×D3 | — | 20 | 2 | no | — |
| 376 | C22×D3 | — | 20 | 1 | no | — |
| 377 | C3×D4 | — | 2 | 2 | no | — |
| 378 | C3×D4 | — | 2 | 2 | no | — |
| 379 | C3×D4 | — | 8 | 2 | no | — |
| 380 | C3×D4 | — | 10 | 2 | no | — |
| 381 | C3×D4 | — | 10 | 2 | no | — |
| 382 | C3×D4 | — | 40 | 2 | no | — |
| 383 | C2×C3×C4 | — | 2 | 1 | no | — |
| 384 | C2×C3×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 385 | #67 | — | 2 | 2 | no | — |
| 386 | #67 | — | 4 | 2 | no | — |
| 387 | #67 | — | 10 | 2 | no | — |
| 388 | #67 | — | 20 | 2 | no | — |
| 389 | #67 | — | 20 | 2 | no | — |
| 390 | #67 | — | 20 | 2 | no | — |
| 391 | C2×Dic3 | — | 4 | 1 | no | — |
| 392 | C2×Dic3 | — | 20 | 2 | no | — |
| 393 | C2×Dic3 | — | 20 | 1 | no | — |
| 394 | D12 | — | 5 | 2 | no | — |
| 395 | D12 | D4×D5 | 1 | 2 | yes | — |
| 396 | C4×D3 | — | 2 | 2 | no | — |
| 397 | C4×D3 | — | 10 | 2 | no | — |
| 398 | Dic6 | — | 5 | 2 | no | — |
| 399 | Dic6 | D4×D5 | 1 | 2 | yes | — |
| 400 | C3×C8 | — | 5 | 2 | no | — |
| 401 | C3×C8 | — | 5 | 2 | no | — |
| 402 | C3⋊C8 | — | 2 | 2 | no | — |
| 403 | C3⋊C8 | — | 10 | 2 | no | — |
| 404 | C22×C5 | — | 4 | 1 | no | — |
| 405 | C22×C5 | — | 4 | 1 | no | — |
| 406 | C22×C5 | — | 6 | 2 | no | — |
| 407 | C22×C5 | — | 8 | 1 | no | — |
| 408 | C22×C5 | — | 8 | 1 | no | — |
| 409 | C22×C5 | — | 48 | 1 | no | — |
| 410 | C22×C5 | #1004 | 1 | 1 | yes | characteristic |
| 411 | C2×D5 | — | 4 | 2 | no | — |
| 412 | C2×D5 | — | 6 | 2 | no | — |
| 413 | C2×D5 | — | 8 | 2 | no | — |
| 414 | C2×D5 | — | 48 | 2 | no | — |
| 415 | C2×D5 | — | 48 | 1 | no | — |
| 416 | C4×C5 | — | 2 | 2 | no | — |
| 417 | C4×C5 | — | 6 | 2 | no | — |
| 418 | C4×C5 | C2×D3×D4 | 1 | 2 | yes | — |
| 419 | Dic5 | — | 6 | 2 | no | — |
| 420 | #41 | — | 3 | 2 | no | — |
| 421 | #41 | — | 6 | 2 | no | — |
| 422 | #41 | — | 15 | 2 | no | — |
| 423 | #41 | — | 30 | 2 | no | — |
| 424 | #41 | — | 30 | 2 | no | — |
| 425 | #41 | — | 30 | 2 | no | — |
| 426 | C2×D4 | — | 4 | 1 | no | — |
| 427 | C2×D4 | — | 5 | 2 | no | — |
| 428 | C2×D4 | — | 6 | 2 | no | — |
| 429 | C2×D4 | — | 12 | 1 | no | — |
| 430 | C2×D4 | — | 20 | 1 | no | — |
| 431 | C2×D4 | — | 30 | 2 | no | — |
| 432 | C2×D4 | — | 30 | 2 | no | — |
| 433 | C2×D4 | — | 30 | 2 | no | — |
| 434 | C2×D4 | — | 60 | 2 | no | — |
| 435 | C2×D4 | — | 60 | 1 | no | — |
| 436 | C2×D4 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 437 | C2×D4 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 438 | Q16 | — | 15 | 2 | no | — |
| 439 | SD16 | — | 6 | 2 | no | — |
| 440 | SD16 | — | 15 | 2 | no | — |
| 441 | SD16 | — | 15 | 2 | no | — |
| 442 | SD16 | — | 30 | 2 | no | — |
| 443 | SD16 | — | 30 | 2 | no | — |
| 444 | SD16 | — | 30 | 2 | no | — |
| 445 | D8 | — | 6 | 2 | no | — |
| 446 | D8 | — | 10 | 2 | no | — |
| 447 | D8 | — | 10 | 2 | no | — |
| 448 | D8 | — | 10 | 2 | no | — |
| 449 | D8 | — | 10 | 2 | no | — |
| 450 | D8 | — | 15 | 2 | no | — |
| 451 | D8 | — | 30 | 2 | no | — |
| 452 | D8 | — | 30 | 2 | no | — |
| 453 | D8 | — | 30 | 2 | no | — |
| 454 | M16 | — | 3 | 2 | no | — |
| 455 | M16 | — | 15 | 2 | no | — |
| 456 | M16 | — | 30 | 2 | no | — |
| 457 | M16 | — | 30 | 2 | no | — |
| 458 | C2×C8 | — | 5 | 2 | no | — |
| 459 | C2×C8 | — | 30 | 2 | no | — |
| 460 | C2×C8 | — | 30 | 2 | no | — |
| 461 | C42 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 462 | C3×C5 | #3292 | 1 | 1 | yes | characteristic, complemented, Hall |
| 463 | C22×C3 | — | 4 | 1 | no | — |
| 464 | C22×C3 | — | 4 | 1 | no | — |
| 465 | C22×C3 | — | 8 | 1 | no | — |
| 466 | C22×C3 | — | 8 | 1 | no | — |
| 467 | C22×C3 | — | 20 | 2 | no | — |
| 468 | C22×C3 | — | 40 | 2 | no | — |
| 469 | C22×C3 | #4144 | 1 | 1 | yes | characteristic |
| 470 | C2×D3 | — | 2 | 2 | no | — |
| 471 | C2×D3 | — | 10 | 2 | no | — |
| 472 | C2×D3 | — | 16 | 1 | no | — |
| 473 | C2×D3 | — | 80 | 2 | no | — |
| 474 | C2×D3 | — | 80 | 1 | no | — |
| 475 | C3×C4 | — | 2 | 2 | no | — |
| 476 | C3×C4 | C2×D4×D5 | 1 | 2 | yes | — |
| 477 | Dic3 | — | 2 | 2 | no | — |
| 478 | Dic3 | — | 10 | 2 | no | — |
| 479 | C2×C5 | — | 2 | 1 | no | — |
| 480 | C2×C5 | — | 8 | 1 | no | — |
| 481 | C2×C5 | — | 8 | 1 | no | — |
| 482 | C2×C5 | — | 12 | 2 | no | — |
| 483 | C2×C5 | #5717 | 1 | 1 | yes | characteristic |
| 484 | D5 | — | 8 | 2 | no | — |
| 485 | D5 | — | 12 | 2 | no | — |
| 486 | C23 | — | 2 | 1 | no | — |
| 487 | C23 | — | 2 | 1 | no | — |
| 488 | C23 | — | 10 | 2 | no | — |
| 489 | C23 | — | 12 | 1 | no | — |
| 490 | C23 | — | 60 | 1 | no | — |
| 491 | C23 | — | 60 | 2 | no | — |
| 492 | Q8 | — | 3 | 2 | no | — |
| 493 | Q8 | — | 15 | 2 | no | — |
| 494 | D4 | — | 2 | 2 | no | — |
| 495 | D4 | — | 2 | 2 | no | — |
| 496 | D4 | — | 3 | 2 | no | — |
| 497 | D4 | — | 6 | 2 | no | — |
| 498 | D4 | — | 8 | 2 | no | — |
| 499 | D4 | — | 10 | 2 | no | — |
| 500 | D4 | — | 10 | 2 | no | — |
| 501 | D4 | — | 12 | 2 | no | — |
| 502 | D4 | — | 15 | 2 | no | — |
| 503 | D4 | — | 30 | 2 | no | — |
| 504 | D4 | — | 40 | 2 | no | — |
| 505 | D4 | — | 60 | 2 | no | — |
| 506 | D4 | — | 60 | 2 | no | — |
| 507 | D4 | — | 60 | 2 | no | — |
| 508 | C2×C4 | — | 2 | 1 | no | — |
| 509 | C2×C4 | — | 6 | 2 | no | — |
| 510 | C2×C4 | — | 12 | 1 | no | — |
| 511 | C2×C4 | — | 30 | 2 | no | — |
| 512 | C2×C4 | — | 60 | 2 | no | — |
| 513 | C2×C4 | — | 60 | 1 | no | — |
| 514 | C2×C4 | C22×D3×D5 | 1 | 1 | yes | characteristic |
| 515 | C8 | — | 5 | 2 | no | — |
| 516 | C8 | — | 5 | 2 | no | — |
| 517 | C8 | — | 6 | 2 | no | — |
| 518 | C8 | — | 30 | 2 | no | — |
| 519 | C2×C3 | — | 2 | 1 | no | — |
| 520 | C2×C3 | — | 8 | 1 | no | — |
| 521 | C2×C3 | — | 8 | 1 | no | — |
| 522 | C2×C3 | — | 40 | 2 | no | — |
| 523 | C2×C3 | #65924 | 1 | 1 | yes | characteristic |
| 524 | D3 | — | 4 | 2 | no | — |
| 525 | D3 | — | 20 | 2 | no | — |
| 526 | C5 | #81791 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 527 | C22 | — | 4 | 1 | no | — |
| 528 | C22 | — | 4 | 1 | no | — |
| 529 | C22 | — | 6 | 2 | no | — |
| 530 | C22 | — | 8 | 1 | no | — |
| 531 | C22 | — | 8 | 1 | no | — |
| 532 | C22 | — | 20 | 2 | no | — |
| 533 | C22 | — | 30 | 2 | no | — |
| 534 | C22 | — | 40 | 2 | no | — |
| 535 | C22 | — | 48 | 1 | no | — |
| 536 | C22 | — | 240 | 1 | no | — |
| 537 | C22 | — | 240 | 2 | no | — |
| 538 | C22 | #92049 | 1 | 1 | yes | characteristic |
| 539 | C4 | — | 2 | 2 | no | — |
| 540 | C4 | — | 6 | 2 | no | — |
| 541 | C4 | — | 30 | 2 | no | — |
| 542 | C4 | D3×D4×D5 | 1 | 2 | yes | — |
| 543 | C3 | #10612013 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 544 | C2 | — | 2 | 1 | no | — |
| 545 | C2 | — | 8 | 1 | no | — |
| 546 | C2 | — | 8 | 1 | no | — |
| 547 | C2 | — | 12 | 2 | no | — |
| 548 | C2 | — | 40 | 2 | no | — |
| 549 | C2 | — | 60 | 2 | no | — |
| 550 | C2 | #11755058 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11754703 | C2 | semidirect |
| 2. #11754697 | C2 | semidirect |
| 3. #11751178 | C2 | semidirect |
| 4. C5×#5077 | C2 | semidirect |
| 5. C3×#65362 | C2 | semidirect |
| 6. #11749139 | C2 | semidirect |
| 7. #11748947 | C2 | semidirect |
| 8. #11747114 | C2 | semidirect |
| 9. #11747018 | C2 | semidirect |
| 11. #92095 | C22 | semidirect |
| 12. C5×#1004 | C22 | semidirect |
| 13. #92017 | C22 | semidirect |
| 14. C3×C5×#127 | C22 | semidirect |
| 15. #91821 | C22 | semidirect |
| 16. C5×#932 | C22 | semidirect |
| 17. C2×C3×#686 | C22 | semidirect |
| 18. C2×C3×#686 | C22 | semidirect |
| 19. C3×#4020 | C22 | semidirect |
| 28. #91312 | C22 | semidirect |
| 30. #91298 | C22 | semidirect |
| 31. #91290 | C22 | semidirect |
| 32. #91286 | C22 | semidirect |
| 33. #91117 | C22 | semidirect |
| 34. #91089 | C22 | semidirect |
| 35. C5×#833 | C22 | semidirect |
| 36. C5×#805 | C22 | semidirect |
| 37. C3×C4×#168 | C22 | semidirect |
| 38. #90991 | C22 | semidirect |
| 39. #90958 | C22 | semidirect |
| 46. #65362 | D3 | semidirect |
| 80. #6663 | D4 | semidirect |
| 81. #6660 | D4 | semidirect |
| 82. #6659 | D4 | semidirect |
| 85. #6654 | D4 | semidirect |
| 99. #5077 | D5 | semidirect |
| 105. C5×#127 | C2×D3 | semidirect |
| 114. C2×#686 | C2×D3 | semidirect |
| 115. C2×#686 | C2×D3 | semidirect |
| 122. #4020 | C2×D3 | semidirect |
| 129. C4×#168 | C2×D3 | semidirect |
| 166. #1004 | C2×D5 | semidirect |
| 170. C3×#127 | C2×D5 | semidirect |
| 174. #932 | C2×D5 | semidirect |
| 189. #833 | C2×D5 | semidirect |
| 192. #805 | C2×D5 | semidirect |
| 356. #127 | D3×D5 | semidirect |
| 462. C3×C5 | #3292 | semidirect |
| 526. C5 | #81791 | semidirect |
| 543. C3 | #10612013 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11754703 | 2 |
| #11754697 | 2 |
| #11751178 | 2 |
| C5×#5077 | 2 |
| C3×#65362 | 2 |
| #11749139 | 2 |
| #11748947 | 2 |
| #11747114 | 2 |
| #11747018 | 2 |
| #10612013 | 3 |
| #81791 | 5 |