Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
920 conjugacy classes of subgroups.
The subgroup lattice has 536 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11754728 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #11754711 | 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×#65365 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11749146 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11748948 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11747120 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11747018 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #10612012 | — | 3 | 1 | no | maximal, Hall |
| 11 | #92095 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | C5×#1004 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | #92004 | C22 | 1 | 2 | yes | — |
| 14 | C3×C5×#127 | C22 | 1 | 1 | yes | characteristic |
| 15 | #91821 | C22 | 1 | 2 | yes | — |
| 16 | C5×#932 | C22 | 1 | 2 | yes | — |
| 17 | C2×C3×#687 | C22 | 1 | 2 | yes | complemented |
| 18 | C2×C3×#687 | C22 | 1 | 2 | yes | complemented |
| 19 | C3×#4015 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | #91500 | — | 2 | 2 | no | — |
| 21 | #91499 | — | 2 | 2 | no | — |
| 22 | #91496 | — | 2 | 2 | no | — |
| 23 | #91495 | — | 2 | 2 | no | — |
| 24 | #91488 | — | 2 | 2 | no | — |
| 25 | #91487 | — | 2 | 2 | no | — |
| 26 | #91486 | — | 2 | 2 | no | — |
| 27 | D3×#687 | — | 2 | 2 | no | — |
| 28 | #91315 | C22 | 1 | 2 | yes | complemented |
| 29 | #91309 | C22 | 1 | 2 | yes | complemented |
| 30 | #91303 | C22 | 1 | 2 | yes | — |
| 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 | #90961 | C22 | 1 | 2 | yes | complemented |
| 40 | #81774 | — | 5 | 1 | no | maximal, Hall |
| 41 | #66170 | — | 3 | 2 | no | — |
| 42 | #66109 | — | 3 | 2 | no | — |
| 43 | C5×#453 | — | 3 | 1 | no | — |
| 44 | #65489 | — | 3 | 2 | no | — |
| 45 | #65366 | — | 3 | 1 | no | — |
| 46 | #65365 | D3 | 1 | 1 | yes | characteristic, complemented |
| 47 | #65115 | — | 3 | 2 | no | — |
| 48 | #65113 | — | 3 | 2 | no | — |
| 49 | #65037 | — | 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×Dic10 | C23 | 1 | 2 | yes | — |
| 62 | #6782 | — | 4 | 2 | no | — |
| 63 | D15⋊Q8 | — | 2 | 2 | no | — |
| 64 | #6769 | — | 2 | 2 | no | — |
| 65 | #6768 | — | 2 | 2 | no | — |
| 66 | D3×Dic10 | — | 2 | 2 | no | — |
| 67 | C3×C42×C5 | C23 | 1 | 1 | yes | characteristic |
| 68 | #6716 | — | 2 | 2 | no | — |
| 69 | #6715 | — | 2 | 2 | no | — |
| 70 | #6710 | C23 | 1 | 2 | yes | — |
| 71 | C5×#214 | — | 2 | 2 | no | — |
| 72 | C5×#213 | — | 2 | 2 | no | — |
| 73 | C5×#208 | C23 | 1 | 2 | yes | — |
| 74 | C3×#687 | — | 2 | 2 | no | — |
| 75 | C3×#687 | — | 2 | 2 | no | — |
| 76 | C3×#687 | — | 2 | 2 | no | — |
| 77 | C3×#687 | — | 2 | 2 | no | — |
| 78 | C3×C4⋊Dic5 | — | 4 | 1 | no | — |
| 79 | C2×C3×#168 | C23 | 1 | 2 | yes | — |
| 80 | #6663 | D4 | 1 | 2 | yes | complemented |
| 81 | #6662 | — | 2 | 2 | no | — |
| 82 | #6661 | — | 2 | 2 | no | — |
| 83 | #6660 | D4 | 1 | 2 | yes | complemented |
| 84 | #6659 | D4 | 1 | 2 | yes | complemented |
| 85 | #6658 | — | 2 | 2 | no | — |
| 86 | #6656 | — | 2 | 2 | no | — |
| 87 | #6654 | D4 | 1 | 2 | yes | complemented |
| 88 | #6651 | — | 2 | 2 | no | — |
| 89 | #6650 | — | 2 | 2 | no | — |
| 90 | #6648 | — | 2 | 2 | no | — |
| 91 | D3×#168 | — | 2 | 2 | no | — |
| 92 | #5762 | — | 5 | 2 | no | — |
| 93 | #5762 | — | 5 | 2 | no | — |
| 94 | C3×#492 | — | 5 | 1 | no | — |
| 95 | #5177 | — | 5 | 2 | no | — |
| 96 | #5177 | — | 5 | 2 | no | — |
| 97 | #5095 | — | 5 | 2 | no | — |
| 98 | #5077 | — | 5 | 1 | no | — |
| 99 | #5077 | D5 | 1 | 1 | yes | characteristic, complemented |
| 100 | #4700 | — | 5 | 2 | no | — |
| 101 | C5×H(5,𝔽2) | — | 3 | 1 | no | — |
| 102 | #4150 | — | 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 |
| 106 | #4097 | — | 3 | 2 | no | — |
| 107 | #4097 | — | 6 | 2 | no | — |
| 108 | #4096 | — | 3 | 2 | no | — |
| 109 | #4096 | — | 6 | 2 | no | — |
| 110 | #4094 | — | 3 | 2 | no | — |
| 111 | C2×#687 | — | 6 | 2 | no | — |
| 112 | C2×#687 | C2×D3 | 1 | 2 | yes | complemented |
| 113 | C2×#687 | C2×D3 | 1 | 2 | yes | complemented |
| 114 | #4078 | — | 3 | 2 | no | — |
| 115 | #4078 | — | 6 | 2 | no | — |
| 116 | #4061 | — | 6 | 2 | no | — |
| 117 | D5×SD16 | — | 6 | 2 | no | — |
| 118 | #4058 | — | 6 | 2 | no | — |
| 119 | #4057 | — | 6 | 2 | no | — |
| 120 | #4055 | — | 3 | 2 | no | — |
| 121 | #4053 | — | 3 | 2 | no | — |
| 122 | #4015 | 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 | #3956 | — | 3 | 2 | no | — |
| 127 | #3954 | — | 3 | 2 | no | — |
| 128 | #3937 | — | 3 | 2 | no | — |
| 129 | C4×#168 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 130 | #3291 | — | 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 | C3×C5×D4 | — | 2 | 2 | no | — |
| 136 | C3×C5×D4 | — | 2 | 2 | no | — |
| 137 | C3×C5×D4 | — | 8 | 2 | no | — |
| 138 | C2×C3×C4×C5 | — | 2 | 1 | no | — |
| 139 | C2×C3×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 140 | #1220 | — | 2 | 2 | no | — |
| 141 | #1220 | — | 4 | 2 | no | — |
| 142 | C2×Dic15 | — | 4 | 1 | no | — |
| 143 | D60 | C2×D4 | 1 | 2 | yes | — |
| 144 | C4×D15 | — | 2 | 2 | no | — |
| 145 | Dic30 | C2×D4 | 1 | 2 | yes | — |
| 146 | C5×#67 | — | 2 | 2 | no | — |
| 147 | C5×#67 | — | 4 | 2 | no | — |
| 148 | C2×C5×Dic3 | — | 4 | 1 | no | — |
| 149 | C5×D12 | C2×D4 | 1 | 2 | yes | — |
| 150 | C4×C5×D3 | — | 2 | 2 | no | — |
| 151 | C5×Dic6 | C2×D4 | 1 | 2 | yes | — |
| 152 | C2×C3×Dic5 | — | 2 | 2 | no | — |
| 153 | C3×Dic10 | — | 2 | 2 | no | — |
| 154 | C3×Dic10 | — | 2 | 2 | no | — |
| 155 | #1204 | — | 4 | 2 | no | — |
| 156 | #1203 | — | 4 | 2 | no | — |
| 157 | #1200 | — | 4 | 2 | no | — |
| 158 | D3×Dic5 | — | 4 | 2 | no | — |
| 159 | C3⋊#168 | — | 2 | 2 | no | — |
| 160 | C3×#168 | C2×D4 | 1 | 2 | yes | — |
| 161 | C3×#168 | C2×D4 | 1 | 2 | yes | — |
| 162 | C5×C3⋊C8 | — | 2 | 2 | no | — |
| 163 | #1007 | — | 5 | 2 | no | — |
| 164 | #1004 | — | 5 | 1 | no | — |
| 165 | #1004 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 166 | C2×C3×SD16 | — | 5 | 2 | no | — |
| 167 | C2×C3×SD16 | — | 5 | 2 | no | — |
| 168 | C3×C4⋊Q8 | — | 5 | 1 | no | — |
| 169 | C3×#127 | C2×D5 | 1 | 1 | yes | characteristic |
| 170 | #942 | — | 5 | 2 | no | — |
| 171 | #942 | — | 5 | 2 | no | — |
| 172 | #932 | — | 5 | 2 | no | — |
| 173 | #932 | C2×D5 | 1 | 2 | yes | — |
| 174 | #916 | — | 10 | 2 | no | — |
| 175 | #916 | — | 10 | 2 | no | — |
| 176 | #915 | — | 10 | 2 | no | — |
| 177 | #915 | — | 10 | 2 | no | — |
| 178 | #914 | — | 10 | 2 | no | — |
| 179 | #914 | — | 10 | 2 | no | — |
| 180 | D3×SD16 | — | 10 | 2 | no | — |
| 181 | D3×SD16 | — | 10 | 2 | no | — |
| 182 | #904 | — | 5 | 2 | no | — |
| 183 | #901 | — | 5 | 2 | no | — |
| 184 | #901 | — | 5 | 2 | no | — |
| 185 | C3×C4×C8 | — | 5 | 1 | no | — |
| 186 | #836 | — | 5 | 2 | no | — |
| 187 | #833 | — | 5 | 1 | no | — |
| 188 | #833 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 189 | #819 | — | 5 | 2 | no | — |
| 190 | #805 | — | 5 | 2 | no | — |
| 191 | #805 | C2×D5 | 1 | 2 | yes | complemented |
| 192 | C5×#41 | — | 3 | 2 | no | — |
| 193 | C5×#41 | — | 6 | 2 | no | — |
| 194 | C2×C5×D4 | — | 4 | 1 | no | — |
| 195 | C2×C5×D4 | — | 6 | 2 | no | — |
| 196 | C2×C5×D4 | — | 12 | 1 | no | — |
| 197 | C2×C5×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 198 | C2×C5×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 199 | C2×C22⋊D5 | — | 12 | 1 | no | — |
| 200 | Q8×D5 | — | 6 | 2 | no | — |
| 201 | #711 | — | 6 | 2 | no | — |
| 202 | #711 | — | 6 | 2 | no | — |
| 203 | #711 | — | 12 | 2 | no | — |
| 204 | D4×D5 | — | 6 | 2 | no | — |
| 205 | #709 | — | 3 | 2 | no | — |
| 206 | #709 | — | 6 | 2 | no | — |
| 207 | C2×Dic10 | — | 6 | 2 | no | — |
| 208 | C2×Dic10 | C22×D3 | 1 | 2 | yes | — |
| 209 | C5×SD16 | — | 6 | 2 | no | — |
| 210 | C5×D8 | — | 6 | 2 | no | — |
| 211 | C5×M16 | — | 3 | 2 | no | — |
| 212 | C42×C5 | C22×D3 | 1 | 1 | yes | characteristic |
| 213 | #689 | — | 3 | 2 | no | — |
| 214 | #689 | — | 6 | 2 | no | — |
| 215 | #688 | — | 3 | 2 | no | — |
| 216 | #687 | — | 2 | 2 | no | — |
| 217 | #687 | — | 2 | 2 | no | — |
| 218 | #687 | — | 2 | 2 | no | — |
| 219 | #687 | — | 2 | 2 | no | — |
| 220 | #687 | — | 3 | 2 | no | — |
| 221 | #687 | — | 6 | 2 | no | — |
| 222 | #687 | — | 6 | 2 | no | — |
| 223 | #686 | — | 3 | 2 | no | — |
| 224 | #686 | — | 6 | 2 | no | — |
| 225 | C4⋊Dic5 | — | 4 | 1 | no | — |
| 226 | #681 | — | 3 | 2 | no | — |
| 227 | #681 | — | 6 | 2 | no | — |
| 228 | C2×#168 | — | 6 | 2 | no | — |
| 229 | C2×#168 | C22×D3 | 1 | 2 | yes | — |
| 230 | Dic20 | — | 6 | 2 | no | — |
| 231 | #677 | — | 6 | 2 | no | — |
| 232 | #676 | — | 6 | 2 | no | — |
| 233 | C8×D5 | — | 6 | 2 | no | — |
| 234 | #577 | — | 15 | 2 | no | — |
| 235 | #577 | — | 15 | 2 | no | — |
| 236 | #492 | — | 5 | 1 | no | — |
| 237 | #471 | — | 15 | 2 | no | — |
| 238 | #471 | — | 15 | 2 | no | — |
| 239 | #456 | — | 15 | 2 | no | — |
| 240 | #453 | — | 3 | 1 | no | — |
| 241 | #453 | — | 15 | 1 | no | — |
| 242 | #443 | — | 15 | 2 | no | — |
| 243 | C22×C3×C5 | — | 4 | 1 | no | — |
| 244 | C22×C3×C5 | — | 4 | 1 | no | — |
| 245 | C22×C3×C5 | — | 8 | 1 | no | — |
| 246 | C22×C3×C5 | — | 8 | 1 | no | — |
| 247 | C22×C3×C5 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 248 | C2×D15 | — | 2 | 2 | no | — |
| 249 | C2×D15 | — | 16 | 1 | no | — |
| 250 | C2×C5×D3 | — | 2 | 2 | no | — |
| 251 | C2×C5×D3 | — | 16 | 1 | no | — |
| 252 | C3×C4×C5 | — | 2 | 2 | no | — |
| 253 | C3×C4×C5 | C22×D4 | 1 | 2 | yes | — |
| 254 | Dic15 | — | 2 | 2 | no | — |
| 255 | C3×Dic5 | — | 4 | 2 | no | — |
| 256 | C5×Dic3 | — | 2 | 2 | no | — |
| 257 | C2×C3×Q8 | — | 5 | 2 | no | — |
| 258 | C2×C3×D4 | — | 4 | 1 | no | — |
| 259 | C2×C3×D4 | C22×D5 | 1 | 1 | yes | characteristic |
| 260 | C2×C3×D4 | C22×D5 | 1 | 1 | yes | characteristic |
| 261 | C2×#67 | — | 4 | 1 | no | — |
| 262 | C2×#67 | — | 20 | 1 | no | — |
| 263 | #239 | — | 10 | 2 | no | — |
| 264 | #239 | — | 10 | 2 | no | — |
| 265 | D3×Q8 | — | 10 | 2 | no | — |
| 266 | D3×Q8 | — | 10 | 2 | no | — |
| 267 | #237 | — | 2 | 2 | no | — |
| 268 | #237 | — | 10 | 2 | no | — |
| 269 | D3×D4 | — | 2 | 2 | no | — |
| 270 | D3×D4 | — | 10 | 2 | no | — |
| 271 | #235 | — | 5 | 2 | no | — |
| 272 | #235 | — | 20 | 2 | no | — |
| 273 | #235 | C22×D5 | 1 | 2 | yes | — |
| 274 | C3×SD16 | — | 10 | 2 | no | — |
| 275 | C3×SD16 | — | 10 | 2 | no | — |
| 276 | C3×SD16 | — | 10 | 2 | no | — |
| 277 | C3×SD16 | — | 10 | 2 | no | — |
| 278 | C2×C3×C8 | — | 5 | 2 | no | — |
| 279 | C3×C4⋊C4 | — | 20 | 1 | no | — |
| 280 | C3×C42 | C22×D5 | 1 | 1 | yes | characteristic |
| 281 | #216 | — | 10 | 2 | no | — |
| 282 | #216 | — | 10 | 2 | no | — |
| 283 | #215 | — | 10 | 2 | no | — |
| 284 | #215 | — | 10 | 2 | no | — |
| 285 | #214 | — | 2 | 2 | no | — |
| 286 | #214 | — | 10 | 2 | no | — |
| 287 | #213 | — | 2 | 2 | no | — |
| 288 | #213 | — | 10 | 2 | no | — |
| 289 | #208 | — | 5 | 2 | no | — |
| 290 | #208 | C22×D5 | 1 | 2 | yes | — |
| 291 | Dic12 | — | 5 | 2 | no | — |
| 292 | D24 | — | 5 | 2 | no | — |
| 293 | #204 | — | 5 | 2 | no | — |
| 294 | #204 | — | 5 | 2 | no | — |
| 295 | ΓL(1,𝔽25) | — | 10 | 2 | no | — |
| 296 | ΓL(1,𝔽25) | — | 10 | 2 | no | — |
| 297 | D3×C8 | — | 10 | 2 | no | — |
| 298 | D3×C8 | — | 10 | 2 | no | — |
| 299 | C23×C5 | — | 2 | 1 | no | — |
| 300 | C23×C5 | — | 2 | 1 | no | — |
| 301 | C23×C5 | — | 12 | 1 | no | — |
| 302 | C22×D5 | — | 12 | 1 | no | — |
| 303 | C5×Q8 | — | 3 | 2 | no | — |
| 304 | C5×D4 | — | 2 | 2 | no | — |
| 305 | C5×D4 | — | 2 | 2 | no | — |
| 306 | C5×D4 | — | 3 | 2 | no | — |
| 307 | C5×D4 | — | 6 | 2 | no | — |
| 308 | C5×D4 | — | 8 | 2 | no | — |
| 309 | C5×D4 | — | 12 | 2 | no | — |
| 310 | C2×C4×C5 | — | 2 | 1 | no | — |
| 311 | C2×C4×C5 | — | 6 | 2 | no | — |
| 312 | C2×C4×C5 | — | 12 | 1 | no | — |
| 313 | C2×C4×C5 | C23×D3 | 1 | 1 | yes | characteristic |
| 314 | C22⋊D5 | — | 6 | 2 | no | — |
| 315 | C22⋊D5 | — | 12 | 2 | no | — |
| 316 | C22⋊D5 | — | 12 | 2 | no | — |
| 317 | C2×Dic5 | — | 2 | 2 | no | — |
| 318 | C2×Dic5 | — | 12 | 2 | no | — |
| 319 | C2×Dic5 | — | 12 | 1 | no | — |
| 320 | D20 | — | 3 | 2 | no | — |
| 321 | C4×D5 | — | 6 | 2 | no | — |
| 322 | C4×D5 | — | 12 | 2 | no | — |
| 323 | Dic10 | — | 2 | 2 | no | — |
| 324 | Dic10 | — | 2 | 2 | no | — |
| 325 | Dic10 | — | 3 | 2 | no | — |
| 326 | Dic10 | — | 12 | 2 | no | — |
| 327 | C5×C8 | — | 6 | 2 | no | — |
| 328 | #168 | — | 6 | 2 | no | — |
| 329 | #168 | D3×D4 | 1 | 2 | yes | — |
| 330 | #168 | D3×D4 | 1 | 2 | yes | — |
| 331 | 2−1+4 | — | 15 | 2 | no | — |
| 332 | H(5,𝔽2) | — | 3 | 1 | no | — |
| 333 | H(5,𝔽2) | — | 15 | 1 | no | — |
| 334 | #137 | — | 15 | 2 | no | — |
| 335 | #137 | — | 15 | 2 | no | — |
| 336 | #137 | — | 30 | 2 | no | — |
| 337 | #137 | — | 30 | 2 | no | — |
| 338 | AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 339 | AGL(1,ℤ/8) | — | 15 | 2 | no | — |
| 340 | AGL(1,ℤ/8) | — | 30 | 2 | no | — |
| 341 | AGL(1,ℤ/8) | — | 30 | 2 | no | — |
| 342 | #135 | — | 15 | 2 | no | — |
| 343 | #135 | — | 30 | 2 | no | — |
| 344 | #135 | — | 30 | 2 | no | — |
| 345 | C2×SD16 | — | 5 | 2 | no | — |
| 346 | C2×SD16 | — | 5 | 2 | no | — |
| 347 | C2×SD16 | — | 30 | 2 | no | — |
| 348 | C2×SD16 | — | 30 | 2 | no | — |
| 349 | #131 | — | 15 | 2 | no | — |
| 350 | #131 | — | 15 | 2 | no | — |
| 351 | C4⋊Q8 | — | 5 | 1 | no | — |
| 352 | #127 | D3×D5 | 1 | 1 | yes | characteristic |
| 353 | #108 | — | 15 | 2 | no | — |
| 354 | #104 | — | 3 | 2 | no | — |
| 355 | #104 | — | 15 | 2 | no | — |
| 356 | #101 | — | 15 | 2 | no | — |
| 357 | #100 | — | 3 | 1 | no | — |
| 358 | #100 | — | 15 | 1 | no | — |
| 359 | C4×C8 | — | 5 | 1 | no | — |
| 360 | C2×C3×C5 | — | 2 | 1 | no | — |
| 361 | C2×C3×C5 | — | 8 | 1 | no | — |
| 362 | C2×C3×C5 | — | 8 | 1 | no | — |
| 363 | C2×C3×C5 | D42 | 1 | 1 | yes | characteristic |
| 364 | D15 | — | 4 | 2 | no | — |
| 365 | C5×D3 | — | 4 | 2 | no | — |
| 366 | C23×C3 | — | 2 | 1 | no | — |
| 367 | C23×C3 | — | 2 | 1 | no | — |
| 368 | C22×D3 | — | 4 | 1 | no | — |
| 369 | C22×D3 | — | 20 | 1 | no | — |
| 370 | C3×Q8 | — | 10 | 2 | no | — |
| 371 | C3×Q8 | — | 10 | 2 | no | — |
| 372 | C3×D4 | — | 2 | 2 | no | — |
| 373 | C3×D4 | — | 2 | 2 | no | — |
| 374 | C3×D4 | — | 8 | 2 | no | — |
| 375 | C2×C3×C4 | — | 2 | 1 | no | — |
| 376 | C2×C3×C4 | — | 10 | 2 | no | — |
| 377 | C2×C3×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 378 | #67 | — | 2 | 2 | no | — |
| 379 | #67 | — | 4 | 2 | no | — |
| 380 | #67 | — | 10 | 2 | no | — |
| 381 | #67 | — | 20 | 2 | no | — |
| 382 | C2×Dic3 | — | 4 | 1 | no | — |
| 383 | C2×Dic3 | — | 20 | 1 | no | — |
| 384 | D12 | — | 5 | 2 | no | — |
| 385 | D12 | — | 20 | 2 | no | — |
| 386 | D12 | D4×D5 | 1 | 2 | yes | — |
| 387 | C4×D3 | — | 2 | 2 | no | — |
| 388 | C4×D3 | — | 10 | 2 | no | — |
| 389 | C4×D3 | — | 20 | 2 | no | — |
| 390 | C4×D3 | — | 20 | 2 | no | — |
| 391 | Dic6 | — | 5 | 2 | no | — |
| 392 | Dic6 | — | 20 | 2 | no | — |
| 393 | Dic6 | D4×D5 | 1 | 2 | yes | — |
| 394 | C3×C8 | — | 5 | 2 | no | — |
| 395 | C3×C8 | — | 5 | 2 | no | — |
| 396 | C3⋊C8 | — | 2 | 2 | no | — |
| 397 | C3⋊C8 | — | 10 | 2 | no | — |
| 398 | C22×C5 | — | 4 | 1 | no | — |
| 399 | C22×C5 | — | 4 | 1 | no | — |
| 400 | C22×C5 | — | 6 | 2 | no | — |
| 401 | C22×C5 | — | 8 | 1 | no | — |
| 402 | C22×C5 | — | 8 | 1 | no | — |
| 403 | C22×C5 | — | 48 | 1 | no | — |
| 404 | C22×C5 | #1004 | 1 | 1 | yes | characteristic |
| 405 | C2×D5 | — | 6 | 2 | no | — |
| 406 | C2×D5 | — | 48 | 1 | no | — |
| 407 | C4×C5 | — | 2 | 2 | no | — |
| 408 | C4×C5 | — | 6 | 2 | no | — |
| 409 | C4×C5 | C2×D3×D4 | 1 | 2 | yes | — |
| 410 | Dic5 | — | 4 | 2 | no | — |
| 411 | Dic5 | — | 6 | 2 | no | — |
| 412 | #41 | — | 3 | 2 | no | — |
| 413 | #41 | — | 6 | 2 | no | — |
| 414 | #41 | — | 15 | 2 | no | — |
| 415 | #41 | — | 30 | 2 | no | — |
| 416 | #41 | — | 30 | 2 | no | — |
| 417 | #41 | — | 30 | 2 | no | — |
| 418 | #41 | — | 60 | 2 | no | — |
| 419 | C2×Q8 | — | 5 | 2 | no | — |
| 420 | C2×Q8 | — | 30 | 2 | no | — |
| 421 | C2×Q8 | — | 30 | 2 | no | — |
| 422 | C2×D4 | — | 4 | 1 | no | — |
| 423 | C2×D4 | — | 6 | 2 | no | — |
| 424 | C2×D4 | — | 12 | 1 | no | — |
| 425 | C2×D4 | — | 30 | 2 | no | — |
| 426 | C2×D4 | — | 60 | 1 | no | — |
| 427 | C2×D4 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 428 | C2×D4 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 429 | Q16 | — | 15 | 2 | no | — |
| 430 | Q16 | — | 30 | 2 | no | — |
| 431 | Q16 | — | 30 | 2 | no | — |
| 432 | SD16 | — | 6 | 2 | no | — |
| 433 | SD16 | — | 10 | 2 | no | — |
| 434 | SD16 | — | 10 | 2 | no | — |
| 435 | SD16 | — | 10 | 2 | no | — |
| 436 | SD16 | — | 10 | 2 | no | — |
| 437 | SD16 | — | 15 | 2 | no | — |
| 438 | SD16 | — | 15 | 2 | no | — |
| 439 | SD16 | — | 30 | 2 | no | — |
| 440 | SD16 | — | 30 | 2 | no | — |
| 441 | SD16 | — | 30 | 2 | no | — |
| 442 | D8 | — | 6 | 2 | no | — |
| 443 | D8 | — | 15 | 2 | no | — |
| 444 | D8 | — | 30 | 2 | no | — |
| 445 | M16 | — | 3 | 2 | no | — |
| 446 | M16 | — | 15 | 2 | no | — |
| 447 | M16 | — | 30 | 2 | no | — |
| 448 | M16 | — | 30 | 2 | no | — |
| 449 | C2×C8 | — | 5 | 2 | no | — |
| 450 | C2×C8 | — | 30 | 2 | no | — |
| 451 | C2×C8 | — | 30 | 2 | no | — |
| 452 | C4⋊C4 | — | 20 | 1 | no | — |
| 453 | C42 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 454 | C3×C5 | #3291 | 1 | 1 | yes | characteristic, complemented, Hall |
| 455 | C22×C3 | — | 4 | 1 | no | — |
| 456 | C22×C3 | — | 4 | 1 | no | — |
| 457 | C22×C3 | — | 8 | 1 | no | — |
| 458 | C22×C3 | — | 8 | 1 | no | — |
| 459 | C22×C3 | #4144 | 1 | 1 | yes | characteristic |
| 460 | C2×D3 | — | 2 | 2 | no | — |
| 461 | C2×D3 | — | 10 | 2 | no | — |
| 462 | C2×D3 | — | 16 | 1 | no | — |
| 463 | C2×D3 | — | 80 | 1 | no | — |
| 464 | C3×C4 | — | 2 | 2 | no | — |
| 465 | C3×C4 | — | 20 | 2 | no | — |
| 466 | C3×C4 | C2×D4×D5 | 1 | 2 | yes | — |
| 467 | Dic3 | — | 2 | 2 | no | — |
| 468 | Dic3 | — | 10 | 2 | no | — |
| 469 | C2×C5 | — | 2 | 1 | no | — |
| 470 | C2×C5 | — | 8 | 1 | no | — |
| 471 | C2×C5 | — | 8 | 1 | no | — |
| 472 | C2×C5 | — | 12 | 2 | no | — |
| 473 | C2×C5 | #5717 | 1 | 1 | yes | characteristic |
| 474 | D5 | — | 12 | 2 | no | — |
| 475 | C23 | — | 2 | 1 | no | — |
| 476 | C23 | — | 2 | 1 | no | — |
| 477 | C23 | — | 12 | 1 | no | — |
| 478 | C23 | — | 60 | 1 | no | — |
| 479 | Q8 | — | 3 | 2 | no | — |
| 480 | Q8 | — | 10 | 2 | no | — |
| 481 | Q8 | — | 10 | 2 | no | — |
| 482 | Q8 | — | 15 | 2 | no | — |
| 483 | Q8 | — | 60 | 2 | no | — |
| 484 | D4 | — | 2 | 2 | no | — |
| 485 | D4 | — | 2 | 2 | no | — |
| 486 | D4 | — | 3 | 2 | no | — |
| 487 | D4 | — | 6 | 2 | no | — |
| 488 | D4 | — | 8 | 2 | no | — |
| 489 | D4 | — | 12 | 2 | no | — |
| 490 | D4 | — | 15 | 2 | no | — |
| 491 | D4 | — | 30 | 2 | no | — |
| 492 | D4 | — | 60 | 2 | no | — |
| 493 | D4 | — | 60 | 2 | no | — |
| 494 | C2×C4 | — | 2 | 1 | no | — |
| 495 | C2×C4 | — | 6 | 2 | no | — |
| 496 | C2×C4 | — | 10 | 2 | no | — |
| 497 | C2×C4 | — | 12 | 1 | no | — |
| 498 | C2×C4 | — | 30 | 2 | no | — |
| 499 | C2×C4 | — | 60 | 2 | no | — |
| 500 | C2×C4 | — | 60 | 2 | no | — |
| 501 | C2×C4 | — | 60 | 1 | no | — |
| 502 | C2×C4 | C22×D3×D5 | 1 | 1 | yes | characteristic |
| 503 | C8 | — | 5 | 2 | no | — |
| 504 | C8 | — | 5 | 2 | no | — |
| 505 | C8 | — | 6 | 2 | no | — |
| 506 | C8 | — | 30 | 2 | no | — |
| 507 | C2×C3 | — | 2 | 1 | no | — |
| 508 | C2×C3 | — | 8 | 1 | no | — |
| 509 | C2×C3 | — | 8 | 1 | no | — |
| 510 | C2×C3 | #65924 | 1 | 1 | yes | characteristic |
| 511 | D3 | — | 4 | 2 | no | — |
| 512 | D3 | — | 20 | 2 | no | — |
| 513 | C5 | #81774 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 514 | C22 | — | 4 | 1 | no | — |
| 515 | C22 | — | 4 | 1 | no | — |
| 516 | C22 | — | 6 | 2 | no | — |
| 517 | C22 | — | 8 | 1 | no | — |
| 518 | C22 | — | 8 | 1 | no | — |
| 519 | C22 | — | 30 | 2 | no | — |
| 520 | C22 | — | 48 | 1 | no | — |
| 521 | C22 | — | 240 | 1 | no | — |
| 522 | C22 | #92049 | 1 | 1 | yes | characteristic |
| 523 | C4 | — | 2 | 2 | no | — |
| 524 | C4 | — | 6 | 2 | no | — |
| 525 | C4 | — | 20 | 2 | no | — |
| 526 | C4 | — | 30 | 2 | no | — |
| 527 | C4 | D3×D4×D5 | 1 | 2 | yes | — |
| 528 | C3 | #10612012 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 529 | C2 | — | 2 | 1 | no | — |
| 530 | C2 | — | 8 | 1 | no | — |
| 531 | C2 | — | 8 | 1 | no | — |
| 532 | C2 | — | 12 | 2 | no | — |
| 533 | C2 | — | 60 | 2 | no | — |
| 534 | C2 | #11755058 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11754728 | C2 | semidirect |
| 2. #11754711 | C2 | semidirect |
| 3. #11751178 | C2 | semidirect |
| 4. C5×#5077 | C2 | semidirect |
| 5. C3×#65365 | C2 | semidirect |
| 6. #11749146 | C2 | semidirect |
| 7. #11748948 | C2 | semidirect |
| 8. #11747120 | C2 | semidirect |
| 9. #11747018 | C2 | semidirect |
| 11. #92095 | C22 | semidirect |
| 12. C5×#1004 | C22 | semidirect |
| 17. C2×C3×#687 | C22 | semidirect |
| 18. C2×C3×#687 | C22 | semidirect |
| 19. C3×#4015 | C22 | semidirect |
| 28. #91315 | C22 | semidirect |
| 29. #91309 | 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. #90961 | C22 | semidirect |
| 46. #65365 | D3 | semidirect |
| 80. #6663 | D4 | semidirect |
| 83. #6660 | D4 | semidirect |
| 84. #6659 | D4 | semidirect |
| 87. #6654 | D4 | semidirect |
| 99. #5077 | D5 | semidirect |
| 112. C2×#687 | C2×D3 | semidirect |
| 113. C2×#687 | C2×D3 | semidirect |
| 122. #4015 | C2×D3 | semidirect |
| 129. C4×#168 | C2×D3 | semidirect |
| 165. #1004 | C2×D5 | semidirect |
| 188. #833 | C2×D5 | semidirect |
| 191. #805 | C2×D5 | semidirect |
| 454. C3×C5 | #3291 | semidirect |
| 513. C5 | #81774 | semidirect |
| 528. C3 | #10612012 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11754728 | 2 |
| #11754711 | 2 |
| #11751178 | 2 |
| C5×#5077 | 2 |
| C3×#65365 | 2 |
| #11749146 | 2 |
| #11748948 | 2 |
| #11747120 | 2 |
| #11747018 | 2 |
| #10612012 | 3 |
| #81774 | 5 |