Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1792 conjugacy classes of subgroups.
The subgroup lattice has 540 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | D15×#125 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C5×C3⋊#564 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×C5⋊#564 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11753620 | C2 | 1 | 4 | yes | maximal |
| 5 | #11753468 | C2 | 1 | 4 | yes | maximal |
| 6 | #11753468 | C2 | 1 | 4 | yes | maximal |
| 7 | #11753395 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #11753393 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #11753333 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #11752631 | C2 | 1 | 2 | yes | maximal |
| 11 | #11752488 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | D5×#564 | — | 3 | 1 | no | maximal, Hall |
| 13 | C3×C5×#125 | C22 | 1 | 1 | yes | characteristic |
| 14 | C4⋊C4×D15 | C22 | 1 | 4 | yes | — |
| 15 | C4⋊C4×D15 | C22 | 1 | 2 | yes | — |
| 16 | #91779 | C22 | 1 | 2 | yes | — |
| 17 | #91778 | C22 | 1 | 4 | yes | — |
| 18 | C42×D15 | C22 | 1 | 1 | yes | characteristic |
| 19 | #91759 | C22 | 1 | 1 | yes | characteristic |
| 20 | C5×#890 | C22 | 1 | 4 | yes | — |
| 21 | C5×#889 | C22 | 1 | 4 | yes | — |
| 22 | C5×#889 | C22 | 1 | 4 | yes | — |
| 23 | C5×#870 | C22 | 1 | 2 | yes | — |
| 24 | C3×#4036 | C22 | 1 | 4 | yes | — |
| 25 | C3×#4035 | C22 | 1 | 4 | yes | — |
| 26 | C3×#4035 | C22 | 1 | 4 | yes | — |
| 27 | C3×#4016 | C22 | 1 | 2 | yes | — |
| 28 | #91437 | C22 | 1 | 2 | yes | — |
| 29 | #91437 | C22 | 1 | 4 | yes | — |
| 30 | #91437 | C22 | 1 | 2 | yes | — |
| 31 | #91404 | C22 | 1 | 4 | yes | — |
| 32 | #91404 | C22 | 1 | 4 | yes | — |
| 33 | #91404 | C22 | 1 | 4 | yes | — |
| 34 | #91404 | C22 | 1 | 4 | yes | — |
| 35 | C4×#1200 | C22 | 1 | 4 | yes | — |
| 36 | #91388 | C22 | 1 | 4 | yes | — |
| 37 | #91384 | C22 | 1 | 2 | yes | — |
| 38 | #91384 | C22 | 1 | 2 | yes | — |
| 39 | #91382 | C22 | 1 | 4 | yes | — |
| 40 | #91382 | C22 | 1 | 4 | yes | — |
| 41 | #91381 | C22 | 1 | 4 | yes | — |
| 42 | #91379 | C22 | 1 | 4 | yes | — |
| 43 | #91379 | C22 | 1 | 4 | yes | — |
| 44 | #91378 | C22 | 1 | 4 | yes | — |
| 45 | #91378 | C22 | 1 | 4 | yes | — |
| 46 | #91346 | C22 | 1 | 4 | yes | — |
| 47 | #91346 | C22 | 1 | 4 | yes | — |
| 48 | #91343 | C22 | 1 | 4 | yes | — |
| 49 | #91343 | C22 | 1 | 4 | yes | — |
| 50 | #91339 | C22 | 1 | 4 | yes | — |
| 51 | #91339 | C22 | 1 | 4 | yes | — |
| 52 | #91336 | C22 | 1 | 4 | yes | — |
| 53 | #91336 | C22 | 1 | 4 | yes | — |
| 54 | #91335 | C22 | 1 | 4 | yes | — |
| 55 | #91335 | C22 | 1 | 4 | yes | — |
| 56 | #91334 | C22 | 1 | 4 | yes | — |
| 57 | #91334 | C22 | 1 | 4 | yes | — |
| 58 | D3×#564 | — | 5 | 1 | no | maximal, Hall |
| 59 | C5×#564 | — | 3 | 1 | no | — |
| 60 | D5×#125 | — | 3 | 4 | no | — |
| 61 | D5×#125 | — | 3 | 4 | no | — |
| 62 | D5×#125 | — | 3 | 4 | no | — |
| 63 | D5×#125 | — | 3 | 2 | no | — |
| 64 | D5×#125 | — | 3 | 1 | no | — |
| 65 | C5⋊#564 | — | 3 | 4 | no | — |
| 66 | C5⋊#564 | — | 3 | 4 | no | — |
| 67 | C5⋊#564 | — | 3 | 4 | no | — |
| 68 | C5⋊#564 | — | 3 | 2 | no | — |
| 69 | C5⋊#564 | D3 | 1 | 1 | yes | characteristic, complemented |
| 70 | C2×C4×D15 | C23 | 1 | 4 | yes | — |
| 71 | C2×C4×D15 | C23 | 1 | 1 | yes | characteristic |
| 72 | C2×C4×D15 | C23 | 1 | 2 | yes | — |
| 73 | C2×#1200 | C23 | 1 | 4 | yes | — |
| 74 | C2×#1200 | C23 | 1 | 4 | yes | — |
| 75 | C3×C5×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 76 | C3×C5×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 77 | C3×C42×C5 | C23 | 1 | 1 | yes | characteristic |
| 78 | C4⋊Dic15 | C23 | 1 | 2 | yes | — |
| 79 | C4⋊Dic15 | C23 | 1 | 4 | yes | — |
| 80 | #6712 | C23 | 1 | 4 | yes | — |
| 81 | #6712 | C23 | 1 | 4 | yes | — |
| 82 | #6712 | C23 | 1 | 4 | yes | — |
| 83 | C4×Dic15 | C23 | 1 | 2 | yes | — |
| 84 | C4×Dic15 | C23 | 1 | 1 | yes | characteristic |
| 85 | C5×C4⋊Dic3 | C23 | 1 | 2 | yes | — |
| 86 | C5×C4⋊Dic3 | C23 | 1 | 2 | yes | — |
| 87 | C5×C4⋊Dic3 | C23 | 1 | 4 | yes | — |
| 88 | C5×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 89 | C5×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 90 | C5×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 91 | C5×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 92 | C4×C5×Dic3 | C23 | 1 | 4 | yes | — |
| 93 | C3×C4⋊Dic5 | C23 | 1 | 2 | yes | — |
| 94 | C3×C4⋊Dic5 | C23 | 1 | 2 | yes | — |
| 95 | C3×C4⋊Dic5 | C23 | 1 | 4 | yes | — |
| 96 | C3×#683 | C23 | 1 | 4 | yes | — |
| 97 | C3×#683 | C23 | 1 | 4 | yes | — |
| 98 | C3×#683 | C23 | 1 | 4 | yes | — |
| 99 | C3×#683 | C23 | 1 | 4 | yes | — |
| 100 | C3×C4×Dic5 | C23 | 1 | 4 | yes | — |
| 101 | Dic3⋊Dic5 | C23 | 1 | 4 | yes | — |
| 102 | Dic3⋊Dic5 | C23 | 1 | 4 | yes | — |
| 103 | Dic3⋊Dic5 | C23 | 1 | 4 | yes | — |
| 104 | Dic3⋊Dic5 | C23 | 1 | 4 | yes | — |
| 105 | #6669 | C23 | 1 | 4 | yes | — |
| 106 | #6669 | C23 | 1 | 4 | yes | — |
| 107 | #6669 | C23 | 1 | 4 | yes | — |
| 108 | #6669 | C23 | 1 | 4 | yes | — |
| 109 | #6668 | C23 | 1 | 4 | yes | — |
| 110 | #6668 | C23 | 1 | 4 | yes | — |
| 111 | #6668 | C23 | 1 | 4 | yes | — |
| 112 | #6668 | C23 | 1 | 4 | yes | — |
| 113 | Dic3×Dic5 | C23 | 1 | 4 | yes | — |
| 114 | Dic3×Dic5 | C23 | 1 | 4 | yes | — |
| 115 | C3×#564 | — | 5 | 1 | no | — |
| 116 | D3×#125 | — | 5 | 1 | no | — |
| 117 | D3×#125 | — | 5 | 4 | no | — |
| 118 | D3×#125 | — | 5 | 4 | no | — |
| 119 | D3×#125 | — | 5 | 4 | no | — |
| 120 | D3×#125 | — | 5 | 2 | no | — |
| 121 | C3⋊#564 | — | 5 | 4 | no | — |
| 122 | C3⋊#564 | — | 5 | 4 | no | — |
| 123 | C3⋊#564 | — | 5 | 4 | no | — |
| 124 | C3⋊#564 | — | 5 | 2 | no | — |
| 125 | C3⋊#564 | D5 | 1 | 1 | yes | characteristic, complemented |
| 126 | C5×#125 | — | 3 | 4 | no | — |
| 127 | C5×#125 | — | 3 | 4 | no | — |
| 128 | C5×#125 | — | 3 | 4 | no | — |
| 129 | C5×#125 | — | 3 | 2 | no | — |
| 130 | C5×#125 | C2×D3 | 1 | 1 | yes | characteristic |
| 131 | D5×C4⋊C4 | — | 3 | 4 | no | — |
| 132 | D5×C4⋊C4 | — | 3 | 2 | no | — |
| 133 | D5×C4⋊C4 | — | 3 | 4 | no | — |
| 134 | D5×C4⋊C4 | — | 3 | 2 | no | — |
| 135 | D5×C4⋊C4 | — | 3 | 2 | no | — |
| 136 | D5×C4⋊C4 | — | 3 | 4 | no | — |
| 137 | D5×C4⋊C4 | — | 3 | 4 | no | — |
| 138 | D5×C4⋊C4 | — | 3 | 4 | no | — |
| 139 | D5×C4⋊C4 | — | 3 | 4 | no | — |
| 140 | #4036 | — | 3 | 2 | no | — |
| 141 | #4036 | — | 3 | 4 | no | — |
| 142 | #4036 | — | 3 | 4 | no | — |
| 143 | #4036 | — | 3 | 2 | no | — |
| 144 | #4036 | — | 3 | 2 | no | — |
| 145 | #4036 | — | 3 | 4 | no | — |
| 146 | #4036 | — | 3 | 4 | no | — |
| 147 | #4036 | — | 3 | 4 | no | — |
| 148 | #4036 | C2×D3 | 1 | 4 | yes | — |
| 149 | #4035 | — | 3 | 4 | no | — |
| 150 | #4035 | — | 3 | 4 | no | — |
| 151 | #4035 | — | 3 | 4 | no | — |
| 152 | #4035 | — | 3 | 4 | no | — |
| 153 | #4035 | — | 3 | 4 | no | — |
| 154 | #4035 | — | 3 | 4 | no | — |
| 155 | #4035 | — | 3 | 4 | no | — |
| 156 | #4035 | — | 3 | 4 | no | — |
| 157 | #4035 | — | 3 | 4 | no | — |
| 158 | #4035 | — | 3 | 4 | no | — |
| 159 | #4035 | — | 3 | 4 | no | — |
| 160 | #4035 | — | 3 | 4 | no | — |
| 161 | #4035 | — | 3 | 4 | no | — |
| 162 | #4035 | C2×D3 | 1 | 4 | yes | — |
| 163 | #4035 | C2×D3 | 1 | 4 | yes | — |
| 164 | C42×D5 | — | 3 | 1 | no | — |
| 165 | C42×D5 | — | 3 | 4 | no | — |
| 166 | #4016 | — | 3 | 1 | no | — |
| 167 | #4016 | — | 3 | 4 | no | — |
| 168 | #4016 | — | 3 | 4 | no | — |
| 169 | #4016 | — | 3 | 4 | no | — |
| 170 | #4016 | C2×D3 | 1 | 2 | yes | — |
| 171 | C2×#564 | — | 15 | 1 | no | Sylow |
| 172 | C22×D15 | C24 | 1 | 1 | yes | characteristic |
| 173 | C2×C3×C4×C5 | C24 | 1 | 4 | yes | — |
| 174 | C2×C3×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 175 | C2×C3×C4×C5 | C24 | 1 | 2 | yes | — |
| 176 | C2×Dic15 | C24 | 1 | 4 | yes | — |
| 177 | C2×Dic15 | C24 | 1 | 1 | yes | characteristic |
| 178 | C2×Dic15 | C24 | 1 | 2 | yes | — |
| 179 | C4×D15 | — | 2 | 2 | no | — |
| 180 | C4×D15 | — | 2 | 8 | no | — |
| 181 | C4×D15 | — | 2 | 4 | no | — |
| 182 | C2×C5×Dic3 | C24 | 1 | 4 | yes | — |
| 183 | C2×C5×Dic3 | C24 | 1 | 4 | yes | — |
| 184 | C2×C3×Dic5 | C24 | 1 | 4 | yes | — |
| 185 | C2×C3×Dic5 | C24 | 1 | 4 | yes | — |
| 186 | #1200 | — | 2 | 8 | no | — |
| 187 | #1200 | — | 2 | 8 | no | — |
| 188 | C3×#125 | — | 5 | 4 | no | — |
| 189 | C3×#125 | — | 5 | 4 | no | — |
| 190 | C3×#125 | — | 5 | 4 | no | — |
| 191 | C3×#125 | — | 5 | 2 | no | — |
| 192 | C3×#125 | C2×D5 | 1 | 1 | yes | characteristic |
| 193 | D3×C4⋊C4 | — | 5 | 4 | no | — |
| 194 | D3×C4⋊C4 | — | 5 | 2 | no | — |
| 195 | D3×C4⋊C4 | — | 5 | 4 | no | — |
| 196 | D3×C4⋊C4 | — | 5 | 2 | no | — |
| 197 | D3×C4⋊C4 | — | 5 | 2 | no | — |
| 198 | D3×C4⋊C4 | — | 5 | 4 | no | — |
| 199 | D3×C4⋊C4 | — | 5 | 4 | no | — |
| 200 | D3×C4⋊C4 | — | 5 | 4 | no | — |
| 201 | D3×C4⋊C4 | — | 5 | 4 | no | — |
| 202 | #890 | — | 5 | 2 | no | — |
| 203 | #890 | — | 5 | 4 | no | — |
| 204 | #890 | — | 5 | 4 | no | — |
| 205 | #890 | — | 5 | 2 | no | — |
| 206 | #890 | — | 5 | 2 | no | — |
| 207 | #890 | — | 5 | 4 | no | — |
| 208 | #890 | — | 5 | 4 | no | — |
| 209 | #890 | — | 5 | 4 | no | — |
| 210 | #890 | C2×D5 | 1 | 4 | yes | — |
| 211 | #889 | — | 5 | 4 | no | — |
| 212 | #889 | — | 5 | 4 | no | — |
| 213 | #889 | — | 5 | 4 | no | — |
| 214 | #889 | — | 5 | 4 | no | — |
| 215 | #889 | — | 5 | 4 | no | — |
| 216 | #889 | — | 5 | 4 | no | — |
| 217 | #889 | — | 5 | 4 | no | — |
| 218 | #889 | — | 5 | 4 | no | — |
| 219 | #889 | — | 5 | 4 | no | — |
| 220 | #889 | — | 5 | 4 | no | — |
| 221 | #889 | — | 5 | 4 | no | — |
| 222 | #889 | — | 5 | 4 | no | — |
| 223 | #889 | — | 5 | 4 | no | — |
| 224 | #889 | C2×D5 | 1 | 4 | yes | — |
| 225 | #889 | C2×D5 | 1 | 4 | yes | — |
| 226 | C42×D3 | — | 5 | 1 | no | — |
| 227 | C42×D3 | — | 5 | 4 | no | — |
| 228 | #870 | — | 5 | 1 | no | — |
| 229 | #870 | — | 5 | 4 | no | — |
| 230 | #870 | — | 5 | 4 | no | — |
| 231 | #870 | — | 5 | 4 | no | — |
| 232 | #870 | C2×D5 | 1 | 2 | yes | — |
| 233 | C2×C4×D5 | — | 3 | 2 | no | — |
| 234 | C2×C4×D5 | — | 3 | 1 | no | — |
| 235 | C2×C4×D5 | — | 3 | 4 | no | — |
| 236 | C2×C4×D5 | — | 3 | 4 | no | — |
| 237 | C2×C4×D5 | — | 3 | 4 | no | — |
| 238 | C5×C4⋊C4 | — | 3 | 4 | no | — |
| 239 | C5×C4⋊C4 | — | 3 | 4 | no | — |
| 240 | C5×C4⋊C4 | — | 3 | 4 | no | — |
| 241 | C5×C4⋊C4 | — | 3 | 4 | no | — |
| 242 | C5×C4⋊C4 | — | 3 | 2 | no | — |
| 243 | C5×C4⋊C4 | — | 3 | 2 | no | — |
| 244 | C5×C4⋊C4 | — | 3 | 4 | no | — |
| 245 | C5×C4⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 246 | C5×C4⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 247 | C42×C5 | — | 3 | 4 | no | — |
| 248 | C42×C5 | C22×D3 | 1 | 1 | yes | characteristic |
| 249 | C4⋊Dic5 | — | 3 | 2 | no | — |
| 250 | C4⋊Dic5 | — | 3 | 4 | no | — |
| 251 | C4⋊Dic5 | — | 3 | 4 | no | — |
| 252 | C4⋊Dic5 | — | 3 | 4 | no | — |
| 253 | C4⋊Dic5 | — | 3 | 4 | no | — |
| 254 | C4⋊Dic5 | — | 3 | 4 | no | — |
| 255 | C4⋊Dic5 | C22×D3 | 1 | 4 | yes | — |
| 256 | C4⋊Dic5 | C22×D3 | 1 | 2 | yes | — |
| 257 | C4⋊Dic5 | C22×D3 | 1 | 2 | yes | — |
| 258 | #683 | — | 3 | 4 | no | — |
| 259 | #683 | — | 3 | 4 | no | — |
| 260 | #683 | — | 3 | 4 | no | — |
| 261 | #683 | — | 3 | 4 | no | — |
| 262 | #683 | — | 3 | 4 | no | — |
| 263 | #683 | — | 3 | 4 | no | — |
| 264 | #683 | — | 3 | 4 | no | — |
| 265 | #683 | — | 3 | 4 | no | — |
| 266 | #683 | — | 3 | 4 | no | — |
| 267 | #683 | — | 3 | 4 | no | — |
| 268 | #683 | — | 3 | 4 | no | — |
| 269 | #683 | C22×D3 | 1 | 4 | yes | — |
| 270 | #683 | C22×D3 | 1 | 4 | yes | — |
| 271 | #683 | C22×D3 | 1 | 4 | yes | — |
| 272 | #683 | C22×D3 | 1 | 4 | yes | — |
| 273 | C4×Dic5 | — | 3 | 2 | no | — |
| 274 | C4×Dic5 | — | 3 | 1 | no | — |
| 275 | C4×Dic5 | — | 3 | 4 | no | — |
| 276 | C4×Dic5 | — | 3 | 4 | no | — |
| 277 | C4×Dic5 | C22×D3 | 1 | 4 | yes | — |
| 278 | #564 | — | 3 | 1 | no | — |
| 279 | #564 | — | 5 | 1 | no | — |
| 280 | #564 | — | 15 | 4 | no | — |
| 281 | #564 | — | 15 | 4 | no | — |
| 282 | #564 | — | 15 | 4 | no | — |
| 283 | #564 | — | 15 | 2 | no | — |
| 284 | C2×#125 | — | 15 | 4 | no | — |
| 285 | C2×#125 | — | 15 | 4 | no | — |
| 286 | C2×#125 | — | 15 | 4 | no | — |
| 287 | C2×#125 | — | 15 | 2 | no | — |
| 288 | C2×#125 | — | 15 | 1 | no | — |
| 289 | C22×C3×C5 | C25 | 1 | 1 | yes | characteristic |
| 290 | C2×D15 | 2−1+4 | 1 | 2 | yes | — |
| 291 | C2×D15 | 2−1+4 | 1 | 4 | yes | — |
| 292 | C3×C4×C5 | — | 2 | 1 | no | — |
| 293 | C3×C4×C5 | — | 2 | 4 | no | — |
| 294 | C3×C4×C5 | — | 2 | 2 | no | — |
| 295 | Dic15 | — | 2 | 1 | no | — |
| 296 | Dic15 | — | 2 | 4 | no | — |
| 297 | Dic15 | — | 2 | 2 | no | — |
| 298 | C3×Dic5 | — | 2 | 4 | no | — |
| 299 | C3×Dic5 | — | 2 | 4 | no | — |
| 300 | C5×Dic3 | — | 2 | 4 | no | — |
| 301 | C5×Dic3 | — | 2 | 4 | no | — |
| 302 | C2×C4×D3 | — | 5 | 2 | no | — |
| 303 | C2×C4×D3 | — | 5 | 1 | no | — |
| 304 | C2×C4×D3 | — | 5 | 4 | no | — |
| 305 | C2×C4×D3 | — | 5 | 4 | no | — |
| 306 | C2×C4×D3 | — | 5 | 4 | no | — |
| 307 | C3×C4⋊C4 | — | 5 | 4 | no | — |
| 308 | C3×C4⋊C4 | — | 5 | 4 | no | — |
| 309 | C3×C4⋊C4 | — | 5 | 4 | no | — |
| 310 | C3×C4⋊C4 | — | 5 | 4 | no | — |
| 311 | C3×C4⋊C4 | — | 5 | 2 | no | — |
| 312 | C3×C4⋊C4 | — | 5 | 2 | no | — |
| 313 | C3×C4⋊C4 | — | 5 | 4 | no | — |
| 314 | C3×C4⋊C4 | C22×D5 | 1 | 4 | yes | — |
| 315 | C3×C4⋊C4 | C22×D5 | 1 | 2 | yes | — |
| 316 | C3×C42 | — | 5 | 4 | no | — |
| 317 | C3×C42 | C22×D5 | 1 | 1 | yes | characteristic |
| 318 | C4⋊Dic3 | — | 5 | 2 | no | — |
| 319 | C4⋊Dic3 | — | 5 | 4 | no | — |
| 320 | C4⋊Dic3 | — | 5 | 4 | no | — |
| 321 | C4⋊Dic3 | — | 5 | 4 | no | — |
| 322 | C4⋊Dic3 | — | 5 | 4 | no | — |
| 323 | C4⋊Dic3 | — | 5 | 4 | no | — |
| 324 | C4⋊Dic3 | C22×D5 | 1 | 4 | yes | — |
| 325 | C4⋊Dic3 | C22×D5 | 1 | 2 | yes | — |
| 326 | C4⋊Dic3 | C22×D5 | 1 | 2 | yes | — |
| 327 | Dic3⋊C4 | — | 5 | 4 | no | — |
| 328 | Dic3⋊C4 | — | 5 | 4 | no | — |
| 329 | Dic3⋊C4 | — | 5 | 4 | no | — |
| 330 | Dic3⋊C4 | — | 5 | 4 | no | — |
| 331 | Dic3⋊C4 | — | 5 | 4 | no | — |
| 332 | Dic3⋊C4 | — | 5 | 4 | no | — |
| 333 | Dic3⋊C4 | — | 5 | 4 | no | — |
| 334 | Dic3⋊C4 | — | 5 | 4 | no | — |
| 335 | Dic3⋊C4 | — | 5 | 4 | no | — |
| 336 | Dic3⋊C4 | — | 5 | 4 | no | — |
| 337 | Dic3⋊C4 | — | 5 | 4 | no | — |
| 338 | Dic3⋊C4 | C22×D5 | 1 | 4 | yes | — |
| 339 | Dic3⋊C4 | C22×D5 | 1 | 4 | yes | — |
| 340 | Dic3⋊C4 | C22×D5 | 1 | 4 | yes | — |
| 341 | Dic3⋊C4 | C22×D5 | 1 | 4 | yes | — |
| 342 | C4×Dic3 | — | 5 | 2 | no | — |
| 343 | C4×Dic3 | — | 5 | 1 | no | — |
| 344 | C4×Dic3 | — | 5 | 4 | no | — |
| 345 | C4×Dic3 | — | 5 | 4 | no | — |
| 346 | C4×Dic3 | C22×D5 | 1 | 4 | yes | — |
| 347 | C22×D5 | — | 3 | 1 | no | — |
| 348 | C2×C4×C5 | — | 3 | 4 | no | — |
| 349 | C2×C4×C5 | — | 3 | 4 | no | — |
| 350 | C2×C4×C5 | C23×D3 | 1 | 2 | yes | — |
| 351 | C2×C4×C5 | C23×D3 | 1 | 1 | yes | characteristic |
| 352 | C2×C4×C5 | C23×D3 | 1 | 4 | yes | — |
| 353 | C2×Dic5 | — | 3 | 1 | no | — |
| 354 | C2×Dic5 | — | 3 | 2 | no | — |
| 355 | C2×Dic5 | — | 3 | 4 | no | — |
| 356 | C2×Dic5 | C23×D3 | 1 | 4 | yes | — |
| 357 | C2×Dic5 | C23×D3 | 1 | 4 | yes | — |
| 358 | C4×D5 | — | 6 | 8 | no | — |
| 359 | C4×D5 | — | 6 | 8 | no | — |
| 360 | C4×D5 | — | 6 | 4 | no | — |
| 361 | C4×D5 | — | 6 | 8 | no | — |
| 362 | C4×D5 | — | 6 | 2 | no | — |
| 363 | #125 | — | 3 | 4 | no | — |
| 364 | #125 | — | 3 | 4 | no | — |
| 365 | #125 | — | 3 | 4 | no | — |
| 366 | #125 | — | 3 | 2 | no | — |
| 367 | #125 | — | 5 | 4 | no | — |
| 368 | #125 | — | 5 | 4 | no | — |
| 369 | #125 | — | 5 | 4 | no | — |
| 370 | #125 | — | 5 | 2 | no | — |
| 371 | #125 | — | 15 | 4 | no | — |
| 372 | #125 | — | 15 | 4 | no | — |
| 373 | #125 | — | 15 | 4 | no | — |
| 374 | #125 | — | 15 | 4 | no | — |
| 375 | #125 | — | 15 | 4 | no | — |
| 376 | #125 | — | 15 | 4 | no | — |
| 377 | #125 | — | 15 | 4 | no | — |
| 378 | #125 | — | 15 | 4 | no | — |
| 379 | #125 | — | 15 | 4 | no | — |
| 380 | #125 | — | 15 | 4 | no | — |
| 381 | #125 | — | 15 | 4 | no | — |
| 382 | #125 | — | 15 | 4 | no | — |
| 383 | #125 | — | 15 | 4 | no | — |
| 384 | #125 | — | 15 | 4 | no | — |
| 385 | #125 | — | 15 | 4 | no | — |
| 386 | #125 | — | 15 | 4 | no | — |
| 387 | #125 | — | 15 | 4 | no | — |
| 388 | #125 | — | 15 | 4 | no | — |
| 389 | #125 | — | 15 | 4 | no | — |
| 390 | #125 | — | 15 | 4 | no | — |
| 391 | #125 | — | 15 | 2 | no | — |
| 392 | #125 | — | 15 | 2 | no | — |
| 393 | #125 | — | 15 | 4 | no | — |
| 394 | #125 | — | 15 | 2 | no | — |
| 395 | #125 | — | 15 | 1 | no | — |
| 396 | #125 | D3×D5 | 1 | 1 | yes | characteristic |
| 397 | C2×C4⋊C4 | — | 15 | 4 | no | — |
| 398 | C2×C4⋊C4 | — | 15 | 4 | no | — |
| 399 | C2×C4⋊C4 | — | 15 | 4 | no | — |
| 400 | C2×C4⋊C4 | — | 15 | 4 | no | — |
| 401 | C2×C4⋊C4 | — | 15 | 4 | no | — |
| 402 | C2×C4⋊C4 | — | 15 | 2 | no | — |
| 403 | C2×C4⋊C4 | — | 15 | 2 | no | — |
| 404 | C2×C4⋊C4 | — | 15 | 4 | no | — |
| 405 | C2×C4⋊C4 | — | 15 | 2 | no | — |
| 406 | C2×C42 | — | 15 | 4 | no | — |
| 407 | C2×C42 | — | 15 | 1 | no | — |
| 408 | C2×C3×C5 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 409 | C2×C3×C5 | C2×2−1+4 | 1 | 2 | yes | — |
| 410 | D15 | #564 | 1 | 4 | yes | complemented |
| 411 | C22×D3 | — | 5 | 1 | no | — |
| 412 | C2×C3×C4 | — | 5 | 4 | no | — |
| 413 | C2×C3×C4 | — | 5 | 4 | no | — |
| 414 | C2×C3×C4 | C23×D5 | 1 | 2 | yes | — |
| 415 | C2×C3×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 416 | C2×C3×C4 | C23×D5 | 1 | 4 | yes | — |
| 417 | C2×Dic3 | — | 5 | 4 | no | — |
| 418 | C2×Dic3 | — | 5 | 1 | no | — |
| 419 | C2×Dic3 | — | 5 | 2 | no | — |
| 420 | C2×Dic3 | C23×D5 | 1 | 4 | yes | — |
| 421 | C2×Dic3 | C23×D5 | 1 | 4 | yes | — |
| 422 | C4×D3 | — | 10 | 8 | no | — |
| 423 | C4×D3 | — | 10 | 8 | no | — |
| 424 | C4×D3 | — | 10 | 4 | no | — |
| 425 | C4×D3 | — | 10 | 8 | no | — |
| 426 | C4×D3 | — | 10 | 2 | no | — |
| 427 | C22×C5 | C24×D3 | 1 | 1 | yes | characteristic |
| 428 | C2×D5 | — | 3 | 4 | no | — |
| 429 | C2×D5 | — | 3 | 2 | no | — |
| 430 | C4×C5 | — | 2 | 2 | no | — |
| 431 | C4×C5 | — | 2 | 4 | no | — |
| 432 | C4×C5 | — | 2 | 1 | no | — |
| 433 | C4×C5 | — | 6 | 4 | no | — |
| 434 | C4×C5 | — | 6 | 4 | no | — |
| 435 | Dic5 | — | 2 | 4 | no | — |
| 436 | Dic5 | — | 2 | 4 | no | — |
| 437 | Dic5 | — | 6 | 4 | no | — |
| 438 | Dic5 | — | 6 | 2 | no | — |
| 439 | Dic5 | — | 6 | 1 | no | — |
| 440 | C22×C4 | — | 15 | 4 | no | — |
| 441 | C22×C4 | — | 15 | 4 | no | — |
| 442 | C22×C4 | — | 15 | 4 | no | — |
| 443 | C22×C4 | — | 15 | 2 | no | — |
| 444 | C22×C4 | — | 15 | 1 | no | — |
| 445 | C4⋊C4 | — | 3 | 4 | no | — |
| 446 | C4⋊C4 | — | 3 | 4 | no | — |
| 447 | C4⋊C4 | — | 3 | 4 | no | — |
| 448 | C4⋊C4 | — | 3 | 4 | no | — |
| 449 | C4⋊C4 | — | 3 | 4 | no | — |
| 450 | C4⋊C4 | — | 3 | 2 | no | — |
| 451 | C4⋊C4 | — | 3 | 2 | no | — |
| 452 | C4⋊C4 | — | 5 | 4 | no | — |
| 453 | C4⋊C4 | — | 5 | 4 | no | — |
| 454 | C4⋊C4 | — | 5 | 4 | no | — |
| 455 | C4⋊C4 | — | 5 | 4 | no | — |
| 456 | C4⋊C4 | — | 5 | 4 | no | — |
| 457 | C4⋊C4 | — | 5 | 2 | no | — |
| 458 | C4⋊C4 | — | 5 | 2 | no | — |
| 459 | C4⋊C4 | — | 15 | 4 | no | — |
| 460 | C4⋊C4 | — | 15 | 4 | no | — |
| 461 | C4⋊C4 | — | 15 | 4 | no | — |
| 462 | C4⋊C4 | — | 15 | 4 | no | — |
| 463 | C4⋊C4 | — | 15 | 4 | no | — |
| 464 | C4⋊C4 | — | 15 | 4 | no | — |
| 465 | C4⋊C4 | — | 15 | 4 | no | — |
| 466 | C4⋊C4 | — | 15 | 4 | no | — |
| 467 | C4⋊C4 | — | 15 | 4 | no | — |
| 468 | C4⋊C4 | — | 15 | 4 | no | — |
| 469 | C4⋊C4 | — | 15 | 4 | no | — |
| 470 | C4⋊C4 | — | 15 | 4 | no | — |
| 471 | C4⋊C4 | — | 15 | 4 | no | — |
| 472 | C4⋊C4 | — | 15 | 4 | no | — |
| 473 | C4⋊C4 | — | 15 | 4 | no | — |
| 474 | C4⋊C4 | — | 15 | 4 | no | — |
| 475 | C4⋊C4 | — | 15 | 2 | no | — |
| 476 | C4⋊C4 | C2×D3×D5 | 1 | 2 | yes | — |
| 477 | C4⋊C4 | C2×D3×D5 | 1 | 4 | yes | — |
| 478 | C42 | — | 3 | 4 | no | — |
| 479 | C42 | — | 5 | 4 | no | — |
| 480 | C42 | — | 15 | 4 | no | — |
| 481 | C42 | — | 15 | 4 | no | — |
| 482 | C42 | — | 15 | 1 | no | — |
| 483 | C42 | — | 15 | 2 | no | — |
| 484 | C42 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 485 | C3×C5 | C2×#564 | 1 | 1 | yes | characteristic, complemented, Hall |
| 486 | C22×C3 | C24×D5 | 1 | 1 | yes | characteristic |
| 487 | C2×D3 | — | 5 | 4 | no | — |
| 488 | C2×D3 | — | 5 | 2 | no | — |
| 489 | C3×C4 | — | 2 | 2 | no | — |
| 490 | C3×C4 | — | 2 | 4 | no | — |
| 491 | C3×C4 | — | 2 | 1 | no | — |
| 492 | C3×C4 | — | 10 | 4 | no | — |
| 493 | C3×C4 | — | 10 | 4 | no | — |
| 494 | Dic3 | — | 2 | 4 | no | — |
| 495 | Dic3 | — | 2 | 4 | no | — |
| 496 | Dic3 | — | 10 | 4 | no | — |
| 497 | Dic3 | — | 10 | 2 | no | — |
| 498 | Dic3 | — | 10 | 1 | no | — |
| 499 | C2×C5 | D3×2−1+4 | 1 | 2 | yes | — |
| 500 | C2×C5 | D3×2−1+4 | 1 | 1 | yes | characteristic |
| 501 | D5 | — | 3 | 4 | no | — |
| 502 | C23 | — | 15 | 1 | no | — |
| 503 | C2×C4 | — | 3 | 4 | no | — |
| 504 | C2×C4 | — | 3 | 4 | no | — |
| 505 | C2×C4 | — | 5 | 4 | no | — |
| 506 | C2×C4 | — | 5 | 4 | no | — |
| 507 | C2×C4 | — | 15 | 4 | no | — |
| 508 | C2×C4 | — | 15 | 2 | no | — |
| 509 | C2×C4 | — | 15 | 1 | no | — |
| 510 | C2×C4 | — | 30 | 8 | no | — |
| 511 | C2×C4 | — | 30 | 4 | no | — |
| 512 | C2×C4 | — | 30 | 2 | no | — |
| 513 | C2×C4 | — | 30 | 8 | no | — |
| 514 | C2×C4 | — | 30 | 8 | no | — |
| 515 | C2×C4 | C22×D3×D5 | 1 | 4 | yes | — |
| 516 | C2×C4 | C22×D3×D5 | 1 | 2 | yes | — |
| 517 | C2×C4 | C22×D3×D5 | 1 | 1 | yes | characteristic |
| 518 | C2×C3 | D5×2−1+4 | 1 | 2 | yes | — |
| 519 | C2×C3 | D5×2−1+4 | 1 | 1 | yes | characteristic |
| 520 | D3 | — | 5 | 4 | no | — |
| 521 | C5 | D3×#564 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 522 | C22 | — | 15 | 4 | no | — |
| 523 | C22 | — | 15 | 2 | no | — |
| 524 | C22 | C23×D3×D5 | 1 | 1 | yes | characteristic |
| 525 | C4 | — | 2 | 4 | no | — |
| 526 | C4 | — | 2 | 2 | no | — |
| 527 | C4 | — | 2 | 1 | no | — |
| 528 | C4 | — | 6 | 4 | no | — |
| 529 | C4 | — | 6 | 4 | no | — |
| 530 | C4 | — | 10 | 4 | no | — |
| 531 | C4 | — | 10 | 4 | no | — |
| 532 | C4 | — | 30 | 4 | no | — |
| 533 | C4 | — | 30 | 2 | no | — |
| 534 | C4 | — | 30 | 1 | no | — |
| 535 | C3 | D5×#564 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 536 | C2 | — | 15 | 4 | no | — |
| 537 | C2 | #11757047 | 1 | 1 | yes | characteristic |
| 538 | C2 | #11757057 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×C3⋊#564 | C2 | semidirect |
| 3. C3×C5⋊#564 | C2 | semidirect |
| 7. #11753395 | C2 | semidirect |
| 8. #11753393 | C2 | semidirect |
| 9. #11753333 | C2 | semidirect |
| 11. #11752488 | C2 | semidirect |
| 69. C5⋊#564 | D3 | semidirect |
| 125. C3⋊#564 | D5 | semidirect |
| 410. D15 | #564 | semidirect |
| 485. C3×C5 | C2×#564 | semidirect |
| 521. C5 | D3×#564 | semidirect |
| 535. C3 | D5×#564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D15×#125 | 2 |
| C5×C3⋊#564 | 2 |
| C3×C5⋊#564 | 2 |
| #11753620 | 2 |
| #11753468 | 2 |
| #11753395 | 2 |
| #11753393 | 2 |
| #11753333 | 2 |
| #11752631 | 2 |
| #11752488 | 2 |
| D5×#564 | 3 |
| D3×#564 | 5 |