Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
888 conjugacy classes of subgroups.
The subgroup lattice has 588 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C5×#5766 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11755105 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #11754011 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11751293 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#65470 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11749414 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11749393 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11749392 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11748094 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11748078 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11748062 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #10615749 | — | 3 | 1 | no | maximal, Hall |
| 13 | C5×#1007 | C22 | 1 | 2 | yes | — |
| 14 | #92004 | C22 | 1 | 2 | yes | — |
| 15 | C2×C3×C5×Q16 | C22 | 1 | 1 | yes | characteristic |
| 16 | #91831 | C22 | 1 | 2 | yes | — |
| 17 | #91790 | C22 | 1 | 1 | yes | characteristic |
| 18 | C5×#942 | C22 | 1 | 2 | yes | — |
| 19 | C5×#919 | — | 2 | 1 | no | — |
| 20 | C5×#918 | — | 2 | 2 | no | — |
| 21 | C5×D3×Q16 | — | 2 | 1 | no | — |
| 22 | C5×#904 | C22 | 1 | 1 | yes | characteristic |
| 23 | C5×#901 | C22 | 1 | 1 | yes | characteristic |
| 24 | C3×#4090 | C22 | 1 | 2 | yes | — |
| 25 | C2×C3×#689 | C22 | 1 | 2 | yes | — |
| 26 | C2×C3×Dic20 | C22 | 1 | 1 | yes | characteristic |
| 27 | #91520 | — | 2 | 2 | no | — |
| 28 | #91519 | — | 2 | 2 | no | — |
| 29 | #91510 | — | 2 | 2 | no | — |
| 30 | D3×#689 | — | 2 | 2 | no | — |
| 31 | #91309 | C22 | 1 | 2 | yes | — |
| 32 | #91309 | C22 | 1 | 2 | yes | — |
| 33 | #91303 | C22 | 1 | 1 | yes | characteristic |
| 34 | #91286 | C22 | 1 | 2 | yes | — |
| 35 | #91280 | — | 2 | 2 | no | — |
| 36 | #91279 | — | 2 | 1 | no | — |
| 37 | #91264 | — | 2 | 1 | no | — |
| 38 | #91120 | C22 | 1 | 2 | yes | — |
| 39 | #91103 | C22 | 1 | 1 | yes | characteristic |
| 40 | C3×C8×Dic5 | C22 | 1 | 1 | yes | characteristic |
| 41 | #90991 | C22 | 1 | 1 | yes | characteristic |
| 42 | #90981 | C22 | 1 | 1 | yes | characteristic |
| 43 | #90979 | C22 | 1 | 1 | yes | characteristic |
| 44 | #90979 | C22 | 1 | 2 | yes | — |
| 45 | #90961 | C22 | 1 | 2 | yes | — |
| 46 | #81808 | — | 5 | 1 | no | maximal, Hall |
| 47 | C5×#578 | — | 3 | 1 | no | — |
| 48 | #66172 | — | 3 | 2 | no | — |
| 49 | #66105 | — | 3 | 1 | no | — |
| 50 | #65535 | — | 3 | 2 | no | — |
| 51 | #65494 | — | 3 | 2 | no | — |
| 52 | #65493 | — | 3 | 2 | no | — |
| 53 | #65485 | — | 3 | 1 | no | — |
| 54 | #65481 | — | 3 | 1 | no | — |
| 55 | #65470 | D3 | 1 | 1 | yes | characteristic, complemented |
| 56 | #65433 | — | 3 | 1 | no | — |
| 57 | #65432 | — | 3 | 1 | no | — |
| 58 | C2×C3×C5×Q8 | C23 | 1 | 2 | yes | — |
| 59 | #6817 | C23 | 1 | 1 | yes | characteristic |
| 60 | C5×#239 | — | 2 | 2 | no | — |
| 61 | C5×#239 | — | 2 | 2 | no | — |
| 62 | C5×D3×Q8 | — | 2 | 2 | no | — |
| 63 | C5×D3×Q8 | — | 2 | 2 | no | — |
| 64 | C5×#235 | — | 4 | 2 | no | — |
| 65 | C5×#235 | C23 | 1 | 1 | yes | characteristic |
| 66 | C5×#235 | C23 | 1 | 2 | yes | — |
| 67 | C2×C3×Dic10 | C23 | 1 | 2 | yes | — |
| 68 | #6782 | — | 4 | 2 | no | — |
| 69 | D15⋊Q8 | — | 2 | 2 | no | — |
| 70 | #6769 | — | 2 | 2 | no | — |
| 71 | #6768 | — | 2 | 2 | no | — |
| 72 | D3×Dic10 | — | 2 | 2 | no | — |
| 73 | C3×C5×Q16 | — | 2 | 1 | no | — |
| 74 | C3×C5×Q16 | — | 2 | 1 | no | — |
| 75 | C2×C3×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 76 | #6718 | — | 2 | 2 | no | — |
| 77 | #6717 | — | 2 | 2 | no | — |
| 78 | #6710 | C23 | 1 | 2 | yes | — |
| 79 | #6710 | C23 | 1 | 1 | yes | characteristic |
| 80 | #6705 | — | 2 | 1 | no | — |
| 81 | C8×D15 | — | 2 | 1 | no | — |
| 82 | C5×#216 | — | 2 | 2 | no | — |
| 83 | C5×#215 | — | 2 | 2 | no | — |
| 84 | C5×#208 | C23 | 1 | 1 | yes | characteristic |
| 85 | C5×Dic12 | D4 | 1 | 1 | yes | characteristic |
| 86 | C5×D24 | D4 | 1 | 1 | yes | characteristic |
| 87 | C5×#204 | D4 | 1 | 2 | yes | — |
| 88 | C5×ΓL(1,𝔽25) | — | 2 | 1 | no | — |
| 89 | C5×D3×C8 | — | 2 | 1 | no | — |
| 90 | C3×#689 | — | 2 | 2 | no | — |
| 91 | C3×#689 | — | 2 | 2 | no | — |
| 92 | C3×#683 | — | 4 | 2 | no | — |
| 93 | C3×C4×Dic5 | C23 | 1 | 1 | yes | characteristic |
| 94 | C2×C3×#168 | C23 | 1 | 1 | yes | characteristic |
| 95 | C3×Dic20 | — | 2 | 1 | no | — |
| 96 | C3×Dic20 | — | 2 | 1 | no | — |
| 97 | #6663 | D4 | 1 | 1 | yes | characteristic |
| 98 | #6661 | — | 2 | 2 | no | — |
| 99 | #6661 | — | 2 | 2 | no | — |
| 100 | #6660 | D4 | 1 | 1 | yes | characteristic |
| 101 | #6659 | D4 | 1 | 1 | yes | characteristic |
| 102 | #6656 | — | 2 | 2 | no | — |
| 103 | #6656 | — | 2 | 2 | no | — |
| 104 | #6654 | D4 | 1 | 1 | yes | characteristic |
| 105 | #6650 | — | 2 | 2 | no | — |
| 106 | D3×#168 | — | 2 | 2 | no | — |
| 107 | #5766 | — | 5 | 2 | no | — |
| 108 | #5766 | — | 5 | 1 | no | — |
| 109 | #5766 | D5 | 1 | 1 | yes | characteristic, complemented |
| 110 | C3×#494 | — | 5 | 1 | no | — |
| 111 | #5192 | — | 5 | 1 | no | — |
| 112 | #5192 | — | 5 | 2 | no | — |
| 113 | #5192 | — | 5 | 1 | no | — |
| 114 | #5095 | — | 5 | 2 | no | — |
| 115 | #5095 | — | 5 | 2 | no | — |
| 116 | #4700 | — | 5 | 1 | no | — |
| 117 | #4700 | — | 5 | 1 | no | — |
| 118 | C5×2−1+4 | — | 3 | 2 | no | — |
| 119 | #4150 | — | 3 | 2 | no | — |
| 120 | C5×#137 | — | 3 | 2 | no | — |
| 121 | C5×#137 | — | 6 | 2 | no | — |
| 122 | C5×#135 | — | 3 | 1 | no | — |
| 123 | C5×#135 | — | 6 | 1 | no | — |
| 124 | C2×C5×Q16 | — | 6 | 1 | no | — |
| 125 | C2×C5×Q16 | C2×D3 | 1 | 1 | yes | characteristic |
| 126 | C5×#131 | — | 3 | 1 | no | — |
| 127 | #4097 | — | 3 | 2 | no | — |
| 128 | #4097 | — | 3 | 2 | no | — |
| 129 | #4097 | — | 6 | 2 | no | — |
| 130 | #4096 | — | 3 | 1 | no | — |
| 131 | #4096 | — | 6 | 2 | no | — |
| 132 | #4094 | — | 3 | 2 | no | — |
| 133 | #4090 | C2×D3 | 1 | 2 | yes | — |
| 134 | C2×#689 | — | 6 | 2 | no | — |
| 135 | C2×#689 | C2×D3 | 1 | 2 | yes | — |
| 136 | #4088 | — | 3 | 2 | no | — |
| 137 | #4088 | — | 6 | 2 | no | — |
| 138 | D5×Q16 | — | 6 | 1 | no | — |
| 139 | #4061 | — | 6 | 2 | no | — |
| 140 | #4058 | — | 6 | 1 | no | — |
| 141 | C2×Dic20 | C2×D3 | 1 | 1 | yes | characteristic |
| 142 | #4047 | — | 3 | 1 | no | — |
| 143 | #3969 | — | 3 | 1 | no | — |
| 144 | #3969 | — | 3 | 2 | no | — |
| 145 | #3968 | — | 3 | 2 | no | — |
| 146 | #3957 | — | 3 | 1 | no | — |
| 147 | #3956 | — | 3 | 2 | no | — |
| 148 | #3954 | — | 3 | 1 | no | — |
| 149 | #3951 | — | 3 | 1 | no | — |
| 150 | C8×Dic5 | C2×D3 | 1 | 1 | yes | characteristic |
| 151 | #3293 | — | 15 | 1 | no | Sylow |
| 152 | C3×C5×Q8 | — | 2 | 2 | no | — |
| 153 | C3×C5×Q8 | — | 2 | 2 | no | — |
| 154 | C2×C3×C4×C5 | — | 2 | 2 | no | — |
| 155 | C2×C3×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 156 | #1220 | — | 2 | 1 | no | — |
| 157 | D60 | C2×D4 | 1 | 1 | yes | characteristic |
| 158 | C4×D15 | — | 2 | 1 | no | — |
| 159 | Dic30 | C2×D4 | 1 | 1 | yes | characteristic |
| 160 | C5×#67 | — | 2 | 2 | no | — |
| 161 | C5×#67 | — | 2 | 1 | no | — |
| 162 | C5×D12 | — | 4 | 2 | no | — |
| 163 | C5×D12 | C2×D4 | 1 | 1 | yes | characteristic |
| 164 | C5×D12 | C2×D4 | 1 | 2 | yes | — |
| 165 | C4×C5×D3 | — | 2 | 1 | no | — |
| 166 | C4×C5×D3 | — | 2 | 2 | no | — |
| 167 | C4×C5×D3 | — | 4 | 2 | no | — |
| 168 | C4×C5×D3 | — | 4 | 2 | no | — |
| 169 | C5×Dic6 | — | 4 | 2 | no | — |
| 170 | C5×Dic6 | C2×D4 | 1 | 1 | yes | characteristic |
| 171 | C5×Dic6 | C2×D4 | 1 | 2 | yes | — |
| 172 | C2×C3×Dic5 | — | 2 | 1 | no | — |
| 173 | C2×C3×Dic5 | — | 2 | 2 | no | — |
| 174 | C3×Dic10 | — | 2 | 2 | no | — |
| 175 | C3×Dic10 | — | 2 | 2 | no | — |
| 176 | #1204 | — | 4 | 2 | no | — |
| 177 | #1203 | — | 4 | 2 | no | — |
| 178 | #1200 | — | 4 | 2 | no | — |
| 179 | D3×Dic5 | — | 4 | 2 | no | — |
| 180 | C3×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 181 | C3×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 182 | C3⋊#168 | — | 2 | 1 | no | — |
| 183 | C3⋊#168 | — | 2 | 2 | no | — |
| 184 | C3×#168 | C2×D4 | 1 | 1 | yes | characteristic |
| 185 | C3×#168 | C2×D4 | 1 | 1 | yes | characteristic |
| 186 | C5×C3⋊C8 | — | 2 | 1 | no | — |
| 187 | #1007 | — | 5 | 2 | no | — |
| 188 | #1007 | C2×D5 | 1 | 2 | yes | — |
| 189 | C2×C3×Q16 | — | 5 | 2 | no | — |
| 190 | C2×C3×Q16 | — | 5 | 1 | no | — |
| 191 | C2×C3×Q16 | C2×D5 | 1 | 1 | yes | characteristic |
| 192 | C3×C4⋊Q8 | — | 5 | 2 | no | — |
| 193 | #942 | — | 5 | 2 | no | — |
| 194 | #942 | — | 5 | 2 | no | — |
| 195 | #942 | — | 5 | 2 | no | — |
| 196 | #942 | C2×D5 | 1 | 2 | yes | — |
| 197 | #919 | — | 2 | 1 | no | — |
| 198 | #919 | — | 10 | 2 | no | — |
| 199 | #919 | — | 10 | 1 | no | — |
| 200 | #918 | — | 2 | 2 | no | — |
| 201 | #918 | — | 10 | 2 | no | — |
| 202 | #918 | — | 10 | 2 | no | — |
| 203 | #918 | — | 10 | 2 | no | — |
| 204 | D3×Q16 | — | 2 | 1 | no | — |
| 205 | D3×Q16 | — | 10 | 2 | no | — |
| 206 | D3×Q16 | — | 10 | 1 | no | — |
| 207 | #904 | — | 5 | 1 | no | — |
| 208 | #904 | C2×D5 | 1 | 1 | yes | characteristic |
| 209 | #901 | — | 5 | 2 | no | — |
| 210 | #901 | — | 5 | 1 | no | — |
| 211 | #901 | C2×D5 | 1 | 1 | yes | characteristic |
| 212 | C3×C4×C8 | — | 5 | 1 | no | — |
| 213 | #836 | — | 5 | 2 | no | — |
| 214 | #836 | — | 5 | 2 | no | — |
| 215 | #819 | — | 5 | 1 | no | — |
| 216 | #819 | — | 5 | 1 | no | — |
| 217 | #805 | — | 5 | 1 | no | — |
| 218 | #805 | — | 5 | 2 | no | — |
| 219 | #805 | — | 5 | 1 | no | — |
| 220 | C5×#41 | — | 3 | 1 | no | — |
| 221 | C5×#41 | — | 3 | 2 | no | — |
| 222 | C5×#41 | — | 6 | 2 | no | — |
| 223 | C5×#41 | — | 6 | 2 | no | — |
| 224 | C5×#41 | — | 12 | 2 | no | — |
| 225 | C2×C5×Q8 | — | 6 | 2 | no | — |
| 226 | C2×C5×Q8 | — | 6 | 2 | no | — |
| 227 | C2×C5×Q8 | C22×D3 | 1 | 2 | yes | — |
| 228 | Q8×D5 | — | 6 | 2 | no | — |
| 229 | #711 | — | 6 | 2 | no | — |
| 230 | #711 | — | 12 | 2 | no | — |
| 231 | #709 | — | 3 | 1 | no | — |
| 232 | #709 | — | 6 | 2 | no | — |
| 233 | C2×Dic10 | — | 6 | 2 | no | — |
| 234 | C2×Dic10 | C22×D3 | 1 | 2 | yes | — |
| 235 | C5×Q16 | — | 2 | 1 | no | — |
| 236 | C5×Q16 | — | 2 | 1 | no | — |
| 237 | C5×Q16 | — | 3 | 1 | no | — |
| 238 | C5×Q16 | — | 6 | 2 | no | — |
| 239 | C5×SD16 | — | 3 | 2 | no | — |
| 240 | C5×SD16 | — | 6 | 2 | no | — |
| 241 | C5×D8 | — | 3 | 1 | no | — |
| 242 | C5×M16 | — | 3 | 1 | no | — |
| 243 | C5×M16 | — | 6 | 1 | no | — |
| 244 | C2×C5×C8 | — | 6 | 1 | no | — |
| 245 | C2×C5×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 246 | #689 | — | 2 | 2 | no | — |
| 247 | #689 | — | 2 | 2 | no | — |
| 248 | #689 | — | 3 | 1 | no | — |
| 249 | #689 | — | 6 | 2 | no | — |
| 250 | #689 | — | 6 | 2 | no | — |
| 251 | #689 | — | 6 | 2 | no | — |
| 252 | #688 | — | 3 | 1 | no | — |
| 253 | #688 | — | 6 | 2 | no | — |
| 254 | #687 | — | 3 | 1 | no | — |
| 255 | #687 | — | 6 | 2 | no | — |
| 256 | #687 | — | 6 | 2 | no | — |
| 257 | #686 | — | 3 | 1 | no | — |
| 258 | #683 | — | 4 | 2 | no | — |
| 259 | C4×Dic5 | C22×D3 | 1 | 1 | yes | characteristic |
| 260 | #681 | — | 3 | 1 | no | — |
| 261 | #681 | — | 3 | 2 | no | — |
| 262 | #681 | — | 6 | 2 | no | — |
| 263 | C2×#168 | — | 6 | 2 | no | — |
| 264 | C2×#168 | C22×D3 | 1 | 1 | yes | characteristic |
| 265 | Dic20 | — | 2 | 1 | no | — |
| 266 | Dic20 | — | 2 | 1 | no | — |
| 267 | #676 | — | 6 | 1 | no | — |
| 268 | C8×D5 | — | 6 | 1 | no | — |
| 269 | #578 | — | 3 | 1 | no | — |
| 270 | #578 | — | 15 | 1 | no | — |
| 271 | #578 | — | 15 | 2 | no | — |
| 272 | #494 | — | 5 | 1 | no | — |
| 273 | #473 | — | 15 | 1 | no | — |
| 274 | #473 | — | 15 | 2 | no | — |
| 275 | #473 | — | 15 | 1 | no | — |
| 276 | #456 | — | 15 | 2 | no | — |
| 277 | #456 | — | 15 | 2 | no | — |
| 278 | #443 | — | 15 | 1 | no | — |
| 279 | #443 | — | 15 | 1 | no | — |
| 280 | C22×C3×C5 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 281 | C2×D15 | — | 2 | 1 | no | — |
| 282 | C2×C5×D3 | — | 2 | 2 | no | — |
| 283 | C2×C5×D3 | — | 2 | 1 | no | — |
| 284 | C3×C4×C5 | — | 4 | 2 | no | — |
| 285 | C3×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 286 | C3×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 287 | Dic15 | — | 2 | 1 | no | — |
| 288 | C3×Dic5 | — | 2 | 2 | no | — |
| 289 | C3×Dic5 | — | 4 | 2 | no | — |
| 290 | C5×Dic3 | — | 2 | 2 | no | — |
| 291 | C5×Dic3 | — | 2 | 1 | no | — |
| 292 | C2×C3×Q8 | — | 5 | 2 | no | — |
| 293 | C2×C3×Q8 | C22×D5 | 1 | 2 | yes | — |
| 294 | #239 | — | 2 | 2 | no | — |
| 295 | #239 | — | 2 | 2 | no | — |
| 296 | #239 | — | 10 | 2 | no | — |
| 297 | #239 | — | 10 | 2 | no | — |
| 298 | D3×Q8 | — | 2 | 2 | no | — |
| 299 | D3×Q8 | — | 2 | 2 | no | — |
| 300 | D3×Q8 | — | 10 | 2 | no | — |
| 301 | D3×Q8 | — | 10 | 2 | no | — |
| 302 | #235 | — | 4 | 2 | no | — |
| 303 | #235 | — | 5 | 1 | no | — |
| 304 | #235 | — | 20 | 2 | no | — |
| 305 | #235 | C22×D5 | 1 | 1 | yes | characteristic |
| 306 | #235 | C22×D5 | 1 | 2 | yes | — |
| 307 | C3×Q16 | — | 2 | 1 | no | — |
| 308 | C3×Q16 | — | 2 | 1 | no | — |
| 309 | C3×Q16 | — | 10 | 2 | no | — |
| 310 | C3×Q16 | — | 10 | 2 | no | — |
| 311 | C3×Q16 | — | 10 | 1 | no | — |
| 312 | C3×Q16 | — | 10 | 1 | no | — |
| 313 | C2×C3×C8 | — | 5 | 1 | no | — |
| 314 | C2×C3×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 315 | C3×C4⋊C4 | — | 20 | 2 | no | — |
| 316 | C3×C42 | — | 5 | 1 | no | — |
| 317 | #216 | — | 2 | 2 | no | — |
| 318 | #216 | — | 10 | 2 | no | — |
| 319 | #216 | — | 10 | 2 | no | — |
| 320 | #216 | — | 10 | 2 | no | — |
| 321 | #215 | — | 2 | 2 | no | — |
| 322 | #215 | — | 10 | 2 | no | — |
| 323 | #215 | — | 10 | 2 | no | — |
| 324 | #215 | — | 10 | 2 | no | — |
| 325 | #208 | — | 5 | 2 | no | — |
| 326 | #208 | — | 5 | 1 | no | — |
| 327 | #208 | C22×D5 | 1 | 1 | yes | characteristic |
| 328 | Dic12 | — | 5 | 1 | no | — |
| 329 | Dic12 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 330 | D24 | — | 5 | 1 | no | — |
| 331 | D24 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 332 | #204 | — | 5 | 1 | no | — |
| 333 | #204 | — | 5 | 1 | no | — |
| 334 | #204 | C22⋊D5 | 1 | 2 | yes | — |
| 335 | ΓL(1,𝔽25) | — | 2 | 1 | no | — |
| 336 | ΓL(1,𝔽25) | — | 10 | 2 | no | — |
| 337 | ΓL(1,𝔽25) | — | 10 | 1 | no | — |
| 338 | D3×C8 | — | 2 | 1 | no | — |
| 339 | D3×C8 | — | 10 | 2 | no | — |
| 340 | D3×C8 | — | 10 | 1 | no | — |
| 341 | C5×Q8 | — | 2 | 2 | no | — |
| 342 | C5×Q8 | — | 2 | 2 | no | — |
| 343 | C5×Q8 | — | 3 | 1 | no | — |
| 344 | C5×Q8 | — | 3 | 2 | no | — |
| 345 | C5×Q8 | — | 12 | 2 | no | — |
| 346 | C5×D4 | — | 3 | 1 | no | — |
| 347 | C5×D4 | — | 3 | 2 | no | — |
| 348 | C5×D4 | — | 6 | 2 | no | — |
| 349 | C5×D4 | — | 6 | 1 | no | — |
| 350 | C5×D4 | — | 12 | 2 | no | — |
| 351 | C2×C4×C5 | — | 2 | 2 | no | — |
| 352 | C2×C4×C5 | — | 6 | 2 | no | — |
| 353 | C2×C4×C5 | — | 6 | 1 | no | — |
| 354 | C2×C4×C5 | — | 12 | 2 | no | — |
| 355 | C2×C4×C5 | — | 12 | 2 | no | — |
| 356 | C2×C4×C5 | C23×D3 | 1 | 1 | yes | characteristic |
| 357 | C22⋊D5 | — | 6 | 1 | no | — |
| 358 | C22⋊D5 | — | 12 | 2 | no | — |
| 359 | C2×Dic5 | — | 2 | 1 | no | — |
| 360 | C2×Dic5 | — | 2 | 2 | no | — |
| 361 | C2×Dic5 | — | 12 | 2 | no | — |
| 362 | D20 | — | 3 | 1 | no | — |
| 363 | C4×D5 | — | 6 | 1 | no | — |
| 364 | C4×D5 | — | 12 | 2 | no | — |
| 365 | Dic10 | — | 2 | 2 | no | — |
| 366 | Dic10 | — | 2 | 2 | no | — |
| 367 | Dic10 | — | 3 | 1 | no | — |
| 368 | Dic10 | — | 12 | 2 | no | — |
| 369 | C5×C8 | — | 6 | 1 | no | — |
| 370 | C5×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 371 | C5×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 372 | #168 | — | 6 | 1 | no | — |
| 373 | #168 | — | 6 | 2 | no | — |
| 374 | #168 | D3×D4 | 1 | 1 | yes | characteristic |
| 375 | #168 | D3×D4 | 1 | 1 | yes | characteristic |
| 376 | 2−1+4 | — | 3 | 2 | no | — |
| 377 | 2−1+4 | — | 15 | 2 | no | — |
| 378 | #137 | — | 3 | 2 | no | — |
| 379 | #137 | — | 6 | 2 | no | — |
| 380 | #137 | — | 15 | 2 | no | — |
| 381 | #137 | — | 15 | 2 | no | — |
| 382 | #137 | — | 15 | 2 | no | — |
| 383 | #137 | — | 30 | 2 | no | — |
| 384 | #137 | — | 30 | 2 | no | — |
| 385 | #137 | — | 30 | 2 | no | — |
| 386 | #135 | — | 3 | 1 | no | — |
| 387 | #135 | — | 6 | 1 | no | — |
| 388 | #135 | — | 15 | 1 | no | — |
| 389 | #135 | — | 30 | 1 | no | — |
| 390 | #135 | — | 30 | 2 | no | — |
| 391 | C2×Q16 | — | 5 | 2 | no | — |
| 392 | C2×Q16 | — | 5 | 1 | no | — |
| 393 | C2×Q16 | — | 6 | 1 | no | — |
| 394 | C2×Q16 | — | 30 | 1 | no | — |
| 395 | C2×Q16 | — | 30 | 2 | no | — |
| 396 | C2×Q16 | D3×D5 | 1 | 1 | yes | characteristic |
| 397 | #131 | — | 3 | 1 | no | — |
| 398 | #131 | — | 15 | 2 | no | — |
| 399 | #131 | — | 15 | 1 | no | — |
| 400 | C4⋊Q8 | — | 5 | 2 | no | — |
| 401 | #108 | — | 15 | 1 | no | — |
| 402 | #108 | — | 15 | 1 | no | — |
| 403 | #104 | — | 15 | 1 | no | — |
| 404 | #104 | — | 15 | 1 | no | — |
| 405 | #104 | — | 15 | 2 | no | — |
| 406 | #101 | — | 15 | 2 | no | — |
| 407 | #101 | — | 15 | 2 | no | — |
| 408 | C4×C8 | — | 5 | 1 | no | — |
| 409 | C2×C3×C5 | — | 2 | 1 | no | — |
| 410 | C2×C3×C5 | D42 | 1 | 1 | yes | characteristic |
| 411 | D15 | — | 4 | 1 | no | — |
| 412 | C5×D3 | — | 4 | 2 | no | — |
| 413 | C5×D3 | — | 4 | 1 | no | — |
| 414 | C3×Q8 | — | 2 | 2 | no | — |
| 415 | C3×Q8 | — | 2 | 2 | no | — |
| 416 | C3×Q8 | — | 10 | 2 | no | — |
| 417 | C3×Q8 | — | 10 | 2 | no | — |
| 418 | C2×C3×C4 | — | 2 | 2 | no | — |
| 419 | C2×C3×C4 | — | 10 | 1 | no | — |
| 420 | C2×C3×C4 | — | 10 | 2 | no | — |
| 421 | C2×C3×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 422 | #67 | — | 2 | 1 | no | — |
| 423 | #67 | — | 2 | 2 | no | — |
| 424 | #67 | — | 10 | 1 | no | — |
| 425 | D12 | — | 4 | 2 | no | — |
| 426 | D12 | — | 5 | 1 | no | — |
| 427 | D12 | — | 20 | 2 | no | — |
| 428 | D12 | D4×D5 | 1 | 1 | yes | characteristic |
| 429 | D12 | C2×C22⋊D5 | 1 | 2 | yes | — |
| 430 | C4×D3 | — | 2 | 2 | no | — |
| 431 | C4×D3 | — | 2 | 1 | no | — |
| 432 | C4×D3 | — | 4 | 2 | no | — |
| 433 | C4×D3 | — | 4 | 2 | no | — |
| 434 | C4×D3 | — | 10 | 1 | no | — |
| 435 | C4×D3 | — | 20 | 2 | no | — |
| 436 | C4×D3 | — | 20 | 2 | no | — |
| 437 | Dic6 | — | 4 | 2 | no | — |
| 438 | Dic6 | — | 5 | 1 | no | — |
| 439 | Dic6 | — | 20 | 2 | no | — |
| 440 | Dic6 | D4×D5 | 1 | 1 | yes | characteristic |
| 441 | Dic6 | C2×C22⋊D5 | 1 | 2 | yes | — |
| 442 | C3×C8 | — | 5 | 1 | no | — |
| 443 | C3×C8 | — | 5 | 1 | no | — |
| 444 | C3×C8 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 445 | C3×C8 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 446 | C3⋊C8 | — | 2 | 1 | no | — |
| 447 | C3⋊C8 | — | 10 | 2 | no | — |
| 448 | C3⋊C8 | — | 10 | 1 | no | — |
| 449 | C22×C5 | — | 6 | 2 | no | — |
| 450 | C22×C5 | — | 6 | 1 | no | — |
| 451 | C22×C5 | #1004 | 1 | 1 | yes | characteristic |
| 452 | C2×D5 | — | 6 | 1 | no | — |
| 453 | C4×C5 | — | 4 | 2 | no | — |
| 454 | C4×C5 | — | 6 | 2 | no | — |
| 455 | C4×C5 | — | 6 | 1 | no | — |
| 456 | C4×C5 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 457 | C4×C5 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 458 | Dic5 | — | 2 | 2 | no | — |
| 459 | Dic5 | — | 4 | 2 | no | — |
| 460 | Dic5 | — | 6 | 1 | no | — |
| 461 | #41 | — | 3 | 1 | no | — |
| 462 | #41 | — | 3 | 2 | no | — |
| 463 | #41 | — | 6 | 2 | no | — |
| 464 | #41 | — | 6 | 2 | no | — |
| 465 | #41 | — | 12 | 2 | no | — |
| 466 | #41 | — | 15 | 1 | no | — |
| 467 | #41 | — | 30 | 2 | no | — |
| 468 | #41 | — | 30 | 2 | no | — |
| 469 | #41 | — | 60 | 2 | no | — |
| 470 | C2×Q8 | — | 5 | 2 | no | — |
| 471 | C2×Q8 | — | 6 | 2 | no | — |
| 472 | C2×Q8 | — | 6 | 2 | no | — |
| 473 | C2×Q8 | — | 30 | 2 | no | — |
| 474 | C2×Q8 | — | 30 | 2 | no | — |
| 475 | C2×Q8 | C2×D3×D5 | 1 | 2 | yes | — |
| 476 | Q16 | — | 2 | 1 | no | — |
| 477 | Q16 | — | 2 | 1 | no | — |
| 478 | Q16 | — | 3 | 1 | no | — |
| 479 | Q16 | — | 6 | 2 | no | — |
| 480 | Q16 | — | 10 | 2 | no | — |
| 481 | Q16 | — | 10 | 2 | no | — |
| 482 | Q16 | — | 10 | 1 | no | — |
| 483 | Q16 | — | 10 | 1 | no | — |
| 484 | Q16 | — | 15 | 1 | no | — |
| 485 | Q16 | — | 30 | 2 | no | — |
| 486 | Q16 | — | 30 | 2 | no | — |
| 487 | Q16 | — | 30 | 2 | no | — |
| 488 | SD16 | — | 3 | 2 | no | — |
| 489 | SD16 | — | 6 | 2 | no | — |
| 490 | SD16 | — | 15 | 1 | no | — |
| 491 | SD16 | — | 15 | 1 | no | — |
| 492 | SD16 | — | 30 | 2 | no | — |
| 493 | SD16 | — | 30 | 2 | no | — |
| 494 | SD16 | — | 30 | 2 | no | — |
| 495 | D8 | — | 3 | 1 | no | — |
| 496 | D8 | — | 15 | 1 | no | — |
| 497 | M16 | — | 3 | 1 | no | — |
| 498 | M16 | — | 6 | 1 | no | — |
| 499 | M16 | — | 15 | 2 | no | — |
| 500 | M16 | — | 15 | 1 | no | — |
| 501 | M16 | — | 30 | 2 | no | — |
| 502 | M16 | — | 30 | 1 | no | — |
| 503 | C2×C8 | — | 5 | 1 | no | — |
| 504 | C2×C8 | — | 6 | 1 | no | — |
| 505 | C2×C8 | — | 30 | 2 | no | — |
| 506 | C2×C8 | — | 30 | 1 | no | — |
| 507 | C2×C8 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 508 | C4⋊C4 | — | 20 | 2 | no | — |
| 509 | C42 | — | 5 | 1 | no | — |
| 510 | C3×C5 | #3293 | 1 | 1 | yes | characteristic, complemented, Hall |
| 511 | C22×C3 | #4144 | 1 | 1 | yes | characteristic |
| 512 | C2×D3 | — | 2 | 1 | no | — |
| 513 | C2×D3 | — | 2 | 2 | no | — |
| 514 | C2×D3 | — | 10 | 1 | no | — |
| 515 | C3×C4 | — | 4 | 2 | no | — |
| 516 | C3×C4 | — | 10 | 2 | no | — |
| 517 | C3×C4 | — | 20 | 2 | no | — |
| 518 | C3×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 519 | C3×C4 | C22×C22⋊D5 | 1 | 1 | yes | characteristic |
| 520 | Dic3 | — | 2 | 1 | no | — |
| 521 | Dic3 | — | 2 | 2 | no | — |
| 522 | Dic3 | — | 10 | 1 | no | — |
| 523 | C2×C5 | — | 2 | 1 | no | — |
| 524 | C2×C5 | — | 12 | 2 | no | — |
| 525 | C2×C5 | — | 12 | 1 | no | — |
| 526 | C2×C5 | #5717 | 1 | 1 | yes | characteristic |
| 527 | D5 | — | 12 | 1 | no | — |
| 528 | Q8 | — | 2 | 2 | no | — |
| 529 | Q8 | — | 2 | 2 | no | — |
| 530 | Q8 | — | 3 | 1 | no | — |
| 531 | Q8 | — | 3 | 2 | no | — |
| 532 | Q8 | — | 10 | 2 | no | — |
| 533 | Q8 | — | 10 | 2 | no | — |
| 534 | Q8 | — | 12 | 2 | no | — |
| 535 | Q8 | — | 15 | 1 | no | — |
| 536 | Q8 | — | 60 | 2 | no | — |
| 537 | D4 | — | 3 | 1 | no | — |
| 538 | D4 | — | 3 | 2 | no | — |
| 539 | D4 | — | 6 | 1 | no | — |
| 540 | D4 | — | 6 | 2 | no | — |
| 541 | D4 | — | 12 | 2 | no | — |
| 542 | D4 | — | 15 | 1 | no | — |
| 543 | D4 | — | 30 | 1 | no | — |
| 544 | D4 | — | 60 | 2 | no | — |
| 545 | C2×C4 | — | 2 | 2 | no | — |
| 546 | C2×C4 | — | 6 | 2 | no | — |
| 547 | C2×C4 | — | 6 | 1 | no | — |
| 548 | C2×C4 | — | 10 | 1 | no | — |
| 549 | C2×C4 | — | 10 | 2 | no | — |
| 550 | C2×C4 | — | 12 | 2 | no | — |
| 551 | C2×C4 | — | 12 | 2 | no | — |
| 552 | C2×C4 | — | 30 | 1 | no | — |
| 553 | C2×C4 | — | 60 | 2 | no | — |
| 554 | C2×C4 | — | 60 | 2 | no | — |
| 555 | C2×C4 | C22×D3×D5 | 1 | 1 | yes | characteristic |
| 556 | C8 | — | 5 | 1 | no | — |
| 557 | C8 | — | 5 | 1 | no | — |
| 558 | C8 | — | 6 | 1 | no | — |
| 559 | C8 | — | 30 | 2 | no | — |
| 560 | C8 | — | 30 | 1 | no | — |
| 561 | C8 | D3×C22⋊D5 | 1 | 1 | yes | characteristic |
| 562 | C8 | D3×C22⋊D5 | 1 | 1 | yes | characteristic |
| 563 | C2×C3 | — | 2 | 1 | no | — |
| 564 | C2×C3 | D4×C22⋊D5 | 1 | 1 | yes | characteristic |
| 565 | D3 | — | 4 | 1 | no | — |
| 566 | D3 | — | 4 | 2 | no | — |
| 567 | D3 | — | 20 | 1 | no | — |
| 568 | C5 | #81808 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 569 | C22 | — | 6 | 1 | no | — |
| 570 | C22 | — | 6 | 2 | no | — |
| 571 | C22 | — | 30 | 1 | no | — |
| 572 | C22 | #92025 | 1 | 1 | yes | characteristic |
| 573 | C4 | — | 4 | 2 | no | — |
| 574 | C4 | — | 6 | 1 | no | — |
| 575 | C4 | — | 6 | 2 | no | — |
| 576 | C4 | — | 10 | 2 | no | — |
| 577 | C4 | — | 20 | 2 | no | — |
| 578 | C4 | — | 30 | 1 | no | — |
| 579 | C4 | D3×D4×D5 | 1 | 1 | yes | characteristic |
| 580 | C4 | C2×D3×C22⋊D5 | 1 | 1 | yes | characteristic |
| 581 | C3 | #10615749 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 582 | C2 | — | 2 | 1 | no | — |
| 583 | C2 | — | 12 | 1 | no | — |
| 584 | C2 | — | 12 | 2 | no | — |
| 585 | C2 | — | 60 | 1 | no | — |
| 586 | C2 | #11755057 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#5766 | C2 | semidirect |
| 2. #11755105 | C2 | semidirect |
| 3. #11754011 | C2 | semidirect |
| 4. #11751293 | C2 | semidirect |
| 5. C3×#65470 | C2 | semidirect |
| 6. #11749414 | C2 | semidirect |
| 7. #11749393 | C2 | semidirect |
| 8. #11749392 | C2 | semidirect |
| 9. #11748094 | C2 | semidirect |
| 10. #11748078 | C2 | semidirect |
| 11. #11748062 | C2 | semidirect |
| 55. #65470 | D3 | semidirect |
| 109. #5766 | D5 | semidirect |
| 510. C3×C5 | #3293 | semidirect |
| 568. C5 | #81808 | semidirect |
| 581. C3 | #10615749 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5766 | 2 |
| #11755105 | 2 |
| #11754011 | 2 |
| #11751293 | 2 |
| C3×#65470 | 2 |
| #11749414 | 2 |
| #11749393 | 2 |
| #11749392 | 2 |
| #11748094 | 2 |
| #11748078 | 2 |
| #11748062 | 2 |
| #10615749 | 3 |
| #81808 | 5 |