← #12122190
Subgroups — #12122190
Order 1280.
844 conjugacy classes of subgroups.
The subgroup lattice has 468 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#65432 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10615516 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #10610552 | C2 | 1 | 2 | yes | maximal |
| 4 | #10610304 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C5×#1764 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #10601158 | C2 | 1 | 2 | yes | maximal |
| 7 | #10600687 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10600572 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #10600568 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #10599723 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #10599557 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | C2×C5×#131 | C22 | 1 | 1 | yes | characteristic |
| 13 | #66161 | C22 | 1 | 2 | yes | — |
| 14 | C2×#4097 | C22 | 1 | 2 | yes | — |
| 15 | C22×Dic20 | C22 | 1 | 1 | yes | characteristic |
| 16 | #65850 | C22 | 1 | 2 | yes | — |
| 17 | C2×C5×#104 | C22 | 1 | 1 | yes | characteristic |
| 18 | C5×#416 | C22 | 1 | 1 | yes | characteristic |
| 19 | C5×#405 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×C4×C5×C8 | C22 | 1 | 1 | yes | characteristic |
| 21 | #65432 | C4 | 1 | 8 | yes | complemented |
| 22 | C2×#3956 | C22 | 1 | 2 | yes | — |
| 23 | #65410 | — | 2 | 2 | no | — |
| 24 | #65410 | C22 | 1 | 2 | yes | — |
| 25 | #65409 | C22 | 1 | 2 | yes | — |
| 26 | C2×#3951 | C22 | 1 | 1 | yes | characteristic |
| 27 | #65395 | — | 2 | 1 | no | — |
| 28 | #65395 | C22 | 1 | 1 | yes | characteristic |
| 29 | C2×#3950 | — | 2 | 1 | no | — |
| 30 | C2×#3950 | C22 | 1 | 1 | yes | characteristic |
| 31 | C2×#3948 | C22 | 1 | 2 | yes | — |
| 32 | #65390 | C22 | 1 | 2 | yes | — |
| 33 | #65284 | C22 | 1 | 2 | yes | — |
| 34 | #65218 | C22 | 1 | 2 | yes | — |
| 35 | #65079 | — | 2 | 2 | no | — |
| 36 | #65078 | — | 2 | 2 | no | — |
| 37 | #65047 | — | 2 | 2 | no | — |
| 38 | #65046 | — | 2 | 2 | no | — |
| 39 | #65005 | — | 2 | 2 | no | — |
| 40 | C4×Dic20 | — | 2 | 1 | no | — |
| 41 | C4×Dic20 | — | 2 | 1 | no | — |
| 42 | C5×#341 | C22 | 1 | 1 | yes | characteristic |
| 43 | C5×#339 | C22 | 1 | 1 | yes | characteristic |
| 44 | #64774 | C22 | 1 | 2 | yes | — |
| 45 | #64743 | C22 | 1 | 2 | yes | — |
| 46 | #23045 | — | 5 | 1 | no | maximal, Sylow |
| 47 | C2×C5×#41 | C23 | 1 | 1 | yes | characteristic |
| 48 | C22×Dic10 | C23 | 1 | 2 | yes | — |
| 49 | C5×#131 | — | 2 | 2 | no | — |
| 50 | C5×#131 | C2×C4 | 1 | 4 | yes | — |
| 51 | C2×C5×M16 | — | 2 | 1 | no | — |
| 52 | C2×C5×M16 | C23 | 1 | 1 | yes | characteristic |
| 53 | C2×C5×M16 | C23 | 1 | 1 | yes | characteristic |
| 54 | C22×C5×C8 | — | 2 | 1 | no | — |
| 55 | C22×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 56 | C22×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 57 | C5×#117 | C23 | 1 | 1 | yes | characteristic |
| 58 | C2×C42×C5 | C23 | 1 | 1 | yes | characteristic |
| 59 | #4097 | — | 2 | 4 | no | — |
| 60 | #4097 | C2×C4 | 1 | 8 | yes | — |
| 61 | Q8×Dic5 | — | 2 | 2 | no | — |
| 62 | C2×#689 | — | 2 | 2 | no | — |
| 63 | D4×Dic5 | — | 2 | 2 | no | — |
| 64 | D4×Dic5 | — | 4 | 2 | no | — |
| 65 | C2×#687 | — | 2 | 2 | no | — |
| 66 | #4072 | — | 2 | 2 | no | — |
| 67 | #4072 | C23 | 1 | 2 | yes | — |
| 68 | C2×C4⋊Dic5 | — | 2 | 2 | no | — |
| 69 | C2×C4⋊Dic5 | C23 | 1 | 2 | yes | — |
| 70 | C2×#681 | C23 | 1 | 2 | yes | — |
| 71 | C2×Dic20 | — | 2 | 1 | no | — |
| 72 | C2×Dic20 | — | 2 | 1 | no | — |
| 73 | C2×Dic20 | — | 2 | 2 | no | — |
| 74 | C2×Dic20 | C2×C4 | 1 | 4 | yes | complemented |
| 75 | #4033 | — | 2 | 2 | no | — |
| 76 | #4033 | — | 2 | 2 | no | — |
| 77 | #4023 | — | 4 | 2 | no | — |
| 78 | C4×Dic10 | — | 2 | 2 | no | — |
| 79 | C4×Dic10 | — | 2 | 2 | no | — |
| 80 | C5×#104 | — | 2 | 2 | no | — |
| 81 | C5×#103 | D4 | 1 | 1 | yes | characteristic |
| 82 | C5×#103 | D4 | 1 | 1 | yes | characteristic |
| 83 | C5×#102 | D4 | 1 | 1 | yes | characteristic |
| 84 | C5×#102 | D4 | 1 | 1 | yes | characteristic |
| 85 | C5×#97 | — | 2 | 1 | no | — |
| 86 | C4×C5×C8 | — | 2 | 1 | no | — |
| 87 | C4×C5×C8 | — | 2 | 2 | no | — |
| 88 | #3963 | — | 4 | 2 | no | — |
| 89 | #3956 | C2×C4 | 1 | 8 | yes | complemented |
| 90 | #3951 | C2×C4 | 1 | 4 | yes | complemented |
| 91 | #3950 | — | 2 | 1 | no | — |
| 92 | #3950 | — | 2 | 1 | no | — |
| 93 | #3950 | — | 2 | 2 | no | — |
| 94 | #3950 | D4 | 1 | 1 | yes | characteristic |
| 95 | #3950 | D4 | 1 | 1 | yes | characteristic |
| 96 | #3949 | — | 2 | 2 | no | — |
| 97 | #3949 | D4 | 1 | 2 | yes | — |
| 98 | #3948 | — | 2 | 2 | no | — |
| 99 | #3948 | — | 2 | 2 | no | — |
| 100 | #3948 | — | 2 | 2 | no | — |
| 101 | #3948 | — | 2 | 2 | no | — |
| 102 | #3947 | — | 2 | 2 | no | — |
| 103 | C8×Dic5 | — | 2 | 2 | no | — |
| 104 | #3940 | — | 2 | 2 | no | — |
| 105 | #3939 | — | 2 | 2 | no | — |
| 106 | C2×#473 | — | 5 | 1 | no | — |
| 107 | #2950 | — | 5 | 1 | no | — |
| 108 | #2947 | — | 5 | 2 | no | — |
| 109 | #2913 | — | 5 | 1 | no | — |
| 110 | #1969 | — | 5 | 1 | no | — |
| 111 | #1952 | — | 5 | 1 | no | — |
| 112 | #1930 | — | 5 | 2 | no | — |
| 113 | #1882 | — | 5 | 2 | no | — |
| 114 | #1857 | — | 5 | 2 | no | — |
| 115 | #1772 | — | 5 | 1 | no | — |
| 116 | #1764 | D5 | 1 | 1 | yes | characteristic |
| 117 | C5×#41 | — | 2 | 1 | no | — |
| 118 | C5×#41 | — | 2 | 1 | no | — |
| 119 | C5×#41 | C22×C4 | 1 | 2 | yes | — |
| 120 | C5×#41 | #41 | 1 | 2 | yes | — |
| 121 | C2×C5×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 122 | C2×C5×D4 | — | 2 | 1 | no | — |
| 123 | C2×C5×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 124 | C22×C4×C5 | — | 2 | 1 | no | — |
| 125 | C22×C4×C5 | — | 2 | 1 | no | — |
| 126 | C22×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 127 | C22×Dic5 | — | 2 | 2 | no | — |
| 128 | C22×Dic5 | — | 2 | 2 | no | — |
| 129 | C22×Dic5 | — | 4 | 2 | no | — |
| 130 | C2×Dic10 | — | 2 | 2 | no | — |
| 131 | C2×Dic10 | — | 2 | 2 | no | — |
| 132 | C2×Dic10 | — | 2 | 2 | no | — |
| 133 | C2×Dic10 | — | 2 | 2 | no | — |
| 134 | C2×Dic10 | — | 2 | 2 | no | — |
| 135 | C2×Dic10 | C22×C4 | 1 | 4 | yes | — |
| 136 | C5×M16 | — | 2 | 1 | no | — |
| 137 | C5×M16 | — | 2 | 4 | no | — |
| 138 | C5×M16 | — | 2 | 1 | no | — |
| 139 | C5×M16 | — | 2 | 1 | no | — |
| 140 | C5×M16 | C22×C4 | 1 | 2 | yes | — |
| 141 | C2×C5×C8 | — | 2 | 1 | no | — |
| 142 | C2×C5×C8 | — | 2 | 1 | no | — |
| 143 | C2×C5×C8 | — | 2 | 1 | no | — |
| 144 | C2×C5×C8 | — | 2 | 4 | no | — |
| 145 | C2×C5×C8 | — | 2 | 1 | no | — |
| 146 | C2×C5×C8 | C22×C4 | 1 | 2 | yes | — |
| 147 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 148 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 149 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 150 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 151 | C2×C5×C8 | #41 | 1 | 2 | yes | — |
| 152 | C5×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 153 | C5×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 154 | C5×C22⋊C4 | — | 2 | 1 | no | — |
| 155 | C42×C5 | — | 2 | 1 | no | — |
| 156 | C42×C5 | — | 2 | 1 | no | — |
| 157 | C42×C5 | — | 2 | 1 | no | — |
| 158 | C22⋊Dic5 | — | 2 | 2 | no | — |
| 159 | C22⋊Dic5 | — | 4 | 2 | no | — |
| 160 | #689 | — | 2 | 8 | no | — |
| 161 | #687 | — | 2 | 8 | no | — |
| 162 | C4⋊Dic5 | — | 2 | 2 | no | — |
| 163 | C4⋊Dic5 | — | 2 | 2 | no | — |
| 164 | C4⋊Dic5 | — | 4 | 2 | no | — |
| 165 | C4⋊Dic5 | C2×D4 | 1 | 2 | yes | — |
| 166 | C4⋊Dic5 | C2×D4 | 1 | 2 | yes | — |
| 167 | #683 | — | 4 | 2 | no | — |
| 168 | #683 | — | 4 | 2 | no | — |
| 169 | C4×Dic5 | — | 2 | 2 | no | — |
| 170 | C4×Dic5 | — | 4 | 2 | no | — |
| 171 | C4×Dic5 | — | 4 | 2 | no | — |
| 172 | C4×Dic5 | — | 4 | 2 | no | — |
| 173 | #681 | — | 2 | 2 | no | — |
| 174 | #681 | C22×C4 | 1 | 4 | yes | — |
| 175 | C2×#168 | — | 2 | 2 | no | — |
| 176 | Dic20 | — | 2 | 4 | no | — |
| 177 | Dic20 | — | 2 | 4 | no | — |
| 178 | C2×#137 | — | 5 | 2 | no | — |
| 179 | C22×Q16 | — | 5 | 1 | no | — |
| 180 | C2×#131 | C2×D5 | 1 | 1 | yes | characteristic |
| 181 | #520 | — | 5 | 2 | no | — |
| 182 | #519 | — | 5 | 2 | no | — |
| 183 | #473 | — | 5 | 8 | no | — |
| 184 | #441 | — | 10 | 2 | no | — |
| 185 | #441 | — | 10 | 2 | no | — |
| 186 | #440 | — | 10 | 2 | no | — |
| 187 | C4×Q16 | — | 10 | 1 | no | — |
| 188 | C4×Q16 | — | 10 | 1 | no | — |
| 189 | C4×Q16 | — | 10 | 2 | no | — |
| 190 | C4×SD16 | — | 10 | 2 | no | — |
| 191 | C2×#108 | — | 5 | 1 | no | — |
| 192 | #428 | — | 5 | 2 | no | — |
| 193 | #428 | — | 5 | 2 | no | — |
| 194 | #428 | — | 10 | 2 | no | — |
| 195 | #427 | — | 5 | 1 | no | — |
| 196 | #427 | — | 10 | 1 | no | — |
| 197 | C2×#107 | — | 5 | 1 | no | — |
| 198 | C2×#107 | — | 10 | 1 | no | — |
| 199 | C2×#104 | C2×D5 | 1 | 1 | yes | characteristic |
| 200 | #419 | — | 5 | 2 | no | — |
| 201 | #416 | C2×D5 | 1 | 1 | yes | characteristic |
| 202 | C2×#103 | — | 5 | 2 | no | — |
| 203 | C2×#101 | — | 5 | 2 | no | — |
| 204 | #405 | — | 5 | 2 | no | — |
| 205 | #405 | C2×D5 | 1 | 1 | yes | characteristic |
| 206 | C2×C4×C8 | C2×D5 | 1 | 1 | yes | characteristic |
| 207 | #391 | — | 5 | 2 | no | — |
| 208 | #343 | — | 5 | 2 | no | — |
| 209 | #341 | C2×D5 | 1 | 1 | yes | characteristic |
| 210 | #339 | — | 5 | 2 | no | — |
| 211 | #339 | C2×D5 | 1 | 1 | yes | characteristic |
| 212 | C23×C5 | — | 2 | 1 | no | — |
| 213 | C23×C5 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 214 | C5×Q8 | — | 2 | 1 | no | — |
| 215 | C5×Q8 | C4×D4 | 1 | 2 | yes | — |
| 216 | C5×D4 | — | 2 | 2 | no | — |
| 217 | C5×D4 | — | 2 | 2 | no | — |
| 218 | C5×D4 | — | 2 | 1 | no | — |
| 219 | C5×D4 | C4×D4 | 1 | 2 | yes | — |
| 220 | C2×C4×C5 | — | 2 | 1 | no | — |
| 221 | C2×C4×C5 | — | 2 | 2 | no | — |
| 222 | C2×C4×C5 | — | 2 | 2 | no | — |
| 223 | C2×C4×C5 | — | 2 | 2 | no | — |
| 224 | C2×C4×C5 | — | 2 | 1 | no | — |
| 225 | C2×C4×C5 | — | 2 | 1 | no | — |
| 226 | C2×C4×C5 | — | 4 | 1 | no | — |
| 227 | C2×C4×C5 | — | 4 | 1 | no | — |
| 228 | C2×C4×C5 | C23×C4 | 1 | 1 | yes | characteristic |
| 229 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 230 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 231 | C2×C4×C5 | C2×#41 | 1 | 1 | yes | characteristic |
| 232 | C2×C4×C5 | C2×#41 | 1 | 1 | yes | characteristic |
| 233 | C2×C4×C5 | 2−1+4 | 1 | 1 | yes | characteristic |
| 234 | C2×Dic5 | — | 2 | 4 | no | — |
| 235 | C2×Dic5 | — | 2 | 2 | no | — |
| 236 | C2×Dic5 | — | 2 | 2 | no | — |
| 237 | C2×Dic5 | — | 4 | 2 | no | — |
| 238 | C2×Dic5 | — | 4 | 2 | no | — |
| 239 | C2×Dic5 | — | 4 | 2 | no | — |
| 240 | C2×Dic5 | — | 8 | 2 | no | — |
| 241 | C2×Dic5 | — | 16 | 2 | no | — |
| 242 | Dic10 | — | 2 | 4 | no | — |
| 243 | Dic10 | — | 2 | 4 | no | — |
| 244 | Dic10 | — | 4 | 2 | no | — |
| 245 | Dic10 | — | 4 | 2 | no | — |
| 246 | C5×C8 | — | 2 | 2 | no | — |
| 247 | C5×C8 | — | 2 | 1 | no | — |
| 248 | C5×C8 | — | 2 | 1 | no | — |
| 249 | C5×C8 | — | 4 | 1 | no | — |
| 250 | C5×C8 | C4×D4 | 1 | 2 | yes | — |
| 251 | C5×C8 | C4×D4 | 1 | 2 | yes | — |
| 252 | #168 | — | 2 | 4 | no | — |
| 253 | C2×#41 | C22×D5 | 1 | 1 | yes | characteristic |
| 254 | C22×Q8 | — | 5 | 2 | no | — |
| 255 | #137 | — | 5 | 8 | no | — |
| 256 | #137 | — | 10 | 4 | no | — |
| 257 | C2×Q16 | — | 5 | 4 | no | — |
| 258 | C2×Q16 | — | 10 | 2 | no | — |
| 259 | C2×Q16 | — | 10 | 1 | no | — |
| 260 | C2×Q16 | — | 10 | 1 | no | — |
| 261 | C2×Q16 | — | 10 | 2 | no | — |
| 262 | C2×SD16 | — | 10 | 2 | no | — |
| 263 | #131 | — | 2 | 2 | no | — |
| 264 | #131 | C4×D5 | 1 | 4 | yes | — |
| 265 | C2×M16 | — | 2 | 1 | no | — |
| 266 | C2×M16 | — | 5 | 2 | no | — |
| 267 | C2×M16 | C22×D5 | 1 | 1 | yes | characteristic |
| 268 | C2×M16 | C22×D5 | 1 | 1 | yes | characteristic |
| 269 | C22×C8 | — | 2 | 1 | no | — |
| 270 | C22×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 271 | C22×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 272 | C4×Q8 | — | 10 | 2 | no | — |
| 273 | C4×Q8 | — | 10 | 2 | no | — |
| 274 | C4×Q8 | — | 10 | 2 | no | — |
| 275 | C4×Q8 | — | 10 | 2 | no | — |
| 276 | C4×Q8 | — | 10 | 2 | no | — |
| 277 | C4×D4 | — | 10 | 2 | no | — |
| 278 | C4×D4 | — | 20 | 2 | no | — |
| 279 | #117 | — | 5 | 2 | no | — |
| 280 | #117 | — | 10 | 2 | no | — |
| 281 | #117 | — | 20 | 2 | no | — |
| 282 | #117 | C22×D5 | 1 | 1 | yes | characteristic |
| 283 | C2×C4⋊C4 | — | 5 | 2 | no | — |
| 284 | C2×C4⋊C4 | — | 10 | 2 | no | — |
| 285 | C2×C42 | C22×D5 | 1 | 1 | yes | characteristic |
| 286 | #108 | — | 5 | 4 | no | — |
| 287 | #107 | — | 5 | 1 | no | — |
| 288 | #107 | — | 5 | 1 | no | — |
| 289 | #107 | — | 10 | 2 | no | — |
| 290 | #107 | — | 10 | 1 | no | — |
| 291 | #107 | — | 10 | 1 | no | — |
| 292 | #107 | — | 10 | 2 | no | — |
| 293 | #106 | — | 5 | 2 | no | — |
| 294 | #106 | — | 10 | 2 | no | — |
| 295 | #106 | — | 10 | 2 | no | — |
| 296 | #104 | — | 2 | 2 | no | — |
| 297 | #103 | — | 10 | 2 | no | — |
| 298 | #103 | — | 10 | 2 | no | — |
| 299 | #103 | — | 10 | 2 | no | — |
| 300 | #103 | — | 10 | 2 | no | — |
| 301 | #103 | D20 | 1 | 1 | yes | characteristic |
| 302 | #103 | D20 | 1 | 1 | yes | characteristic |
| 303 | #102 | D20 | 1 | 1 | yes | characteristic |
| 304 | #102 | D20 | 1 | 1 | yes | characteristic |
| 305 | #101 | — | 5 | 8 | no | — |
| 306 | #97 | — | 2 | 1 | no | — |
| 307 | #97 | — | 10 | 2 | no | — |
| 308 | C4×C8 | — | 2 | 1 | no | — |
| 309 | C4×C8 | — | 2 | 2 | no | — |
| 310 | C4×C8 | — | 10 | 2 | no | — |
| 311 | #95 | — | 20 | 2 | no | — |
| 312 | C22×C5 | — | 2 | 1 | no | — |
| 313 | C22×C5 | — | 2 | 1 | no | — |
| 314 | C22×C5 | — | 2 | 2 | no | — |
| 315 | C22×C5 | — | 4 | 1 | no | — |
| 316 | C22×C5 | — | 4 | 1 | no | — |
| 317 | C22×C5 | #520 | 1 | 1 | yes | characteristic |
| 318 | C22×C5 | D42 | 1 | 1 | yes | characteristic |
| 319 | C22×C5 | #553 | 1 | 1 | yes | characteristic |
| 320 | C4×C5 | — | 2 | 2 | no | — |
| 321 | C4×C5 | — | 4 | 2 | no | — |
| 322 | C4×C5 | — | 4 | 1 | no | — |
| 323 | C4×C5 | — | 4 | 1 | no | — |
| 324 | C4×C5 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 325 | C4×C5 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 326 | C4×C5 | #547 | 1 | 1 | yes | characteristic |
| 327 | C4×C5 | #548 | 1 | 1 | yes | characteristic |
| 328 | Dic5 | — | 4 | 4 | no | — |
| 329 | Dic5 | — | 4 | 2 | no | — |
| 330 | Dic5 | — | 4 | 2 | no | — |
| 331 | Dic5 | — | 8 | 2 | no | — |
| 332 | #41 | — | 2 | 1 | no | — |
| 333 | #41 | — | 2 | 1 | no | — |
| 334 | #41 | C2×C4×D5 | 1 | 2 | yes | — |
| 335 | #41 | #709 | 1 | 2 | yes | — |
| 336 | C2×Q8 | — | 5 | 4 | no | — |
| 337 | C2×Q8 | — | 10 | 2 | no | — |
| 338 | C2×Q8 | — | 10 | 2 | no | — |
| 339 | C2×Q8 | — | 10 | 2 | no | — |
| 340 | C2×Q8 | — | 10 | 2 | no | — |
| 341 | C2×Q8 | — | 10 | 2 | no | — |
| 342 | C2×Q8 | C2×D20 | 1 | 1 | yes | characteristic |
| 343 | C2×D4 | — | 2 | 1 | no | — |
| 344 | C2×D4 | C2×D20 | 1 | 1 | yes | characteristic |
| 345 | C22×C4 | — | 2 | 1 | no | — |
| 346 | C22×C4 | — | 2 | 1 | no | — |
| 347 | C22×C4 | — | 10 | 2 | no | — |
| 348 | C22×C4 | — | 10 | 2 | no | — |
| 349 | C22×C4 | — | 20 | 2 | no | — |
| 350 | C22×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 351 | Q16 | — | 10 | 8 | no | — |
| 352 | Q16 | — | 10 | 4 | no | — |
| 353 | Q16 | — | 10 | 4 | no | — |
| 354 | SD16 | — | 10 | 8 | no | — |
| 355 | M16 | — | 2 | 1 | no | — |
| 356 | M16 | — | 2 | 4 | no | — |
| 357 | M16 | — | 2 | 1 | no | — |
| 358 | M16 | — | 2 | 1 | no | — |
| 359 | M16 | — | 5 | 4 | no | — |
| 360 | M16 | — | 10 | 2 | no | — |
| 361 | M16 | C2×C4×D5 | 1 | 2 | yes | — |
| 362 | C2×C8 | — | 2 | 1 | no | — |
| 363 | C2×C8 | — | 2 | 1 | no | — |
| 364 | C2×C8 | — | 2 | 1 | no | — |
| 365 | C2×C8 | — | 2 | 4 | no | — |
| 366 | C2×C8 | — | 2 | 1 | no | — |
| 367 | C2×C8 | — | 10 | 2 | no | — |
| 368 | C2×C8 | C2×C4×D5 | 1 | 2 | yes | — |
| 369 | C2×C8 | C2×D20 | 1 | 1 | yes | characteristic |
| 370 | C2×C8 | C2×D20 | 1 | 1 | yes | characteristic |
| 371 | C2×C8 | D4×D5 | 1 | 1 | yes | characteristic |
| 372 | C2×C8 | D4×D5 | 1 | 1 | yes | characteristic |
| 373 | C2×C8 | #711 | 1 | 2 | yes | — |
| 374 | C4⋊C4 | — | 5 | 2 | no | — |
| 375 | C4⋊C4 | — | 5 | 2 | no | — |
| 376 | C4⋊C4 | — | 10 | 2 | no | — |
| 377 | C4⋊C4 | — | 10 | 2 | no | — |
| 378 | C4⋊C4 | — | 20 | 2 | no | — |
| 379 | C4⋊C4 | — | 20 | 2 | no | — |
| 380 | C4⋊C4 | — | 20 | 2 | no | — |
| 381 | C4⋊C4 | C2×D20 | 1 | 1 | yes | characteristic |
| 382 | C4⋊C4 | C2×D20 | 1 | 1 | yes | characteristic |
| 383 | C22⋊C4 | — | 2 | 1 | no | — |
| 384 | C22⋊C4 | — | 10 | 2 | no | — |
| 385 | C22⋊C4 | — | 20 | 2 | no | — |
| 386 | C42 | — | 2 | 1 | no | — |
| 387 | C42 | — | 2 | 1 | no | — |
| 388 | C42 | — | 2 | 1 | no | — |
| 389 | C42 | — | 10 | 2 | no | — |
| 390 | C42 | — | 20 | 2 | no | — |
| 391 | C42 | — | 20 | 2 | no | — |
| 392 | C42 | — | 20 | 2 | no | — |
| 393 | C2×C5 | — | 2 | 1 | no | — |
| 394 | C2×C5 | — | 2 | 1 | no | — |
| 395 | C2×C5 | — | 4 | 2 | no | — |
| 396 | C2×C5 | #2361 | 1 | 1 | yes | characteristic |
| 397 | C2×C5 | #3290 | 1 | 1 | yes | characteristic |
| 398 | C2×C5 | #3293 | 1 | 1 | yes | characteristic |
| 399 | C23 | — | 2 | 1 | no | — |
| 400 | C23 | #4149 | 1 | 1 | yes | characteristic |
| 401 | Q8 | — | 2 | 1 | no | — |
| 402 | Q8 | — | 10 | 4 | no | — |
| 403 | Q8 | — | 10 | 4 | no | — |
| 404 | Q8 | — | 20 | 2 | no | — |
| 405 | Q8 | — | 20 | 2 | no | — |
| 406 | Q8 | C4×D20 | 1 | 2 | yes | — |
| 407 | D4 | — | 2 | 2 | no | — |
| 408 | D4 | — | 2 | 2 | no | — |
| 409 | D4 | — | 2 | 1 | no | — |
| 410 | D4 | C4×D20 | 1 | 2 | yes | — |
| 411 | C2×C4 | — | 2 | 1 | no | — |
| 412 | C2×C4 | — | 2 | 2 | no | — |
| 413 | C2×C4 | — | 2 | 2 | no | — |
| 414 | C2×C4 | — | 2 | 2 | no | — |
| 415 | C2×C4 | — | 2 | 1 | no | — |
| 416 | C2×C4 | — | 2 | 1 | no | — |
| 417 | C2×C4 | — | 4 | 1 | no | — |
| 418 | C2×C4 | — | 4 | 1 | no | — |
| 419 | C2×C4 | — | 10 | 4 | no | — |
| 420 | C2×C4 | — | 10 | 2 | no | — |
| 421 | C2×C4 | — | 10 | 2 | no | — |
| 422 | C2×C4 | — | 20 | 2 | no | — |
| 423 | C2×C4 | — | 20 | 2 | no | — |
| 424 | C2×C4 | — | 20 | 2 | no | — |
| 425 | C2×C4 | — | 40 | 2 | no | — |
| 426 | C2×C4 | — | 80 | 2 | no | — |
| 427 | C2×C4 | C22×C4×D5 | 1 | 1 | yes | characteristic |
| 428 | C2×C4 | C22×D20 | 1 | 1 | yes | characteristic |
| 429 | C2×C4 | C2×#709 | 1 | 1 | yes | characteristic |
| 430 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 431 | C2×C4 | C2×#711 | 1 | 1 | yes | characteristic |
| 432 | C2×C4 | #4150 | 1 | 1 | yes | characteristic |
| 433 | C8 | — | 2 | 2 | no | — |
| 434 | C8 | — | 2 | 1 | no | — |
| 435 | C8 | — | 2 | 1 | no | — |
| 436 | C8 | — | 4 | 1 | no | — |
| 437 | C8 | — | 10 | 4 | no | — |
| 438 | C8 | #4027 | 1 | 2 | yes | — |
| 439 | C8 | #4027 | 1 | 2 | yes | — |
| 440 | C5 | #23045 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 441 | C22 | — | 2 | 1 | no | — |
| 442 | C22 | — | 2 | 1 | no | — |
| 443 | C22 | — | 2 | 2 | no | — |
| 444 | C22 | — | 4 | 1 | no | — |
| 445 | C22 | — | 4 | 1 | no | — |
| 446 | C22 | #65857 | 1 | 1 | yes | characteristic |
| 447 | C22 | D4×D20 | 1 | 1 | yes | characteristic |
| 448 | C22 | #65899 | 1 | 1 | yes | characteristic |
| 449 | C4 | — | 2 | 2 | no | — |
| 450 | C4 | — | 4 | 2 | no | — |
| 451 | C4 | — | 4 | 1 | no | — |
| 452 | C4 | — | 4 | 1 | no | — |
| 453 | C4 | — | 20 | 4 | no | — |
| 454 | C4 | — | 20 | 2 | no | — |
| 455 | C4 | — | 20 | 2 | no | — |
| 456 | C4 | — | 40 | 2 | no | — |
| 457 | C4 | C2×C4×D20 | 1 | 1 | yes | characteristic |
| 458 | C4 | C2×#4027 | 1 | 1 | yes | characteristic |
| 459 | C4 | #65886 | 1 | 1 | yes | characteristic |
| 460 | C4 | #65889 | 1 | 1 | yes | characteristic |
| 461 | C2 | — | 2 | 1 | no | — |
| 462 | C2 | — | 2 | 1 | no | — |
| 463 | C2 | — | 4 | 2 | no | — |
| 464 | C2 | #10605198 | 1 | 1 | yes | characteristic |
| 465 | C2 | #10611622 | 1 | 1 | yes | characteristic |
| 466 | C2 | #10611626 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta