← #30555928
Subgroups — #30555928
Order 15616.
2658 conjugacy classes of subgroups.
The subgroup lattice has 522 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#16840575 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #21459590 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #21457406 | C2 | 1 | 8 | yes | maximal, complemented |
| 4 | #21457391 | C2 | 1 | 8 | yes | maximal, complemented |
| 5 | #21456265 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #21455482 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #21455291 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #21455139 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #21454538 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×C61×#441 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C2×#14519825 | C22 | 1 | 4 | yes | — |
| 12 | #16840575 | — | 2 | 16 | no | — |
| 13 | C2×#14519809 | C22 | 1 | 8 | yes | — |
| 14 | C2×#14519808 | C22 | 1 | 4 | yes | — |
| 15 | C2×#14519800 | C22 | 1 | 4 | yes | — |
| 16 | C2×#14519799 | C22 | 1 | 2 | yes | — |
| 17 | C2×#14519799 | C22 | 1 | 2 | yes | — |
| 18 | C2×Q16×D61 | C22 | 1 | 4 | yes | — |
| 19 | C2×#14519783 | C22 | 1 | 2 | yes | — |
| 20 | #16840434 | — | 2 | 2 | no | — |
| 21 | #16840434 | C22 | 1 | 4 | yes | — |
| 22 | Q8×D244 | — | 2 | 2 | no | — |
| 23 | Q8×D244 | C22 | 1 | 4 | yes | — |
| 24 | #16840424 | — | 2 | 4 | no | — |
| 25 | #16840424 | C22 | 1 | 8 | yes | — |
| 26 | #16840343 | — | 2 | 4 | no | — |
| 27 | #16840343 | C22 | 1 | 4 | yes | — |
| 28 | #16840312 | — | 2 | 4 | no | — |
| 29 | #16840312 | C22 | 1 | 2 | yes | — |
| 30 | #16840312 | C22 | 1 | 1 | yes | characteristic |
| 31 | #16840156 | C22 | 1 | 4 | yes | — |
| 32 | #16840151 | C22 | 1 | 4 | yes | — |
| 33 | #16840021 | C22 | 1 | 4 | yes | — |
| 34 | #16840016 | C22 | 1 | 4 | yes | — |
| 35 | #16839992 | C22 | 1 | 8 | yes | — |
| 36 | #16839984 | C22 | 1 | 8 | yes | — |
| 37 | #16839972 | C22 | 1 | 4 | yes | — |
| 38 | #16839962 | C22 | 1 | 4 | yes | — |
| 39 | #16839927 | C22 | 1 | 8 | yes | — |
| 40 | #16839919 | C22 | 1 | 8 | yes | — |
| 41 | #16839910 | C22 | 1 | 8 | yes | — |
| 42 | #16839902 | C22 | 1 | 8 | yes | — |
| 43 | #16839835 | C22 | 1 | 8 | yes | — |
| 44 | #16839786 | C22 | 1 | 1 | yes | characteristic |
| 45 | #16839761 | C22 | 1 | 4 | yes | — |
| 46 | #16839728 | C22 | 1 | 2 | yes | — |
| 47 | C22×Q16×C61 | C22 | 1 | 1 | yes | characteristic |
| 48 | C2×C4×Q8×C61 | C22 | 1 | 2 | yes | — |
| 49 | C61×#441 | C22 | 1 | 8 | yes | — |
| 50 | C2×#106×C61 | C22 | 1 | 1 | yes | characteristic |
| 51 | C2×#103×C61 | C22 | 1 | 2 | yes | — |
| 52 | C2×#97×C61 | C22 | 1 | 1 | yes | characteristic |
| 53 | #14519825 | — | 2 | 16 | no | — |
| 54 | #14519825 | — | 4 | 8 | no | — |
| 55 | C2×#11758226 | — | 2 | 4 | no | — |
| 56 | C2×#11758226 | C23 | 1 | 8 | yes | — |
| 57 | C2×#11758222 | — | 2 | 8 | no | — |
| 58 | C2×#11758222 | C23 | 1 | 2 | yes | — |
| 59 | C2×#11758222 | C23 | 1 | 4 | yes | — |
| 60 | C2×Q8×D61 | — | 2 | 4 | no | — |
| 61 | C2×Q8×D61 | C23 | 1 | 8 | yes | — |
| 62 | #14519809 | — | 2 | 32 | no | — |
| 63 | #14519808 | — | 2 | 16 | no | — |
| 64 | #14519800 | — | 2 | 16 | no | — |
| 65 | #14519799 | — | 2 | 8 | no | — |
| 66 | #14519799 | — | 4 | 4 | no | — |
| 67 | C2×Dic244 | C23 | 1 | 2 | yes | — |
| 68 | C2×Dic244 | C23 | 1 | 2 | yes | — |
| 69 | C2×#11758202 | C23 | 1 | 8 | yes | — |
| 70 | Q16×D61 | — | 2 | 16 | no | — |
| 71 | C2×#11758190 | C23 | 1 | 4 | yes | — |
| 72 | C2×#11758190 | C23 | 1 | 4 | yes | — |
| 73 | C2×#11758201 | C23 | 1 | 8 | yes | — |
| 74 | C2×D488 | C23 | 1 | 2 | yes | — |
| 75 | C2×D488 | C23 | 1 | 2 | yes | — |
| 76 | #14519783 | — | 2 | 8 | no | — |
| 77 | C2×#11758194 | C23 | 1 | 2 | yes | — |
| 78 | C2×#11758189 | C23 | 1 | 4 | yes | — |
| 79 | C2×C8×D61 | C23 | 1 | 4 | yes | — |
| 80 | #14519777 | — | 2 | 4 | no | — |
| 81 | #14519777 | D4 | 1 | 1 | yes | characteristic |
| 82 | #14519777 | C23 | 1 | 2 | yes | — |
| 83 | #14519774 | — | 2 | 4 | no | — |
| 84 | #14519774 | D4 | 1 | 1 | yes | characteristic |
| 85 | #14519774 | C23 | 1 | 2 | yes | — |
| 86 | #14519765 | — | 2 | 8 | no | — |
| 87 | #14519765 | D4 | 1 | 2 | yes | — |
| 88 | #14519765 | C23 | 1 | 4 | yes | — |
| 89 | #14519757 | — | 2 | 4 | no | — |
| 90 | #14519757 | — | 2 | 8 | no | — |
| 91 | #14519757 | — | 2 | 8 | no | — |
| 92 | #14519757 | C23 | 1 | 8 | yes | — |
| 93 | #14519752 | — | 2 | 8 | no | — |
| 94 | #14519752 | — | 2 | 4 | no | — |
| 95 | #14519752 | — | 2 | 8 | no | — |
| 96 | #14519752 | C23 | 1 | 8 | yes | — |
| 97 | #14519751 | — | 2 | 2 | no | — |
| 98 | #14519751 | — | 2 | 2 | no | — |
| 99 | #14519751 | — | 2 | 8 | no | — |
| 100 | #14519751 | D4 | 1 | 4 | yes | — |
| 101 | C4×D244 | — | 2 | 4 | no | — |
| 102 | C4×D244 | — | 2 | 2 | no | — |
| 103 | C4×D244 | — | 2 | 2 | no | — |
| 104 | C4×D244 | — | 2 | 8 | no | — |
| 105 | C4×D244 | — | 2 | 4 | no | — |
| 106 | C4×D244 | C23 | 1 | 4 | yes | — |
| 107 | C4⋊#92418 | C23 | 1 | 4 | yes | — |
| 108 | #14519700 | C23 | 1 | 8 | yes | — |
| 109 | #14519697 | C23 | 1 | 8 | yes | — |
| 110 | #14519689 | C23 | 1 | 8 | yes | — |
| 111 | C22×Q8×C61 | C23 | 1 | 2 | yes | — |
| 112 | C2×Q16×C61 | D4 | 1 | 8 | yes | complemented |
| 113 | C2×Q16×C61 | C23 | 1 | 4 | yes | — |
| 114 | C22×C8×C61 | C23 | 1 | 1 | yes | characteristic |
| 115 | C22×C8×C61 | C23 | 1 | 1 | yes | characteristic |
| 116 | C4×Q8×C61 | — | 2 | 2 | no | — |
| 117 | C4×Q8×C61 | — | 2 | 2 | no | — |
| 118 | C4×Q8×C61 | C23 | 1 | 4 | yes | — |
| 119 | C4×Q8×C61 | C23 | 1 | 4 | yes | — |
| 120 | C2×C4⋊C4×C61 | — | 2 | 2 | no | — |
| 121 | C2×C4⋊C4×C61 | C23 | 1 | 2 | yes | — |
| 122 | C2×C42×C61 | — | 2 | 2 | no | — |
| 123 | C2×C42×C61 | C23 | 1 | 1 | yes | characteristic |
| 124 | #106×C61 | C23 | 1 | 4 | yes | — |
| 125 | #103×C61 | C23 | 1 | 8 | yes | — |
| 126 | #97×C61 | C23 | 1 | 4 | yes | — |
| 127 | C2×Q8×C61 | — | 2 | 2 | no | — |
| 128 | C2×Q8×C61 | — | 2 | 4 | no | — |
| 129 | C2×Q8×C61 | C2×D4 | 1 | 8 | yes | — |
| 130 | C2×Q8×C61 | C24 | 1 | 4 | yes | — |
| 131 | C22×C4×C61 | — | 2 | 2 | no | — |
| 132 | C22×C4×C61 | — | 2 | 2 | no | — |
| 133 | C22×C4×C61 | C2×D4 | 1 | 2 | yes | — |
| 134 | C22×C4×C61 | C24 | 1 | 1 | yes | characteristic |
| 135 | C2×C22⋊D61 | — | 2 | 4 | no | — |
| 136 | C2×C22⋊D61 | C2×D4 | 1 | 4 | yes | — |
| 137 | #11758226 | — | 2 | 16 | no | — |
| 138 | #11758226 | — | 4 | 8 | no | — |
| 139 | #11758226 | — | 4 | 16 | no | — |
| 140 | Q8×D61 | — | 2 | 16 | no | — |
| 141 | Q8×D61 | — | 4 | 8 | no | — |
| 142 | Q8×D61 | — | 4 | 16 | no | — |
| 143 | #11758222 | — | 2 | 4 | no | — |
| 144 | #11758222 | — | 2 | 4 | no | — |
| 145 | #11758222 | — | 2 | 8 | no | — |
| 146 | #11758222 | — | 2 | 8 | no | — |
| 147 | #11758222 | — | 4 | 32 | no | — |
| 148 | C2×D244 | — | 2 | 8 | no | — |
| 149 | C2×D244 | — | 2 | 2 | no | — |
| 150 | C2×D244 | — | 2 | 8 | no | — |
| 151 | C2×D244 | — | 2 | 2 | no | — |
| 152 | C2×D244 | C2×D4 | 1 | 2 | yes | — |
| 153 | C2×D244 | C2×D4 | 1 | 4 | yes | — |
| 154 | C2×D244 | C24 | 1 | 4 | yes | — |
| 155 | C2×C4×D61 | — | 2 | 8 | no | — |
| 156 | C2×C4×D61 | — | 2 | 4 | no | — |
| 157 | C2×C4×D61 | — | 2 | 8 | no | — |
| 158 | C2×C4×D61 | C24 | 1 | 4 | yes | — |
| 159 | C2×Dic122 | — | 2 | 8 | no | — |
| 160 | C2×Dic122 | C2×D4 | 1 | 2 | yes | — |
| 161 | C2×Dic122 | C24 | 1 | 4 | yes | — |
| 162 | Q16×C61 | C2×D4 | 1 | 16 | yes | — |
| 163 | C2×C8×C61 | — | 2 | 2 | no | — |
| 164 | C2×C8×C61 | C2×D4 | 1 | 4 | yes | — |
| 165 | C2×C8×C61 | C24 | 1 | 2 | yes | — |
| 166 | C2×C8×C61 | C24 | 1 | 2 | yes | — |
| 167 | C4⋊C4×C61 | — | 2 | 4 | no | — |
| 168 | C4⋊C4×C61 | — | 2 | 4 | no | — |
| 169 | C4⋊C4×C61 | — | 2 | 2 | no | — |
| 170 | C4⋊C4×C61 | C24 | 1 | 4 | yes | — |
| 171 | C42×C61 | — | 2 | 4 | no | — |
| 172 | C42×C61 | — | 2 | 4 | no | — |
| 173 | C42×C61 | C2×D4 | 1 | 1 | yes | characteristic |
| 174 | C42×C61 | C2×D4 | 1 | 1 | yes | characteristic |
| 175 | C42×C61 | C24 | 1 | 2 | yes | — |
| 176 | #11758202 | — | 2 | 16 | no | — |
| 177 | #11758201 | — | 2 | 16 | no | — |
| 178 | #11758198 | — | 2 | 8 | no | — |
| 179 | #11758198 | — | 2 | 4 | no | — |
| 180 | #11758198 | — | 2 | 4 | no | — |
| 181 | #11758198 | — | 2 | 8 | no | — |
| 182 | #11758198 | C2×D4 | 1 | 8 | yes | — |
| 183 | C4⋊Dic61 | — | 2 | 2 | no | — |
| 184 | C4⋊Dic61 | — | 2 | 2 | no | — |
| 185 | C4⋊Dic61 | — | 2 | 8 | no | — |
| 186 | C4⋊Dic61 | C2×D4 | 1 | 4 | yes | — |
| 187 | #11758194 | — | 2 | 4 | no | — |
| 188 | C2×#92418 | C24 | 1 | 4 | yes | — |
| 189 | Dic244 | — | 2 | 4 | no | — |
| 190 | Dic244 | — | 4 | 2 | no | — |
| 191 | D488 | — | 2 | 4 | no | — |
| 192 | D488 | — | 4 | 2 | no | — |
| 193 | #11758190 | — | 2 | 8 | no | — |
| 194 | #11758190 | — | 4 | 4 | no | — |
| 195 | #11758189 | — | 2 | 8 | no | — |
| 196 | C8×D61 | — | 2 | 8 | no | — |
| 197 | C23×C61 | C22×D4 | 1 | 1 | yes | characteristic |
| 198 | C22×D61 | — | 2 | 4 | no | — |
| 199 | C22×D61 | C22×D4 | 1 | 4 | yes | — |
| 200 | Q8×C61 | — | 2 | 8 | no | — |
| 201 | Q8×C61 | — | 2 | 4 | no | — |
| 202 | Q8×C61 | C22×D4 | 1 | 8 | yes | — |
| 203 | C2×C4×C61 | — | 2 | 8 | no | — |
| 204 | C2×C4×C61 | — | 2 | 4 | no | — |
| 205 | C2×C4×C61 | — | 2 | 4 | no | — |
| 206 | C2×C4×C61 | — | 4 | 2 | no | — |
| 207 | C2×C4×C61 | — | 8 | 2 | no | — |
| 208 | C2×C4×C61 | C22×D4 | 1 | 2 | yes | — |
| 209 | C2×C4×C61 | C22×D4 | 1 | 2 | yes | — |
| 210 | C2×C4×C61 | C22×D4 | 1 | 1 | yes | characteristic |
| 211 | C2×C4×C61 | C22×D4 | 1 | 2 | yes | — |
| 212 | C2×C4×C61 | H(5,𝔽2) | 1 | 2 | yes | — |
| 213 | C2×C4×C61 | C25 | 1 | 1 | yes | characteristic |
| 214 | C22⋊D61 | — | 2 | 8 | no | — |
| 215 | C22⋊D61 | — | 4 | 8 | no | — |
| 216 | C2×Dic61 | — | 2 | 4 | no | — |
| 217 | C2×Dic61 | C22×D4 | 1 | 4 | yes | — |
| 218 | D244 | — | 2 | 4 | no | — |
| 219 | D244 | — | 2 | 4 | no | — |
| 220 | D244 | — | 2 | 4 | no | — |
| 221 | D244 | — | 4 | 4 | no | — |
| 222 | D244 | — | 4 | 16 | no | — |
| 223 | D244 | — | 4 | 4 | no | — |
| 224 | D244 | — | 8 | 2 | no | — |
| 225 | D244 | — | 8 | 8 | no | — |
| 226 | C4×D61 | — | 2 | 4 | no | — |
| 227 | C4×D61 | — | 2 | 4 | no | — |
| 228 | C4×D61 | — | 4 | 16 | no | — |
| 229 | C4×D61 | — | 4 | 16 | no | — |
| 230 | C4×D61 | — | 4 | 8 | no | — |
| 231 | Dic122 | — | 2 | 4 | no | — |
| 232 | Dic122 | — | 2 | 4 | no | — |
| 233 | Dic122 | — | 2 | 4 | no | — |
| 234 | Dic122 | — | 4 | 16 | no | — |
| 235 | C8×C61 | — | 2 | 2 | no | — |
| 236 | C8×C61 | C22×D4 | 1 | 4 | yes | — |
| 237 | #92418 | — | 2 | 4 | no | — |
| 238 | #61081 | — | 61 | 1 | no | maximal, Sylow |
| 239 | C22×C61 | — | 2 | 2 | no | — |
| 240 | C22×C61 | D42 | 1 | 2 | yes | — |
| 241 | C22×C61 | C23×D4 | 1 | 1 | yes | characteristic |
| 242 | C2×D61 | — | 2 | 8 | no | — |
| 243 | C2×D61 | — | 2 | 4 | no | — |
| 244 | C2×D61 | — | 4 | 4 | no | — |
| 245 | C2×D61 | — | 4 | 4 | no | — |
| 246 | C2×D61 | — | 4 | 4 | no | — |
| 247 | C4×C61 | — | 2 | 2 | no | — |
| 248 | C4×C61 | — | 2 | 2 | no | — |
| 249 | C4×C61 | — | 2 | 8 | no | — |
| 250 | C4×C61 | — | 4 | 4 | no | — |
| 251 | C4×C61 | D42 | 1 | 2 | yes | — |
| 252 | C4×C61 | C23×D4 | 1 | 1 | yes | characteristic |
| 253 | C4×C61 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 254 | Dic61 | — | 2 | 4 | no | — |
| 255 | Dic61 | — | 4 | 4 | no | — |
| 256 | C2×#578 | — | 61 | 2 | no | — |
| 257 | #3497 | — | 61 | 2 | no | — |
| 258 | #3271 | — | 61 | 8 | no | — |
| 259 | #3270 | — | 61 | 8 | no | — |
| 260 | #3150 | — | 61 | 1 | no | — |
| 261 | #3060 | — | 61 | 2 | no | — |
| 262 | #3037 | — | 61 | 2 | no | — |
| 263 | #3013 | — | 61 | 4 | no | — |
| 264 | C2×#441 | D61 | 1 | 1 | yes | characteristic, complemented |
| 265 | #2932 | — | 61 | 1 | no | — |
| 266 | C2×C61 | — | 2 | 2 | no | — |
| 267 | C2×C61 | C2×D42 | 1 | 1 | yes | characteristic |
| 268 | C2×C61 | #3586 | 1 | 2 | yes | — |
| 269 | D61 | — | 4 | 4 | no | — |
| 270 | D61 | — | 8 | 4 | no | — |
| 271 | C2×2−1+4 | — | 61 | 4 | no | — |
| 272 | #578 | — | 122 | 16 | no | — |
| 273 | C2×#137 | — | 61 | 4 | no | — |
| 274 | C2×#137 | — | 61 | 8 | no | — |
| 275 | C2×#135 | — | 61 | 4 | no | — |
| 276 | C2×#135 | — | 61 | 2 | no | — |
| 277 | C2×#135 | — | 61 | 2 | no | — |
| 278 | C22×Q16 | — | 61 | 4 | no | — |
| 279 | C22×Q16 | C2×D61 | 1 | 1 | yes | characteristic |
| 280 | C2×#131 | — | 61 | 2 | no | — |
| 281 | #550 | — | 61 | 4 | no | — |
| 282 | #550 | — | 122 | 2 | no | — |
| 283 | D4×Q8 | — | 61 | 4 | no | — |
| 284 | D4×Q8 | — | 122 | 2 | no | — |
| 285 | #548 | — | 61 | 8 | no | — |
| 286 | #548 | — | 122 | 4 | no | — |
| 287 | #537 | — | 61 | 4 | no | — |
| 288 | #537 | — | 122 | 4 | no | — |
| 289 | #532 | — | 61 | 1 | no | — |
| 290 | #532 | — | 61 | 2 | no | — |
| 291 | #532 | — | 122 | 4 | no | — |
| 292 | C2×C4×Q8 | C2×D61 | 1 | 2 | yes | — |
| 293 | #497 | — | 61 | 4 | no | — |
| 294 | #496 | — | 61 | 4 | no | — |
| 295 | #470 | — | 61 | 4 | no | — |
| 296 | #469 | — | 61 | 4 | no | — |
| 297 | #465 | — | 61 | 8 | no | — |
| 298 | #464 | — | 61 | 8 | no | — |
| 299 | #462 | — | 61 | 4 | no | — |
| 300 | #460 | — | 61 | 4 | no | — |
| 301 | #452 | — | 61 | 8 | no | — |
| 302 | #451 | — | 61 | 8 | no | — |
| 303 | #449 | — | 61 | 8 | no | — |
| 304 | #448 | — | 61 | 8 | no | — |
| 305 | #441 | C2×D61 | 1 | 8 | yes | — |
| 306 | #435 | — | 61 | 8 | no | — |
| 307 | C2×#106 | C2×D61 | 1 | 1 | yes | characteristic |
| 308 | #423 | — | 61 | 1 | no | — |
| 309 | #417 | — | 61 | 4 | no | — |
| 310 | C2×#103 | C2×D61 | 1 | 2 | yes | — |
| 311 | #408 | — | 61 | 2 | no | — |
| 312 | C2×#97 | C2×D61 | 1 | 1 | yes | characteristic |
| 313 | C61 | #61081 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 314 | 2−1+4 | — | 122 | 16 | no | — |
| 315 | 2−1+4 | — | 244 | 8 | no | — |
| 316 | C2×#41 | — | 61 | 2 | no | — |
| 317 | C2×#41 | — | 61 | 8 | no | — |
| 318 | C2×#41 | — | 61 | 4 | no | — |
| 319 | C2×#41 | — | 122 | 8 | no | — |
| 320 | C2×#41 | — | 122 | 4 | no | — |
| 321 | C22×Q8 | — | 61 | 8 | no | — |
| 322 | C22×Q8 | — | 122 | 4 | no | — |
| 323 | C22×Q8 | C22×D61 | 1 | 2 | yes | — |
| 324 | #137 | — | 122 | 16 | no | — |
| 325 | #137 | — | 122 | 32 | no | — |
| 326 | #135 | — | 122 | 16 | no | — |
| 327 | #135 | — | 122 | 8 | no | — |
| 328 | #135 | — | 244 | 4 | no | — |
| 329 | C2×Q16 | — | 61 | 8 | no | — |
| 330 | C2×Q16 | — | 61 | 2 | no | — |
| 331 | C2×Q16 | — | 61 | 2 | no | — |
| 332 | C2×Q16 | — | 122 | 16 | no | — |
| 333 | C2×Q16 | D244 | 1 | 8 | yes | complemented |
| 334 | C2×Q16 | C22×D61 | 1 | 4 | yes | — |
| 335 | C2×SD16 | — | 61 | 8 | no | — |
| 336 | C2×SD16 | — | 61 | 4 | no | — |
| 337 | C2×SD16 | — | 61 | 4 | no | — |
| 338 | C2×D8 | — | 61 | 2 | no | — |
| 339 | C2×D8 | — | 61 | 2 | no | — |
| 340 | #131 | — | 122 | 8 | no | — |
| 341 | C2×M16 | — | 61 | 2 | no | — |
| 342 | C2×M16 | — | 61 | 4 | no | — |
| 343 | C22×C8 | — | 61 | 4 | no | — |
| 344 | C22×C8 | C22×D61 | 1 | 1 | yes | characteristic |
| 345 | C22×C8 | C22×D61 | 1 | 1 | yes | characteristic |
| 346 | C4⋊Q8 | — | 61 | 1 | no | — |
| 347 | C4⋊Q8 | — | 61 | 2 | no | — |
| 348 | C4⋊Q8 | — | 122 | 4 | no | — |
| 349 | #127 | — | 61 | 1 | no | — |
| 350 | #127 | — | 61 | 2 | no | — |
| 351 | #127 | — | 122 | 4 | no | — |
| 352 | #124 | — | 61 | 2 | no | — |
| 353 | #124 | — | 61 | 4 | no | — |
| 354 | #124 | — | 122 | 8 | no | — |
| 355 | C22⋊Q8 | — | 61 | 8 | no | — |
| 356 | C22⋊Q8 | — | 122 | 8 | no | — |
| 357 | C22⋊Q8 | — | 122 | 8 | no | — |
| 358 | C22⋊Q8 | — | 122 | 4 | no | — |
| 359 | #121 | — | 61 | 4 | no | — |
| 360 | #121 | — | 61 | 8 | no | — |
| 361 | #121 | — | 122 | 8 | no | — |
| 362 | #121 | — | 122 | 4 | no | — |
| 363 | #121 | — | 122 | 8 | no | — |
| 364 | #121 | — | 122 | 8 | no | — |
| 365 | #121 | — | 122 | 2 | no | — |
| 366 | #121 | — | 122 | 2 | no | — |
| 367 | C4×Q8 | — | 2 | 2 | no | — |
| 368 | C4×Q8 | — | 2 | 2 | no | — |
| 369 | C4×Q8 | C22×D61 | 1 | 4 | yes | — |
| 370 | C4×Q8 | C22×D61 | 1 | 4 | yes | — |
| 371 | C4×D4 | — | 61 | 4 | no | — |
| 372 | C4×D4 | — | 122 | 8 | no | — |
| 373 | C4×D4 | — | 122 | 4 | no | — |
| 374 | C4×D4 | — | 122 | 4 | no | — |
| 375 | C4×D4 | — | 122 | 2 | no | — |
| 376 | C4×D4 | — | 122 | 2 | no | — |
| 377 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 378 | C2×C4⋊C4 | C22×D61 | 1 | 2 | yes | — |
| 379 | C2×C42 | — | 2 | 2 | no | — |
| 380 | C2×C42 | C22×D61 | 1 | 1 | yes | characteristic |
| 381 | #106 | C22×D61 | 1 | 4 | yes | — |
| 382 | C4⋊C8 | — | 61 | 4 | no | — |
| 383 | #103 | — | 61 | 8 | no | — |
| 384 | #103 | C22×D61 | 1 | 8 | yes | — |
| 385 | #102 | — | 61 | 8 | no | — |
| 386 | C22⋊C8 | — | 61 | 8 | no | — |
| 387 | #97 | C22×D61 | 1 | 4 | yes | — |
| 388 | #41 | — | 122 | 4 | no | — |
| 389 | #41 | — | 122 | 4 | no | — |
| 390 | #41 | — | 122 | 16 | no | — |
| 391 | #41 | — | 122 | 8 | no | — |
| 392 | #41 | — | 122 | 8 | no | — |
| 393 | #41 | — | 244 | 32 | no | — |
| 394 | #41 | — | 244 | 8 | no | — |
| 395 | #41 | — | 244 | 16 | no | — |
| 396 | C2×Q8 | — | 2 | 2 | no | — |
| 397 | C2×Q8 | — | 2 | 4 | no | — |
| 398 | C2×Q8 | — | 61 | 2 | no | — |
| 399 | C2×Q8 | — | 61 | 4 | no | — |
| 400 | C2×Q8 | — | 122 | 8 | no | — |
| 401 | C2×Q8 | — | 122 | 16 | no | — |
| 402 | C2×Q8 | — | 244 | 8 | no | — |
| 403 | C2×Q8 | — | 244 | 16 | no | — |
| 404 | C2×Q8 | C2×D244 | 1 | 8 | yes | — |
| 405 | C2×Q8 | C23×D61 | 1 | 4 | yes | — |
| 406 | C2×D4 | — | 61 | 4 | no | — |
| 407 | C2×D4 | — | 61 | 2 | no | — |
| 408 | C2×D4 | — | 61 | 4 | no | — |
| 409 | C2×D4 | — | 61 | 4 | no | — |
| 410 | C2×D4 | — | 122 | 8 | no | — |
| 411 | C2×D4 | — | 122 | 8 | no | — |
| 412 | C2×D4 | — | 122 | 4 | no | — |
| 413 | C2×D4 | — | 122 | 2 | no | — |
| 414 | C2×D4 | — | 122 | 2 | no | — |
| 415 | C22×C4 | — | 2 | 2 | no | — |
| 416 | C22×C4 | — | 2 | 2 | no | — |
| 417 | C22×C4 | — | 61 | 4 | no | — |
| 418 | C22×C4 | — | 122 | 8 | no | — |
| 419 | C22×C4 | — | 122 | 8 | no | — |
| 420 | C22×C4 | — | 122 | 4 | no | — |
| 421 | C22×C4 | D4×D61 | 1 | 2 | yes | — |
| 422 | C22×C4 | C23×D61 | 1 | 1 | yes | characteristic |
| 423 | Q16 | — | 122 | 16 | no | — |
| 424 | Q16 | — | 122 | 4 | no | — |
| 425 | Q16 | — | 244 | 2 | no | — |
| 426 | Q16 | C2×D244 | 1 | 16 | yes | — |
| 427 | SD16 | — | 122 | 16 | no | — |
| 428 | SD16 | — | 122 | 8 | no | — |
| 429 | SD16 | — | 244 | 4 | no | — |
| 430 | D8 | — | 122 | 4 | no | — |
| 431 | D8 | — | 244 | 2 | no | — |
| 432 | M16 | — | 122 | 4 | no | — |
| 433 | M16 | — | 122 | 8 | no | — |
| 434 | C2×C8 | — | 2 | 2 | no | — |
| 435 | C2×C8 | — | 61 | 4 | no | — |
| 436 | C2×C8 | — | 122 | 8 | no | — |
| 437 | C2×C8 | C2×D244 | 1 | 4 | yes | — |
| 438 | C2×C8 | C23×D61 | 1 | 2 | yes | — |
| 439 | C2×C8 | C23×D61 | 1 | 2 | yes | — |
| 440 | C4⋊C4 | — | 2 | 4 | no | — |
| 441 | C4⋊C4 | — | 2 | 4 | no | — |
| 442 | C4⋊C4 | — | 2 | 2 | no | — |
| 443 | C4⋊C4 | — | 61 | 4 | no | — |
| 444 | C4⋊C4 | — | 122 | 8 | no | — |
| 445 | C4⋊C4 | — | 122 | 2 | no | — |
| 446 | C4⋊C4 | — | 122 | 2 | no | — |
| 447 | C4⋊C4 | C23×D61 | 1 | 4 | yes | — |
| 448 | C22⋊C4 | — | 61 | 8 | no | — |
| 449 | C22⋊C4 | — | 122 | 8 | no | — |
| 450 | C22⋊C4 | — | 122 | 8 | no | — |
| 451 | C22⋊C4 | — | 122 | 4 | no | — |
| 452 | C22⋊C4 | — | 122 | 4 | no | — |
| 453 | C42 | — | 2 | 4 | no | — |
| 454 | C42 | — | 2 | 4 | no | — |
| 455 | C42 | D4×D61 | 1 | 1 | yes | characteristic |
| 456 | C42 | D4×D61 | 1 | 1 | yes | characteristic |
| 457 | C42 | C23×D61 | 1 | 2 | yes | — |
| 458 | C23 | — | 61 | 4 | no | — |
| 459 | C23 | — | 122 | 4 | no | — |
| 460 | C23 | C2×D4×D61 | 1 | 1 | yes | characteristic |
| 461 | Q8 | — | 2 | 4 | no | — |
| 462 | Q8 | — | 2 | 8 | no | — |
| 463 | Q8 | — | 122 | 4 | no | — |
| 464 | Q8 | — | 122 | 4 | no | — |
| 465 | Q8 | — | 122 | 4 | no | — |
| 466 | Q8 | — | 244 | 16 | no | — |
| 467 | Q8 | C22×D244 | 1 | 8 | yes | — |
| 468 | D4 | — | 122 | 8 | no | — |
| 469 | D4 | — | 122 | 4 | no | — |
| 470 | D4 | — | 122 | 4 | no | — |
| 471 | D4 | — | 122 | 4 | no | — |
| 472 | D4 | — | 488 | 2 | no | — |
| 473 | D4 | — | 488 | 8 | no | — |
| 474 | D4 | — | 244 | 4 | no | — |
| 475 | D4 | — | 244 | 16 | no | — |
| 476 | D4 | — | 244 | 4 | no | — |
| 477 | D4 | — | 244 | 8 | no | — |
| 478 | C2×C4 | — | 2 | 4 | no | — |
| 479 | C2×C4 | — | 2 | 8 | no | — |
| 480 | C2×C4 | — | 2 | 4 | no | — |
| 481 | C2×C4 | — | 4 | 2 | no | — |
| 482 | C2×C4 | — | 8 | 2 | no | — |
| 483 | C2×C4 | — | 61 | 4 | no | — |
| 484 | C2×C4 | — | 122 | 4 | no | — |
| 485 | C2×C4 | — | 122 | 4 | no | — |
| 486 | C2×C4 | — | 122 | 4 | no | — |
| 487 | C2×C4 | — | 244 | 16 | no | — |
| 488 | C2×C4 | — | 244 | 16 | no | — |
| 489 | C2×C4 | — | 244 | 8 | no | — |
| 490 | C2×C4 | C2×D4×D61 | 1 | 2 | yes | — |
| 491 | C2×C4 | C2×D4×D61 | 1 | 2 | yes | — |
| 492 | C2×C4 | C2×D4×D61 | 1 | 1 | yes | characteristic |
| 493 | C2×C4 | C22×D244 | 1 | 2 | yes | — |
| 494 | C2×C4 | #14519823 | 1 | 2 | yes | — |
| 495 | C2×C4 | C24×D61 | 1 | 1 | yes | characteristic |
| 496 | C8 | — | 2 | 2 | no | — |
| 497 | C8 | — | 122 | 4 | no | — |
| 498 | C8 | C22×D244 | 1 | 4 | yes | — |
| 499 | C22 | — | 2 | 2 | no | — |
| 500 | C22 | — | 122 | 4 | no | — |
| 501 | C22 | — | 122 | 8 | no | — |
| 502 | C22 | — | 244 | 4 | no | — |
| 503 | C22 | — | 244 | 4 | no | — |
| 504 | C22 | — | 244 | 4 | no | — |
| 505 | C22 | D4×D244 | 1 | 2 | yes | — |
| 506 | C22 | C22×D4×D61 | 1 | 1 | yes | characteristic |
| 507 | C4 | — | 2 | 8 | no | — |
| 508 | C4 | — | 2 | 2 | no | — |
| 509 | C4 | — | 2 | 2 | no | — |
| 510 | C4 | — | 4 | 4 | no | — |
| 511 | C4 | — | 122 | 4 | no | — |
| 512 | C4 | — | 244 | 4 | no | — |
| 513 | C4 | D4×D244 | 1 | 2 | yes | — |
| 514 | C4 | C23×D244 | 1 | 1 | yes | characteristic |
| 515 | C4 | C2×#14519823 | 1 | 1 | yes | characteristic |
| 516 | C2 | — | 2 | 2 | no | — |
| 517 | C2 | — | 488 | 4 | no | — |
| 518 | C2 | — | 244 | 4 | no | — |
| 519 | C2 | C2×D4×D244 | 1 | 1 | yes | characteristic |
| 520 | C2 | #21460602 | 1 | 2 | yes | — |
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