Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
866 conjugacy classes of subgroups.
The subgroup lattice has 706 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10618934 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10613667 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #10612748 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10612187 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C5×#1648 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10602729 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10602168 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10601921 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #10601853 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #10599251 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #10599219 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #10599053 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #10599053 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #10599032 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #10599028 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C5×#557 | C22 | 1 | 1 | yes | characteristic |
| 17 | #66066 | — | 2 | 1 | no | — |
| 18 | #66062 | C22 | 1 | 1 | yes | characteristic |
| 19 | #66059 | C22 | 1 | 1 | yes | characteristic |
| 20 | #66058 | — | 2 | 1 | no | — |
| 21 | #66055 | C22 | 1 | 1 | yes | characteristic |
| 22 | #66027 | — | 2 | 2 | no | — |
| 23 | #66026 | — | 2 | 2 | no | — |
| 24 | #66025 | — | 2 | 1 | no | — |
| 25 | #66024 | — | 2 | 1 | no | — |
| 26 | #65919 | C22 | 1 | 1 | yes | characteristic |
| 27 | #65919 | C22 | 1 | 1 | yes | characteristic |
| 28 | #65914 | — | 2 | 1 | no | — |
| 29 | #65912 | C22 | 1 | 1 | yes | characteristic |
| 30 | #65908 | — | 2 | 1 | no | — |
| 31 | C4×Q8×D5 | C22 | 1 | 1 | yes | characteristic |
| 32 | #65902 | — | 2 | 1 | no | — |
| 33 | #65902 | — | 2 | 1 | no | — |
| 34 | C5×#500 | C22 | 1 | 1 | yes | characteristic |
| 35 | C5×#475 | C22 | 1 | 1 | yes | characteristic |
| 36 | C5×#462 | C22 | 1 | 1 | yes | characteristic |
| 37 | #65475 | — | 2 | 1 | no | — |
| 38 | Q16×Dic5 | — | 2 | 1 | no | — |
| 39 | #65383 | C22 | 1 | 1 | yes | characteristic |
| 40 | #65382 | C22 | 1 | 1 | yes | characteristic |
| 41 | #65379 | C22 | 1 | 1 | yes | characteristic |
| 42 | #65377 | C22 | 1 | 1 | yes | characteristic |
| 43 | #65310 | C22 | 1 | 1 | yes | characteristic |
| 44 | #65310 | C22 | 1 | 1 | yes | characteristic |
| 45 | #65178 | — | 2 | 2 | no | — |
| 46 | #65175 | — | 2 | 2 | no | — |
| 47 | #65156 | — | 2 | 1 | no | — |
| 48 | #65145 | — | 2 | 1 | no | — |
| 49 | #65139 | C22 | 1 | 1 | yes | characteristic |
| 50 | #65139 | C22 | 1 | 1 | yes | characteristic |
| 51 | #65124 | C22 | 1 | 1 | yes | characteristic |
| 52 | #65122 | C22 | 1 | 1 | yes | characteristic |
| 53 | #65103 | — | 2 | 1 | no | — |
| 54 | #65098 | — | 2 | 1 | no | — |
| 55 | #65086 | — | 2 | 1 | no | — |
| 56 | #65079 | — | 2 | 1 | no | — |
| 57 | #64982 | C22 | 1 | 1 | yes | characteristic |
| 58 | C4×#676 | C22 | 1 | 1 | yes | characteristic |
| 59 | C5×#332 | C22 | 1 | 1 | yes | characteristic |
| 60 | C5×Q8⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 61 | C5×Q8⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 62 | #64767 | C22 | 1 | 1 | yes | characteristic |
| 63 | Q8⋊#168 | C22 | 1 | 1 | yes | characteristic |
| 64 | Q8⋊#168 | C22 | 1 | 1 | yes | characteristic |
| 65 | #64705 | C22 | 1 | 1 | yes | characteristic |
| 66 | #64705 | C22 | 1 | 1 | yes | characteristic |
| 67 | #64704 | C22 | 1 | 1 | yes | characteristic |
| 68 | #64704 | C22 | 1 | 1 | yes | characteristic |
| 69 | #64676 | C22 | 1 | 1 | yes | characteristic |
| 70 | #64676 | C22 | 1 | 1 | yes | characteristic |
| 71 | #18603 | — | 5 | 1 | no | maximal, Sylow |
| 72 | C2×#713 | — | 2 | 1 | no | — |
| 73 | C2×Q8×D5 | D4 | 1 | 1 | yes | characteristic |
| 74 | C2×C5×Q16 | — | 2 | 1 | no | — |
| 75 | C5×C4⋊Q8 | — | 2 | 1 | no | — |
| 76 | C5×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 77 | C5×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 78 | C5×#125 | — | 2 | 1 | no | — |
| 79 | C5×#125 | — | 2 | 2 | no | — |
| 80 | C4×C5×Q8 | — | 2 | 1 | no | — |
| 81 | C4×C5×Q8 | — | 2 | 1 | no | — |
| 82 | C4×C5×Q8 | C23 | 1 | 1 | yes | characteristic |
| 83 | C4×C5×Q8 | C23 | 1 | 1 | yes | characteristic |
| 84 | #4093 | — | 2 | 1 | no | — |
| 85 | #4093 | — | 2 | 1 | no | — |
| 86 | #4093 | — | 2 | 1 | no | — |
| 87 | #4092 | — | 2 | 1 | no | — |
| 88 | #4092 | D4 | 1 | 1 | yes | characteristic |
| 89 | Q8×Dic5 | — | 2 | 1 | no | — |
| 90 | Q8×Dic5 | — | 2 | 1 | no | — |
| 91 | Q8×Dic5 | D4 | 1 | 1 | yes | characteristic |
| 92 | #4090 | — | 2 | 1 | no | — |
| 93 | #4090 | D4 | 1 | 1 | yes | characteristic |
| 94 | C2×#689 | — | 2 | 1 | no | — |
| 95 | C2×#677 | — | 2 | 2 | no | — |
| 96 | C2×#676 | — | 2 | 1 | no | — |
| 97 | #4044 | — | 2 | 2 | no | — |
| 98 | #4044 | — | 2 | 2 | no | — |
| 99 | #4044 | — | 2 | 2 | no | — |
| 100 | #4043 | — | 2 | 2 | no | — |
| 101 | #4043 | — | 2 | 1 | no | — |
| 102 | #4043 | D4 | 1 | 1 | yes | characteristic |
| 103 | #4042 | — | 2 | 2 | no | — |
| 104 | #4042 | — | 2 | 2 | no | — |
| 105 | #4042 | — | 2 | 2 | no | — |
| 106 | #4042 | — | 2 | 1 | no | — |
| 107 | #4041 | — | 2 | 1 | no | — |
| 108 | #4041 | D4 | 1 | 2 | yes | — |
| 109 | #4040 | — | 2 | 2 | no | — |
| 110 | #4040 | — | 2 | 2 | no | — |
| 111 | #4040 | — | 2 | 2 | no | — |
| 112 | #4040 | — | 2 | 2 | no | — |
| 113 | #4039 | — | 2 | 2 | no | — |
| 114 | #4039 | — | 2 | 1 | no | — |
| 115 | #4039 | — | 2 | 1 | no | — |
| 116 | #4039 | — | 2 | 1 | no | — |
| 117 | #4039 | D4 | 1 | 2 | yes | — |
| 118 | #4038 | — | 2 | 2 | no | — |
| 119 | #4038 | — | 2 | 1 | no | — |
| 120 | D5×C4⋊C4 | — | 2 | 2 | no | — |
| 121 | D5×C4⋊C4 | — | 2 | 1 | no | — |
| 122 | D5×C4⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 123 | #4036 | — | 2 | 1 | no | — |
| 124 | #4036 | — | 2 | 1 | no | — |
| 125 | #4035 | — | 2 | 2 | no | — |
| 126 | #4035 | — | 2 | 1 | no | — |
| 127 | #4034 | D4 | 1 | 1 | yes | characteristic |
| 128 | #4033 | — | 2 | 1 | no | — |
| 129 | #4033 | — | 2 | 1 | no | — |
| 130 | #4033 | — | 2 | 1 | no | — |
| 131 | #4033 | D4 | 1 | 1 | yes | characteristic |
| 132 | #4022 | — | 2 | 2 | no | — |
| 133 | #4021 | — | 2 | 1 | no | — |
| 134 | #4021 | — | 2 | 1 | no | — |
| 135 | #4020 | C23 | 1 | 1 | yes | characteristic |
| 136 | C4×D20 | — | 2 | 2 | no | — |
| 137 | C4×D20 | — | 2 | 1 | no | — |
| 138 | C4×D20 | — | 2 | 1 | no | — |
| 139 | #4018 | — | 2 | 2 | no | — |
| 140 | #4018 | — | 2 | 2 | no | — |
| 141 | #4018 | — | 2 | 1 | no | — |
| 142 | C42×D5 | — | 2 | 1 | no | — |
| 143 | C42×D5 | C23 | 1 | 1 | yes | characteristic |
| 144 | #4015 | C23 | 1 | 1 | yes | characteristic |
| 145 | C4×Dic10 | — | 2 | 1 | no | — |
| 146 | C4×Dic10 | — | 2 | 1 | no | — |
| 147 | C4×Dic10 | C23 | 1 | 1 | yes | characteristic |
| 148 | C4×Dic10 | C23 | 1 | 1 | yes | characteristic |
| 149 | C5×#107 | — | 2 | 2 | no | — |
| 150 | C5×#106 | — | 2 | 1 | no | — |
| 151 | C5×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 152 | C5×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 153 | C5×#103 | — | 2 | 1 | no | — |
| 154 | C5×#103 | — | 2 | 1 | no | — |
| 155 | C4×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 156 | #3967 | — | 2 | 1 | no | — |
| 157 | #3967 | — | 2 | 1 | no | — |
| 158 | #3967 | — | 2 | 1 | no | — |
| 159 | #3952 | — | 2 | 1 | no | — |
| 160 | #3952 | — | 2 | 1 | no | — |
| 161 | #3950 | — | 2 | 1 | no | — |
| 162 | #3950 | — | 2 | 1 | no | — |
| 163 | #3948 | — | 2 | 1 | no | — |
| 164 | #3948 | — | 2 | 1 | no | — |
| 165 | #3947 | — | 2 | 1 | no | — |
| 166 | #3947 | — | 2 | 1 | no | — |
| 167 | C8×Dic5 | — | 2 | 1 | no | — |
| 168 | #3942 | — | 2 | 1 | no | — |
| 169 | #3942 | — | 2 | 2 | no | — |
| 170 | #3941 | — | 2 | 2 | no | — |
| 171 | #3940 | — | 2 | 1 | no | — |
| 172 | #3939 | — | 2 | 1 | no | — |
| 173 | #3939 | — | 2 | 1 | no | — |
| 174 | C4⋊#168 | C23 | 1 | 1 | yes | characteristic |
| 175 | C4⋊#168 | C23 | 1 | 1 | yes | characteristic |
| 176 | C4×#168 | C23 | 1 | 1 | yes | characteristic |
| 177 | #3507 | — | 5 | 1 | no | — |
| 178 | #3237 | — | 5 | 1 | no | — |
| 179 | #3182 | — | 5 | 1 | no | — |
| 180 | #3104 | — | 5 | 1 | no | — |
| 181 | #1648 | — | 5 | 1 | no | — |
| 182 | #1648 | D5 | 1 | 1 | yes | characteristic, complemented |
| 183 | #1640 | — | 5 | 1 | no | — |
| 184 | #1640 | — | 5 | 1 | no | — |
| 185 | #1636 | — | 5 | 1 | no | — |
| 186 | #1636 | — | 5 | 1 | no | — |
| 187 | #1630 | — | 5 | 1 | no | — |
| 188 | #1630 | — | 5 | 1 | no | — |
| 189 | #1553 | — | 5 | 1 | no | — |
| 190 | #1491 | — | 5 | 1 | no | — |
| 191 | #1485 | — | 5 | 1 | no | — |
| 192 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 193 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 194 | C2×C5×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 195 | C2×C5×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 196 | #713 | — | 4 | 2 | no | — |
| 197 | #713 | — | 4 | 2 | no | — |
| 198 | Q8×D5 | — | 4 | 1 | no | — |
| 199 | Q8×D5 | — | 4 | 1 | no | — |
| 200 | C2×D20 | — | 2 | 2 | no | — |
| 201 | C2×D20 | — | 2 | 1 | no | — |
| 202 | C2×D20 | — | 2 | 1 | no | — |
| 203 | C2×D20 | C2×D4 | 1 | 2 | yes | — |
| 204 | C2×C4×D5 | — | 2 | 1 | no | — |
| 205 | C2×C4×D5 | — | 2 | 2 | no | — |
| 206 | C2×C4×D5 | — | 2 | 2 | no | — |
| 207 | C2×C4×D5 | — | 2 | 2 | no | — |
| 208 | C2×C4×D5 | — | 2 | 1 | no | — |
| 209 | C2×C4×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 210 | C2×C4×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 211 | C2×C4×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 212 | C2×Dic10 | — | 2 | 1 | no | — |
| 213 | C2×Dic10 | — | 2 | 1 | no | — |
| 214 | C2×Dic10 | — | 2 | 1 | no | — |
| 215 | C2×Dic10 | C2×D4 | 1 | 1 | yes | characteristic |
| 216 | C2×Dic10 | C2×D4 | 1 | 1 | yes | characteristic |
| 217 | C5×Q16 | — | 4 | 2 | no | — |
| 218 | C2×C5×C8 | — | 2 | 1 | no | — |
| 219 | C2×C5×C8 | — | 2 | 1 | no | — |
| 220 | C2×C5×C8 | — | 2 | 1 | no | — |
| 221 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 222 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 223 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 224 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 225 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 226 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 227 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 228 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 229 | C5×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 230 | C5×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 231 | C5×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 232 | C42×C5 | — | 2 | 2 | no | — |
| 233 | C42×C5 | — | 2 | 1 | no | — |
| 234 | C42×C5 | — | 2 | 1 | no | — |
| 235 | C42×C5 | C24 | 1 | 1 | yes | characteristic |
| 236 | #689 | — | 4 | 2 | no | — |
| 237 | #685 | — | 2 | 2 | no | — |
| 238 | #685 | — | 2 | 2 | no | — |
| 239 | #685 | — | 2 | 2 | no | — |
| 240 | #685 | — | 2 | 2 | no | — |
| 241 | #685 | — | 2 | 2 | no | — |
| 242 | #685 | — | 2 | 2 | no | — |
| 243 | #685 | — | 2 | 1 | no | — |
| 244 | #685 | — | 2 | 1 | no | — |
| 245 | #685 | — | 2 | 2 | no | — |
| 246 | #685 | — | 2 | 2 | no | — |
| 247 | #685 | — | 4 | 1 | no | — |
| 248 | C4⋊Dic5 | — | 2 | 2 | no | — |
| 249 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 250 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 251 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 252 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 253 | C4⋊Dic5 | — | 4 | 1 | no | — |
| 254 | C4⋊Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 255 | C4⋊Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 256 | #683 | — | 2 | 2 | no | — |
| 257 | #683 | — | 2 | 2 | no | — |
| 258 | #683 | — | 2 | 1 | no | — |
| 259 | #683 | — | 2 | 1 | no | — |
| 260 | #683 | — | 2 | 1 | no | — |
| 261 | #683 | — | 2 | 1 | no | — |
| 262 | #683 | — | 2 | 1 | no | — |
| 263 | #683 | — | 2 | 1 | no | — |
| 264 | #683 | — | 2 | 1 | no | — |
| 265 | #683 | — | 2 | 1 | no | — |
| 266 | #683 | — | 4 | 1 | no | — |
| 267 | C4×Dic5 | — | 2 | 2 | no | — |
| 268 | C4×Dic5 | — | 2 | 1 | no | — |
| 269 | C4×Dic5 | — | 2 | 1 | no | — |
| 270 | C4×Dic5 | — | 2 | 1 | no | — |
| 271 | C4×Dic5 | — | 2 | 1 | no | — |
| 272 | C4×Dic5 | — | 4 | 1 | no | — |
| 273 | C4×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 274 | C4×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 275 | C4×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 276 | C2×#168 | — | 2 | 1 | no | — |
| 277 | C2×#168 | — | 2 | 1 | no | — |
| 278 | C2×#168 | — | 2 | 1 | no | — |
| 279 | #677 | — | 4 | 4 | no | — |
| 280 | #676 | — | 4 | 2 | no | — |
| 281 | #559 | — | 5 | 1 | no | — |
| 282 | #559 | — | 5 | 1 | no | — |
| 283 | #557 | — | 5 | 1 | no | — |
| 284 | #557 | C2×D5 | 1 | 1 | yes | characteristic |
| 285 | #556 | — | 10 | 1 | no | — |
| 286 | #556 | — | 10 | 1 | no | — |
| 287 | #556 | — | 10 | 1 | no | — |
| 288 | #554 | — | 10 | 1 | no | — |
| 289 | #552 | — | 10 | 2 | no | — |
| 290 | #539 | — | 10 | 2 | no | — |
| 291 | #536 | — | 10 | 1 | no | — |
| 292 | #533 | — | 5 | 1 | no | — |
| 293 | #533 | — | 5 | 1 | no | — |
| 294 | #532 | — | 5 | 1 | no | — |
| 295 | #529 | — | 10 | 1 | no | — |
| 296 | #529 | — | 10 | 1 | no | — |
| 297 | #520 | — | 10 | 1 | no | — |
| 298 | C2×C4×Q8 | — | 5 | 1 | no | — |
| 299 | #501 | — | 10 | 1 | no | — |
| 300 | #500 | C2×D5 | 1 | 1 | yes | characteristic |
| 301 | #492 | — | 5 | 1 | no | — |
| 302 | #491 | — | 10 | 1 | no | — |
| 303 | #487 | — | 5 | 1 | no | — |
| 304 | #486 | — | 5 | 1 | no | — |
| 305 | #485 | — | 10 | 1 | no | — |
| 306 | #485 | — | 10 | 1 | no | — |
| 307 | #484 | — | 10 | 1 | no | — |
| 308 | #477 | — | 5 | 1 | no | — |
| 309 | #477 | — | 5 | 1 | no | — |
| 310 | #477 | — | 5 | 1 | no | — |
| 311 | #477 | — | 5 | 1 | no | — |
| 312 | #475 | — | 5 | 1 | no | — |
| 313 | #475 | C2×D5 | 1 | 1 | yes | characteristic |
| 314 | #468 | — | 10 | 2 | no | — |
| 315 | #462 | — | 5 | 1 | no | — |
| 316 | #462 | C2×D5 | 1 | 1 | yes | characteristic |
| 317 | #451 | — | 10 | 1 | no | — |
| 318 | #440 | — | 10 | 2 | no | — |
| 319 | C4×Q16 | — | 10 | 1 | no | — |
| 320 | C4×Q16 | — | 10 | 1 | no | — |
| 321 | #432 | — | 5 | 1 | no | — |
| 322 | #431 | — | 5 | 1 | no | — |
| 323 | C4×M16 | — | 5 | 1 | no | — |
| 324 | #332 | — | 5 | 1 | no | — |
| 325 | #332 | C2×D5 | 1 | 1 | yes | characteristic |
| 326 | #331 | — | 5 | 1 | no | — |
| 327 | #331 | — | 5 | 1 | no | — |
| 328 | Q8⋊C8 | — | 5 | 1 | no | — |
| 329 | Q8⋊C8 | — | 5 | 1 | no | — |
| 330 | Q8⋊C8 | — | 5 | 1 | no | — |
| 331 | Q8⋊C8 | — | 5 | 1 | no | — |
| 332 | Q8⋊C8 | — | 5 | 1 | no | — |
| 333 | Q8⋊C8 | — | 5 | 1 | no | — |
| 334 | Q8⋊C8 | C2×D5 | 1 | 1 | yes | characteristic |
| 335 | Q8⋊C8 | C2×D5 | 1 | 1 | yes | characteristic |
| 336 | C22×D5 | — | 2 | 2 | no | — |
| 337 | C22×D5 | #120 | 1 | 1 | yes | characteristic |
| 338 | C5×Q8 | — | 2 | 1 | no | — |
| 339 | C5×Q8 | — | 2 | 1 | no | — |
| 340 | C5×Q8 | — | 2 | 1 | no | — |
| 341 | C5×Q8 | — | 2 | 1 | no | — |
| 342 | C5×Q8 | — | 4 | 1 | no | — |
| 343 | C5×Q8 | — | 4 | 1 | no | — |
| 344 | C5×Q8 | — | 4 | 1 | no | — |
| 345 | C5×Q8 | — | 4 | 1 | no | — |
| 346 | C2×C4×C5 | — | 2 | 2 | no | — |
| 347 | C2×C4×C5 | — | 2 | 1 | no | — |
| 348 | C2×C4×C5 | — | 2 | 1 | no | — |
| 349 | C2×C4×C5 | — | 2 | 1 | no | — |
| 350 | C2×C4×C5 | — | 2 | 1 | no | — |
| 351 | C2×C4×C5 | — | 4 | 1 | no | — |
| 352 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 353 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 354 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 355 | C2×Dic5 | — | 2 | 1 | no | — |
| 356 | C2×Dic5 | — | 2 | 1 | no | — |
| 357 | C2×Dic5 | — | 2 | 1 | no | — |
| 358 | C2×Dic5 | — | 2 | 1 | no | — |
| 359 | C2×Dic5 | — | 4 | 1 | no | — |
| 360 | C2×Dic5 | #120 | 1 | 1 | yes | characteristic |
| 361 | C2×Dic5 | #120 | 1 | 1 | yes | characteristic |
| 362 | C2×Dic5 | #120 | 1 | 1 | yes | characteristic |
| 363 | D20 | — | 4 | 2 | no | — |
| 364 | D20 | — | 4 | 4 | no | — |
| 365 | D20 | — | 4 | 1 | no | — |
| 366 | D20 | — | 4 | 1 | no | — |
| 367 | D20 | — | 4 | 1 | no | — |
| 368 | D20 | — | 4 | 1 | no | — |
| 369 | C4×D5 | — | 2 | 1 | no | — |
| 370 | C4×D5 | — | 2 | 1 | no | — |
| 371 | C4×D5 | — | 2 | 1 | no | — |
| 372 | C4×D5 | — | 2 | 1 | no | — |
| 373 | C4×D5 | — | 4 | 1 | no | — |
| 374 | C4×D5 | — | 4 | 4 | no | — |
| 375 | C4×D5 | — | 4 | 2 | no | — |
| 376 | C4×D5 | — | 8 | 1 | no | — |
| 377 | C4×D5 | — | 8 | 2 | no | — |
| 378 | C4×D5 | — | 8 | 2 | no | — |
| 379 | Dic10 | — | 2 | 1 | no | — |
| 380 | Dic10 | — | 2 | 1 | no | — |
| 381 | Dic10 | — | 2 | 1 | no | — |
| 382 | Dic10 | — | 2 | 1 | no | — |
| 383 | Dic10 | — | 4 | 2 | no | — |
| 384 | Dic10 | — | 4 | 2 | no | — |
| 385 | Dic10 | — | 8 | 1 | no | — |
| 386 | C5×C8 | — | 2 | 2 | no | — |
| 387 | C5×C8 | — | 4 | 1 | no | — |
| 388 | C5×C8 | — | 4 | 1 | no | — |
| 389 | #168 | — | 4 | 1 | no | — |
| 390 | #168 | — | 4 | 1 | no | — |
| 391 | #168 | — | 4 | 1 | no | — |
| 392 | C2×#41 | — | 10 | 1 | no | — |
| 393 | C22×Q8 | — | 5 | 1 | no | — |
| 394 | C2×Q16 | — | 2 | 1 | no | — |
| 395 | C2×Q16 | — | 10 | 1 | no | — |
| 396 | C2×SD16 | — | 10 | 2 | no | — |
| 397 | C2×M16 | — | 10 | 1 | no | — |
| 398 | C4⋊Q8 | — | 2 | 1 | no | — |
| 399 | C4⋊Q8 | — | 5 | 1 | no | — |
| 400 | C4⋊Q8 | — | 5 | 1 | no | — |
| 401 | C4⋊Q8 | — | 5 | 1 | no | — |
| 402 | C4⋊Q8 | — | 10 | 1 | no | — |
| 403 | C4⋊Q8 | C22×D5 | 1 | 1 | yes | characteristic |
| 404 | C4⋊Q8 | C22×D5 | 1 | 1 | yes | characteristic |
| 405 | #127 | — | 5 | 1 | no | — |
| 406 | #126 | — | 10 | 2 | no | — |
| 407 | #126 | — | 10 | 2 | no | — |
| 408 | #126 | — | 10 | 2 | no | — |
| 409 | #126 | — | 10 | 2 | no | — |
| 410 | #125 | — | 2 | 1 | no | — |
| 411 | #125 | — | 2 | 2 | no | — |
| 412 | #125 | — | 10 | 1 | no | — |
| 413 | #125 | — | 10 | 1 | no | — |
| 414 | #125 | — | 10 | 1 | no | — |
| 415 | #125 | — | 10 | 2 | no | — |
| 416 | #124 | — | 10 | 1 | no | — |
| 417 | #124 | — | 10 | 1 | no | — |
| 418 | #124 | — | 10 | 1 | no | — |
| 419 | #124 | — | 10 | 1 | no | — |
| 420 | #124 | — | 10 | 1 | no | — |
| 421 | #123 | — | 10 | 2 | no | — |
| 422 | #123 | — | 10 | 2 | no | — |
| 423 | #123 | — | 10 | 2 | no | — |
| 424 | #123 | — | 10 | 2 | no | — |
| 425 | C22⋊Q8 | — | 5 | 1 | no | — |
| 426 | C22⋊Q8 | — | 5 | 1 | no | — |
| 427 | C22⋊Q8 | — | 10 | 1 | no | — |
| 428 | C22⋊Q8 | — | 10 | 2 | no | — |
| 429 | C22⋊Q8 | — | 10 | 2 | no | — |
| 430 | C22⋊Q8 | — | 10 | 2 | no | — |
| 431 | C22⋊Q8 | — | 10 | 2 | no | — |
| 432 | C22⋊Q8 | — | 10 | 1 | no | — |
| 433 | C22⋊Q8 | — | 10 | 1 | no | — |
| 434 | #121 | — | 5 | 2 | no | — |
| 435 | #121 | — | 10 | 1 | no | — |
| 436 | C4×Q8 | — | 2 | 1 | no | — |
| 437 | C4×Q8 | — | 2 | 1 | no | — |
| 438 | C4×Q8 | — | 5 | 1 | no | — |
| 439 | C4×Q8 | — | 5 | 1 | no | — |
| 440 | C4×Q8 | — | 5 | 1 | no | — |
| 441 | C4×Q8 | — | 5 | 1 | no | — |
| 442 | C4×Q8 | — | 10 | 1 | no | — |
| 443 | C4×Q8 | — | 10 | 1 | no | — |
| 444 | C4×Q8 | — | 10 | 1 | no | — |
| 445 | C4×Q8 | — | 10 | 1 | no | — |
| 446 | C4×Q8 | — | 10 | 1 | no | — |
| 447 | C4×Q8 | — | 10 | 1 | no | — |
| 448 | C4×Q8 | — | 10 | 1 | no | — |
| 449 | C4×Q8 | C22×D5 | 1 | 1 | yes | characteristic |
| 450 | C4×Q8 | C22×D5 | 1 | 1 | yes | characteristic |
| 451 | C4×D4 | — | 5 | 2 | no | — |
| 452 | C4×D4 | — | 10 | 1 | no | — |
| 453 | C4×D4 | — | 10 | 1 | no | — |
| 454 | C4×D4 | — | 10 | 2 | no | — |
| 455 | C4×D4 | — | 10 | 1 | no | — |
| 456 | C4×D4 | — | 10 | 2 | no | — |
| 457 | C4×D4 | — | 10 | 1 | no | — |
| 458 | C4×D4 | — | 10 | 1 | no | — |
| 459 | #117 | — | 10 | 1 | no | — |
| 460 | #117 | — | 10 | 2 | no | — |
| 461 | #117 | — | 10 | 2 | no | — |
| 462 | #117 | — | 10 | 2 | no | — |
| 463 | #117 | — | 10 | 1 | no | — |
| 464 | C2×C4⋊C4 | — | 5 | 1 | no | — |
| 465 | C2×C4⋊C4 | — | 10 | 1 | no | — |
| 466 | C2×C4⋊C4 | — | 10 | 2 | no | — |
| 467 | C2×C42 | — | 5 | 1 | no | — |
| 468 | C2×C42 | — | 10 | 1 | no | — |
| 469 | #107 | — | 2 | 2 | no | — |
| 470 | #107 | — | 10 | 1 | no | — |
| 471 | #107 | — | 10 | 1 | no | — |
| 472 | #107 | — | 10 | 1 | no | — |
| 473 | #107 | — | 10 | 1 | no | — |
| 474 | #106 | — | 2 | 1 | no | — |
| 475 | #106 | — | 10 | 1 | no | — |
| 476 | C4⋊C8 | — | 5 | 1 | no | — |
| 477 | C4⋊C8 | — | 5 | 1 | no | — |
| 478 | C4⋊C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 479 | C4⋊C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 480 | #103 | — | 2 | 1 | no | — |
| 481 | #103 | — | 2 | 1 | no | — |
| 482 | #103 | — | 10 | 1 | no | — |
| 483 | #103 | — | 10 | 1 | no | — |
| 484 | #103 | — | 10 | 1 | no | — |
| 485 | #103 | — | 10 | 1 | no | — |
| 486 | #103 | — | 10 | 1 | no | — |
| 487 | #103 | — | 10 | 1 | no | — |
| 488 | #103 | — | 10 | 2 | no | — |
| 489 | #102 | — | 10 | 2 | no | — |
| 490 | C22⋊C8 | — | 10 | 1 | no | — |
| 491 | C22⋊C8 | — | 10 | 1 | no | — |
| 492 | #97 | — | 10 | 1 | no | — |
| 493 | #97 | — | 10 | 1 | no | — |
| 494 | C4×C8 | — | 5 | 1 | no | — |
| 495 | C4×C8 | — | 10 | 1 | no | — |
| 496 | C4×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 497 | C22×C5 | C2×#120 | 1 | 1 | yes | characteristic |
| 498 | C2×D5 | — | 2 | 1 | no | — |
| 499 | C2×D5 | — | 2 | 1 | no | — |
| 500 | C2×D5 | — | 2 | 1 | no | — |
| 501 | C2×D5 | — | 4 | 2 | no | — |
| 502 | C2×D5 | — | 4 | 2 | no | — |
| 503 | C2×D5 | — | 4 | 2 | no | — |
| 504 | C4×C5 | — | 2 | 1 | no | — |
| 505 | C4×C5 | — | 4 | 1 | no | — |
| 506 | C4×C5 | — | 4 | 2 | no | — |
| 507 | C4×C5 | — | 4 | 1 | no | — |
| 508 | C4×C5 | — | 4 | 1 | no | — |
| 509 | C4×C5 | — | 4 | 1 | no | — |
| 510 | C4×C5 | — | 8 | 1 | no | — |
| 511 | C4×C5 | #575 | 1 | 1 | yes | characteristic |
| 512 | C4×C5 | #575 | 1 | 1 | yes | characteristic |
| 513 | C4×C5 | #578 | 1 | 1 | yes | characteristic |
| 514 | C4×C5 | #578 | 1 | 1 | yes | characteristic |
| 515 | Dic5 | — | 2 | 1 | no | — |
| 516 | Dic5 | — | 2 | 1 | no | — |
| 517 | Dic5 | — | 2 | 1 | no | — |
| 518 | Dic5 | — | 4 | 1 | no | — |
| 519 | Dic5 | — | 4 | 1 | no | — |
| 520 | Dic5 | — | 4 | 1 | no | — |
| 521 | Dic5 | — | 4 | 1 | no | — |
| 522 | Dic5 | — | 8 | 1 | no | — |
| 523 | #41 | — | 20 | 2 | no | — |
| 524 | #41 | — | 20 | 2 | no | — |
| 525 | C2×Q8 | — | 2 | 1 | no | — |
| 526 | C2×Q8 | — | 2 | 1 | no | — |
| 527 | C2×Q8 | — | 5 | 1 | no | — |
| 528 | C2×Q8 | — | 5 | 1 | no | — |
| 529 | C2×Q8 | — | 10 | 1 | no | — |
| 530 | C2×Q8 | — | 10 | 1 | no | — |
| 531 | C2×Q8 | — | 10 | 1 | no | — |
| 532 | C2×Q8 | — | 20 | 1 | no | — |
| 533 | C2×Q8 | — | 20 | 1 | no | — |
| 534 | C2×Q8 | D4×D5 | 1 | 1 | yes | characteristic |
| 535 | C2×Q8 | D4×D5 | 1 | 1 | yes | characteristic |
| 536 | C2×D4 | — | 5 | 2 | no | — |
| 537 | C2×D4 | — | 10 | 2 | no | — |
| 538 | C2×D4 | — | 10 | 1 | no | — |
| 539 | C2×D4 | — | 10 | 1 | no | — |
| 540 | C22×C4 | — | 5 | 1 | no | — |
| 541 | C22×C4 | — | 5 | 1 | no | — |
| 542 | C22×C4 | — | 5 | 1 | no | — |
| 543 | C22×C4 | — | 10 | 2 | no | — |
| 544 | C22×C4 | — | 10 | 1 | no | — |
| 545 | C22×C4 | — | 10 | 1 | no | — |
| 546 | C22×C4 | — | 10 | 2 | no | — |
| 547 | C22×C4 | — | 10 | 2 | no | — |
| 548 | Q16 | — | 4 | 2 | no | — |
| 549 | Q16 | — | 20 | 2 | no | — |
| 550 | SD16 | — | 20 | 4 | no | — |
| 551 | M16 | — | 20 | 2 | no | — |
| 552 | C2×C8 | — | 2 | 1 | no | — |
| 553 | C2×C8 | — | 2 | 1 | no | — |
| 554 | C2×C8 | — | 2 | 1 | no | — |
| 555 | C2×C8 | — | 10 | 1 | no | — |
| 556 | C2×C8 | — | 10 | 1 | no | — |
| 557 | C2×C8 | — | 10 | 1 | no | — |
| 558 | C4⋊C4 | — | 2 | 2 | no | — |
| 559 | C4⋊C4 | — | 2 | 2 | no | — |
| 560 | C4⋊C4 | — | 2 | 2 | no | — |
| 561 | C4⋊C4 | — | 2 | 1 | no | — |
| 562 | C4⋊C4 | — | 2 | 1 | no | — |
| 563 | C4⋊C4 | — | 2 | 1 | no | — |
| 564 | C4⋊C4 | — | 2 | 1 | no | — |
| 565 | C4⋊C4 | — | 2 | 1 | no | — |
| 566 | C4⋊C4 | — | 5 | 1 | no | — |
| 567 | C4⋊C4 | — | 5 | 1 | no | — |
| 568 | C4⋊C4 | — | 10 | 1 | no | — |
| 569 | C4⋊C4 | — | 10 | 1 | no | — |
| 570 | C4⋊C4 | — | 10 | 1 | no | — |
| 571 | C4⋊C4 | — | 10 | 1 | no | — |
| 572 | C4⋊C4 | — | 10 | 1 | no | — |
| 573 | C4⋊C4 | — | 10 | 1 | no | — |
| 574 | C4⋊C4 | — | 10 | 1 | no | — |
| 575 | C4⋊C4 | — | 10 | 1 | no | — |
| 576 | C4⋊C4 | — | 10 | 2 | no | — |
| 577 | C4⋊C4 | — | 10 | 2 | no | — |
| 578 | C4⋊C4 | — | 10 | 2 | no | — |
| 579 | C4⋊C4 | — | 10 | 1 | no | — |
| 580 | C4⋊C4 | — | 10 | 1 | no | — |
| 581 | C4⋊C4 | — | 10 | 1 | no | — |
| 582 | C4⋊C4 | — | 10 | 1 | no | — |
| 583 | C4⋊C4 | — | 20 | 1 | no | — |
| 584 | C4⋊C4 | — | 20 | 1 | no | — |
| 585 | C4⋊C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 586 | C4⋊C4 | D4×D5 | 1 | 2 | yes | — |
| 587 | C4⋊C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 588 | C22⋊C4 | — | 10 | 2 | no | — |
| 589 | C22⋊C4 | — | 10 | 2 | no | — |
| 590 | C22⋊C4 | — | 10 | 1 | no | — |
| 591 | C22⋊C4 | — | 10 | 1 | no | — |
| 592 | C22⋊C4 | — | 10 | 2 | no | — |
| 593 | C22⋊C4 | — | 10 | 2 | no | — |
| 594 | C22⋊C4 | — | 10 | 2 | no | — |
| 595 | C22⋊C4 | — | 10 | 2 | no | — |
| 596 | C22⋊C4 | — | 10 | 2 | no | — |
| 597 | C22⋊C4 | — | 10 | 2 | no | — |
| 598 | C22⋊C4 | — | 20 | 1 | no | — |
| 599 | C42 | — | 2 | 2 | no | — |
| 600 | C42 | — | 2 | 1 | no | — |
| 601 | C42 | — | 2 | 1 | no | — |
| 602 | C42 | — | 5 | 1 | no | — |
| 603 | C42 | — | 5 | 1 | no | — |
| 604 | C42 | — | 5 | 1 | no | — |
| 605 | C42 | — | 10 | 1 | no | — |
| 606 | C42 | — | 10 | 1 | no | — |
| 607 | C42 | — | 10 | 2 | no | — |
| 608 | C42 | — | 10 | 1 | no | — |
| 609 | C42 | — | 10 | 1 | no | — |
| 610 | C42 | — | 20 | 1 | no | — |
| 611 | C42 | C23×D5 | 1 | 1 | yes | characteristic |
| 612 | C2×C5 | #3005 | 1 | 1 | yes | characteristic |
| 613 | C2×C5 | #3011 | 1 | 1 | yes | characteristic |
| 614 | C2×C5 | #3018 | 1 | 1 | yes | characteristic |
| 615 | D5 | — | 4 | 1 | no | — |
| 616 | D5 | — | 8 | 2 | no | — |
| 617 | C23 | — | 5 | 1 | no | — |
| 618 | C23 | — | 10 | 2 | no | — |
| 619 | Q8 | — | 2 | 1 | no | — |
| 620 | Q8 | — | 2 | 1 | no | — |
| 621 | Q8 | — | 2 | 1 | no | — |
| 622 | Q8 | — | 2 | 1 | no | — |
| 623 | Q8 | — | 4 | 1 | no | — |
| 624 | Q8 | — | 4 | 1 | no | — |
| 625 | Q8 | — | 4 | 1 | no | — |
| 626 | Q8 | — | 4 | 1 | no | — |
| 627 | Q8 | — | 10 | 1 | no | — |
| 628 | Q8 | — | 10 | 1 | no | — |
| 629 | Q8 | — | 10 | 1 | no | — |
| 630 | Q8 | — | 10 | 1 | no | — |
| 631 | Q8 | — | 20 | 2 | no | — |
| 632 | Q8 | — | 20 | 2 | no | — |
| 633 | Q8 | — | 40 | 1 | no | — |
| 634 | D4 | — | 20 | 2 | no | — |
| 635 | D4 | — | 20 | 4 | no | — |
| 636 | D4 | — | 20 | 1 | no | — |
| 637 | D4 | — | 20 | 1 | no | — |
| 638 | D4 | — | 20 | 1 | no | — |
| 639 | D4 | — | 20 | 1 | no | — |
| 640 | C2×C4 | — | 2 | 1 | no | — |
| 641 | C2×C4 | — | 2 | 1 | no | — |
| 642 | C2×C4 | — | 2 | 1 | no | — |
| 643 | C2×C4 | — | 2 | 2 | no | — |
| 644 | C2×C4 | — | 2 | 1 | no | — |
| 645 | C2×C4 | — | 4 | 1 | no | — |
| 646 | C2×C4 | — | 5 | 1 | no | — |
| 647 | C2×C4 | — | 5 | 1 | no | — |
| 648 | C2×C4 | — | 5 | 1 | no | — |
| 649 | C2×C4 | — | 10 | 1 | no | — |
| 650 | C2×C4 | — | 10 | 1 | no | — |
| 651 | C2×C4 | — | 10 | 1 | no | — |
| 652 | C2×C4 | — | 10 | 1 | no | — |
| 653 | C2×C4 | — | 10 | 1 | no | — |
| 654 | C2×C4 | — | 10 | 1 | no | — |
| 655 | C2×C4 | — | 10 | 1 | no | — |
| 656 | C2×C4 | — | 10 | 1 | no | — |
| 657 | C2×C4 | — | 20 | 1 | no | — |
| 658 | C2×C4 | — | 20 | 4 | no | — |
| 659 | C2×C4 | — | 20 | 2 | no | — |
| 660 | C2×C4 | — | 20 | 1 | no | — |
| 661 | C2×C4 | — | 40 | 1 | no | — |
| 662 | C2×C4 | — | 40 | 2 | no | — |
| 663 | C2×C4 | — | 40 | 2 | no | — |
| 664 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 665 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 666 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 667 | C8 | — | 2 | 2 | no | — |
| 668 | C8 | — | 4 | 1 | no | — |
| 669 | C8 | — | 4 | 1 | no | — |
| 670 | C8 | — | 20 | 1 | no | — |
| 671 | C8 | — | 20 | 1 | no | — |
| 672 | C8 | — | 20 | 1 | no | — |
| 673 | C5 | #18603 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 674 | C22 | — | 10 | 1 | no | — |
| 675 | C22 | — | 10 | 1 | no | — |
| 676 | C22 | — | 10 | 1 | no | — |
| 677 | C22 | — | 20 | 2 | no | — |
| 678 | C22 | — | 20 | 2 | no | — |
| 679 | C22 | — | 20 | 2 | no | — |
| 680 | C22 | D5×#120 | 1 | 1 | yes | characteristic |
| 681 | C4 | — | 2 | 1 | no | — |
| 682 | C4 | — | 4 | 1 | no | — |
| 683 | C4 | — | 4 | 1 | no | — |
| 684 | C4 | — | 4 | 2 | no | — |
| 685 | C4 | — | 4 | 1 | no | — |
| 686 | C4 | — | 4 | 1 | no | — |
| 687 | C4 | — | 8 | 1 | no | — |
| 688 | C4 | — | 10 | 1 | no | — |
| 689 | C4 | — | 10 | 1 | no | — |
| 690 | C4 | — | 10 | 1 | no | — |
| 691 | C4 | — | 20 | 1 | no | — |
| 692 | C4 | — | 20 | 1 | no | — |
| 693 | C4 | — | 20 | 1 | no | — |
| 694 | C4 | — | 20 | 1 | no | — |
| 695 | C4 | — | 40 | 1 | no | — |
| 696 | C4 | #66100 | 1 | 1 | yes | characteristic |
| 697 | C4 | #66102 | 1 | 1 | yes | characteristic |
| 698 | C4 | #66107 | 1 | 1 | yes | characteristic |
| 699 | C4 | #66113 | 1 | 1 | yes | characteristic |
| 700 | C2 | — | 20 | 1 | no | — |
| 701 | C2 | — | 40 | 2 | no | — |
| 702 | C2 | #10611814 | 1 | 1 | yes | characteristic |
| 703 | C2 | #10611916 | 1 | 1 | yes | characteristic |
| 704 | C2 | #10612029 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #10612748 | C2 | semidirect |
| 4. #10612187 | C2 | semidirect |
| 5. C5×#1648 | C2 | semidirect |
| 6. #10602729 | C2 | semidirect |
| 7. #10602168 | C2 | semidirect |
| 8. #10601921 | C2 | semidirect |
| 9. #10601853 | C2 | semidirect |
| 10. #10599251 | C2 | semidirect |
| 12. #10599053 | C2 | semidirect |
| 13. #10599053 | C2 | semidirect |
| 14. #10599032 | C2 | semidirect |
| 15. #10599028 | C2 | semidirect |
| 182. #1648 | D5 | semidirect |
| 673. C5 | #18603 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10618934 | 2 |
| #10613667 | 2 |
| #10612748 | 2 |
| #10612187 | 2 |
| C5×#1648 | 2 |
| #10602729 | 2 |
| #10602168 | 2 |
| #10601921 | 2 |
| #10601853 | 2 |
| #10599251 | 2 |
| #10599219 | 2 |
| #10599053 | 2 |
| #10599032 | 2 |
| #10599028 | 2 |
| #18603 | 5 |