Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
992 conjugacy classes of subgroups.
The subgroup lattice has 540 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10618153 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C5×#3216 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10615089 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10615066 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10602591 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10602122 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #10602037 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #10601604 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #10601599 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C5×#533 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | C5×#532 | C22 | 1 | 1 | yes | characteristic |
| 12 | #66164 | — | 2 | 2 | no | — |
| 13 | #66068 | — | 2 | 1 | no | — |
| 14 | #66051 | — | 2 | 1 | no | — |
| 15 | #66017 | C22 | 1 | 4 | yes | — |
| 16 | #65941 | — | 2 | 2 | no | — |
| 17 | #65941 | — | 2 | 2 | no | — |
| 18 | #65897 | — | 2 | 1 | no | — |
| 19 | #65897 | — | 2 | 1 | no | — |
| 20 | D4×D20 | — | 2 | 1 | no | — |
| 21 | D4×D20 | — | 2 | 1 | no | — |
| 22 | #65811 | C22 | 1 | 1 | yes | characteristic |
| 23 | #65811 | C22 | 1 | 1 | yes | characteristic |
| 24 | C5×#497 | C22 | 1 | 2 | yes | complemented |
| 25 | C5×#489 | C22 | 1 | 2 | yes | complemented |
| 26 | C5×#462 | — | 2 | 1 | no | — |
| 27 | C5×#460 | — | 2 | 1 | no | — |
| 28 | C5×#452 | — | 2 | 2 | no | — |
| 29 | C5×#432 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | #65378 | C22 | 1 | 2 | yes | complemented |
| 31 | #65378 | C22 | 1 | 2 | yes | complemented |
| 32 | #65378 | C22 | 1 | 2 | yes | complemented |
| 33 | #65375 | C22 | 1 | 2 | yes | complemented |
| 34 | #65358 | — | 2 | 1 | no | — |
| 35 | #65356 | — | 2 | 1 | no | — |
| 36 | #65336 | — | 2 | 2 | no | — |
| 37 | #65320 | — | 2 | 1 | no | — |
| 38 | #65316 | — | 2 | 1 | no | — |
| 39 | #65291 | — | 2 | 2 | no | — |
| 40 | #65215 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | C2×#3935 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | #64760 | C22 | 1 | 4 | yes | complemented |
| 43 | #64684 | C22 | 1 | 4 | yes | complemented |
| 44 | #64684 | C22 | 1 | 4 | yes | complemented |
| 45 | #19056 | — | 5 | 1 | no | maximal, Sylow |
| 46 | C2×C5×#41 | D4 | 1 | 2 | yes | — |
| 47 | C2×D4×D5 | — | 2 | 2 | no | — |
| 48 | C2×D4×D5 | — | 2 | 2 | no | — |
| 49 | C2×#709 | D4 | 1 | 2 | yes | — |
| 50 | C2×#709 | D4 | 1 | 2 | yes | — |
| 51 | C22×D20 | — | 2 | 2 | no | — |
| 52 | C2×C5×Q16 | — | 2 | 2 | no | — |
| 53 | C2×C5×SD16 | — | 2 | 2 | no | — |
| 54 | C5×C4⋊Q8 | D4 | 1 | 1 | yes | characteristic |
| 55 | C5×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 56 | C5×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 57 | C5×#127 | D4 | 1 | 1 | yes | characteristic |
| 58 | C5×#125 | — | 2 | 1 | no | — |
| 59 | C5×#124 | C23 | 1 | 2 | yes | — |
| 60 | C5×C22⋊Q8 | — | 2 | 1 | no | — |
| 61 | C5×C22⋊Q8 | — | 2 | 1 | no | — |
| 62 | C5×#121 | — | 2 | 1 | no | — |
| 63 | C5×#121 | — | 2 | 1 | no | — |
| 64 | C4×C5×Q8 | — | 2 | 1 | no | — |
| 65 | C4×C5×Q8 | — | 2 | 1 | no | — |
| 66 | C4×C5×D4 | — | 2 | 1 | no | — |
| 67 | C4×C5×D4 | — | 2 | 1 | no | — |
| 68 | C5×#117 | — | 2 | 1 | no | — |
| 69 | C2×C42×C5 | C23 | 1 | 1 | yes | characteristic |
| 70 | #4093 | — | 2 | 4 | no | — |
| 71 | C2×#689 | — | 2 | 2 | no | — |
| 72 | C2×#688 | — | 2 | 2 | no | — |
| 73 | #4086 | — | 2 | 4 | no | — |
| 74 | #4084 | — | 2 | 2 | no | — |
| 75 | #4084 | — | 2 | 2 | no | — |
| 76 | #4083 | — | 2 | 4 | no | — |
| 77 | #4083 | — | 2 | 4 | no | — |
| 78 | #4076 | — | 2 | 2 | no | — |
| 79 | #4076 | — | 2 | 2 | no | — |
| 80 | #4076 | — | 2 | 1 | no | — |
| 81 | #4076 | — | 2 | 1 | no | — |
| 82 | #4076 | — | 2 | 1 | no | — |
| 83 | #4076 | — | 2 | 1 | no | — |
| 84 | #4072 | — | 2 | 2 | no | — |
| 85 | C22×#168 | — | 2 | 1 | no | — |
| 86 | #4041 | — | 2 | 2 | no | — |
| 87 | #4041 | — | 2 | 2 | no | — |
| 88 | #4038 | — | 2 | 2 | no | — |
| 89 | #4038 | — | 2 | 2 | no | — |
| 90 | #4031 | — | 2 | 4 | no | — |
| 91 | #4031 | — | 2 | 4 | no | — |
| 92 | #4028 | — | 2 | 4 | no | — |
| 93 | #4028 | — | 2 | 4 | no | — |
| 94 | #4021 | C23 | 1 | 2 | yes | — |
| 95 | #4021 | C23 | 1 | 2 | yes | — |
| 96 | #4020 | D4 | 1 | 1 | yes | characteristic |
| 97 | #4020 | D4 | 1 | 1 | yes | characteristic |
| 98 | C4×D20 | — | 2 | 1 | no | — |
| 99 | C4×D20 | — | 2 | 1 | no | — |
| 100 | C4×D20 | — | 2 | 1 | no | — |
| 101 | C4×D20 | — | 2 | 1 | no | — |
| 102 | #4015 | D4 | 1 | 1 | yes | characteristic |
| 103 | #4015 | D4 | 1 | 1 | yes | characteristic |
| 104 | C5×C4⋊C8 | — | 2 | 1 | no | — |
| 105 | C5×#103 | — | 2 | 2 | no | — |
| 106 | C5×#102 | — | 2 | 2 | no | — |
| 107 | C5×C22⋊C8 | — | 2 | 1 | no | — |
| 108 | C5×#97 | C23 | 1 | 2 | yes | — |
| 109 | C22⋊#168 | — | 2 | 1 | no | — |
| 110 | #3942 | — | 2 | 2 | no | — |
| 111 | #3942 | — | 2 | 2 | no | — |
| 112 | #3942 | — | 2 | 2 | no | — |
| 113 | #3941 | — | 2 | 2 | no | — |
| 114 | #3941 | — | 2 | 2 | no | — |
| 115 | #3941 | — | 2 | 2 | no | — |
| 116 | C4⋊#168 | — | 2 | 1 | no | — |
| 117 | #3935 | — | 2 | 1 | no | — |
| 118 | #3935 | C23 | 1 | 2 | yes | — |
| 119 | #3935 | C23 | 1 | 2 | yes | — |
| 120 | #3549 | — | 5 | 1 | no | — |
| 121 | #3216 | — | 5 | 1 | no | — |
| 122 | #3216 | D5 | 1 | 1 | yes | characteristic, complemented |
| 123 | #3135 | — | 5 | 1 | no | — |
| 124 | #1659 | — | 5 | 4 | no | — |
| 125 | #1659 | — | 5 | 4 | no | — |
| 126 | #1536 | — | 5 | 1 | no | — |
| 127 | #1530 | — | 5 | 1 | no | — |
| 128 | #1530 | — | 5 | 1 | no | — |
| 129 | C23×D5 | — | 2 | 4 | no | — |
| 130 | C5×#41 | — | 8 | 2 | no | — |
| 131 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 132 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 133 | C2×C5×Q8 | C2×D4 | 1 | 2 | yes | — |
| 134 | C2×C5×D4 | — | 2 | 2 | no | — |
| 135 | C2×C5×D4 | — | 2 | 1 | no | — |
| 136 | C2×C5×D4 | — | 2 | 1 | no | — |
| 137 | C2×C5×D4 | C2×D4 | 1 | 2 | yes | — |
| 138 | C22×C4×C5 | — | 2 | 2 | no | — |
| 139 | C22×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 140 | C22×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 141 | C22×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 142 | C2×C22⋊D5 | — | 2 | 4 | no | — |
| 143 | C2×C22⋊D5 | — | 2 | 4 | no | — |
| 144 | C2×C22⋊D5 | — | 2 | 2 | no | — |
| 145 | C2×C22⋊D5 | — | 2 | 2 | no | — |
| 146 | D4×D5 | — | 8 | 4 | no | — |
| 147 | D4×D5 | — | 8 | 4 | no | — |
| 148 | #709 | — | 4 | 4 | no | — |
| 149 | #709 | — | 8 | 2 | no | — |
| 150 | C2×D20 | — | 2 | 1 | no | — |
| 151 | C2×D20 | — | 2 | 1 | no | — |
| 152 | C2×D20 | — | 2 | 1 | no | — |
| 153 | C2×D20 | — | 2 | 1 | no | — |
| 154 | C2×D20 | — | 2 | 4 | no | — |
| 155 | C2×D20 | — | 8 | 4 | no | — |
| 156 | C2×D20 | C2×D4 | 1 | 2 | yes | — |
| 157 | C2×D20 | C2×D4 | 1 | 2 | yes | — |
| 158 | C2×C4×D5 | — | 2 | 2 | no | — |
| 159 | C2×C4×D5 | — | 2 | 2 | no | — |
| 160 | C2×Dic10 | C2×D4 | 1 | 2 | yes | — |
| 161 | C2×Dic10 | C2×D4 | 1 | 2 | yes | — |
| 162 | C5×Q16 | — | 8 | 2 | no | — |
| 163 | C5×SD16 | — | 8 | 2 | no | — |
| 164 | C2×C5×C8 | — | 2 | 2 | no | — |
| 165 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 166 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 167 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 168 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 169 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 170 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 171 | C5×C4⋊C4 | — | 4 | 1 | no | — |
| 172 | C5×C4⋊C4 | — | 4 | 1 | no | — |
| 173 | C5×C22⋊C4 | — | 2 | 2 | no | — |
| 174 | C5×C22⋊C4 | — | 2 | 2 | no | — |
| 175 | C5×C22⋊C4 | — | 4 | 1 | no | — |
| 176 | C42×C5 | — | 4 | 1 | no | — |
| 177 | C42×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 178 | C42×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 179 | C42×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 180 | C42×C5 | C24 | 1 | 1 | yes | characteristic |
| 181 | C22⋊Dic5 | — | 2 | 4 | no | — |
| 182 | #689 | — | 8 | 2 | no | — |
| 183 | #688 | — | 8 | 2 | no | — |
| 184 | #685 | — | 2 | 4 | no | — |
| 185 | #685 | — | 2 | 4 | no | — |
| 186 | #685 | — | 2 | 2 | no | — |
| 187 | #685 | — | 2 | 2 | no | — |
| 188 | #685 | — | 2 | 2 | no | — |
| 189 | #685 | — | 2 | 2 | no | — |
| 190 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 191 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 192 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 193 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 194 | C4×Dic5 | — | 2 | 4 | no | — |
| 195 | C2×#168 | — | 2 | 2 | no | — |
| 196 | C2×#168 | — | 2 | 2 | no | — |
| 197 | C2×#168 | — | 4 | 2 | no | — |
| 198 | H(3,𝔽4) | — | 5 | 4 | no | — |
| 199 | #555 | — | 10 | 1 | no | — |
| 200 | #555 | — | 10 | 1 | no | — |
| 201 | #555 | — | 10 | 1 | no | — |
| 202 | D42 | — | 10 | 1 | no | — |
| 203 | D42 | — | 10 | 1 | no | — |
| 204 | D42 | — | 10 | 1 | no | — |
| 205 | #535 | — | 10 | 2 | no | — |
| 206 | #535 | — | 10 | 2 | no | — |
| 207 | #535 | — | 10 | 2 | no | — |
| 208 | #533 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 209 | #532 | — | 5 | 1 | no | — |
| 210 | #532 | — | 5 | 1 | no | — |
| 211 | #532 | C2×D5 | 1 | 1 | yes | characteristic |
| 212 | #497 | — | 5 | 2 | no | — |
| 213 | #497 | C2×D5 | 1 | 2 | yes | complemented |
| 214 | #491 | — | 10 | 1 | no | — |
| 215 | #490 | — | 10 | 1 | no | — |
| 216 | #489 | — | 5 | 2 | no | — |
| 217 | #489 | — | 5 | 2 | no | — |
| 218 | #489 | — | 5 | 2 | no | — |
| 219 | #489 | C2×D5 | 1 | 2 | yes | complemented |
| 220 | #462 | — | 2 | 1 | no | — |
| 221 | #462 | — | 10 | 1 | no | — |
| 222 | #460 | — | 2 | 1 | no | — |
| 223 | #460 | — | 10 | 1 | no | — |
| 224 | #452 | — | 2 | 2 | no | — |
| 225 | #452 | — | 10 | 2 | no | — |
| 226 | #432 | — | 5 | 1 | no | — |
| 227 | #432 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 228 | #416 | — | 10 | 2 | no | — |
| 229 | C2×#97 | — | 5 | 1 | no | — |
| 230 | #329 | — | 5 | 4 | no | — |
| 231 | #329 | — | 5 | 4 | no | — |
| 232 | #329 | — | 5 | 4 | no | — |
| 233 | C23×C5 | — | 2 | 2 | no | — |
| 234 | C23×C5 | #120 | 1 | 1 | yes | characteristic |
| 235 | C22×D5 | — | 2 | 2 | no | — |
| 236 | C22×D5 | — | 2 | 2 | no | — |
| 237 | C22×D5 | — | 8 | 4 | no | — |
| 238 | C22×D5 | — | 8 | 4 | no | — |
| 239 | C22×D5 | — | 8 | 4 | no | — |
| 240 | C5×Q8 | — | 4 | 2 | no | — |
| 241 | C5×Q8 | — | 4 | 1 | no | — |
| 242 | C5×Q8 | — | 4 | 1 | no | — |
| 243 | C5×Q8 | — | 4 | 1 | no | — |
| 244 | C5×Q8 | — | 4 | 1 | no | — |
| 245 | C5×D4 | — | 4 | 2 | no | — |
| 246 | C5×D4 | — | 4 | 2 | no | — |
| 247 | C5×D4 | — | 4 | 2 | no | — |
| 248 | C5×D4 | — | 8 | 2 | no | — |
| 249 | C2×C4×C5 | — | 2 | 2 | no | — |
| 250 | C2×C4×C5 | — | 2 | 2 | no | — |
| 251 | C2×C4×C5 | — | 4 | 1 | no | — |
| 252 | C2×C4×C5 | — | 4 | 1 | no | — |
| 253 | C2×C4×C5 | — | 4 | 4 | no | — |
| 254 | C2×C4×C5 | — | 4 | 1 | no | — |
| 255 | C2×C4×C5 | — | 4 | 1 | no | — |
| 256 | C2×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 257 | C2×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 258 | C2×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 259 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 260 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 261 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 262 | C22⋊D5 | — | 8 | 2 | no | — |
| 263 | C22⋊D5 | — | 8 | 2 | no | — |
| 264 | C22⋊D5 | — | 8 | 4 | no | — |
| 265 | C22⋊D5 | — | 8 | 4 | no | — |
| 266 | C2×Dic5 | — | 2 | 2 | no | — |
| 267 | C2×Dic5 | — | 2 | 2 | no | — |
| 268 | D20 | — | 4 | 2 | no | — |
| 269 | D20 | — | 4 | 2 | no | — |
| 270 | D20 | — | 4 | 2 | no | — |
| 271 | D20 | — | 4 | 2 | no | — |
| 272 | D20 | — | 4 | 2 | no | — |
| 273 | D20 | — | 4 | 2 | no | — |
| 274 | D20 | — | 8 | 4 | no | — |
| 275 | C4×D5 | — | 4 | 4 | no | — |
| 276 | C4×D5 | — | 4 | 4 | no | — |
| 277 | Dic10 | — | 4 | 2 | no | — |
| 278 | Dic10 | — | 4 | 2 | no | — |
| 279 | C5×C8 | — | 4 | 2 | no | — |
| 280 | #168 | — | 4 | 2 | no | — |
| 281 | #168 | — | 4 | 2 | no | — |
| 282 | C2×#41 | — | 5 | 2 | no | — |
| 283 | C2×#41 | — | 5 | 2 | no | — |
| 284 | C2×#41 | C22⋊D5 | 1 | 2 | yes | — |
| 285 | C22×D4 | — | 10 | 2 | no | — |
| 286 | C22×D4 | — | 10 | 2 | no | — |
| 287 | C22×D4 | — | 10 | 2 | no | — |
| 288 | C2×Q16 | — | 2 | 2 | no | — |
| 289 | C2×Q16 | — | 10 | 2 | no | — |
| 290 | C2×SD16 | — | 2 | 2 | no | — |
| 291 | C2×SD16 | — | 10 | 2 | no | — |
| 292 | C22×C8 | — | 10 | 1 | no | — |
| 293 | C4⋊Q8 | — | 5 | 1 | no | — |
| 294 | C4⋊Q8 | — | 5 | 1 | no | — |
| 295 | C4⋊Q8 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 296 | C4⋊Q8 | C22×D5 | 1 | 1 | yes | characteristic |
| 297 | C4⋊Q8 | C22×D5 | 1 | 1 | yes | characteristic |
| 298 | #127 | — | 5 | 1 | no | — |
| 299 | #127 | — | 5 | 1 | no | — |
| 300 | #127 | — | 10 | 4 | no | — |
| 301 | #127 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 302 | #125 | — | 2 | 1 | no | — |
| 303 | #124 | — | 5 | 2 | no | — |
| 304 | #124 | — | 5 | 2 | no | — |
| 305 | #124 | — | 10 | 4 | no | — |
| 306 | #124 | — | 10 | 4 | no | — |
| 307 | #124 | — | 10 | 4 | no | — |
| 308 | #124 | C22×D5 | 1 | 2 | yes | — |
| 309 | C22⋊Q8 | — | 2 | 1 | no | — |
| 310 | C22⋊Q8 | — | 2 | 1 | no | — |
| 311 | #121 | — | 2 | 1 | no | — |
| 312 | #121 | — | 2 | 1 | no | — |
| 313 | #121 | — | 10 | 2 | no | — |
| 314 | #121 | — | 10 | 2 | no | — |
| 315 | #121 | — | 10 | 2 | no | — |
| 316 | #121 | — | 10 | 2 | no | — |
| 317 | #121 | — | 10 | 2 | no | — |
| 318 | #121 | — | 10 | 2 | no | — |
| 319 | #121 | — | 10 | 1 | no | — |
| 320 | #121 | — | 10 | 1 | no | — |
| 321 | #121 | — | 10 | 1 | no | — |
| 322 | #121 | — | 10 | 1 | no | — |
| 323 | #120 | — | 10 | 4 | no | — |
| 324 | #120 | — | 10 | 4 | no | — |
| 325 | #120 | — | 10 | 4 | no | — |
| 326 | #120 | — | 10 | 4 | no | — |
| 327 | C4×Q8 | — | 2 | 1 | no | — |
| 328 | C4×Q8 | — | 2 | 1 | no | — |
| 329 | C4×D4 | — | 2 | 1 | no | — |
| 330 | C4×D4 | — | 2 | 1 | no | — |
| 331 | C4×D4 | — | 10 | 1 | no | — |
| 332 | C4×D4 | — | 10 | 1 | no | — |
| 333 | C4×D4 | — | 10 | 1 | no | — |
| 334 | C4×D4 | — | 10 | 1 | no | — |
| 335 | #117 | — | 2 | 1 | no | — |
| 336 | #117 | — | 10 | 2 | no | — |
| 337 | #117 | — | 10 | 2 | no | — |
| 338 | #117 | — | 10 | 2 | no | — |
| 339 | C2×C42 | C22×D5 | 1 | 1 | yes | characteristic |
| 340 | C4⋊C8 | — | 2 | 1 | no | — |
| 341 | C4⋊C8 | — | 10 | 1 | no | — |
| 342 | #103 | — | 2 | 2 | no | — |
| 343 | #103 | — | 10 | 2 | no | — |
| 344 | #103 | — | 10 | 2 | no | — |
| 345 | #103 | — | 10 | 2 | no | — |
| 346 | #102 | — | 2 | 2 | no | — |
| 347 | #102 | — | 10 | 2 | no | — |
| 348 | #102 | — | 10 | 2 | no | — |
| 349 | #102 | — | 10 | 2 | no | — |
| 350 | C22⋊C8 | — | 2 | 1 | no | — |
| 351 | C22⋊C8 | — | 10 | 1 | no | — |
| 352 | #97 | — | 5 | 2 | no | — |
| 353 | #97 | — | 5 | 2 | no | — |
| 354 | #97 | — | 10 | 1 | no | — |
| 355 | #97 | C22×D5 | 1 | 2 | yes | — |
| 356 | C22×C5 | — | 2 | 1 | no | — |
| 357 | C22×C5 | — | 2 | 1 | no | — |
| 358 | C22×C5 | — | 2 | 1 | no | — |
| 359 | C22×C5 | — | 4 | 2 | no | — |
| 360 | C22×C5 | — | 4 | 2 | no | — |
| 361 | C22×C5 | — | 4 | 2 | no | — |
| 362 | C22×C5 | C2×#120 | 1 | 1 | yes | characteristic |
| 363 | C2×D5 | — | 4 | 2 | no | — |
| 364 | C2×D5 | — | 4 | 2 | no | — |
| 365 | C2×D5 | — | 4 | 2 | no | — |
| 366 | C2×D5 | — | 4 | 2 | no | — |
| 367 | C2×D5 | — | 4 | 2 | no | — |
| 368 | C2×D5 | — | 4 | 2 | no | — |
| 369 | C2×D5 | — | 16 | 8 | no | — |
| 370 | C4×C5 | — | 2 | 1 | no | — |
| 371 | C4×C5 | — | 2 | 1 | no | — |
| 372 | C4×C5 | — | 2 | 1 | no | — |
| 373 | C4×C5 | — | 2 | 1 | no | — |
| 374 | C4×C5 | — | 2 | 1 | no | — |
| 375 | C4×C5 | — | 4 | 2 | no | — |
| 376 | C4×C5 | — | 8 | 1 | no | — |
| 377 | C4×C5 | — | 8 | 1 | no | — |
| 378 | C4×C5 | #455 | 1 | 2 | yes | — |
| 379 | Dic5 | — | 4 | 2 | no | — |
| 380 | Dic5 | — | 4 | 2 | no | — |
| 381 | C24 | — | 10 | 4 | no | — |
| 382 | #41 | — | 8 | 2 | no | — |
| 383 | #41 | — | 20 | 4 | no | — |
| 384 | #41 | — | 40 | 2 | no | — |
| 385 | C2×Q8 | — | 2 | 1 | no | — |
| 386 | C2×Q8 | — | 2 | 1 | no | — |
| 387 | C2×Q8 | — | 5 | 2 | no | — |
| 388 | C2×Q8 | — | 5 | 2 | no | — |
| 389 | C2×Q8 | C2×C22⋊D5 | 1 | 2 | yes | — |
| 390 | C2×D4 | — | 2 | 2 | no | — |
| 391 | C2×D4 | — | 2 | 1 | no | — |
| 392 | C2×D4 | — | 2 | 1 | no | — |
| 393 | C2×D4 | — | 5 | 2 | no | — |
| 394 | C2×D4 | — | 5 | 2 | no | — |
| 395 | C2×D4 | — | 10 | 4 | no | — |
| 396 | C2×D4 | — | 10 | 4 | no | — |
| 397 | C2×D4 | — | 10 | 4 | no | — |
| 398 | C2×D4 | — | 10 | 2 | no | — |
| 399 | C2×D4 | — | 10 | 2 | no | — |
| 400 | C2×D4 | — | 10 | 1 | no | — |
| 401 | C2×D4 | — | 10 | 1 | no | — |
| 402 | C2×D4 | — | 10 | 1 | no | — |
| 403 | C2×D4 | — | 10 | 1 | no | — |
| 404 | C2×D4 | — | 40 | 4 | no | — |
| 405 | C2×D4 | — | 40 | 4 | no | — |
| 406 | C2×D4 | — | 40 | 4 | no | — |
| 407 | C2×D4 | C2×C22⋊D5 | 1 | 2 | yes | — |
| 408 | C22×C4 | — | 2 | 2 | no | — |
| 409 | C22×C4 | — | 10 | 2 | no | — |
| 410 | C22×C4 | — | 10 | 2 | no | — |
| 411 | C22×C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 412 | C22×C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 413 | C22×C4 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 414 | Q16 | — | 8 | 2 | no | — |
| 415 | Q16 | — | 40 | 2 | no | — |
| 416 | SD16 | — | 8 | 2 | no | — |
| 417 | SD16 | — | 40 | 2 | no | — |
| 418 | C2×C8 | — | 2 | 2 | no | — |
| 419 | C2×C8 | — | 10 | 2 | no | — |
| 420 | C2×C8 | — | 10 | 2 | no | — |
| 421 | C2×C8 | — | 20 | 2 | no | — |
| 422 | C4⋊C4 | — | 2 | 1 | no | — |
| 423 | C4⋊C4 | — | 2 | 1 | no | — |
| 424 | C4⋊C4 | — | 2 | 1 | no | — |
| 425 | C4⋊C4 | — | 2 | 1 | no | — |
| 426 | C4⋊C4 | — | 2 | 1 | no | — |
| 427 | C4⋊C4 | — | 2 | 1 | no | — |
| 428 | C4⋊C4 | — | 4 | 1 | no | — |
| 429 | C4⋊C4 | — | 4 | 1 | no | — |
| 430 | C4⋊C4 | — | 10 | 1 | no | — |
| 431 | C4⋊C4 | — | 10 | 1 | no | — |
| 432 | C4⋊C4 | — | 10 | 1 | no | — |
| 433 | C4⋊C4 | — | 10 | 1 | no | — |
| 434 | C22⋊C4 | — | 2 | 2 | no | — |
| 435 | C22⋊C4 | — | 2 | 2 | no | — |
| 436 | C22⋊C4 | — | 4 | 1 | no | — |
| 437 | C22⋊C4 | — | 10 | 4 | no | — |
| 438 | C22⋊C4 | — | 10 | 4 | no | — |
| 439 | C22⋊C4 | — | 10 | 4 | no | — |
| 440 | C22⋊C4 | — | 10 | 2 | no | — |
| 441 | C22⋊C4 | — | 10 | 2 | no | — |
| 442 | C22⋊C4 | — | 10 | 2 | no | — |
| 443 | C22⋊C4 | — | 10 | 2 | no | — |
| 444 | C42 | — | 4 | 1 | no | — |
| 445 | C42 | — | 10 | 4 | no | — |
| 446 | C42 | D4×D5 | 1 | 1 | yes | characteristic |
| 447 | C42 | D4×D5 | 1 | 1 | yes | characteristic |
| 448 | C42 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 449 | C42 | C23×D5 | 1 | 1 | yes | characteristic |
| 450 | C2×C5 | — | 4 | 1 | no | — |
| 451 | C2×C5 | — | 8 | 2 | no | — |
| 452 | C2×C5 | C2×#455 | 1 | 1 | yes | characteristic |
| 453 | C2×C5 | #3019 | 1 | 1 | yes | characteristic |
| 454 | C2×C5 | #3019 | 1 | 1 | yes | characteristic |
| 455 | D5 | — | 8 | 2 | no | — |
| 456 | D5 | — | 8 | 2 | no | — |
| 457 | C23 | — | 2 | 2 | no | — |
| 458 | C23 | — | 10 | 2 | no | — |
| 459 | C23 | — | 10 | 2 | no | — |
| 460 | C23 | — | 40 | 4 | no | — |
| 461 | C23 | — | 40 | 4 | no | — |
| 462 | C23 | — | 40 | 4 | no | — |
| 463 | C23 | #4083 | 1 | 1 | yes | characteristic |
| 464 | Q8 | — | 4 | 2 | no | — |
| 465 | Q8 | — | 4 | 1 | no | — |
| 466 | Q8 | — | 4 | 1 | no | — |
| 467 | Q8 | — | 4 | 1 | no | — |
| 468 | Q8 | — | 4 | 1 | no | — |
| 469 | Q8 | — | 20 | 2 | no | — |
| 470 | Q8 | — | 20 | 2 | no | — |
| 471 | D4 | — | 4 | 2 | no | — |
| 472 | D4 | — | 4 | 2 | no | — |
| 473 | D4 | — | 4 | 2 | no | — |
| 474 | D4 | — | 8 | 2 | no | — |
| 475 | D4 | — | 20 | 2 | no | — |
| 476 | D4 | — | 20 | 2 | no | — |
| 477 | D4 | — | 20 | 2 | no | — |
| 478 | D4 | — | 20 | 2 | no | — |
| 479 | D4 | — | 20 | 2 | no | — |
| 480 | D4 | — | 20 | 2 | no | — |
| 481 | D4 | — | 40 | 4 | no | — |
| 482 | D4 | — | 40 | 2 | no | — |
| 483 | D4 | — | 40 | 2 | no | — |
| 484 | D4 | — | 40 | 4 | no | — |
| 485 | D4 | — | 40 | 4 | no | — |
| 486 | C2×C4 | — | 2 | 2 | no | — |
| 487 | C2×C4 | — | 2 | 2 | no | — |
| 488 | C2×C4 | — | 4 | 1 | no | — |
| 489 | C2×C4 | — | 4 | 1 | no | — |
| 490 | C2×C4 | — | 4 | 4 | no | — |
| 491 | C2×C4 | — | 4 | 1 | no | — |
| 492 | C2×C4 | — | 4 | 1 | no | — |
| 493 | C2×C4 | — | 10 | 2 | no | — |
| 494 | C2×C4 | — | 10 | 2 | no | — |
| 495 | C2×C4 | — | 20 | 4 | no | — |
| 496 | C2×C4 | — | 20 | 4 | no | — |
| 497 | C2×C4 | #4083 | 1 | 1 | yes | characteristic |
| 498 | C2×C4 | #4083 | 1 | 1 | yes | characteristic |
| 499 | C2×C4 | #4083 | 1 | 1 | yes | characteristic |
| 500 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 501 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 502 | C2×C4 | C22×C22⋊D5 | 1 | 1 | yes | characteristic |
| 503 | C8 | — | 4 | 2 | no | — |
| 504 | C8 | — | 20 | 2 | no | — |
| 505 | C8 | — | 20 | 2 | no | — |
| 506 | C5 | #19056 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 507 | C22 | — | 2 | 1 | no | — |
| 508 | C22 | — | 2 | 1 | no | — |
| 509 | C22 | — | 2 | 1 | no | — |
| 510 | C22 | — | 4 | 2 | no | — |
| 511 | C22 | — | 4 | 2 | no | — |
| 512 | C22 | — | 4 | 2 | no | — |
| 513 | C22 | — | 20 | 2 | no | — |
| 514 | C22 | — | 20 | 2 | no | — |
| 515 | C22 | — | 20 | 2 | no | — |
| 516 | C22 | — | 20 | 2 | no | — |
| 517 | C22 | — | 20 | 2 | no | — |
| 518 | C22 | — | 20 | 2 | no | — |
| 519 | C22 | — | 80 | 8 | no | — |
| 520 | C22 | C2×#4083 | 1 | 1 | yes | characteristic |
| 521 | C4 | — | 2 | 1 | no | — |
| 522 | C4 | — | 2 | 1 | no | — |
| 523 | C4 | — | 2 | 1 | no | — |
| 524 | C4 | — | 2 | 1 | no | — |
| 525 | C4 | — | 2 | 1 | no | — |
| 526 | C4 | — | 4 | 2 | no | — |
| 527 | C4 | — | 8 | 1 | no | — |
| 528 | C4 | — | 8 | 1 | no | — |
| 529 | C4 | — | 20 | 2 | no | — |
| 530 | C4 | — | 20 | 2 | no | — |
| 531 | C4 | #65491 | 1 | 2 | yes | — |
| 532 | C2 | — | 4 | 1 | no | — |
| 533 | C2 | — | 8 | 2 | no | — |
| 534 | C2 | — | 40 | 2 | no | — |
| 535 | C2 | — | 40 | 2 | no | — |
| 536 | C2 | #10615125 | 1 | 1 | yes | characteristic |
| 537 | C2 | C2×#65491 | 1 | 1 | yes | characteristic |
| 538 | C2 | #10615736 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#3216 | C2 | semidirect |
| 3. #10615089 | C2 | semidirect |
| 4. #10615066 | C2 | semidirect |
| 5. #10602591 | C2 | semidirect |
| 6. #10602122 | C2 | semidirect |
| 7. #10602037 | C2 | semidirect |
| 8. #10601604 | C2 | semidirect |
| 9. #10601599 | C2 | semidirect |
| 10. C5×#533 | C22 | semidirect |
| 24. C5×#497 | C22 | semidirect |
| 25. C5×#489 | C22 | semidirect |
| 29. C5×#432 | C22 | semidirect |
| 30. #65378 | C22 | semidirect |
| 31. #65378 | C22 | semidirect |
| 32. #65378 | C22 | semidirect |
| 33. #65375 | C22 | semidirect |
| 40. #65215 | C22 | semidirect |
| 41. C2×#3935 | C22 | semidirect |
| 42. #64760 | C22 | semidirect |
| 43. #64684 | C22 | semidirect |
| 44. #64684 | C22 | semidirect |
| 122. #3216 | D5 | semidirect |
| 208. #533 | C2×D5 | semidirect |
| 213. #497 | C2×D5 | semidirect |
| 219. #489 | C2×D5 | semidirect |
| 227. #432 | C2×D5 | semidirect |
| 506. C5 | #19056 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10618153 | 2 |
| C5×#3216 | 2 |
| #10615089 | 2 |
| #10615066 | 2 |
| #10602591 | 2 |
| #10602122 | 2 |
| #10602037 | 2 |
| #10601604 | 2 |
| #10601599 | 2 |
| #19056 | 5 |