Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1852 conjugacy classes of subgroups.
The subgroup lattice has 416 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10618918 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C5×#3395 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10615419 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10613537 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #10613523 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #10612223 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #10612188 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | Q8×D40 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C8×#713 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #10611474 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | C4×#4065 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | C5×#557 | C22 | 1 | 2 | yes | — |
| 13 | C2×#4065 | C22 | 1 | 3 | yes | — |
| 14 | #66062 | C22 | 1 | 6 | yes | — |
| 15 | #66060 | C22 | 1 | 6 | yes | — |
| 16 | #66028 | — | 2 | 6 | no | — |
| 17 | #66025 | — | 2 | 6 | no | — |
| 18 | #65918 | C22 | 1 | 6 | yes | — |
| 19 | #65910 | — | 2 | 2 | no | — |
| 20 | Q8×D20 | C22 | 1 | 2 | yes | — |
| 21 | C4×#713 | C22 | 1 | 1 | yes | characteristic |
| 22 | C4×#713 | C22 | 1 | 6 | yes | — |
| 23 | C4×Q8×D5 | — | 2 | 2 | no | — |
| 24 | C5×#494 | C22 | 1 | 3 | yes | — |
| 25 | C5×#462 | C22 | 1 | 6 | yes | — |
| 26 | C5×C8×Q8 | C22 | 1 | 1 | yes | characteristic |
| 27 | C4×C5×Q16 | C22 | 1 | 3 | yes | — |
| 28 | #65477 | C22 | 1 | 6 | yes | — |
| 29 | #65477 | C22 | 1 | 6 | yes | — |
| 30 | #65476 | C22 | 1 | 12 | yes | — |
| 31 | Q16×Dic5 | C22 | 1 | 3 | yes | — |
| 32 | Q16×Dic5 | C22 | 1 | 6 | yes | — |
| 33 | #65372 | C22 | 1 | 6 | yes | — |
| 34 | #65370 | C22 | 1 | 6 | yes | — |
| 35 | C4×#688 | C22 | 1 | 6 | yes | — |
| 36 | Q8×#168 | C22 | 1 | 1 | yes | characteristic |
| 37 | #65309 | C22 | 1 | 6 | yes | — |
| 38 | #65169 | C22 | 1 | 3 | yes | — |
| 39 | #65161 | C22 | 1 | 1 | yes | characteristic |
| 40 | #65135 | C22 | 1 | 6 | yes | — |
| 41 | #65123 | C22 | 1 | 3 | yes | — |
| 42 | #65122 | C22 | 1 | 3 | yes | — |
| 43 | #65103 | C22 | 1 | 12 | yes | — |
| 44 | #65093 | C22 | 1 | 6 | yes | — |
| 45 | #65077 | C22 | 1 | 6 | yes | — |
| 46 | C4×D40 | C22 | 1 | 3 | yes | — |
| 47 | C8×D20 | C22 | 1 | 3 | yes | — |
| 48 | C4×C8×D5 | C22 | 1 | 3 | yes | — |
| 49 | #64971 | C22 | 1 | 3 | yes | — |
| 50 | #61435 | — | 5 | 1 | no | maximal, Sylow |
| 51 | C2×#713 | D4 | 1 | 1 | yes | characteristic |
| 52 | C2×#713 | C23 | 1 | 6 | yes | — |
| 53 | C2×Q8×D5 | — | 2 | 2 | no | — |
| 54 | C2×C5×Q16 | C23 | 1 | 3 | yes | — |
| 55 | C2×C5×Q16 | C23 | 1 | 6 | yes | — |
| 56 | C5×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 57 | C5×#125 | — | 2 | 6 | no | — |
| 58 | C4×C5×Q8 | — | 2 | 2 | no | — |
| 59 | C4×C5×Q8 | C23 | 1 | 6 | yes | — |
| 60 | C4×C5×Q8 | C23 | 1 | 1 | yes | characteristic |
| 61 | #4092 | C23 | 1 | 12 | yes | — |
| 62 | Q8×Dic5 | D4 | 1 | 1 | yes | characteristic |
| 63 | Q8×Dic5 | C23 | 1 | 6 | yes | — |
| 64 | C2×#688 | C23 | 1 | 6 | yes | — |
| 65 | #4065 | — | 2 | 12 | no | — |
| 66 | C2×D40 | C23 | 1 | 1 | yes | characteristic |
| 67 | C2×C8×D5 | C23 | 1 | 3 | yes | — |
| 68 | C2×C8×D5 | C23 | 1 | 3 | yes | — |
| 69 | #4044 | — | 2 | 12 | no | — |
| 70 | #4043 | — | 2 | 6 | no | — |
| 71 | #4043 | — | 2 | 6 | no | — |
| 72 | #4041 | — | 2 | 6 | no | — |
| 73 | #4040 | — | 2 | 12 | no | — |
| 74 | #4039 | — | 2 | 6 | no | — |
| 75 | #4039 | D4 | 1 | 3 | yes | — |
| 76 | #4039 | C23 | 1 | 2 | yes | — |
| 77 | #4038 | — | 2 | 6 | no | — |
| 78 | #4038 | — | 2 | 6 | no | — |
| 79 | #4038 | D4 | 1 | 3 | yes | — |
| 80 | #4038 | C23 | 1 | 6 | yes | — |
| 81 | D5×C4⋊C4 | — | 2 | 6 | no | — |
| 82 | #4036 | — | 2 | 6 | no | — |
| 83 | #4033 | — | 2 | 6 | no | — |
| 84 | #4021 | — | 2 | 6 | no | — |
| 85 | C4×D20 | — | 2 | 6 | no | — |
| 86 | C4×D20 | C23 | 1 | 3 | yes | — |
| 87 | C4×D20 | C23 | 1 | 6 | yes | — |
| 88 | C42×D5 | — | 2 | 6 | no | — |
| 89 | C42×D5 | C23 | 1 | 3 | yes | — |
| 90 | #4015 | C23 | 1 | 6 | yes | — |
| 91 | C4×Dic10 | — | 2 | 6 | no | — |
| 92 | C5×#107 | C23 | 1 | 1 | yes | characteristic |
| 93 | C5×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 94 | C5×#103 | C23 | 1 | 6 | yes | — |
| 95 | C4×C5×C8 | C23 | 1 | 3 | yes | — |
| 96 | #3967 | C23 | 1 | 12 | yes | — |
| 97 | #3967 | C23 | 1 | 6 | yes | — |
| 98 | #3953 | C23 | 1 | 6 | yes | — |
| 99 | #3952 | C23 | 1 | 6 | yes | — |
| 100 | #3950 | C23 | 1 | 6 | yes | — |
| 101 | #3950 | C23 | 1 | 3 | yes | — |
| 102 | C8×Dic5 | C23 | 1 | 3 | yes | — |
| 103 | C8×Dic5 | C23 | 1 | 1 | yes | characteristic |
| 104 | #3941 | C23 | 1 | 2 | yes | — |
| 105 | #3940 | C23 | 1 | 6 | yes | — |
| 106 | C4⋊#168 | C23 | 1 | 3 | yes | — |
| 107 | C4×#168 | C23 | 1 | 3 | yes | — |
| 108 | #3482 | — | 5 | 2 | no | — |
| 109 | #3395 | D5 | 1 | 1 | yes | characteristic, complemented |
| 110 | Q8×D8 | — | 5 | 1 | no | — |
| 111 | #3359 | — | 5 | 2 | no | — |
| 112 | #3342 | — | 5 | 3 | no | — |
| 113 | #3302 | — | 5 | 6 | no | — |
| 114 | #3283 | — | 5 | 3 | no | — |
| 115 | #3170 | — | 5 | 3 | no | — |
| 116 | #3107 | — | 5 | 6 | no | — |
| 117 | C8×#41 | — | 5 | 1 | no | — |
| 118 | C4×#135 | — | 5 | 3 | no | — |
| 119 | C2×C5×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 120 | C2×C5×Q8 | C24 | 1 | 6 | yes | — |
| 121 | #713 | — | 2 | 4 | no | — |
| 122 | #713 | — | 2 | 12 | no | — |
| 123 | #713 | — | 4 | 6 | no | — |
| 124 | Q8×D5 | — | 4 | 8 | no | — |
| 125 | C2×D20 | — | 2 | 6 | no | — |
| 126 | C2×D20 | C2×D4 | 1 | 3 | yes | — |
| 127 | C2×D20 | C24 | 1 | 2 | yes | — |
| 128 | C2×C4×D5 | — | 2 | 6 | no | — |
| 129 | C2×C4×D5 | — | 2 | 6 | no | — |
| 130 | C2×C4×D5 | — | 2 | 2 | no | — |
| 131 | C2×C4×D5 | C2×D4 | 1 | 3 | yes | — |
| 132 | C2×C4×D5 | C2×D4 | 1 | 3 | yes | — |
| 133 | C2×C4×D5 | C24 | 1 | 3 | yes | — |
| 134 | C2×Dic10 | — | 2 | 6 | no | — |
| 135 | C5×Q16 | — | 2 | 6 | no | — |
| 136 | C5×Q16 | — | 4 | 6 | no | — |
| 137 | C2×C5×C8 | C24 | 1 | 3 | yes | — |
| 138 | C2×C5×C8 | C24 | 1 | 1 | yes | characteristic |
| 139 | C5×C4⋊C4 | — | 2 | 6 | no | — |
| 140 | C5×C4⋊C4 | — | 2 | 6 | no | — |
| 141 | C5×C4⋊C4 | — | 2 | 6 | no | — |
| 142 | C5×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 143 | C5×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 144 | C42×C5 | — | 2 | 6 | no | — |
| 145 | C42×C5 | C24 | 1 | 3 | yes | — |
| 146 | #688 | — | 2 | 12 | no | — |
| 147 | #685 | — | 2 | 6 | no | — |
| 148 | #685 | — | 2 | 12 | no | — |
| 149 | #685 | — | 2 | 6 | no | — |
| 150 | #685 | — | 2 | 2 | no | — |
| 151 | #685 | C2×D4 | 1 | 6 | yes | — |
| 152 | C4⋊Dic5 | — | 2 | 6 | no | — |
| 153 | C4⋊Dic5 | — | 2 | 6 | no | — |
| 154 | C4⋊Dic5 | C2×D4 | 1 | 3 | yes | — |
| 155 | C4⋊Dic5 | C24 | 1 | 6 | yes | — |
| 156 | #683 | — | 2 | 12 | no | — |
| 157 | C4×Dic5 | — | 2 | 6 | no | — |
| 158 | C4×Dic5 | — | 2 | 6 | no | — |
| 159 | C4×Dic5 | C2×D4 | 1 | 3 | yes | — |
| 160 | C4×Dic5 | C2×D4 | 1 | 3 | yes | — |
| 161 | C4×Dic5 | C24 | 1 | 1 | yes | characteristic |
| 162 | C2×#168 | C24 | 1 | 1 | yes | characteristic |
| 163 | C2×#168 | C24 | 1 | 3 | yes | — |
| 164 | D40 | #41 | 1 | 4 | yes | complemented |
| 165 | C8×D5 | — | 2 | 6 | no | — |
| 166 | C8×D5 | — | 4 | 3 | no | — |
| 167 | C2×#135 | — | 5 | 3 | no | — |
| 168 | #557 | C2×D5 | 1 | 2 | yes | — |
| 169 | #556 | — | 5 | 6 | no | — |
| 170 | #552 | — | 10 | 6 | no | — |
| 171 | D4×Q8 | — | 5 | 2 | no | — |
| 172 | #548 | — | 10 | 2 | no | — |
| 173 | #547 | — | 5 | 6 | no | — |
| 174 | #533 | — | 5 | 6 | no | — |
| 175 | #529 | — | 10 | 6 | no | — |
| 176 | C4×#41 | — | 5 | 1 | no | — |
| 177 | C4×#41 | — | 5 | 6 | no | — |
| 178 | C2×C4×Q8 | — | 10 | 2 | no | — |
| 179 | #500 | — | 5 | 3 | no | — |
| 180 | #494 | C2×D5 | 1 | 3 | yes | — |
| 181 | #487 | — | 5 | 6 | no | — |
| 182 | #485 | — | 5 | 12 | no | — |
| 183 | #475 | — | 5 | 6 | no | — |
| 184 | #474 | — | 5 | 6 | no | — |
| 185 | #467 | — | 5 | 6 | no | — |
| 186 | #467 | — | 5 | 6 | no | — |
| 187 | #462 | C2×D5 | 1 | 6 | yes | — |
| 188 | #461 | — | 5 | 6 | no | — |
| 189 | #452 | — | 5 | 12 | no | — |
| 190 | C8×Q8 | — | 5 | 1 | no | — |
| 191 | C8×Q8 | C2×D5 | 1 | 1 | yes | characteristic |
| 192 | C4×Q16 | — | 5 | 6 | no | — |
| 193 | C4×Q16 | — | 5 | 3 | no | — |
| 194 | C4×Q16 | C2×D5 | 1 | 3 | yes | — |
| 195 | C4×SD16 | — | 5 | 6 | no | — |
| 196 | C4×SD16 | — | 5 | 6 | no | — |
| 197 | C4×D8 | — | 5 | 1 | no | — |
| 198 | C4×D8 | — | 5 | 3 | no | — |
| 199 | C8×D4 | — | 5 | 3 | no | — |
| 200 | C8×D4 | — | 5 | 3 | no | — |
| 201 | #431 | — | 5 | 3 | no | — |
| 202 | #427 | — | 5 | 3 | no | — |
| 203 | #416 | — | 5 | 6 | no | — |
| 204 | C2×C4×C8 | — | 5 | 3 | no | — |
| 205 | C22×D5 | — | 2 | 2 | no | — |
| 206 | C22×D5 | C22×D4 | 1 | 3 | yes | — |
| 207 | C5×Q8 | — | 2 | 6 | no | — |
| 208 | C5×Q8 | — | 2 | 6 | no | — |
| 209 | C5×Q8 | #135 | 1 | 4 | yes | complemented |
| 210 | C2×C4×C5 | — | 2 | 2 | no | — |
| 211 | C2×C4×C5 | — | 2 | 6 | no | — |
| 212 | C2×C4×C5 | C22×D4 | 1 | 3 | yes | — |
| 213 | C2×C4×C5 | C22×D4 | 1 | 3 | yes | — |
| 214 | C2×C4×C5 | C25 | 1 | 1 | yes | characteristic |
| 215 | C2×Dic5 | — | 2 | 6 | no | — |
| 216 | C2×Dic5 | C22×D4 | 1 | 3 | yes | — |
| 217 | C2×Dic5 | C22×D4 | 1 | 1 | yes | characteristic |
| 218 | C2×Dic5 | C22×D4 | 1 | 1 | yes | characteristic |
| 219 | D20 | — | 2 | 6 | no | — |
| 220 | D20 | — | 2 | 2 | no | — |
| 221 | D20 | — | 4 | 12 | no | — |
| 222 | D20 | C2×#41 | 1 | 4 | yes | — |
| 223 | C4×D5 | — | 2 | 6 | no | — |
| 224 | C4×D5 | — | 2 | 3 | no | — |
| 225 | C4×D5 | — | 2 | 3 | no | — |
| 226 | C4×D5 | — | 2 | 6 | no | — |
| 227 | C4×D5 | — | 4 | 12 | no | — |
| 228 | C4×D5 | — | 4 | 12 | no | — |
| 229 | C4×D5 | — | 4 | 4 | no | — |
| 230 | Dic10 | — | 4 | 12 | no | — |
| 231 | C5×C8 | — | 2 | 3 | no | — |
| 232 | C5×C8 | C2×#41 | 1 | 2 | yes | — |
| 233 | #168 | — | 2 | 3 | no | — |
| 234 | #168 | — | 2 | 1 | no | — |
| 235 | C2×#41 | — | 5 | 1 | no | — |
| 236 | C2×#41 | — | 5 | 6 | no | — |
| 237 | C22×Q8 | — | 10 | 2 | no | — |
| 238 | #135 | — | 10 | 12 | no | — |
| 239 | C2×Q16 | C22×D5 | 1 | 3 | yes | — |
| 240 | C2×Q16 | C22×D5 | 1 | 6 | yes | — |
| 241 | C2×SD16 | — | 5 | 6 | no | — |
| 242 | C2×D8 | — | 5 | 1 | no | — |
| 243 | C22×C8 | — | 5 | 3 | no | — |
| 244 | C22×C8 | — | 5 | 3 | no | — |
| 245 | C4⋊Q8 | — | 5 | 6 | no | — |
| 246 | C4⋊Q8 | C22×D5 | 1 | 6 | yes | — |
| 247 | #126 | — | 10 | 12 | no | — |
| 248 | #125 | — | 2 | 6 | no | — |
| 249 | #125 | — | 10 | 6 | no | — |
| 250 | #124 | — | 10 | 6 | no | — |
| 251 | #123 | — | 10 | 12 | no | — |
| 252 | C22⋊Q8 | — | 5 | 12 | no | — |
| 253 | C22⋊Q8 | — | 10 | 6 | no | — |
| 254 | C22⋊Q8 | — | 10 | 6 | no | — |
| 255 | #121 | — | 10 | 6 | no | — |
| 256 | C4×Q8 | — | 2 | 2 | no | — |
| 257 | C4×Q8 | — | 5 | 1 | no | — |
| 258 | C4×Q8 | — | 5 | 6 | no | — |
| 259 | C4×Q8 | — | 10 | 6 | no | — |
| 260 | C4×Q8 | — | 10 | 6 | no | — |
| 261 | C4×Q8 | C22×D5 | 1 | 6 | yes | — |
| 262 | C4×Q8 | C22×D5 | 1 | 1 | yes | characteristic |
| 263 | C4×D4 | — | 5 | 3 | no | — |
| 264 | C4×D4 | — | 5 | 2 | no | — |
| 265 | C4×D4 | — | 5 | 3 | no | — |
| 266 | C4×D4 | — | 5 | 6 | no | — |
| 267 | C4×D4 | — | 10 | 6 | no | — |
| 268 | C4×D4 | — | 10 | 6 | no | — |
| 269 | #117 | — | 5 | 3 | no | — |
| 270 | #117 | — | 5 | 6 | no | — |
| 271 | #117 | — | 10 | 6 | no | — |
| 272 | #117 | — | 10 | 6 | no | — |
| 273 | C2×C4⋊C4 | — | 10 | 6 | no | — |
| 274 | C2×C42 | — | 5 | 3 | no | — |
| 275 | C2×C42 | — | 10 | 6 | no | — |
| 276 | #107 | — | 5 | 3 | no | — |
| 277 | #107 | — | 5 | 6 | no | — |
| 278 | #107 | C22×D5 | 1 | 1 | yes | characteristic |
| 279 | #106 | — | 5 | 6 | no | — |
| 280 | C4⋊C8 | — | 5 | 3 | no | — |
| 281 | C4⋊C8 | C22×D5 | 1 | 3 | yes | — |
| 282 | #103 | — | 5 | 6 | no | — |
| 283 | #103 | — | 5 | 12 | no | — |
| 284 | #103 | C22×D5 | 1 | 6 | yes | — |
| 285 | #102 | — | 5 | 6 | no | — |
| 286 | #102 | — | 5 | 2 | no | — |
| 287 | C22⋊C8 | — | 5 | 6 | no | — |
| 288 | C4×C8 | — | 5 | 1 | no | — |
| 289 | C4×C8 | — | 5 | 3 | no | — |
| 290 | C4×C8 | — | 5 | 3 | no | — |
| 291 | C4×C8 | C22×D5 | 1 | 3 | yes | — |
| 292 | C22×C5 | C23×D4 | 1 | 1 | yes | characteristic |
| 293 | C2×D5 | — | 2 | 3 | no | — |
| 294 | C2×D5 | — | 2 | 4 | no | — |
| 295 | C2×D5 | — | 2 | 3 | no | — |
| 296 | C2×D5 | — | 2 | 3 | no | — |
| 297 | C2×D5 | — | 4 | 2 | no | — |
| 298 | C2×D5 | — | 4 | 2 | no | — |
| 299 | C4×C5 | — | 2 | 3 | no | — |
| 300 | C4×C5 | — | 4 | 6 | no | — |
| 301 | C4×C5 | — | 4 | 2 | no | — |
| 302 | C4×C5 | C2×#135 | 1 | 6 | yes | — |
| 303 | C4×C5 | C22×#41 | 1 | 1 | yes | characteristic |
| 304 | C4×C5 | #585 | 1 | 1 | yes | characteristic |
| 305 | Dic5 | — | 2 | 3 | no | — |
| 306 | Dic5 | — | 2 | 1 | no | — |
| 307 | Dic5 | — | 4 | 6 | no | — |
| 308 | Dic5 | #578 | 1 | 2 | yes | — |
| 309 | #41 | — | 10 | 4 | no | — |
| 310 | #41 | — | 10 | 12 | no | — |
| 311 | #41 | — | 20 | 6 | no | — |
| 312 | C2×Q8 | — | 10 | 6 | no | — |
| 313 | C2×Q8 | — | 20 | 8 | no | — |
| 314 | C2×Q8 | D4×D5 | 1 | 1 | yes | characteristic |
| 315 | C2×Q8 | C23×D5 | 1 | 6 | yes | — |
| 316 | C2×D4 | — | 5 | 3 | no | — |
| 317 | C2×D4 | — | 5 | 2 | no | — |
| 318 | C2×D4 | — | 10 | 6 | no | — |
| 319 | C22×C4 | — | 5 | 3 | no | — |
| 320 | C22×C4 | — | 5 | 3 | no | — |
| 321 | C22×C4 | — | 5 | 3 | no | — |
| 322 | C22×C4 | — | 10 | 2 | no | — |
| 323 | C22×C4 | — | 10 | 6 | no | — |
| 324 | C22×C4 | — | 10 | 6 | no | — |
| 325 | Q16 | — | 2 | 6 | no | — |
| 326 | Q16 | — | 4 | 6 | no | — |
| 327 | SD16 | — | 10 | 12 | no | — |
| 328 | D8 | — | 5 | 4 | no | — |
| 329 | C2×C8 | — | 5 | 1 | no | — |
| 330 | C2×C8 | — | 5 | 3 | no | — |
| 331 | C2×C8 | — | 10 | 6 | no | — |
| 332 | C2×C8 | — | 20 | 3 | no | — |
| 333 | C2×C8 | C23×D5 | 1 | 3 | yes | — |
| 334 | C2×C8 | C23×D5 | 1 | 1 | yes | characteristic |
| 335 | C4⋊C4 | — | 2 | 6 | no | — |
| 336 | C4⋊C4 | — | 2 | 6 | no | — |
| 337 | C4⋊C4 | — | 2 | 6 | no | — |
| 338 | C4⋊C4 | — | 5 | 3 | no | — |
| 339 | C4⋊C4 | — | 5 | 6 | no | — |
| 340 | C4⋊C4 | — | 10 | 12 | no | — |
| 341 | C4⋊C4 | — | 10 | 6 | no | — |
| 342 | C4⋊C4 | — | 10 | 6 | no | — |
| 343 | C4⋊C4 | D4×D5 | 1 | 3 | yes | — |
| 344 | C4⋊C4 | C23×D5 | 1 | 2 | yes | — |
| 345 | C22⋊C4 | — | 5 | 6 | no | — |
| 346 | C22⋊C4 | — | 10 | 2 | no | — |
| 347 | C22⋊C4 | — | 10 | 6 | no | — |
| 348 | C22⋊C4 | — | 10 | 12 | no | — |
| 349 | C22⋊C4 | — | 10 | 6 | no | — |
| 350 | C42 | — | 2 | 6 | no | — |
| 351 | C42 | — | 5 | 3 | no | — |
| 352 | C42 | — | 5 | 3 | no | — |
| 353 | C42 | — | 5 | 1 | no | — |
| 354 | C42 | — | 10 | 6 | no | — |
| 355 | C42 | — | 10 | 6 | no | — |
| 356 | C42 | C23×D5 | 1 | 3 | yes | — |
| 357 | C2×C5 | D4×#41 | 1 | 1 | yes | characteristic |
| 358 | C2×C5 | C22×#135 | 1 | 1 | yes | characteristic |
| 359 | C2×C5 | C2×#578 | 1 | 1 | yes | characteristic |
| 360 | D5 | — | 4 | 3 | no | — |
| 361 | D5 | — | 4 | 4 | no | — |
| 362 | C23 | — | 5 | 3 | no | — |
| 363 | C23 | — | 10 | 2 | no | — |
| 364 | Q8 | — | 2 | 6 | no | — |
| 365 | Q8 | — | 2 | 6 | no | — |
| 366 | Q8 | — | 20 | 12 | no | — |
| 367 | Q8 | #4065 | 1 | 4 | yes | complemented |
| 368 | D4 | — | 5 | 4 | no | — |
| 369 | D4 | — | 10 | 6 | no | — |
| 370 | D4 | — | 10 | 2 | no | — |
| 371 | D4 | — | 20 | 12 | no | — |
| 372 | C2×C4 | — | 2 | 2 | no | — |
| 373 | C2×C4 | — | 2 | 6 | no | — |
| 374 | C2×C4 | — | 5 | 1 | no | — |
| 375 | C2×C4 | — | 5 | 1 | no | — |
| 376 | C2×C4 | — | 5 | 3 | no | — |
| 377 | C2×C4 | — | 10 | 6 | no | — |
| 378 | C2×C4 | — | 10 | 6 | no | — |
| 379 | C2×C4 | — | 10 | 3 | no | — |
| 380 | C2×C4 | — | 10 | 3 | no | — |
| 381 | C2×C4 | — | 10 | 6 | no | — |
| 382 | C2×C4 | — | 20 | 4 | no | — |
| 383 | C2×C4 | — | 20 | 12 | no | — |
| 384 | C2×C4 | — | 20 | 12 | no | — |
| 385 | C2×C4 | C2×D4×D5 | 1 | 3 | yes | — |
| 386 | C2×C4 | C2×D4×D5 | 1 | 3 | yes | — |
| 387 | C2×C4 | C24×D5 | 1 | 1 | yes | characteristic |
| 388 | C8 | — | 2 | 3 | no | — |
| 389 | C8 | — | 10 | 3 | no | — |
| 390 | C8 | — | 10 | 1 | no | — |
| 391 | C8 | D5×#41 | 1 | 2 | yes | — |
| 392 | C5 | #61435 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 393 | C22 | — | 10 | 3 | no | — |
| 394 | C22 | — | 10 | 4 | no | — |
| 395 | C22 | — | 10 | 3 | no | — |
| 396 | C22 | — | 10 | 3 | no | — |
| 397 | C22 | — | 20 | 2 | no | — |
| 398 | C22 | — | 20 | 2 | no | — |
| 399 | C22 | C22×D4×D5 | 1 | 1 | yes | characteristic |
| 400 | C4 | — | 2 | 3 | no | — |
| 401 | C4 | — | 4 | 6 | no | — |
| 402 | C4 | — | 4 | 2 | no | — |
| 403 | C4 | — | 5 | 2 | no | — |
| 404 | C4 | — | 10 | 3 | no | — |
| 405 | C4 | — | 10 | 1 | no | — |
| 406 | C4 | — | 20 | 6 | no | — |
| 407 | C4 | C2×#4065 | 1 | 6 | yes | — |
| 408 | C4 | C2×D5×#41 | 1 | 1 | yes | characteristic |
| 409 | C4 | #66285 | 1 | 1 | yes | characteristic |
| 410 | C2 | — | 20 | 3 | no | — |
| 411 | C2 | — | 20 | 4 | no | — |
| 412 | C2 | #10618667 | 1 | 1 | yes | characteristic |
| 413 | C2 | C22×#4065 | 1 | 1 | yes | characteristic |
| 414 | C2 | D5×#578 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10618918 | C2 | semidirect |
| 2. C5×#3395 | C2 | semidirect |
| 3. #10615419 | C2 | semidirect |
| 4. #10613537 | C2 | semidirect |
| 5. #10613523 | C2 | semidirect |
| 6. #10612223 | C2 | semidirect |
| 7. #10612188 | C2 | semidirect |
| 8. Q8×D40 | C2 | semidirect |
| 9. C8×#713 | C2 | semidirect |
| 10. #10611474 | C2 | semidirect |
| 11. C4×#4065 | C2 | semidirect |
| 109. #3395 | D5 | semidirect |
| 164. D40 | #41 | semidirect |
| 209. C5×Q8 | #135 | semidirect |
| 367. Q8 | #4065 | semidirect |
| 392. C5 | #61435 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10618918 | 2 |
| C5×#3395 | 2 |
| #10615419 | 2 |
| #10613537 | 2 |
| #10613523 | 2 |
| #10612223 | 2 |
| #10612188 | 2 |
| Q8×D40 | 2 |
| C8×#713 | 2 |
| #10611474 | 2 |
| C4×#4065 | 2 |
| #61435 | 5 |