Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
934 conjugacy classes of subgroups.
The subgroup lattice has 526 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#65431 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10615531 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10610571 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10610296 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#65006 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C5×#1765 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10601185 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #10600686 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #10600618 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #10599741 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #10599526 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | C2×C5×#131 | C22 | 1 | 1 | yes | characteristic |
| 13 | #66167 | C22 | 1 | 2 | yes | — |
| 14 | C2×#4095 | C22 | 1 | 2 | yes | — |
| 15 | C2×#4054 | C22 | 1 | 2 | yes | — |
| 16 | C2×#4050 | C22 | 1 | 1 | yes | characteristic |
| 17 | C22×D40 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#4047 | C22 | 1 | 2 | yes | — |
| 19 | #65859 | C22 | 1 | 2 | yes | — |
| 20 | C2×C5×#104 | C22 | 1 | 1 | yes | characteristic |
| 21 | C5×#416 | C22 | 1 | 1 | yes | characteristic |
| 22 | C5×#405 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×C5×#97 | C22 | 1 | 1 | yes | characteristic |
| 24 | #65431 | — | 2 | 4 | no | — |
| 25 | #65426 | — | 2 | 1 | no | — |
| 26 | #65424 | — | 2 | 1 | no | — |
| 27 | #65422 | C22 | 1 | 2 | yes | — |
| 28 | C2×#3955 | C22 | 1 | 2 | yes | — |
| 29 | #65403 | — | 2 | 2 | no | — |
| 30 | C2×#3953 | C22 | 1 | 2 | yes | — |
| 31 | C2×#3951 | C22 | 1 | 1 | yes | characteristic |
| 32 | C2×#3949 | C22 | 1 | 1 | yes | characteristic |
| 33 | #65284 | C22 | 1 | 2 | yes | — |
| 34 | #65228 | C22 | 1 | 2 | yes | — |
| 35 | C2×#3937 | C22 | 1 | 2 | yes | — |
| 36 | #65101 | — | 2 | 2 | no | — |
| 37 | #65096 | — | 2 | 2 | no | — |
| 38 | #65071 | — | 2 | 2 | no | — |
| 39 | #65064 | — | 2 | 2 | no | — |
| 40 | #65006 | — | 2 | 4 | no | — |
| 41 | #65001 | — | 2 | 2 | no | — |
| 42 | #64985 | — | 2 | 1 | no | — |
| 43 | #64984 | — | 2 | 1 | no | — |
| 44 | C5×#341 | C22 | 1 | 1 | yes | characteristic |
| 45 | C5×#339 | C22 | 1 | 1 | yes | characteristic |
| 46 | #64774 | C22 | 1 | 2 | yes | — |
| 47 | #25444 | — | 5 | 1 | no | maximal, Sylow |
| 48 | C2×C5×#41 | C23 | 1 | 1 | yes | characteristic |
| 49 | C2×#709 | C23 | 1 | 2 | yes | — |
| 50 | C22×D20 | C23 | 1 | 2 | yes | — |
| 51 | C5×#131 | — | 2 | 2 | no | — |
| 52 | C5×#131 | — | 2 | 2 | no | — |
| 53 | C2×C5×M16 | — | 2 | 1 | no | — |
| 54 | C2×C5×M16 | C23 | 1 | 1 | yes | characteristic |
| 55 | C2×C5×M16 | C23 | 1 | 1 | yes | characteristic |
| 56 | C22×C5×C8 | — | 2 | 1 | no | — |
| 57 | C22×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 58 | C22×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 59 | C5×#117 | C23 | 1 | 1 | yes | characteristic |
| 60 | C2×C42×C5 | C23 | 1 | 1 | yes | characteristic |
| 61 | #4095 | — | 2 | 4 | no | — |
| 62 | #4095 | — | 4 | 2 | no | — |
| 63 | #4092 | — | 2 | 2 | no | — |
| 64 | C2×#688 | — | 2 | 2 | no | — |
| 65 | #4085 | — | 4 | 2 | no | — |
| 66 | #4084 | — | 2 | 2 | no | — |
| 67 | C2×#686 | — | 2 | 2 | no | — |
| 68 | #4076 | — | 2 | 2 | no | — |
| 69 | C2×#685 | — | 4 | 2 | no | — |
| 70 | C2×C4⋊Dic5 | C23 | 1 | 2 | yes | — |
| 71 | #4070 | — | 2 | 2 | no | — |
| 72 | C2×#681 | C23 | 1 | 2 | yes | — |
| 73 | #4054 | — | 2 | 4 | no | — |
| 74 | #4054 | — | 4 | 2 | no | — |
| 75 | C2×Dic20 | D4 | 1 | 1 | yes | characteristic |
| 76 | #4050 | — | 2 | 2 | no | — |
| 77 | #4050 | — | 2 | 2 | no | — |
| 78 | C2×D40 | — | 2 | 2 | no | — |
| 79 | C2×D40 | — | 2 | 2 | no | — |
| 80 | C2×D40 | — | 2 | 1 | no | — |
| 81 | C2×D40 | — | 2 | 1 | no | — |
| 82 | C2×D40 | — | 2 | 2 | no | — |
| 83 | C2×D40 | D4 | 1 | 1 | yes | characteristic |
| 84 | C2×#677 | — | 2 | 2 | no | — |
| 85 | C2×#677 | D4 | 1 | 2 | yes | — |
| 86 | #4047 | — | 2 | 4 | no | — |
| 87 | #4047 | — | 4 | 2 | no | — |
| 88 | C2×#676 | — | 2 | 2 | no | — |
| 89 | C2×C8×D5 | — | 2 | 2 | no | — |
| 90 | #4041 | — | 2 | 2 | no | — |
| 91 | #4041 | — | 2 | 2 | no | — |
| 92 | #4028 | — | 4 | 2 | no | — |
| 93 | #4021 | — | 2 | 2 | no | — |
| 94 | #4020 | — | 2 | 2 | no | — |
| 95 | C5×#104 | — | 2 | 2 | no | — |
| 96 | C5×#103 | D4 | 1 | 2 | yes | — |
| 97 | C5×#102 | D4 | 1 | 2 | yes | — |
| 98 | C5×#97 | — | 2 | 2 | no | — |
| 99 | C5×#97 | — | 2 | 1 | no | — |
| 100 | C4×C5×C8 | — | 2 | 1 | no | — |
| 101 | #3955 | — | 2 | 4 | no | — |
| 102 | #3953 | — | 2 | 2 | no | — |
| 103 | #3953 | — | 2 | 2 | no | — |
| 104 | #3953 | — | 2 | 2 | no | — |
| 105 | #3951 | D4 | 1 | 4 | yes | complemented |
| 106 | #3949 | — | 2 | 1 | no | — |
| 107 | #3949 | — | 2 | 1 | no | — |
| 108 | #3948 | — | 2 | 2 | no | — |
| 109 | #3940 | — | 2 | 2 | no | — |
| 110 | #3939 | — | 2 | 2 | no | — |
| 111 | #3937 | — | 2 | 4 | no | — |
| 112 | #3155 | — | 5 | 1 | no | — |
| 113 | C2×#472 | — | 5 | 1 | no | — |
| 114 | #3062 | — | 5 | 2 | no | — |
| 115 | #3060 | — | 5 | 1 | no | — |
| 116 | C2×#444 | — | 5 | 1 | no | — |
| 117 | #2037 | — | 5 | 2 | no | — |
| 118 | #2006 | — | 5 | 2 | no | — |
| 119 | #1972 | — | 5 | 1 | no | — |
| 120 | #1951 | — | 5 | 1 | no | — |
| 121 | #1907 | — | 5 | 2 | no | — |
| 122 | #1765 | D5 | 1 | 1 | yes | characteristic, complemented |
| 123 | C23×D5 | — | 2 | 2 | no | — |
| 124 | C5×#41 | — | 2 | 1 | no | — |
| 125 | C5×#41 | — | 2 | 1 | no | — |
| 126 | C5×#41 | — | 2 | 1 | no | — |
| 127 | C5×#41 | — | 2 | 1 | no | — |
| 128 | C2×C5×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 129 | C2×C5×D4 | — | 2 | 1 | no | — |
| 130 | C2×C5×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 131 | C22×C4×C5 | — | 2 | 1 | no | — |
| 132 | C22×C4×C5 | — | 2 | 1 | no | — |
| 133 | C22×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 134 | C2×C22⋊D5 | — | 2 | 2 | no | — |
| 135 | C2×C22⋊D5 | — | 4 | 2 | no | — |
| 136 | C22×Dic5 | — | 2 | 2 | no | — |
| 137 | #709 | — | 2 | 2 | no | — |
| 138 | #709 | — | 2 | 2 | no | — |
| 139 | #709 | — | 2 | 2 | no | — |
| 140 | #709 | — | 2 | 2 | no | — |
| 141 | C2×D20 | — | 2 | 2 | no | — |
| 142 | C2×D20 | — | 2 | 2 | no | — |
| 143 | C2×D20 | — | 2 | 2 | no | — |
| 144 | C2×D20 | — | 2 | 2 | no | — |
| 145 | C2×D20 | — | 2 | 2 | no | — |
| 146 | C2×D20 | — | 2 | 2 | no | — |
| 147 | C2×D20 | — | 4 | 2 | no | — |
| 148 | C2×D20 | — | 4 | 2 | no | — |
| 149 | C2×D20 | C2×D4 | 1 | 2 | yes | — |
| 150 | C2×C4×D5 | — | 2 | 2 | no | — |
| 151 | C2×Dic10 | C2×D4 | 1 | 2 | yes | — |
| 152 | C5×M16 | — | 2 | 1 | no | — |
| 153 | C5×M16 | — | 2 | 1 | no | — |
| 154 | C5×M16 | — | 2 | 1 | no | — |
| 155 | C5×M16 | — | 4 | 2 | no | — |
| 156 | C5×M16 | #41 | 1 | 2 | yes | — |
| 157 | C2×C5×C8 | — | 2 | 1 | no | — |
| 158 | C2×C5×C8 | — | 2 | 1 | no | — |
| 159 | C2×C5×C8 | — | 2 | 1 | no | — |
| 160 | C2×C5×C8 | — | 2 | 1 | no | — |
| 161 | C2×C5×C8 | — | 4 | 2 | no | — |
| 162 | C2×C5×C8 | C2×D4 | 1 | 2 | yes | — |
| 163 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 164 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 165 | C2×C5×C8 | C2×D4 | 1 | 2 | yes | — |
| 166 | C2×C5×C8 | #41 | 1 | 2 | yes | — |
| 167 | C5×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 168 | C5×C22⋊C4 | — | 2 | 1 | no | — |
| 169 | C42×C5 | — | 2 | 1 | no | — |
| 170 | C42×C5 | — | 2 | 1 | no | — |
| 171 | C42×C5 | — | 2 | 1 | no | — |
| 172 | C22⋊Dic5 | — | 4 | 2 | no | — |
| 173 | #688 | — | 4 | 4 | no | — |
| 174 | #686 | — | 4 | 4 | no | — |
| 175 | #685 | — | 4 | 2 | no | — |
| 176 | #685 | — | 4 | 2 | no | — |
| 177 | #685 | — | 4 | 2 | no | — |
| 178 | #685 | — | 8 | 4 | no | — |
| 179 | C4⋊Dic5 | — | 2 | 2 | no | — |
| 180 | C4⋊Dic5 | — | 2 | 2 | no | — |
| 181 | #683 | — | 4 | 2 | no | — |
| 182 | #681 | — | 2 | 2 | no | — |
| 183 | #681 | C2×D4 | 1 | 4 | yes | — |
| 184 | C2×#168 | — | 2 | 2 | no | — |
| 185 | Dic20 | — | 2 | 2 | no | — |
| 186 | D40 | — | 2 | 2 | no | — |
| 187 | D40 | — | 4 | 4 | no | — |
| 188 | D40 | — | 4 | 2 | no | — |
| 189 | D40 | — | 4 | 2 | no | — |
| 190 | #677 | — | 2 | 4 | no | — |
| 191 | #677 | — | 4 | 4 | no | — |
| 192 | #676 | — | 4 | 4 | no | — |
| 193 | C8×D5 | — | 4 | 4 | no | — |
| 194 | C2×AGL(1,ℤ/8) | — | 5 | 2 | no | — |
| 195 | C2×AGL(1,ℤ/8) | — | 5 | 2 | no | — |
| 196 | C2×#135 | — | 5 | 1 | no | — |
| 197 | C22×D8 | — | 5 | 1 | no | — |
| 198 | C2×#131 | — | 5 | 2 | no | — |
| 199 | C2×#131 | C2×D5 | 1 | 1 | yes | characteristic |
| 200 | #537 | — | 5 | 2 | no | — |
| 201 | #535 | — | 5 | 2 | no | — |
| 202 | #496 | — | 10 | 2 | no | — |
| 203 | #495 | — | 10 | 1 | no | — |
| 204 | #493 | — | 10 | 1 | no | — |
| 205 | #472 | — | 10 | 4 | no | — |
| 206 | #470 | — | 10 | 1 | no | — |
| 207 | #469 | — | 10 | 1 | no | — |
| 208 | #469 | — | 10 | 2 | no | — |
| 209 | #468 | — | 10 | 2 | no | — |
| 210 | #466 | — | 10 | 2 | no | — |
| 211 | #465 | — | 10 | 2 | no | — |
| 212 | #465 | — | 10 | 2 | no | — |
| 213 | #444 | — | 10 | 4 | no | — |
| 214 | C2×#108 | — | 5 | 1 | no | — |
| 215 | #428 | — | 5 | 2 | no | — |
| 216 | C2×#106 | — | 5 | 1 | no | — |
| 217 | C2×#104 | — | 5 | 2 | no | — |
| 218 | C2×#104 | C2×D5 | 1 | 1 | yes | characteristic |
| 219 | #417 | — | 5 | 2 | no | — |
| 220 | #416 | C2×D5 | 1 | 1 | yes | characteristic |
| 221 | C2×#102 | — | 5 | 2 | no | — |
| 222 | C2×#100 | — | 5 | 2 | no | — |
| 223 | #405 | C2×D5 | 1 | 1 | yes | characteristic |
| 224 | C2×#97 | C2×D5 | 1 | 1 | yes | characteristic |
| 225 | #390 | — | 5 | 2 | no | — |
| 226 | #343 | — | 5 | 2 | no | — |
| 227 | #341 | C2×D5 | 1 | 1 | yes | characteristic |
| 228 | #339 | C2×D5 | 1 | 1 | yes | characteristic |
| 229 | C23×C5 | — | 2 | 1 | no | — |
| 230 | C23×C5 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 231 | C22×D5 | — | 2 | 2 | no | — |
| 232 | C22×D5 | — | 4 | 2 | no | — |
| 233 | C22×D5 | — | 4 | 2 | no | — |
| 234 | C22×D5 | — | 4 | 2 | no | — |
| 235 | C22×D5 | — | 8 | 2 | no | — |
| 236 | C22×D5 | — | 8 | 2 | no | — |
| 237 | C5×Q8 | — | 2 | 1 | no | — |
| 238 | C5×Q8 | — | 2 | 1 | no | — |
| 239 | C5×D4 | — | 2 | 1 | no | — |
| 240 | C5×D4 | — | 2 | 1 | no | — |
| 241 | C5×D4 | — | 4 | 1 | no | — |
| 242 | C5×D4 | — | 4 | 1 | no | — |
| 243 | C2×C4×C5 | — | 2 | 1 | no | — |
| 244 | C2×C4×C5 | — | 2 | 2 | no | — |
| 245 | C2×C4×C5 | — | 4 | 1 | no | — |
| 246 | C2×C4×C5 | — | 4 | 1 | no | — |
| 247 | C2×C4×C5 | — | 4 | 2 | no | — |
| 248 | C2×C4×C5 | — | 4 | 1 | no | — |
| 249 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 250 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 251 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 252 | C2×C4×C5 | C2×#41 | 1 | 1 | yes | characteristic |
| 253 | C2×C4×C5 | C2×#41 | 1 | 1 | yes | characteristic |
| 254 | C2×C4×C5 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 255 | C22⋊D5 | — | 4 | 2 | no | — |
| 256 | C22⋊D5 | — | 4 | 2 | no | — |
| 257 | C22⋊D5 | — | 16 | 2 | no | — |
| 258 | C2×Dic5 | — | 2 | 2 | no | — |
| 259 | C2×Dic5 | — | 4 | 2 | no | — |
| 260 | C2×Dic5 | — | 8 | 2 | no | — |
| 261 | D20 | — | 2 | 2 | no | — |
| 262 | D20 | — | 2 | 2 | no | — |
| 263 | D20 | — | 4 | 2 | no | — |
| 264 | D20 | — | 4 | 2 | no | — |
| 265 | D20 | — | 4 | 2 | no | — |
| 266 | D20 | — | 4 | 2 | no | — |
| 267 | D20 | — | 16 | 2 | no | — |
| 268 | D20 | — | 16 | 2 | no | — |
| 269 | C4×D5 | — | 4 | 2 | no | — |
| 270 | C4×D5 | — | 4 | 2 | no | — |
| 271 | Dic10 | — | 2 | 2 | no | — |
| 272 | Dic10 | — | 2 | 2 | no | — |
| 273 | C5×C8 | — | 2 | 2 | no | — |
| 274 | C5×C8 | — | 2 | 2 | no | — |
| 275 | C5×C8 | — | 4 | 1 | no | — |
| 276 | C5×C8 | #121 | 1 | 2 | yes | — |
| 277 | C5×C8 | #121 | 1 | 2 | yes | — |
| 278 | #168 | — | 2 | 4 | no | — |
| 279 | C2×#41 | — | 5 | 2 | no | — |
| 280 | C2×#41 | C22×D5 | 1 | 1 | yes | characteristic |
| 281 | C22×D4 | — | 5 | 2 | no | — |
| 282 | AGL(1,ℤ/8) | — | 10 | 4 | no | — |
| 283 | AGL(1,ℤ/8) | — | 10 | 4 | no | — |
| 284 | AGL(1,ℤ/8) | — | 20 | 2 | no | — |
| 285 | AGL(1,ℤ/8) | — | 20 | 2 | no | — |
| 286 | #135 | — | 10 | 2 | no | — |
| 287 | #135 | — | 10 | 2 | no | — |
| 288 | C2×Q16 | — | 5 | 1 | no | — |
| 289 | C2×SD16 | — | 5 | 2 | no | — |
| 290 | C2×SD16 | — | 10 | 2 | no | — |
| 291 | C2×SD16 | — | 10 | 2 | no | — |
| 292 | C2×D8 | — | 5 | 1 | no | — |
| 293 | C2×D8 | — | 10 | 2 | no | — |
| 294 | C2×D8 | — | 10 | 2 | no | — |
| 295 | C2×D8 | — | 10 | 2 | no | — |
| 296 | C2×D8 | — | 10 | 2 | no | — |
| 297 | C2×D8 | — | 10 | 1 | no | — |
| 298 | C2×D8 | — | 10 | 1 | no | — |
| 299 | #131 | — | 2 | 2 | no | — |
| 300 | #131 | — | 2 | 2 | no | — |
| 301 | #131 | — | 10 | 4 | no | — |
| 302 | #131 | — | 20 | 2 | no | — |
| 303 | C2×M16 | — | 2 | 1 | no | — |
| 304 | C2×M16 | — | 5 | 2 | no | — |
| 305 | C2×M16 | — | 10 | 2 | no | — |
| 306 | C2×M16 | C22×D5 | 1 | 1 | yes | characteristic |
| 307 | C2×M16 | C22×D5 | 1 | 1 | yes | characteristic |
| 308 | C22×C8 | — | 2 | 1 | no | — |
| 309 | C22×C8 | — | 10 | 2 | no | — |
| 310 | C22×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 311 | C22×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 312 | #127 | — | 10 | 2 | no | — |
| 313 | #124 | — | 10 | 2 | no | — |
| 314 | C22⋊Q8 | — | 10 | 2 | no | — |
| 315 | C22⋊Q8 | — | 10 | 2 | no | — |
| 316 | #121 | — | 10 | 2 | no | — |
| 317 | #121 | — | 10 | 2 | no | — |
| 318 | #121 | — | 10 | 2 | no | — |
| 319 | #121 | — | 10 | 2 | no | — |
| 320 | #121 | — | 20 | 2 | no | — |
| 321 | #120 | — | 20 | 2 | no | — |
| 322 | #117 | C22×D5 | 1 | 1 | yes | characteristic |
| 323 | C2×C4⋊C4 | — | 5 | 2 | no | — |
| 324 | C2×C22⋊C4 | — | 20 | 2 | no | — |
| 325 | C2×C42 | C22×D5 | 1 | 1 | yes | characteristic |
| 326 | #108 | — | 5 | 4 | no | — |
| 327 | #107 | — | 10 | 2 | no | — |
| 328 | #106 | — | 10 | 1 | no | — |
| 329 | #106 | — | 10 | 1 | no | — |
| 330 | #106 | — | 10 | 2 | no | — |
| 331 | #104 | — | 2 | 2 | no | — |
| 332 | #104 | — | 10 | 4 | no | — |
| 333 | #103 | — | 10 | 2 | no | — |
| 334 | #103 | D20 | 1 | 2 | yes | — |
| 335 | #102 | — | 10 | 2 | no | — |
| 336 | #102 | — | 10 | 2 | no | — |
| 337 | #102 | — | 10 | 2 | no | — |
| 338 | #102 | D20 | 1 | 2 | yes | — |
| 339 | #100 | — | 10 | 4 | no | — |
| 340 | #97 | — | 2 | 2 | no | — |
| 341 | #97 | — | 2 | 1 | no | — |
| 342 | C4×C8 | — | 2 | 1 | no | — |
| 343 | C22×C5 | — | 2 | 2 | no | — |
| 344 | C22×C5 | — | 4 | 1 | no | — |
| 345 | C22×C5 | — | 4 | 2 | no | — |
| 346 | C22×C5 | #540 | 1 | 1 | yes | characteristic |
| 347 | C22×C5 | D42 | 1 | 1 | yes | characteristic |
| 348 | C22×C5 | #550 | 1 | 1 | yes | characteristic |
| 349 | C2×D5 | — | 4 | 2 | no | — |
| 350 | C2×D5 | — | 4 | 2 | no | — |
| 351 | C2×D5 | — | 4 | 2 | no | — |
| 352 | C2×D5 | — | 8 | 4 | no | — |
| 353 | C2×D5 | — | 8 | 2 | no | — |
| 354 | C2×D5 | — | 8 | 2 | no | — |
| 355 | C2×D5 | — | 8 | 2 | no | — |
| 356 | C2×D5 | — | 16 | 2 | no | — |
| 357 | C4×C5 | — | 4 | 1 | no | — |
| 358 | C4×C5 | — | 4 | 2 | no | — |
| 359 | C4×C5 | — | 8 | 1 | no | — |
| 360 | C4×C5 | C2×#121 | 1 | 1 | yes | characteristic |
| 361 | C4×C5 | #532 | 1 | 1 | yes | characteristic |
| 362 | C4×C5 | D42 | 1 | 1 | yes | characteristic |
| 363 | C4×C5 | #546 | 1 | 1 | yes | characteristic |
| 364 | Dic5 | — | 4 | 2 | no | — |
| 365 | Dic5 | — | 8 | 2 | no | — |
| 366 | C24 | — | 10 | 2 | no | — |
| 367 | #41 | — | 2 | 1 | no | — |
| 368 | #41 | — | 2 | 1 | no | — |
| 369 | #41 | — | 2 | 1 | no | — |
| 370 | #41 | — | 2 | 1 | no | — |
| 371 | #41 | — | 10 | 2 | no | — |
| 372 | #41 | — | 10 | 2 | no | — |
| 373 | #41 | — | 10 | 2 | no | — |
| 374 | #41 | — | 10 | 2 | no | — |
| 375 | C2×Q8 | — | 5 | 2 | no | — |
| 376 | C2×Q8 | C2×D20 | 1 | 1 | yes | characteristic |
| 377 | C2×D4 | — | 2 | 1 | no | — |
| 378 | C2×D4 | — | 5 | 2 | no | — |
| 379 | C2×D4 | — | 10 | 2 | no | — |
| 380 | C2×D4 | — | 10 | 2 | no | — |
| 381 | C2×D4 | — | 10 | 2 | no | — |
| 382 | C2×D4 | — | 10 | 2 | no | — |
| 383 | C2×D4 | — | 10 | 2 | no | — |
| 384 | C2×D4 | — | 10 | 2 | no | — |
| 385 | C2×D4 | — | 10 | 2 | no | — |
| 386 | C2×D4 | — | 20 | 2 | no | — |
| 387 | C2×D4 | — | 20 | 2 | no | — |
| 388 | C2×D4 | — | 20 | 2 | no | — |
| 389 | C2×D4 | C2×D20 | 1 | 1 | yes | characteristic |
| 390 | C22×C4 | — | 2 | 1 | no | — |
| 391 | C22×C4 | — | 2 | 1 | no | — |
| 392 | C22×C4 | — | 10 | 2 | no | — |
| 393 | C22×C4 | — | 10 | 2 | no | — |
| 394 | C22×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 395 | Q16 | — | 10 | 2 | no | — |
| 396 | SD16 | — | 10 | 4 | no | — |
| 397 | SD16 | — | 20 | 4 | no | — |
| 398 | SD16 | — | 20 | 4 | no | — |
| 399 | D8 | — | 10 | 2 | no | — |
| 400 | D8 | — | 20 | 4 | no | — |
| 401 | D8 | — | 20 | 4 | no | — |
| 402 | D8 | — | 20 | 2 | no | — |
| 403 | D8 | — | 20 | 2 | no | — |
| 404 | M16 | — | 2 | 1 | no | — |
| 405 | M16 | — | 2 | 1 | no | — |
| 406 | M16 | — | 2 | 1 | no | — |
| 407 | M16 | — | 4 | 2 | no | — |
| 408 | M16 | — | 5 | 4 | no | — |
| 409 | M16 | — | 10 | 2 | no | — |
| 410 | M16 | — | 20 | 4 | no | — |
| 411 | M16 | #709 | 1 | 2 | yes | — |
| 412 | C2×C8 | — | 2 | 1 | no | — |
| 413 | C2×C8 | — | 2 | 1 | no | — |
| 414 | C2×C8 | — | 2 | 1 | no | — |
| 415 | C2×C8 | — | 2 | 1 | no | — |
| 416 | C2×C8 | — | 4 | 2 | no | — |
| 417 | C2×C8 | — | 10 | 2 | no | — |
| 418 | C2×C8 | — | 20 | 4 | no | — |
| 419 | C2×C8 | C2×D20 | 1 | 2 | yes | — |
| 420 | C2×C8 | #709 | 1 | 2 | yes | — |
| 421 | C2×C8 | D4×D5 | 1 | 1 | yes | characteristic |
| 422 | C2×C8 | D4×D5 | 1 | 1 | yes | characteristic |
| 423 | C2×C8 | D4×D5 | 1 | 2 | yes | — |
| 424 | C4⋊C4 | — | 10 | 2 | no | — |
| 425 | C4⋊C4 | — | 10 | 2 | no | — |
| 426 | C4⋊C4 | — | 20 | 2 | no | — |
| 427 | C4⋊C4 | C2×D20 | 1 | 2 | yes | — |
| 428 | C22⋊C4 | — | 2 | 1 | no | — |
| 429 | C22⋊C4 | — | 20 | 2 | no | — |
| 430 | C22⋊C4 | — | 20 | 2 | no | — |
| 431 | C22⋊C4 | — | 20 | 2 | no | — |
| 432 | C22⋊C4 | — | 20 | 2 | no | — |
| 433 | C22⋊C4 | — | 40 | 4 | no | — |
| 434 | C42 | — | 2 | 1 | no | — |
| 435 | C42 | — | 2 | 1 | no | — |
| 436 | C42 | — | 2 | 1 | no | — |
| 437 | C2×C5 | — | 2 | 1 | no | — |
| 438 | C2×C5 | — | 2 | 1 | no | — |
| 439 | C2×C5 | — | 8 | 1 | no | — |
| 440 | C2×C5 | #2428 | 1 | 1 | yes | characteristic |
| 441 | C2×C5 | #3288 | 1 | 2 | yes | — |
| 442 | D5 | — | 8 | 2 | no | — |
| 443 | D5 | — | 16 | 2 | no | — |
| 444 | C23 | — | 2 | 1 | no | — |
| 445 | C23 | — | 10 | 2 | no | — |
| 446 | C23 | — | 20 | 2 | no | — |
| 447 | C23 | — | 20 | 2 | no | — |
| 448 | C23 | — | 20 | 2 | no | — |
| 449 | C23 | — | 40 | 2 | no | — |
| 450 | C23 | — | 40 | 2 | no | — |
| 451 | C23 | #4149 | 1 | 1 | yes | characteristic |
| 452 | Q8 | — | 2 | 1 | no | — |
| 453 | Q8 | — | 2 | 1 | no | — |
| 454 | Q8 | — | 10 | 2 | no | — |
| 455 | Q8 | — | 10 | 2 | no | — |
| 456 | D4 | — | 2 | 1 | no | — |
| 457 | D4 | — | 2 | 1 | no | — |
| 458 | D4 | — | 4 | 1 | no | — |
| 459 | D4 | — | 4 | 1 | no | — |
| 460 | D4 | — | 10 | 2 | no | — |
| 461 | D4 | — | 10 | 2 | no | — |
| 462 | D4 | — | 20 | 2 | no | — |
| 463 | D4 | — | 20 | 2 | no | — |
| 464 | D4 | — | 20 | 2 | no | — |
| 465 | D4 | — | 20 | 2 | no | — |
| 466 | D4 | — | 20 | 2 | no | — |
| 467 | D4 | — | 20 | 2 | no | — |
| 468 | D4 | — | 80 | 2 | no | — |
| 469 | D4 | — | 80 | 2 | no | — |
| 470 | D4 | — | 80 | 2 | no | — |
| 471 | C2×C4 | — | 2 | 2 | no | — |
| 472 | C2×C4 | — | 2 | 1 | no | — |
| 473 | C2×C4 | — | 4 | 1 | no | — |
| 474 | C2×C4 | — | 4 | 1 | no | — |
| 475 | C2×C4 | — | 4 | 2 | no | — |
| 476 | C2×C4 | — | 4 | 1 | no | — |
| 477 | C2×C4 | — | 10 | 2 | no | — |
| 478 | C2×C4 | — | 20 | 2 | no | — |
| 479 | C2×C4 | — | 20 | 2 | no | — |
| 480 | C2×C4 | — | 20 | 2 | no | — |
| 481 | C2×C4 | — | 40 | 2 | no | — |
| 482 | C2×C4 | C22×D20 | 1 | 1 | yes | characteristic |
| 483 | C2×C4 | C2×#709 | 1 | 1 | yes | characteristic |
| 484 | C2×C4 | C2×#709 | 1 | 1 | yes | characteristic |
| 485 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 486 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 487 | C2×C4 | #4149 | 1 | 1 | yes | characteristic |
| 488 | C8 | — | 2 | 2 | no | — |
| 489 | C8 | — | 2 | 2 | no | — |
| 490 | C8 | — | 4 | 1 | no | — |
| 491 | C8 | — | 10 | 4 | no | — |
| 492 | C8 | #4030 | 1 | 2 | yes | — |
| 493 | C8 | #4030 | 1 | 2 | yes | — |
| 494 | C5 | #25444 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 495 | C22 | — | 2 | 2 | no | — |
| 496 | C22 | — | 4 | 1 | no | — |
| 497 | C22 | — | 4 | 2 | no | — |
| 498 | C22 | — | 20 | 2 | no | — |
| 499 | C22 | — | 20 | 2 | no | — |
| 500 | C22 | — | 20 | 2 | no | — |
| 501 | C22 | — | 40 | 4 | no | — |
| 502 | C22 | — | 40 | 2 | no | — |
| 503 | C22 | — | 40 | 2 | no | — |
| 504 | C22 | — | 40 | 2 | no | — |
| 505 | C22 | — | 80 | 2 | no | — |
| 506 | C22 | #65869 | 1 | 1 | yes | characteristic |
| 507 | C22 | D4×D20 | 1 | 1 | yes | characteristic |
| 508 | C22 | #65887 | 1 | 1 | yes | characteristic |
| 509 | C4 | — | 4 | 1 | no | — |
| 510 | C4 | — | 4 | 2 | no | — |
| 511 | C4 | — | 8 | 1 | no | — |
| 512 | C4 | — | 20 | 2 | no | — |
| 513 | C4 | — | 40 | 2 | no | — |
| 514 | C4 | #65811 | 1 | 1 | yes | characteristic |
| 515 | C4 | C2×#4030 | 1 | 1 | yes | characteristic |
| 516 | C4 | D4×D20 | 1 | 1 | yes | characteristic |
| 517 | C4 | #65884 | 1 | 1 | yes | characteristic |
| 518 | C2 | — | 2 | 1 | no | — |
| 519 | C2 | — | 2 | 1 | no | — |
| 520 | C2 | — | 8 | 1 | no | — |
| 521 | C2 | — | 40 | 2 | no | — |
| 522 | C2 | — | 80 | 2 | no | — |
| 523 | C2 | #10605218 | 1 | 1 | yes | characteristic |
| 524 | C2 | #10611631 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#65431 | C2 | semidirect |
| 2. #10615531 | C2 | semidirect |
| 3. #10610571 | C2 | semidirect |
| 4. #10610296 | C2 | semidirect |
| 5. C2×#65006 | C2 | semidirect |
| 6. C5×#1765 | C2 | semidirect |
| 7. #10601185 | C2 | semidirect |
| 8. #10600686 | C2 | semidirect |
| 9. #10600618 | C2 | semidirect |
| 10. #10599741 | C2 | semidirect |
| 11. #10599526 | C2 | semidirect |
| 105. #3951 | D4 | semidirect |
| 122. #1765 | D5 | semidirect |
| 494. C5 | #25444 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65431 | 2 |
| #10615531 | 2 |
| #10610571 | 2 |
| #10610296 | 2 |
| C2×#65006 | 2 |
| C5×#1765 | 2 |
| #10601185 | 2 |
| #10600686 | 2 |
| #10600618 | 2 |
| #10599741 | 2 |
| #10599526 | 2 |
| #25444 | 5 |