Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
894 conjugacy classes of subgroups.
The subgroup lattice has 544 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#65186 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10610914 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10610910 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10610819 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C2×#64989 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C5×#1945 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10601514 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10601335 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10600569 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #10599569 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #10599526 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | C2×#4054 | C22 | 1 | 2 | yes | — |
| 13 | C2×#4050 | C22 | 1 | 1 | yes | characteristic |
| 14 | C22×D40 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×#4047 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×#4047 | C22 | 1 | 1 | yes | characteristic |
| 17 | #65859 | C22 | 1 | 2 | yes | — |
| 18 | #65857 | C22 | 1 | 2 | yes | — |
| 19 | C2×C5×#108 | C22 | 1 | 1 | yes | characteristic |
| 20 | C5×#427 | C22 | 1 | 1 | yes | characteristic |
| 21 | C5×#424 | C22 | 1 | 2 | yes | — |
| 22 | C2×C4×C5×C8 | C22 | 1 | 1 | yes | characteristic |
| 23 | #65422 | C22 | 1 | 2 | yes | — |
| 24 | C2×#3955 | C22 | 1 | 2 | yes | — |
| 25 | C2×#3953 | C22 | 1 | 2 | yes | — |
| 26 | C2×#3951 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×#3950 | C22 | 1 | 1 | yes | characteristic |
| 28 | #65290 | C22 | 1 | 2 | yes | — |
| 29 | #65284 | C22 | 1 | 2 | yes | — |
| 30 | #65228 | C22 | 1 | 2 | yes | — |
| 31 | C2×#3937 | C22 | 1 | 1 | yes | characteristic |
| 32 | C2×#3937 | C22 | 1 | 1 | yes | characteristic |
| 33 | #65186 | — | 2 | 4 | no | — |
| 34 | #65172 | — | 2 | 1 | no | — |
| 35 | #65172 | — | 2 | 1 | no | — |
| 36 | #65169 | — | 2 | 1 | no | — |
| 37 | D5×#107 | — | 2 | 1 | no | — |
| 38 | #65154 | — | 2 | 2 | no | — |
| 39 | #65150 | — | 2 | 2 | no | — |
| 40 | #65137 | — | 2 | 2 | no | — |
| 41 | #65134 | — | 2 | 2 | no | — |
| 42 | #65133 | — | 2 | 2 | no | — |
| 43 | #65132 | — | 2 | 2 | no | — |
| 44 | #64989 | — | 2 | 4 | no | — |
| 45 | C5×#339 | C22 | 1 | 2 | yes | — |
| 46 | #64774 | C22 | 1 | 2 | yes | — |
| 47 | #24797 | — | 5 | 1 | no | maximal, Sylow |
| 48 | C2×#709 | C23 | 1 | 1 | yes | characteristic |
| 49 | C2×#709 | C23 | 1 | 1 | yes | characteristic |
| 50 | C22×D20 | C23 | 1 | 2 | yes | — |
| 51 | C2×C5×M16 | C23 | 1 | 2 | yes | — |
| 52 | C22×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 53 | C22×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 54 | C5×#117 | C23 | 1 | 2 | yes | — |
| 55 | C2×C42×C5 | C23 | 1 | 1 | yes | characteristic |
| 56 | C2×#685 | — | 4 | 2 | no | — |
| 57 | C2×C4⋊Dic5 | C23 | 1 | 2 | yes | — |
| 58 | C2×#681 | C23 | 1 | 1 | yes | characteristic |
| 59 | C2×#681 | C23 | 1 | 1 | yes | characteristic |
| 60 | #4054 | — | 2 | 4 | no | — |
| 61 | #4054 | — | 2 | 4 | no | — |
| 62 | C2×Dic20 | D4 | 1 | 1 | yes | characteristic |
| 63 | #4050 | — | 2 | 2 | no | — |
| 64 | #4050 | — | 2 | 2 | no | — |
| 65 | C2×D40 | — | 2 | 2 | no | — |
| 66 | C2×D40 | — | 2 | 1 | no | — |
| 67 | C2×D40 | — | 2 | 1 | no | — |
| 68 | C2×D40 | — | 2 | 2 | no | — |
| 69 | C2×D40 | — | 2 | 2 | no | — |
| 70 | C2×D40 | D4 | 1 | 1 | yes | characteristic |
| 71 | C2×#677 | — | 2 | 2 | no | — |
| 72 | C2×#677 | D4 | 1 | 1 | yes | characteristic |
| 73 | C2×#677 | D4 | 1 | 1 | yes | characteristic |
| 74 | #4047 | — | 2 | 2 | no | — |
| 75 | #4047 | — | 2 | 2 | no | — |
| 76 | #4047 | — | 2 | 2 | no | — |
| 77 | #4047 | D4 | 1 | 4 | yes | complemented |
| 78 | C2×#676 | — | 2 | 1 | no | — |
| 79 | C2×#676 | — | 2 | 1 | no | — |
| 80 | C2×C8×D5 | — | 2 | 1 | no | — |
| 81 | C2×C8×D5 | — | 2 | 1 | no | — |
| 82 | #4041 | — | 2 | 2 | no | — |
| 83 | #4041 | — | 2 | 2 | no | — |
| 84 | #4038 | — | 2 | 2 | no | — |
| 85 | D5×C4⋊C4 | — | 2 | 2 | no | — |
| 86 | #4028 | — | 4 | 2 | no | — |
| 87 | #4027 | — | 4 | 2 | no | — |
| 88 | #4021 | — | 2 | 2 | no | — |
| 89 | #4020 | — | 2 | 2 | no | — |
| 90 | C4×D20 | — | 2 | 2 | no | — |
| 91 | C4×Dic10 | — | 2 | 2 | no | — |
| 92 | C5×#108 | — | 2 | 2 | no | — |
| 93 | C5×#107 | D4 | 1 | 1 | yes | characteristic |
| 94 | C5×#107 | D4 | 1 | 1 | yes | characteristic |
| 95 | C5×#106 | D4 | 1 | 2 | yes | — |
| 96 | C5×C4⋊C8 | — | 2 | 2 | no | — |
| 97 | C5×C4⋊C8 | — | 2 | 2 | no | — |
| 98 | C4×C5×C8 | — | 2 | 2 | no | — |
| 99 | #3955 | — | 2 | 4 | no | — |
| 100 | #3953 | — | 2 | 2 | no | — |
| 101 | #3953 | — | 2 | 2 | no | — |
| 102 | #3953 | — | 2 | 2 | no | — |
| 103 | #3951 | — | 2 | 2 | no | — |
| 104 | #3950 | — | 2 | 1 | no | — |
| 105 | #3950 | — | 2 | 1 | no | — |
| 106 | #3948 | — | 2 | 2 | no | — |
| 107 | #3941 | — | 2 | 2 | no | — |
| 108 | #3941 | — | 2 | 2 | no | — |
| 109 | #3940 | — | 2 | 2 | no | — |
| 110 | #3939 | — | 2 | 2 | no | — |
| 111 | #3937 | — | 2 | 2 | no | — |
| 112 | #3937 | — | 2 | 2 | no | — |
| 113 | C2×#472 | — | 5 | 1 | no | — |
| 114 | #3058 | — | 5 | 1 | no | — |
| 115 | #3045 | — | 5 | 2 | no | — |
| 116 | C2×#443 | — | 5 | 1 | no | — |
| 117 | #2913 | — | 5 | 1 | no | — |
| 118 | #2063 | — | 5 | 2 | no | — |
| 119 | #2037 | — | 5 | 2 | no | — |
| 120 | #1970 | — | 5 | 1 | no | — |
| 121 | #1945 | D5 | 1 | 1 | yes | characteristic, complemented |
| 122 | #1883 | — | 5 | 2 | no | — |
| 123 | #1816 | — | 5 | 1 | no | — |
| 124 | C23×D5 | — | 2 | 2 | no | — |
| 125 | C22×C4×C5 | — | 2 | 1 | no | — |
| 126 | C22×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 127 | C2×C22⋊D5 | — | 2 | 1 | no | — |
| 128 | C2×C22⋊D5 | — | 2 | 1 | no | — |
| 129 | C22×Dic5 | — | 2 | 2 | no | — |
| 130 | #709 | — | 2 | 1 | no | — |
| 131 | #709 | — | 2 | 1 | no | — |
| 132 | #709 | — | 2 | 1 | no | — |
| 133 | #709 | — | 2 | 1 | no | — |
| 134 | #709 | — | 2 | 1 | no | — |
| 135 | #709 | — | 2 | 1 | no | — |
| 136 | #709 | C2×D4 | 1 | 2 | yes | — |
| 137 | #709 | #41 | 1 | 2 | yes | — |
| 138 | C2×D20 | — | 2 | 2 | no | — |
| 139 | C2×D20 | — | 2 | 2 | no | — |
| 140 | C2×D20 | — | 2 | 2 | no | — |
| 141 | C2×D20 | — | 2 | 2 | no | — |
| 142 | C2×D20 | — | 2 | 2 | no | — |
| 143 | C2×D20 | — | 2 | 2 | no | — |
| 144 | C2×D20 | — | 4 | 2 | no | — |
| 145 | C2×D20 | — | 4 | 2 | no | — |
| 146 | C2×D20 | C2×D4 | 1 | 1 | yes | characteristic |
| 147 | C2×D20 | C2×D4 | 1 | 1 | yes | characteristic |
| 148 | C2×C4×D5 | — | 2 | 1 | no | — |
| 149 | C2×C4×D5 | — | 2 | 1 | no | — |
| 150 | C2×C4×D5 | — | 4 | 2 | no | — |
| 151 | C2×Dic10 | C2×D4 | 1 | 1 | yes | characteristic |
| 152 | C2×Dic10 | C2×D4 | 1 | 1 | yes | characteristic |
| 153 | C5×M16 | — | 2 | 2 | no | — |
| 154 | C5×M16 | — | 2 | 2 | no | — |
| 155 | C2×C5×C8 | — | 2 | 1 | no | — |
| 156 | C2×C5×C8 | — | 2 | 1 | no | — |
| 157 | C2×C5×C8 | — | 2 | 2 | no | — |
| 158 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 159 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 160 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 161 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 162 | C2×C5×C8 | C2×D4 | 1 | 2 | yes | — |
| 163 | C2×C5×C8 | #41 | 1 | 2 | yes | — |
| 164 | C5×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 165 | C5×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 166 | C5×C22⋊C4 | — | 2 | 2 | no | — |
| 167 | C42×C5 | — | 2 | 2 | no | — |
| 168 | C42×C5 | — | 2 | 1 | no | — |
| 169 | C42×C5 | — | 2 | 1 | no | — |
| 170 | #685 | — | 4 | 2 | no | — |
| 171 | #685 | — | 4 | 2 | no | — |
| 172 | #685 | — | 4 | 2 | no | — |
| 173 | #685 | — | 8 | 4 | no | — |
| 174 | C4⋊Dic5 | — | 2 | 2 | no | — |
| 175 | C4⋊Dic5 | — | 2 | 2 | no | — |
| 176 | #683 | — | 4 | 2 | no | — |
| 177 | C4×Dic5 | — | 4 | 2 | no | — |
| 178 | #681 | — | 2 | 1 | no | — |
| 179 | #681 | — | 2 | 1 | no | — |
| 180 | #681 | — | 2 | 1 | no | — |
| 181 | #681 | C2×D4 | 1 | 2 | yes | — |
| 182 | C2×#168 | — | 2 | 1 | no | — |
| 183 | C2×#168 | — | 2 | 1 | no | — |
| 184 | Dic20 | — | 2 | 2 | no | — |
| 185 | D40 | — | 2 | 2 | no | — |
| 186 | D40 | — | 4 | 4 | no | — |
| 187 | D40 | — | 4 | 2 | no | — |
| 188 | D40 | — | 4 | 2 | no | — |
| 189 | #677 | — | 2 | 2 | no | — |
| 190 | #677 | — | 2 | 2 | no | — |
| 191 | #677 | — | 4 | 4 | no | — |
| 192 | #676 | — | 2 | 4 | no | — |
| 193 | #676 | — | 4 | 2 | no | — |
| 194 | C8×D5 | — | 2 | 4 | no | — |
| 195 | C8×D5 | — | 4 | 2 | no | — |
| 196 | C2×AGL(1,ℤ/8) | — | 5 | 2 | no | — |
| 197 | C2×#135 | — | 5 | 1 | no | — |
| 198 | C22×D8 | — | 5 | 1 | no | — |
| 199 | C2×#131 | — | 5 | 1 | no | — |
| 200 | C2×#131 | — | 5 | 1 | no | — |
| 201 | #535 | — | 5 | 2 | no | — |
| 202 | #520 | — | 5 | 2 | no | — |
| 203 | #472 | — | 10 | 4 | no | — |
| 204 | #469 | — | 10 | 2 | no | — |
| 205 | #466 | — | 10 | 1 | no | — |
| 206 | #466 | — | 10 | 1 | no | — |
| 207 | #464 | — | 10 | 2 | no | — |
| 208 | #463 | — | 10 | 2 | no | — |
| 209 | #460 | — | 10 | 2 | no | — |
| 210 | #459 | — | 10 | 2 | no | — |
| 211 | #443 | — | 10 | 4 | no | — |
| 212 | C2×#108 | — | 5 | 1 | no | — |
| 213 | C2×#108 | C2×D5 | 1 | 1 | yes | characteristic |
| 214 | #428 | — | 5 | 2 | no | — |
| 215 | #428 | — | 10 | 2 | no | — |
| 216 | #427 | — | 10 | 1 | no | — |
| 217 | #427 | C2×D5 | 1 | 1 | yes | characteristic |
| 218 | C2×#107 | — | 5 | 1 | no | — |
| 219 | C2×#107 | — | 10 | 1 | no | — |
| 220 | #424 | C2×D5 | 1 | 2 | yes | — |
| 221 | C2×#104 | — | 5 | 1 | no | — |
| 222 | C2×#104 | — | 5 | 1 | no | — |
| 223 | #418 | — | 5 | 2 | no | — |
| 224 | #417 | — | 5 | 2 | no | — |
| 225 | C2×#102 | — | 5 | 2 | no | — |
| 226 | C2×#100 | — | 5 | 2 | no | — |
| 227 | C2×C4×C8 | C2×D5 | 1 | 1 | yes | characteristic |
| 228 | #390 | — | 5 | 2 | no | — |
| 229 | #343 | — | 5 | 2 | no | — |
| 230 | #339 | C2×D5 | 1 | 2 | yes | — |
| 231 | C23×C5 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 232 | C22×D5 | — | 2 | 1 | no | — |
| 233 | C22×D5 | — | 2 | 1 | no | — |
| 234 | C22×D5 | — | 4 | 2 | no | — |
| 235 | C22×D5 | — | 4 | 2 | no | — |
| 236 | C22×D5 | — | 4 | 2 | no | — |
| 237 | C22×D5 | — | 8 | 2 | no | — |
| 238 | C22×D5 | — | 8 | 2 | no | — |
| 239 | C2×C4×C5 | — | 2 | 2 | no | — |
| 240 | C2×C4×C5 | — | 2 | 2 | no | — |
| 241 | C2×C4×C5 | — | 2 | 2 | no | — |
| 242 | C2×C4×C5 | — | 4 | 1 | no | — |
| 243 | C2×C4×C5 | — | 4 | 1 | no | — |
| 244 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 245 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 246 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 247 | C2×C4×C5 | C2×#41 | 1 | 1 | yes | characteristic |
| 248 | C2×C4×C5 | C2×#41 | 1 | 1 | yes | characteristic |
| 249 | C2×C4×C5 | 2−1+4 | 1 | 1 | yes | characteristic |
| 250 | C22⋊D5 | — | 2 | 2 | no | — |
| 251 | C22⋊D5 | — | 2 | 2 | no | — |
| 252 | C22⋊D5 | — | 4 | 1 | no | — |
| 253 | C22⋊D5 | — | 4 | 1 | no | — |
| 254 | C2×Dic5 | — | 2 | 1 | no | — |
| 255 | C2×Dic5 | — | 2 | 1 | no | — |
| 256 | C2×Dic5 | — | 4 | 2 | no | — |
| 257 | C2×Dic5 | — | 8 | 2 | no | — |
| 258 | D20 | — | 2 | 1 | no | — |
| 259 | D20 | — | 2 | 1 | no | — |
| 260 | D20 | — | 2 | 1 | no | — |
| 261 | D20 | — | 4 | 2 | no | — |
| 262 | D20 | — | 4 | 2 | no | — |
| 263 | D20 | — | 4 | 2 | no | — |
| 264 | D20 | — | 4 | 2 | no | — |
| 265 | D20 | — | 16 | 2 | no | — |
| 266 | D20 | — | 16 | 2 | no | — |
| 267 | D20 | #121 | 1 | 2 | yes | — |
| 268 | C4×D5 | — | 2 | 2 | no | — |
| 269 | C4×D5 | — | 2 | 2 | no | — |
| 270 | C4×D5 | — | 4 | 1 | no | — |
| 271 | C4×D5 | — | 4 | 1 | no | — |
| 272 | C4×D5 | — | 16 | 2 | no | — |
| 273 | Dic10 | — | 2 | 1 | no | — |
| 274 | Dic10 | — | 2 | 1 | no | — |
| 275 | Dic10 | — | 2 | 1 | no | — |
| 276 | Dic10 | #121 | 1 | 2 | yes | — |
| 277 | C5×C8 | — | 2 | 1 | no | — |
| 278 | C5×C8 | — | 2 | 1 | no | — |
| 279 | C5×C8 | — | 4 | 2 | no | — |
| 280 | C5×C8 | #121 | 1 | 2 | yes | — |
| 281 | C5×C8 | #121 | 1 | 2 | yes | — |
| 282 | #168 | — | 2 | 2 | no | — |
| 283 | #168 | — | 4 | 1 | no | — |
| 284 | C2×#41 | — | 5 | 1 | no | — |
| 285 | C2×#41 | — | 5 | 1 | no | — |
| 286 | C22×D4 | — | 5 | 2 | no | — |
| 287 | AGL(1,ℤ/8) | — | 10 | 4 | no | — |
| 288 | AGL(1,ℤ/8) | — | 10 | 4 | no | — |
| 289 | #135 | — | 10 | 2 | no | — |
| 290 | #135 | — | 10 | 2 | no | — |
| 291 | C2×Q16 | — | 5 | 1 | no | — |
| 292 | C2×SD16 | — | 5 | 1 | no | — |
| 293 | C2×SD16 | — | 5 | 1 | no | — |
| 294 | C2×SD16 | — | 10 | 2 | no | — |
| 295 | C2×D8 | — | 5 | 1 | no | — |
| 296 | C2×D8 | — | 10 | 2 | no | — |
| 297 | C2×D8 | — | 10 | 1 | no | — |
| 298 | C2×D8 | — | 10 | 1 | no | — |
| 299 | C2×D8 | — | 10 | 2 | no | — |
| 300 | C2×D8 | — | 10 | 2 | no | — |
| 301 | #131 | — | 5 | 4 | no | — |
| 302 | #131 | — | 10 | 2 | no | — |
| 303 | #131 | — | 10 | 2 | no | — |
| 304 | #131 | — | 10 | 2 | no | — |
| 305 | C2×M16 | — | 5 | 1 | no | — |
| 306 | C2×M16 | — | 5 | 1 | no | — |
| 307 | C2×M16 | — | 10 | 1 | no | — |
| 308 | C2×M16 | — | 10 | 1 | no | — |
| 309 | C2×M16 | C22×D5 | 1 | 2 | yes | — |
| 310 | C22×C8 | — | 10 | 1 | no | — |
| 311 | C22×C8 | — | 10 | 1 | no | — |
| 312 | C22×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 313 | C22×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 314 | #127 | — | 10 | 2 | no | — |
| 315 | #124 | — | 10 | 2 | no | — |
| 316 | #121 | — | 10 | 2 | no | — |
| 317 | #121 | — | 10 | 2 | no | — |
| 318 | #120 | — | 20 | 2 | no | — |
| 319 | C4×Q8 | — | 10 | 2 | no | — |
| 320 | C4×D4 | — | 10 | 2 | no | — |
| 321 | C4×D4 | — | 20 | 2 | no | — |
| 322 | #117 | — | 10 | 2 | no | — |
| 323 | #117 | C22×D5 | 1 | 2 | yes | — |
| 324 | C2×C4⋊C4 | — | 5 | 2 | no | — |
| 325 | C2×C4⋊C4 | — | 10 | 2 | no | — |
| 326 | C2×C22⋊C4 | — | 20 | 2 | no | — |
| 327 | C2×C42 | C22×D5 | 1 | 1 | yes | characteristic |
| 328 | #108 | — | 2 | 2 | no | — |
| 329 | #108 | — | 10 | 2 | no | — |
| 330 | #107 | — | 10 | 1 | no | — |
| 331 | #107 | — | 10 | 1 | no | — |
| 332 | #107 | — | 10 | 2 | no | — |
| 333 | #107 | D20 | 1 | 1 | yes | characteristic |
| 334 | #107 | D20 | 1 | 1 | yes | characteristic |
| 335 | #106 | — | 10 | 2 | no | — |
| 336 | #106 | D20 | 1 | 2 | yes | — |
| 337 | C4⋊C8 | — | 2 | 2 | no | — |
| 338 | C4⋊C8 | — | 2 | 2 | no | — |
| 339 | #104 | — | 10 | 2 | no | — |
| 340 | #104 | — | 10 | 2 | no | — |
| 341 | #103 | — | 10 | 2 | no | — |
| 342 | #102 | — | 10 | 2 | no | — |
| 343 | #102 | — | 10 | 2 | no | — |
| 344 | #102 | — | 10 | 2 | no | — |
| 345 | #102 | — | 10 | 2 | no | — |
| 346 | #102 | — | 10 | 2 | no | — |
| 347 | #100 | — | 10 | 4 | no | — |
| 348 | C4×C8 | — | 2 | 2 | no | — |
| 349 | C22×C5 | — | 2 | 1 | no | — |
| 350 | C22×C5 | — | 2 | 1 | no | — |
| 351 | C22×C5 | #537 | 1 | 1 | yes | characteristic |
| 352 | C22×C5 | D42 | 1 | 1 | yes | characteristic |
| 353 | C22×C5 | #553 | 1 | 1 | yes | characteristic |
| 354 | C2×D5 | — | 2 | 2 | no | — |
| 355 | C2×D5 | — | 4 | 1 | no | — |
| 356 | C2×D5 | — | 4 | 1 | no | — |
| 357 | C2×D5 | — | 4 | 1 | no | — |
| 358 | C2×D5 | — | 4 | 1 | no | — |
| 359 | C2×D5 | — | 4 | 1 | no | — |
| 360 | C2×D5 | — | 8 | 4 | no | — |
| 361 | C2×D5 | — | 8 | 2 | no | — |
| 362 | C2×D5 | — | 8 | 2 | no | — |
| 363 | C2×D5 | — | 8 | 2 | no | — |
| 364 | C2×D5 | — | 16 | 2 | no | — |
| 365 | C4×C5 | — | 4 | 2 | no | — |
| 366 | C4×C5 | — | 4 | 2 | no | — |
| 367 | C4×C5 | — | 4 | 2 | no | — |
| 368 | C4×C5 | C2×#121 | 1 | 1 | yes | characteristic |
| 369 | C4×C5 | C2×#121 | 1 | 1 | yes | characteristic |
| 370 | C4×C5 | #547 | 1 | 1 | yes | characteristic |
| 371 | C4×C5 | #548 | 1 | 1 | yes | characteristic |
| 372 | Dic5 | — | 2 | 2 | no | — |
| 373 | Dic5 | — | 4 | 1 | no | — |
| 374 | Dic5 | — | 8 | 2 | no | — |
| 375 | C24 | — | 10 | 2 | no | — |
| 376 | #41 | — | 5 | 2 | no | — |
| 377 | #41 | — | 5 | 2 | no | — |
| 378 | #41 | — | 10 | 1 | no | — |
| 379 | #41 | — | 10 | 1 | no | — |
| 380 | #41 | — | 10 | 1 | no | — |
| 381 | #41 | — | 10 | 1 | no | — |
| 382 | #41 | — | 10 | 1 | no | — |
| 383 | #41 | — | 10 | 1 | no | — |
| 384 | C2×Q8 | — | 5 | 1 | no | — |
| 385 | C2×Q8 | — | 5 | 1 | no | — |
| 386 | C2×D4 | — | 5 | 1 | no | — |
| 387 | C2×D4 | — | 5 | 1 | no | — |
| 388 | C2×D4 | — | 10 | 1 | no | — |
| 389 | C2×D4 | — | 10 | 1 | no | — |
| 390 | C2×D4 | — | 10 | 2 | no | — |
| 391 | C2×D4 | — | 10 | 2 | no | — |
| 392 | C2×D4 | — | 10 | 2 | no | — |
| 393 | C2×D4 | — | 10 | 2 | no | — |
| 394 | C2×D4 | — | 10 | 2 | no | — |
| 395 | C2×D4 | — | 10 | 2 | no | — |
| 396 | C2×D4 | — | 20 | 2 | no | — |
| 397 | C2×D4 | — | 20 | 2 | no | — |
| 398 | C22×C4 | — | 2 | 1 | no | — |
| 399 | C22×C4 | — | 10 | 1 | no | — |
| 400 | C22×C4 | — | 10 | 1 | no | — |
| 401 | C22×C4 | — | 10 | 2 | no | — |
| 402 | C22×C4 | — | 20 | 2 | no | — |
| 403 | C22×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 404 | Q16 | — | 10 | 2 | no | — |
| 405 | SD16 | — | 10 | 2 | no | — |
| 406 | SD16 | — | 10 | 2 | no | — |
| 407 | SD16 | — | 20 | 4 | no | — |
| 408 | D8 | — | 10 | 2 | no | — |
| 409 | D8 | — | 20 | 4 | no | — |
| 410 | D8 | — | 20 | 2 | no | — |
| 411 | D8 | — | 20 | 2 | no | — |
| 412 | M16 | — | 2 | 2 | no | — |
| 413 | M16 | — | 2 | 2 | no | — |
| 414 | M16 | — | 5 | 2 | no | — |
| 415 | M16 | — | 10 | 1 | no | — |
| 416 | M16 | — | 10 | 4 | no | — |
| 417 | M16 | — | 10 | 1 | no | — |
| 418 | M16 | — | 10 | 1 | no | — |
| 419 | M16 | — | 20 | 2 | no | — |
| 420 | C2×C8 | — | 2 | 1 | no | — |
| 421 | C2×C8 | — | 2 | 1 | no | — |
| 422 | C2×C8 | — | 2 | 2 | no | — |
| 423 | C2×C8 | — | 10 | 1 | no | — |
| 424 | C2×C8 | — | 10 | 4 | no | — |
| 425 | C2×C8 | — | 10 | 1 | no | — |
| 426 | C2×C8 | — | 20 | 2 | no | — |
| 427 | C2×C8 | C2×D20 | 1 | 1 | yes | characteristic |
| 428 | C2×C8 | C2×D20 | 1 | 1 | yes | characteristic |
| 429 | C2×C8 | D4×D5 | 1 | 1 | yes | characteristic |
| 430 | C2×C8 | D4×D5 | 1 | 1 | yes | characteristic |
| 431 | C2×C8 | D4×D5 | 1 | 2 | yes | — |
| 432 | C2×C8 | #713 | 1 | 2 | yes | — |
| 433 | C4⋊C4 | — | 10 | 2 | no | — |
| 434 | C4⋊C4 | — | 10 | 2 | no | — |
| 435 | C4⋊C4 | — | 20 | 2 | no | — |
| 436 | C4⋊C4 | C2×D20 | 1 | 2 | yes | — |
| 437 | C4⋊C4 | C2×D20 | 1 | 2 | yes | — |
| 438 | C22⋊C4 | — | 2 | 2 | no | — |
| 439 | C22⋊C4 | — | 20 | 2 | no | — |
| 440 | C22⋊C4 | — | 20 | 2 | no | — |
| 441 | C22⋊C4 | — | 20 | 2 | no | — |
| 442 | C22⋊C4 | — | 40 | 4 | no | — |
| 443 | C42 | — | 2 | 2 | no | — |
| 444 | C42 | — | 2 | 1 | no | — |
| 445 | C42 | — | 2 | 1 | no | — |
| 446 | C42 | — | 20 | 2 | no | — |
| 447 | C2×C5 | — | 2 | 1 | no | — |
| 448 | C2×C5 | — | 2 | 1 | no | — |
| 449 | C2×C5 | #2416 | 1 | 1 | yes | characteristic |
| 450 | C2×C5 | #3290 | 1 | 1 | yes | characteristic |
| 451 | C2×C5 | #3292 | 1 | 1 | yes | characteristic |
| 452 | D5 | — | 4 | 2 | no | — |
| 453 | D5 | — | 8 | 1 | no | — |
| 454 | D5 | — | 16 | 2 | no | — |
| 455 | C23 | — | 10 | 1 | no | — |
| 456 | C23 | — | 10 | 1 | no | — |
| 457 | C23 | — | 20 | 2 | no | — |
| 458 | C23 | — | 20 | 2 | no | — |
| 459 | C23 | — | 20 | 2 | no | — |
| 460 | C23 | — | 40 | 2 | no | — |
| 461 | C23 | — | 40 | 2 | no | — |
| 462 | C23 | #4149 | 1 | 1 | yes | characteristic |
| 463 | Q8 | — | 5 | 2 | no | — |
| 464 | Q8 | — | 10 | 1 | no | — |
| 465 | Q8 | — | 10 | 1 | no | — |
| 466 | Q8 | — | 10 | 1 | no | — |
| 467 | D4 | — | 5 | 2 | no | — |
| 468 | D4 | — | 10 | 2 | no | — |
| 469 | D4 | — | 10 | 2 | no | — |
| 470 | D4 | — | 10 | 1 | no | — |
| 471 | D4 | — | 10 | 1 | no | — |
| 472 | D4 | — | 10 | 1 | no | — |
| 473 | D4 | — | 20 | 1 | no | — |
| 474 | D4 | — | 20 | 1 | no | — |
| 475 | D4 | — | 20 | 2 | no | — |
| 476 | D4 | — | 20 | 2 | no | — |
| 477 | D4 | — | 20 | 2 | no | — |
| 478 | D4 | — | 20 | 2 | no | — |
| 479 | D4 | — | 80 | 2 | no | — |
| 480 | D4 | — | 80 | 2 | no | — |
| 481 | C2×C4 | — | 2 | 2 | no | — |
| 482 | C2×C4 | — | 2 | 2 | no | — |
| 483 | C2×C4 | — | 2 | 2 | no | — |
| 484 | C2×C4 | — | 4 | 1 | no | — |
| 485 | C2×C4 | — | 4 | 1 | no | — |
| 486 | C2×C4 | — | 10 | 1 | no | — |
| 487 | C2×C4 | — | 10 | 2 | no | — |
| 488 | C2×C4 | — | 10 | 2 | no | — |
| 489 | C2×C4 | — | 10 | 1 | no | — |
| 490 | C2×C4 | — | 20 | 1 | no | — |
| 491 | C2×C4 | — | 20 | 1 | no | — |
| 492 | C2×C4 | — | 20 | 2 | no | — |
| 493 | C2×C4 | — | 40 | 2 | no | — |
| 494 | C2×C4 | — | 80 | 2 | no | — |
| 495 | C2×C4 | C22×D20 | 1 | 1 | yes | characteristic |
| 496 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 497 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 498 | C2×C4 | C2×#713 | 1 | 1 | yes | characteristic |
| 499 | C2×C4 | #4147 | 1 | 1 | yes | characteristic |
| 500 | C2×C4 | D5×#41 | 1 | 1 | yes | characteristic |
| 501 | C8 | — | 2 | 1 | no | — |
| 502 | C8 | — | 2 | 1 | no | — |
| 503 | C8 | — | 4 | 2 | no | — |
| 504 | C8 | — | 10 | 2 | no | — |
| 505 | C8 | — | 20 | 1 | no | — |
| 506 | C8 | #4041 | 1 | 2 | yes | — |
| 507 | C8 | #4041 | 1 | 2 | yes | — |
| 508 | C5 | #24797 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 509 | C22 | — | 2 | 1 | no | — |
| 510 | C22 | — | 2 | 1 | no | — |
| 511 | C22 | — | 10 | 2 | no | — |
| 512 | C22 | — | 20 | 1 | no | — |
| 513 | C22 | — | 20 | 1 | no | — |
| 514 | C22 | — | 20 | 1 | no | — |
| 515 | C22 | — | 20 | 1 | no | — |
| 516 | C22 | — | 20 | 1 | no | — |
| 517 | C22 | — | 40 | 4 | no | — |
| 518 | C22 | — | 40 | 2 | no | — |
| 519 | C22 | — | 40 | 2 | no | — |
| 520 | C22 | — | 40 | 2 | no | — |
| 521 | C22 | — | 80 | 2 | no | — |
| 522 | C22 | D4×D20 | 1 | 1 | yes | characteristic |
| 523 | C22 | #65963 | 1 | 1 | yes | characteristic |
| 524 | C22 | #66029 | 1 | 1 | yes | characteristic |
| 525 | C4 | — | 4 | 2 | no | — |
| 526 | C4 | — | 4 | 2 | no | — |
| 527 | C4 | — | 4 | 2 | no | — |
| 528 | C4 | — | 10 | 2 | no | — |
| 529 | C4 | — | 20 | 1 | no | — |
| 530 | C4 | — | 40 | 2 | no | — |
| 531 | C4 | C2×#4041 | 1 | 1 | yes | characteristic |
| 532 | C4 | #65910 | 1 | 1 | yes | characteristic |
| 533 | C4 | D5×#121 | 1 | 1 | yes | characteristic |
| 534 | C4 | #66060 | 1 | 1 | yes | characteristic |
| 535 | C2 | — | 2 | 1 | no | — |
| 536 | C2 | — | 2 | 1 | no | — |
| 537 | C2 | — | 20 | 2 | no | — |
| 538 | C2 | — | 40 | 1 | no | — |
| 539 | C2 | — | 80 | 2 | no | — |
| 540 | C2 | #10607942 | 1 | 1 | yes | characteristic |
| 541 | C2 | #10611623 | 1 | 1 | yes | characteristic |
| 542 | C2 | #10611625 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#65186 | C2 | semidirect |
| 2. #10610914 | C2 | semidirect |
| 3. #10610910 | C2 | semidirect |
| 4. #10610819 | C2 | semidirect |
| 5. C2×#64989 | C2 | semidirect |
| 6. C5×#1945 | C2 | semidirect |
| 7. #10601514 | C2 | semidirect |
| 8. #10601335 | C2 | semidirect |
| 9. #10600569 | C2 | semidirect |
| 10. #10599569 | C2 | semidirect |
| 11. #10599526 | C2 | semidirect |
| 77. #4047 | D4 | semidirect |
| 121. #1945 | D5 | semidirect |
| 508. C5 | #24797 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65186 | 2 |
| #10610914 | 2 |
| #10610910 | 2 |
| #10610819 | 2 |
| C2×#64989 | 2 |
| C5×#1945 | 2 |
| #10601514 | 2 |
| #10601335 | 2 |
| #10600569 | 2 |
| #10599569 | 2 |
| #10599526 | 2 |
| #24797 | 5 |