Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1362 conjugacy classes of subgroups.
The subgroup lattice has 642 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#66103 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10615648 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#65186 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10610403 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C2×#64989 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C5×#1974 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10601514 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10601185 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10601177 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #10600796 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #10600569 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#4149 | C22 | 1 | 2 | yes | — |
| 13 | C2×C5×#135 | C22 | 1 | 1 | yes | characteristic |
| 14 | #66167 | C22 | 1 | 2 | yes | complemented |
| 15 | C2×#4095 | C22 | 1 | 2 | yes | — |
| 16 | #66103 | — | 2 | 4 | no | — |
| 17 | #66103 | — | 2 | 4 | no | — |
| 18 | C2×#4065 | — | 2 | 1 | no | — |
| 19 | C2×#4060 | — | 2 | 2 | no | — |
| 20 | C2×D5×D8 | — | 2 | 1 | no | — |
| 21 | C2×#4054 | C22 | 1 | 2 | yes | complemented |
| 22 | C2×#4050 | C22 | 1 | 1 | yes | characteristic |
| 23 | C22×D40 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×#4047 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#4047 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | C2×C5×#108 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | C2×C5×#104 | C22 | 1 | 2 | yes | complemented |
| 28 | C5×#408 | C22 | 1 | 2 | yes | complemented |
| 29 | C2×C4×C5×C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | #65521 | C22 | 1 | 2 | yes | complemented |
| 31 | #65477 | — | 2 | 1 | no | — |
| 32 | #65463 | — | 2 | 2 | no | — |
| 33 | #65446 | — | 2 | 1 | no | — |
| 34 | #65422 | C22 | 1 | 2 | yes | — |
| 35 | C2×#3955 | C22 | 1 | 2 | yes | complemented |
| 36 | C2×#3953 | C22 | 1 | 2 | yes | complemented |
| 37 | C2×#3951 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | C2×#3950 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | #65228 | C22 | 1 | 2 | yes | complemented |
| 40 | C2×#3937 | C22 | 1 | 1 | yes | characteristic |
| 41 | C2×#3937 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | #65186 | — | 2 | 4 | no | — |
| 43 | #65023 | — | 2 | 2 | no | — |
| 44 | #65022 | — | 2 | 2 | no | — |
| 45 | #65021 | — | 2 | 2 | no | — |
| 46 | #65020 | — | 2 | 2 | no | — |
| 47 | #64989 | — | 2 | 4 | no | — |
| 48 | #64774 | C22 | 1 | 2 | yes | complemented |
| 49 | #24291 | — | 5 | 1 | no | maximal, Sylow |
| 50 | C2×C5×#41 | C23 | 1 | 2 | yes | — |
| 51 | #4149 | — | 2 | 4 | no | — |
| 52 | #4149 | — | 2 | 4 | no | — |
| 53 | #4149 | — | 2 | 4 | no | — |
| 54 | #4149 | — | 4 | 2 | no | — |
| 55 | C2×#713 | — | 2 | 2 | no | — |
| 56 | C2×D4×D5 | — | 2 | 2 | no | — |
| 57 | C2×D4×D5 | — | 4 | 2 | no | — |
| 58 | C2×#709 | — | 2 | 2 | no | — |
| 59 | C2×#709 | C23 | 1 | 1 | yes | characteristic |
| 60 | C2×#709 | C23 | 1 | 1 | yes | characteristic |
| 61 | C22×D20 | — | 2 | 2 | no | — |
| 62 | C22×D20 | C23 | 1 | 2 | yes | — |
| 63 | C5×#135 | — | 2 | 2 | no | — |
| 64 | C5×#135 | — | 2 | 2 | no | — |
| 65 | C2×C5×Q16 | D4 | 1 | 1 | yes | characteristic |
| 66 | C2×C5×SD16 | D4 | 1 | 2 | yes | — |
| 67 | C2×C5×D8 | D4 | 1 | 1 | yes | characteristic |
| 68 | C2×C5×M16 | C23 | 1 | 2 | yes | — |
| 69 | C22×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 70 | C22×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 71 | C2×C42×C5 | C23 | 1 | 1 | yes | characteristic |
| 72 | #4095 | — | 2 | 4 | no | — |
| 73 | #4095 | — | 2 | 4 | no | — |
| 74 | #4092 | — | 2 | 2 | no | — |
| 75 | C2×#688 | — | 2 | 2 | no | — |
| 76 | #4085 | — | 4 | 2 | no | — |
| 77 | #4084 | — | 2 | 2 | no | — |
| 78 | C2×#686 | — | 2 | 2 | no | — |
| 79 | #4076 | — | 2 | 2 | no | — |
| 80 | C2×#685 | — | 4 | 2 | no | — |
| 81 | C2×C4⋊Dic5 | C23 | 1 | 2 | yes | — |
| 82 | #4070 | — | 2 | 2 | no | — |
| 83 | C2×#681 | C23 | 1 | 1 | yes | characteristic |
| 84 | C2×#681 | C23 | 1 | 1 | yes | characteristic |
| 85 | #4065 | — | 2 | 8 | no | — |
| 86 | #4060 | — | 2 | 16 | no | — |
| 87 | D5×D8 | — | 2 | 8 | no | — |
| 88 | #4054 | — | 2 | 4 | no | — |
| 89 | #4054 | — | 4 | 2 | no | — |
| 90 | C2×Dic20 | D4 | 1 | 1 | yes | characteristic |
| 91 | #4050 | — | 2 | 2 | no | — |
| 92 | #4050 | — | 2 | 2 | no | — |
| 93 | C2×D40 | — | 2 | 1 | no | — |
| 94 | C2×D40 | — | 2 | 1 | no | — |
| 95 | C2×D40 | — | 2 | 2 | no | — |
| 96 | C2×D40 | — | 2 | 2 | no | — |
| 97 | C2×D40 | D4 | 1 | 1 | yes | characteristic |
| 98 | C2×D40 | D4 | 1 | 4 | yes | complemented |
| 99 | C2×#677 | — | 2 | 2 | no | — |
| 100 | C2×#677 | D4 | 1 | 1 | yes | characteristic |
| 101 | C2×#677 | D4 | 1 | 1 | yes | characteristic |
| 102 | #4047 | — | 2 | 2 | no | — |
| 103 | #4047 | — | 2 | 2 | no | — |
| 104 | #4047 | — | 2 | 2 | no | — |
| 105 | #4047 | D4 | 1 | 4 | yes | complemented |
| 106 | C2×#676 | — | 2 | 1 | no | — |
| 107 | C2×#676 | — | 2 | 1 | no | — |
| 108 | C2×C8×D5 | — | 2 | 1 | no | — |
| 109 | C2×C8×D5 | — | 2 | 1 | no | — |
| 110 | C5×#108 | — | 2 | 2 | no | — |
| 111 | C5×#104 | — | 4 | 2 | no | — |
| 112 | C5×C22⋊C8 | — | 2 | 2 | no | — |
| 113 | C5×C22⋊C8 | — | 2 | 2 | no | — |
| 114 | C4×C5×C8 | — | 2 | 2 | no | — |
| 115 | #3967 | — | 2 | 2 | no | — |
| 116 | #3964 | — | 2 | 2 | no | — |
| 117 | #3955 | — | 2 | 4 | no | — |
| 118 | #3953 | — | 2 | 2 | no | — |
| 119 | #3953 | — | 2 | 2 | no | — |
| 120 | #3953 | — | 2 | 2 | no | — |
| 121 | #3951 | — | 2 | 2 | no | — |
| 122 | #3950 | — | 2 | 1 | no | — |
| 123 | #3950 | — | 2 | 1 | no | — |
| 124 | #3948 | — | 2 | 2 | no | — |
| 125 | #3937 | — | 2 | 2 | no | — |
| 126 | #3937 | — | 2 | 2 | no | — |
| 127 | C2×#576 | — | 5 | 1 | no | — |
| 128 | C2×#472 | — | 5 | 1 | no | — |
| 129 | #3061 | — | 5 | 1 | no | — |
| 130 | #3012 | — | 5 | 2 | no | — |
| 131 | C2×#443 | — | 5 | 1 | no | — |
| 132 | #2051 | — | 5 | 2 | no | — |
| 133 | #2006 | — | 5 | 2 | no | — |
| 134 | #1974 | D5 | 1 | 1 | yes | characteristic, complemented |
| 135 | #1970 | — | 5 | 1 | no | — |
| 136 | #1816 | — | 5 | 1 | no | — |
| 137 | #1792 | — | 5 | 2 | no | — |
| 138 | C23×D5 | — | 2 | 2 | no | — |
| 139 | C23×D5 | — | 4 | 2 | no | — |
| 140 | C5×#41 | — | 2 | 2 | no | — |
| 141 | C5×#41 | — | 2 | 2 | no | — |
| 142 | C5×#41 | — | 2 | 2 | no | — |
| 143 | C5×#41 | — | 2 | 2 | no | — |
| 144 | C2×C5×Q8 | C2×D4 | 1 | 2 | yes | — |
| 145 | C2×C5×D4 | — | 2 | 2 | no | — |
| 146 | C2×C5×D4 | C2×D4 | 1 | 2 | yes | — |
| 147 | C22×C4×C5 | — | 2 | 1 | no | — |
| 148 | C22×C4×C5 | — | 2 | 2 | no | — |
| 149 | C22×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 150 | C2×C22⋊D5 | — | 2 | 1 | no | — |
| 151 | C2×C22⋊D5 | — | 2 | 1 | no | — |
| 152 | C2×C22⋊D5 | — | 4 | 2 | no | — |
| 153 | C2×C22⋊D5 | — | 4 | 2 | no | — |
| 154 | C22×Dic5 | — | 2 | 2 | no | — |
| 155 | #713 | — | 2 | 8 | no | — |
| 156 | #713 | — | 4 | 4 | no | — |
| 157 | D4×D5 | — | 2 | 8 | no | — |
| 158 | D4×D5 | — | 4 | 4 | no | — |
| 159 | D4×D5 | — | 4 | 8 | no | — |
| 160 | D4×D5 | — | 4 | 8 | no | — |
| 161 | #709 | — | 2 | 1 | no | — |
| 162 | #709 | — | 2 | 1 | no | — |
| 163 | #709 | — | 2 | 1 | no | — |
| 164 | #709 | — | 2 | 1 | no | — |
| 165 | #709 | — | 2 | 1 | no | — |
| 166 | #709 | — | 2 | 1 | no | — |
| 167 | #709 | — | 4 | 4 | no | — |
| 168 | #709 | — | 4 | 4 | no | — |
| 169 | #709 | C2×D4 | 1 | 2 | yes | — |
| 170 | #709 | #41 | 1 | 2 | yes | — |
| 171 | C2×D20 | — | 2 | 2 | no | — |
| 172 | C2×D20 | — | 2 | 2 | no | — |
| 173 | C2×D20 | — | 2 | 2 | no | — |
| 174 | C2×D20 | — | 2 | 2 | no | — |
| 175 | C2×D20 | — | 2 | 2 | no | — |
| 176 | C2×D20 | — | 4 | 4 | no | — |
| 177 | C2×D20 | — | 4 | 2 | no | — |
| 178 | C2×D20 | — | 4 | 4 | no | — |
| 179 | C2×D20 | C2×D4 | 1 | 4 | yes | — |
| 180 | C2×D20 | C2×D4 | 1 | 1 | yes | characteristic |
| 181 | C2×D20 | C2×D4 | 1 | 1 | yes | characteristic |
| 182 | C2×C4×D5 | — | 2 | 1 | no | — |
| 183 | C2×C4×D5 | — | 2 | 1 | no | — |
| 184 | C2×C4×D5 | — | 4 | 2 | no | — |
| 185 | C2×Dic10 | C2×D4 | 1 | 1 | yes | characteristic |
| 186 | C2×Dic10 | C2×D4 | 1 | 1 | yes | characteristic |
| 187 | C5×Q16 | — | 2 | 2 | no | — |
| 188 | C5×SD16 | — | 2 | 4 | no | — |
| 189 | C5×D8 | — | 2 | 2 | no | — |
| 190 | C5×M16 | — | 2 | 2 | no | — |
| 191 | C5×M16 | — | 2 | 2 | no | — |
| 192 | C2×C5×C8 | — | 2 | 1 | no | — |
| 193 | C2×C5×C8 | — | 2 | 1 | no | — |
| 194 | C2×C5×C8 | — | 2 | 2 | no | — |
| 195 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 196 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 197 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 198 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 199 | C2×C5×C8 | C2×D4 | 1 | 2 | yes | — |
| 200 | C2×C5×C8 | C2×D4 | 1 | 2 | yes | — |
| 201 | C42×C5 | — | 2 | 1 | no | — |
| 202 | C42×C5 | — | 2 | 1 | no | — |
| 203 | C22⋊Dic5 | — | 4 | 2 | no | — |
| 204 | #688 | — | 2 | 8 | no | — |
| 205 | #686 | — | 2 | 8 | no | — |
| 206 | #685 | — | 4 | 2 | no | — |
| 207 | #685 | — | 8 | 4 | no | — |
| 208 | C4⋊Dic5 | — | 2 | 2 | no | — |
| 209 | C4⋊Dic5 | — | 2 | 2 | no | — |
| 210 | #683 | — | 4 | 2 | no | — |
| 211 | #681 | — | 2 | 1 | no | — |
| 212 | #681 | — | 2 | 1 | no | — |
| 213 | #681 | — | 2 | 1 | no | — |
| 214 | #681 | C2×D4 | 1 | 2 | yes | — |
| 215 | C2×#168 | — | 2 | 1 | no | — |
| 216 | C2×#168 | — | 2 | 1 | no | — |
| 217 | Dic20 | — | 2 | 2 | no | — |
| 218 | D40 | — | 2 | 2 | no | — |
| 219 | D40 | — | 2 | 4 | no | — |
| 220 | D40 | — | 2 | 4 | no | — |
| 221 | D40 | — | 4 | 4 | no | — |
| 222 | #677 | — | 2 | 2 | no | — |
| 223 | #677 | — | 2 | 2 | no | — |
| 224 | #677 | — | 4 | 4 | no | — |
| 225 | #676 | — | 2 | 4 | no | — |
| 226 | #676 | — | 4 | 2 | no | — |
| 227 | C8×D5 | — | 2 | 4 | no | — |
| 228 | C8×D5 | — | 4 | 2 | no | — |
| 229 | C2×H(5,𝔽2) | — | 5 | 2 | no | — |
| 230 | #576 | — | 10 | 4 | no | — |
| 231 | #576 | — | 10 | 4 | no | — |
| 232 | C2×AGL(1,ℤ/8) | — | 5 | 2 | no | — |
| 233 | C2×AGL(1,ℤ/8) | — | 5 | 2 | no | — |
| 234 | C2×AGL(1,ℤ/8) | — | 10 | 2 | no | — |
| 235 | C2×#135 | — | 5 | 1 | no | — |
| 236 | C2×#135 | — | 10 | 1 | no | — |
| 237 | C2×#135 | C2×D5 | 1 | 1 | yes | characteristic |
| 238 | C22×D8 | — | 5 | 1 | no | — |
| 239 | C22×D8 | — | 10 | 1 | no | — |
| 240 | C2×#131 | — | 5 | 1 | no | — |
| 241 | C2×#131 | — | 5 | 1 | no | — |
| 242 | #537 | — | 5 | 2 | no | — |
| 243 | #472 | — | 10 | 4 | no | — |
| 244 | #468 | — | 10 | 2 | no | — |
| 245 | #467 | — | 10 | 1 | no | — |
| 246 | #466 | — | 10 | 1 | no | — |
| 247 | #452 | — | 10 | 2 | no | — |
| 248 | #450 | — | 10 | 2 | no | — |
| 249 | #449 | — | 10 | 2 | no | — |
| 250 | #447 | — | 10 | 2 | no | — |
| 251 | #443 | — | 10 | 4 | no | — |
| 252 | C2×#108 | — | 5 | 1 | no | — |
| 253 | C2×#108 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 254 | C2×#107 | — | 5 | 1 | no | — |
| 255 | C2×#104 | — | 5 | 1 | no | — |
| 256 | C2×#104 | — | 5 | 1 | no | — |
| 257 | C2×#104 | C2×D5 | 1 | 2 | yes | complemented |
| 258 | #417 | — | 5 | 2 | no | — |
| 259 | #417 | — | 5 | 2 | no | — |
| 260 | C2×#102 | — | 5 | 2 | no | — |
| 261 | C2×#100 | — | 5 | 2 | no | — |
| 262 | #408 | C2×D5 | 1 | 2 | yes | complemented |
| 263 | C2×C4×C8 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 264 | #390 | — | 5 | 2 | no | — |
| 265 | #343 | — | 5 | 2 | no | — |
| 266 | C23×C5 | — | 2 | 2 | no | — |
| 267 | C23×C5 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 268 | C22×D5 | — | 2 | 1 | no | — |
| 269 | C22×D5 | — | 2 | 1 | no | — |
| 270 | C22×D5 | — | 2 | 4 | no | — |
| 271 | C22×D5 | — | 4 | 8 | no | — |
| 272 | C22×D5 | — | 4 | 2 | no | — |
| 273 | C22×D5 | — | 4 | 2 | no | — |
| 274 | C22×D5 | — | 8 | 2 | no | — |
| 275 | C22×D5 | — | 8 | 2 | no | — |
| 276 | C22×D5 | — | 16 | 2 | no | — |
| 277 | C22×D5 | — | 16 | 2 | no | — |
| 278 | C5×Q8 | — | 2 | 2 | no | — |
| 279 | C5×Q8 | — | 2 | 2 | no | — |
| 280 | C5×D4 | — | 2 | 2 | no | — |
| 281 | C5×D4 | — | 2 | 2 | no | — |
| 282 | C5×D4 | — | 4 | 2 | no | — |
| 283 | C5×D4 | — | 4 | 2 | no | — |
| 284 | C2×C4×C5 | — | 2 | 2 | no | — |
| 285 | C2×C4×C5 | — | 2 | 2 | no | — |
| 286 | C2×C4×C5 | — | 4 | 1 | no | — |
| 287 | C2×C4×C5 | — | 4 | 1 | no | — |
| 288 | C2×C4×C5 | — | 4 | 2 | no | — |
| 289 | C2×C4×C5 | — | 4 | 2 | no | — |
| 290 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 291 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 292 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 293 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 294 | C2×C4×C5 | C2×#41 | 1 | 1 | yes | characteristic |
| 295 | C2×C4×C5 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 296 | C22⋊D5 | — | 2 | 2 | no | — |
| 297 | C22⋊D5 | — | 2 | 2 | no | — |
| 298 | C22⋊D5 | — | 4 | 8 | no | — |
| 299 | C22⋊D5 | — | 4 | 1 | no | — |
| 300 | C22⋊D5 | — | 4 | 1 | no | — |
| 301 | C22⋊D5 | — | 16 | 2 | no | — |
| 302 | C2×Dic5 | — | 2 | 1 | no | — |
| 303 | C2×Dic5 | — | 2 | 1 | no | — |
| 304 | C2×Dic5 | — | 4 | 2 | no | — |
| 305 | C2×Dic5 | — | 8 | 2 | no | — |
| 306 | D20 | — | 2 | 4 | no | — |
| 307 | D20 | — | 2 | 1 | no | — |
| 308 | D20 | — | 2 | 1 | no | — |
| 309 | D20 | — | 2 | 4 | no | — |
| 310 | D20 | — | 2 | 1 | no | — |
| 311 | D20 | — | 4 | 8 | no | — |
| 312 | D20 | — | 4 | 2 | no | — |
| 313 | D20 | — | 4 | 2 | no | — |
| 314 | D20 | #121 | 1 | 2 | yes | — |
| 315 | C4×D5 | — | 2 | 2 | no | — |
| 316 | C4×D5 | — | 2 | 2 | no | — |
| 317 | C4×D5 | — | 4 | 8 | no | — |
| 318 | C4×D5 | — | 4 | 1 | no | — |
| 319 | C4×D5 | — | 4 | 1 | no | — |
| 320 | Dic10 | — | 2 | 1 | no | — |
| 321 | Dic10 | — | 2 | 1 | no | — |
| 322 | Dic10 | — | 2 | 1 | no | — |
| 323 | Dic10 | #121 | 1 | 2 | yes | — |
| 324 | C5×C8 | — | 2 | 1 | no | — |
| 325 | C5×C8 | — | 2 | 1 | no | — |
| 326 | C5×C8 | — | 4 | 2 | no | — |
| 327 | C5×C8 | #120 | 1 | 2 | yes | — |
| 328 | C5×C8 | #120 | 1 | 2 | yes | — |
| 329 | #168 | — | 2 | 2 | no | — |
| 330 | #168 | — | 4 | 1 | no | — |
| 331 | H(5,𝔽2) | — | 10 | 4 | no | — |
| 332 | H(5,𝔽2) | — | 10 | 4 | no | — |
| 333 | H(5,𝔽2) | — | 10 | 4 | no | — |
| 334 | H(5,𝔽2) | — | 20 | 2 | no | — |
| 335 | C2×#41 | — | 5 | 1 | no | — |
| 336 | C2×#41 | — | 5 | 1 | no | — |
| 337 | C2×#41 | — | 10 | 2 | no | — |
| 338 | C2×#41 | — | 10 | 2 | no | — |
| 339 | C2×#41 | C22×D5 | 1 | 2 | yes | — |
| 340 | C22×D4 | — | 5 | 2 | no | — |
| 341 | C22×D4 | — | 10 | 2 | no | — |
| 342 | C22×D4 | — | 10 | 2 | no | — |
| 343 | C22×D4 | — | 20 | 2 | no | — |
| 344 | AGL(1,ℤ/8) | — | 10 | 4 | no | — |
| 345 | AGL(1,ℤ/8) | — | 10 | 4 | no | — |
| 346 | AGL(1,ℤ/8) | — | 10 | 16 | no | — |
| 347 | AGL(1,ℤ/8) | — | 10 | 4 | no | — |
| 348 | AGL(1,ℤ/8) | — | 20 | 2 | no | — |
| 349 | #135 | — | 2 | 2 | no | — |
| 350 | #135 | — | 2 | 2 | no | — |
| 351 | #135 | — | 10 | 2 | no | — |
| 352 | #135 | — | 10 | 2 | no | — |
| 353 | #135 | — | 10 | 8 | no | — |
| 354 | C2×Q16 | — | 5 | 1 | no | — |
| 355 | C2×Q16 | D20 | 1 | 1 | yes | characteristic |
| 356 | C2×SD16 | — | 5 | 1 | no | — |
| 357 | C2×SD16 | — | 5 | 1 | no | — |
| 358 | C2×SD16 | — | 10 | 2 | no | — |
| 359 | C2×SD16 | — | 10 | 2 | no | — |
| 360 | C2×SD16 | D20 | 1 | 2 | yes | — |
| 361 | C2×D8 | — | 5 | 4 | no | — |
| 362 | C2×D8 | — | 5 | 1 | no | — |
| 363 | C2×D8 | — | 10 | 2 | no | — |
| 364 | C2×D8 | — | 10 | 8 | no | — |
| 365 | C2×D8 | — | 10 | 2 | no | — |
| 366 | C2×D8 | — | 10 | 1 | no | — |
| 367 | C2×D8 | — | 10 | 1 | no | — |
| 368 | C2×D8 | — | 10 | 2 | no | — |
| 369 | C2×D8 | D20 | 1 | 1 | yes | characteristic |
| 370 | #131 | — | 5 | 4 | no | — |
| 371 | #131 | — | 10 | 2 | no | — |
| 372 | #131 | — | 10 | 2 | no | — |
| 373 | #131 | — | 10 | 2 | no | — |
| 374 | C2×M16 | — | 5 | 1 | no | — |
| 375 | C2×M16 | — | 5 | 1 | no | — |
| 376 | C2×M16 | — | 10 | 1 | no | — |
| 377 | C2×M16 | — | 10 | 1 | no | — |
| 378 | C2×M16 | C22×D5 | 1 | 2 | yes | — |
| 379 | C22×C8 | — | 10 | 1 | no | — |
| 380 | C22×C8 | — | 10 | 1 | no | — |
| 381 | C22×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 382 | C22×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 383 | C22⋊Q8 | — | 10 | 2 | no | — |
| 384 | C22⋊Q8 | — | 10 | 2 | no | — |
| 385 | #121 | — | 10 | 2 | no | — |
| 386 | #121 | — | 10 | 2 | no | — |
| 387 | #121 | — | 20 | 2 | no | — |
| 388 | C2×C4⋊C4 | — | 5 | 2 | no | — |
| 389 | C2×C22⋊C4 | — | 20 | 2 | no | — |
| 390 | C2×C42 | C22×D5 | 1 | 1 | yes | characteristic |
| 391 | #108 | — | 2 | 2 | no | — |
| 392 | #108 | — | 10 | 2 | no | — |
| 393 | #107 | — | 10 | 1 | no | — |
| 394 | #107 | — | 10 | 1 | no | — |
| 395 | #104 | — | 4 | 2 | no | — |
| 396 | #104 | — | 10 | 2 | no | — |
| 397 | #104 | — | 10 | 2 | no | — |
| 398 | #103 | — | 10 | 2 | no | — |
| 399 | #103 | — | 10 | 2 | no | — |
| 400 | #102 | — | 10 | 2 | no | — |
| 401 | #102 | — | 10 | 2 | no | — |
| 402 | #102 | — | 10 | 2 | no | — |
| 403 | #102 | — | 10 | 2 | no | — |
| 404 | #100 | — | 10 | 4 | no | — |
| 405 | C22⋊C8 | — | 2 | 2 | no | — |
| 406 | C22⋊C8 | — | 2 | 2 | no | — |
| 407 | C4×C8 | — | 2 | 2 | no | — |
| 408 | C22×C5 | — | 2 | 1 | no | — |
| 409 | C22×C5 | — | 2 | 1 | no | — |
| 410 | C22×C5 | — | 4 | 2 | no | — |
| 411 | C22×C5 | — | 4 | 2 | no | — |
| 412 | C22×C5 | — | 4 | 2 | no | — |
| 413 | C22×C5 | #535 | 1 | 1 | yes | characteristic |
| 414 | C22×C5 | D42 | 1 | 1 | yes | characteristic |
| 415 | C22×C5 | #546 | 1 | 1 | yes | characteristic |
| 416 | C2×D5 | — | 2 | 2 | no | — |
| 417 | C2×D5 | — | 4 | 1 | no | — |
| 418 | C2×D5 | — | 4 | 1 | no | — |
| 419 | C2×D5 | — | 4 | 4 | no | — |
| 420 | C2×D5 | — | 4 | 1 | no | — |
| 421 | C2×D5 | — | 4 | 1 | no | — |
| 422 | C2×D5 | — | 4 | 1 | no | — |
| 423 | C2×D5 | — | 8 | 2 | no | — |
| 424 | C2×D5 | — | 8 | 2 | no | — |
| 425 | C2×D5 | — | 8 | 4 | no | — |
| 426 | C2×D5 | — | 16 | 8 | no | — |
| 427 | C2×D5 | — | 16 | 2 | no | — |
| 428 | C4×C5 | — | 4 | 2 | no | — |
| 429 | C4×C5 | — | 4 | 2 | no | — |
| 430 | C4×C5 | C2×#120 | 1 | 1 | yes | characteristic |
| 431 | C4×C5 | C2×#121 | 1 | 1 | yes | characteristic |
| 432 | C4×C5 | D42 | 1 | 1 | yes | characteristic |
| 433 | C4×C5 | #546 | 1 | 1 | yes | characteristic |
| 434 | Dic5 | — | 2 | 2 | no | — |
| 435 | Dic5 | — | 4 | 1 | no | — |
| 436 | Dic5 | — | 8 | 2 | no | — |
| 437 | C24 | — | 10 | 2 | no | — |
| 438 | C24 | — | 20 | 2 | no | — |
| 439 | #41 | — | 2 | 2 | no | — |
| 440 | #41 | — | 2 | 2 | no | — |
| 441 | #41 | — | 2 | 2 | no | — |
| 442 | #41 | — | 2 | 2 | no | — |
| 443 | #41 | — | 5 | 2 | no | — |
| 444 | #41 | — | 5 | 2 | no | — |
| 445 | #41 | — | 10 | 1 | no | — |
| 446 | #41 | — | 10 | 1 | no | — |
| 447 | #41 | — | 10 | 8 | no | — |
| 448 | #41 | — | 10 | 1 | no | — |
| 449 | #41 | — | 10 | 1 | no | — |
| 450 | #41 | — | 10 | 1 | no | — |
| 451 | #41 | — | 10 | 1 | no | — |
| 452 | #41 | — | 20 | 4 | no | — |
| 453 | #41 | — | 20 | 4 | no | — |
| 454 | #41 | — | 20 | 4 | no | — |
| 455 | C2×Q8 | — | 5 | 1 | no | — |
| 456 | C2×Q8 | — | 5 | 1 | no | — |
| 457 | C2×Q8 | C2×D20 | 1 | 2 | yes | — |
| 458 | C2×D4 | — | 2 | 2 | no | — |
| 459 | C2×D4 | — | 5 | 1 | no | — |
| 460 | C2×D4 | — | 5 | 4 | no | — |
| 461 | C2×D4 | — | 5 | 1 | no | — |
| 462 | C2×D4 | — | 10 | 8 | no | — |
| 463 | C2×D4 | — | 10 | 1 | no | — |
| 464 | C2×D4 | — | 10 | 1 | no | — |
| 465 | C2×D4 | — | 10 | 2 | no | — |
| 466 | C2×D4 | — | 10 | 2 | no | — |
| 467 | C2×D4 | — | 10 | 2 | no | — |
| 468 | C2×D4 | — | 10 | 2 | no | — |
| 469 | C2×D4 | — | 10 | 2 | no | — |
| 470 | C2×D4 | — | 20 | 2 | no | — |
| 471 | C2×D4 | — | 20 | 4 | no | — |
| 472 | C2×D4 | — | 20 | 4 | no | — |
| 473 | C2×D4 | — | 20 | 4 | no | — |
| 474 | C2×D4 | — | 20 | 2 | no | — |
| 475 | C2×D4 | — | 20 | 8 | no | — |
| 476 | C2×D4 | — | 20 | 8 | no | — |
| 477 | C2×D4 | — | 20 | 2 | no | — |
| 478 | C2×D4 | C2×D20 | 1 | 2 | yes | — |
| 479 | C22×C4 | — | 2 | 1 | no | — |
| 480 | C22×C4 | — | 2 | 2 | no | — |
| 481 | C22×C4 | — | 10 | 1 | no | — |
| 482 | C22×C4 | — | 10 | 1 | no | — |
| 483 | C22×C4 | — | 10 | 2 | no | — |
| 484 | C22×C4 | — | 20 | 2 | no | — |
| 485 | C22×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 486 | Q16 | — | 2 | 2 | no | — |
| 487 | Q16 | — | 10 | 2 | no | — |
| 488 | SD16 | — | 2 | 4 | no | — |
| 489 | SD16 | — | 10 | 2 | no | — |
| 490 | SD16 | — | 10 | 2 | no | — |
| 491 | SD16 | — | 10 | 8 | no | — |
| 492 | SD16 | — | 20 | 4 | no | — |
| 493 | D8 | — | 2 | 2 | no | — |
| 494 | D8 | — | 10 | 2 | no | — |
| 495 | D8 | — | 10 | 8 | no | — |
| 496 | D8 | — | 10 | 4 | no | — |
| 497 | D8 | — | 10 | 4 | no | — |
| 498 | D8 | — | 20 | 4 | no | — |
| 499 | M16 | — | 2 | 2 | no | — |
| 500 | M16 | — | 2 | 2 | no | — |
| 501 | M16 | — | 5 | 2 | no | — |
| 502 | M16 | — | 10 | 1 | no | — |
| 503 | M16 | — | 10 | 4 | no | — |
| 504 | M16 | — | 10 | 1 | no | — |
| 505 | M16 | — | 10 | 1 | no | — |
| 506 | M16 | — | 20 | 2 | no | — |
| 507 | C2×C8 | — | 2 | 1 | no | — |
| 508 | C2×C8 | — | 2 | 1 | no | — |
| 509 | C2×C8 | — | 2 | 2 | no | — |
| 510 | C2×C8 | — | 10 | 1 | no | — |
| 511 | C2×C8 | — | 10 | 4 | no | — |
| 512 | C2×C8 | — | 10 | 1 | no | — |
| 513 | C2×C8 | — | 20 | 2 | no | — |
| 514 | C2×C8 | C2×D20 | 1 | 1 | yes | characteristic |
| 515 | C2×C8 | C2×D20 | 1 | 1 | yes | characteristic |
| 516 | C2×C8 | D4×D5 | 1 | 1 | yes | characteristic |
| 517 | C2×C8 | D4×D5 | 1 | 1 | yes | characteristic |
| 518 | C2×C8 | D4×D5 | 1 | 2 | yes | — |
| 519 | C2×C8 | D4×D5 | 1 | 2 | yes | — |
| 520 | C4⋊C4 | — | 10 | 2 | no | — |
| 521 | C4⋊C4 | — | 10 | 2 | no | — |
| 522 | C4⋊C4 | — | 20 | 2 | no | — |
| 523 | C22⋊C4 | — | 20 | 2 | no | — |
| 524 | C22⋊C4 | — | 20 | 2 | no | — |
| 525 | C22⋊C4 | — | 40 | 4 | no | — |
| 526 | C42 | — | 2 | 1 | no | — |
| 527 | C42 | — | 2 | 1 | no | — |
| 528 | C2×C5 | — | 2 | 1 | no | — |
| 529 | C2×C5 | — | 2 | 1 | no | — |
| 530 | C2×C5 | — | 8 | 2 | no | — |
| 531 | C2×C5 | #2408 | 1 | 1 | yes | characteristic |
| 532 | C2×C5 | #3290 | 1 | 1 | yes | characteristic |
| 533 | C2×C5 | #3292 | 1 | 1 | yes | characteristic |
| 534 | D5 | — | 4 | 2 | no | — |
| 535 | D5 | — | 8 | 1 | no | — |
| 536 | D5 | — | 8 | 4 | no | — |
| 537 | C23 | — | 2 | 2 | no | — |
| 538 | C23 | — | 10 | 1 | no | — |
| 539 | C23 | — | 10 | 1 | no | — |
| 540 | C23 | — | 10 | 4 | no | — |
| 541 | C23 | — | 20 | 8 | no | — |
| 542 | C23 | — | 20 | 2 | no | — |
| 543 | C23 | — | 20 | 2 | no | — |
| 544 | C23 | — | 40 | 2 | no | — |
| 545 | C23 | — | 40 | 2 | no | — |
| 546 | C23 | — | 80 | 2 | no | — |
| 547 | C23 | — | 80 | 2 | no | — |
| 548 | C23 | #4149 | 1 | 1 | yes | characteristic |
| 549 | Q8 | — | 2 | 2 | no | — |
| 550 | Q8 | — | 2 | 2 | no | — |
| 551 | Q8 | — | 5 | 2 | no | — |
| 552 | Q8 | — | 10 | 1 | no | — |
| 553 | Q8 | — | 10 | 1 | no | — |
| 554 | Q8 | — | 10 | 1 | no | — |
| 555 | D4 | — | 2 | 2 | no | — |
| 556 | D4 | — | 2 | 2 | no | — |
| 557 | D4 | — | 4 | 2 | no | — |
| 558 | D4 | — | 4 | 2 | no | — |
| 559 | D4 | — | 5 | 2 | no | — |
| 560 | D4 | — | 10 | 2 | no | — |
| 561 | D4 | — | 10 | 2 | no | — |
| 562 | D4 | — | 10 | 1 | no | — |
| 563 | D4 | — | 10 | 1 | no | — |
| 564 | D4 | — | 10 | 4 | no | — |
| 565 | D4 | — | 10 | 4 | no | — |
| 566 | D4 | — | 10 | 1 | no | — |
| 567 | D4 | — | 20 | 8 | no | — |
| 568 | D4 | — | 20 | 8 | no | — |
| 569 | D4 | — | 20 | 1 | no | — |
| 570 | D4 | — | 20 | 1 | no | — |
| 571 | D4 | — | 20 | 2 | no | — |
| 572 | D4 | — | 20 | 2 | no | — |
| 573 | D4 | — | 80 | 2 | no | — |
| 574 | C2×C4 | — | 2 | 2 | no | — |
| 575 | C2×C4 | — | 2 | 2 | no | — |
| 576 | C2×C4 | — | 4 | 1 | no | — |
| 577 | C2×C4 | — | 4 | 1 | no | — |
| 578 | C2×C4 | — | 4 | 2 | no | — |
| 579 | C2×C4 | — | 4 | 2 | no | — |
| 580 | C2×C4 | — | 10 | 1 | no | — |
| 581 | C2×C4 | — | 10 | 2 | no | — |
| 582 | C2×C4 | — | 10 | 2 | no | — |
| 583 | C2×C4 | — | 10 | 1 | no | — |
| 584 | C2×C4 | — | 20 | 8 | no | — |
| 585 | C2×C4 | — | 20 | 1 | no | — |
| 586 | C2×C4 | — | 20 | 1 | no | — |
| 587 | C2×C4 | — | 20 | 2 | no | — |
| 588 | C2×C4 | — | 40 | 2 | no | — |
| 589 | C2×C4 | C22×D20 | 1 | 1 | yes | characteristic |
| 590 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 591 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 592 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 593 | C2×C4 | #4144 | 1 | 1 | yes | characteristic |
| 594 | C2×C4 | D5×#41 | 1 | 1 | yes | characteristic |
| 595 | C8 | — | 2 | 1 | no | — |
| 596 | C8 | — | 2 | 1 | no | — |
| 597 | C8 | — | 4 | 2 | no | — |
| 598 | C8 | — | 10 | 2 | no | — |
| 599 | C8 | — | 20 | 1 | no | — |
| 600 | C8 | #4028 | 1 | 2 | yes | — |
| 601 | C8 | #4028 | 1 | 2 | yes | — |
| 602 | C5 | #24291 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 603 | C22 | — | 2 | 1 | no | — |
| 604 | C22 | — | 2 | 1 | no | — |
| 605 | C22 | — | 4 | 2 | no | — |
| 606 | C22 | — | 4 | 2 | no | — |
| 607 | C22 | — | 4 | 2 | no | — |
| 608 | C22 | — | 10 | 2 | no | — |
| 609 | C22 | — | 20 | 1 | no | — |
| 610 | C22 | — | 20 | 1 | no | — |
| 611 | C22 | — | 20 | 4 | no | — |
| 612 | C22 | — | 20 | 1 | no | — |
| 613 | C22 | — | 20 | 1 | no | — |
| 614 | C22 | — | 20 | 1 | no | — |
| 615 | C22 | — | 40 | 4 | no | — |
| 616 | C22 | — | 40 | 2 | no | — |
| 617 | C22 | — | 40 | 2 | no | — |
| 618 | C22 | — | 80 | 2 | no | — |
| 619 | C22 | — | 80 | 8 | no | — |
| 620 | C22 | D4×D20 | 1 | 1 | yes | characteristic |
| 621 | C22 | #65941 | 1 | 1 | yes | characteristic |
| 622 | C22 | #66010 | 1 | 1 | yes | characteristic |
| 623 | C4 | — | 4 | 2 | no | — |
| 624 | C4 | — | 4 | 2 | no | — |
| 625 | C4 | — | 10 | 2 | no | — |
| 626 | C4 | — | 20 | 1 | no | — |
| 627 | C4 | — | 40 | 2 | no | — |
| 628 | C4 | C2×#4028 | 1 | 1 | yes | characteristic |
| 629 | C4 | #65888 | 1 | 1 | yes | characteristic |
| 630 | C4 | D5×#121 | 1 | 1 | yes | characteristic |
| 631 | C4 | #66051 | 1 | 1 | yes | characteristic |
| 632 | C2 | — | 2 | 1 | no | — |
| 633 | C2 | — | 2 | 1 | no | — |
| 634 | C2 | — | 8 | 2 | no | — |
| 635 | C2 | — | 20 | 2 | no | — |
| 636 | C2 | — | 40 | 1 | no | — |
| 637 | C2 | — | 40 | 4 | no | — |
| 638 | C2 | #10608167 | 1 | 1 | yes | characteristic |
| 639 | C2 | #10611623 | 1 | 1 | yes | characteristic |
| 640 | C2 | #10611625 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#66103 | C2 | semidirect |
| 2. #10615648 | C2 | semidirect |
| 3. C2×#65186 | C2 | semidirect |
| 4. #10610403 | C2 | semidirect |
| 5. C2×#64989 | C2 | semidirect |
| 6. C5×#1974 | C2 | semidirect |
| 7. #10601514 | C2 | semidirect |
| 8. #10601185 | C2 | semidirect |
| 9. #10601177 | C2 | semidirect |
| 10. #10600796 | C2 | semidirect |
| 11. #10600569 | C2 | semidirect |
| 14. #66167 | C22 | semidirect |
| 21. C2×#4054 | C22 | semidirect |
| 25. C2×#4047 | C22 | semidirect |
| 26. C2×C5×#108 | C22 | semidirect |
| 27. C2×C5×#104 | C22 | semidirect |
| 28. C5×#408 | C22 | semidirect |
| 29. C2×C4×C5×C8 | C22 | semidirect |
| 30. #65521 | C22 | semidirect |
| 35. C2×#3955 | C22 | semidirect |
| 36. C2×#3953 | C22 | semidirect |
| 37. C2×#3951 | C22 | semidirect |
| 38. C2×#3950 | C22 | semidirect |
| 39. #65228 | C22 | semidirect |
| 41. C2×#3937 | C22 | semidirect |
| 48. #64774 | C22 | semidirect |
| 98. C2×D40 | D4 | semidirect |
| 105. #4047 | D4 | semidirect |
| 134. #1974 | D5 | semidirect |
| 253. C2×#108 | C2×D5 | semidirect |
| 257. C2×#104 | C2×D5 | semidirect |
| 262. #408 | C2×D5 | semidirect |
| 263. C2×C4×C8 | C2×D5 | semidirect |
| 602. C5 | #24291 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66103 | 2 |
| #10615648 | 2 |
| C2×#65186 | 2 |
| #10610403 | 2 |
| C2×#64989 | 2 |
| C5×#1974 | 2 |
| #10601514 | 2 |
| #10601185 | 2 |
| #10601177 | 2 |
| #10600796 | 2 |
| #10600569 | 2 |
| #24291 | 5 |