Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1098 conjugacy classes of subgroups.
The subgroup lattice has 494 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#66087 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10615532 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#65198 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#65193 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C5×#2113 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10602232 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C2×#64723 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10599906 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10599905 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #10599904 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #10599902 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | C2×#4150 | — | 2 | 1 | no | — |
| 13 | C2×C5×#131 | C22 | 1 | 1 | yes | characteristic |
| 14 | #66167 | — | 2 | 1 | no | — |
| 15 | #66087 | — | 2 | 4 | no | — |
| 16 | #66087 | — | 2 | 4 | no | — |
| 17 | C2×#4055 | — | 2 | 1 | no | — |
| 18 | C2×#4055 | — | 2 | 2 | no | — |
| 19 | C22×Dic20 | C22 | 1 | 2 | yes | — |
| 20 | C22×Dic20 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#4050 | C22 | 1 | 2 | yes | — |
| 22 | C2×#4050 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#4050 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×C5×M32 | C22 | 1 | 1 | yes | characteristic |
| 25 | C22×C5×C16 | C22 | 1 | 1 | yes | characteristic |
| 26 | #65423 | — | 2 | 2 | no | — |
| 27 | #65422 | — | 2 | 1 | no | — |
| 28 | #65405 | C22 | 1 | 2 | yes | — |
| 29 | #65404 | C22 | 1 | 2 | yes | — |
| 30 | C2×#3950 | C22 | 1 | 1 | yes | characteristic |
| 31 | #65198 | — | 2 | 4 | no | — |
| 32 | C2×Dic40 | C22 | 1 | 2 | yes | — |
| 33 | C2×Dic40 | C22 | 1 | 1 | yes | characteristic |
| 34 | #65193 | — | 2 | 4 | no | — |
| 35 | C2×#3932 | C22 | 1 | 2 | yes | — |
| 36 | C2×#3932 | C22 | 1 | 1 | yes | characteristic |
| 37 | C2×#3932 | C22 | 1 | 1 | yes | characteristic |
| 38 | C2×D80 | C22 | 1 | 1 | yes | characteristic |
| 39 | C5×C22⋊C16 | C22 | 1 | 2 | yes | — |
| 40 | C5×C22⋊C16 | C22 | 1 | 2 | yes | — |
| 41 | #64729 | C22 | 1 | 2 | yes | — |
| 42 | #64723 | C22 | 1 | 2 | yes | — |
| 43 | #64723 | C22 | 1 | 2 | yes | — |
| 44 | #64723 | C22 | 1 | 2 | yes | — |
| 45 | #33527 | — | 5 | 1 | no | maximal, Sylow |
| 46 | C2×C5×#41 | D4 | 1 | 1 | yes | characteristic |
| 47 | #4150 | — | 2 | 8 | no | — |
| 48 | #4150 | — | 4 | 4 | no | — |
| 49 | C2×Q8×D5 | — | 4 | 1 | no | — |
| 50 | C2×#711 | — | 4 | 1 | no | — |
| 51 | C2×#711 | — | 4 | 2 | no | — |
| 52 | C2×#709 | — | 2 | 2 | no | — |
| 53 | C2×#709 | — | 2 | 1 | no | — |
| 54 | C2×#709 | — | 2 | 1 | no | — |
| 55 | C22×Dic10 | — | 2 | 2 | no | — |
| 56 | C22×Dic10 | — | 2 | 1 | no | — |
| 57 | C5×#131 | — | 2 | 2 | no | — |
| 58 | C5×#131 | — | 2 | 2 | no | — |
| 59 | C2×C5×M16 | D4 | 1 | 1 | yes | characteristic |
| 60 | C2×C5×M16 | D4 | 1 | 2 | yes | — |
| 61 | C22×C5×C8 | C23 | 1 | 2 | yes | — |
| 62 | C22×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 63 | #4092 | — | 4 | 1 | no | — |
| 64 | #4085 | — | 4 | 2 | no | — |
| 65 | #4084 | — | 4 | 1 | no | — |
| 66 | #4076 | — | 2 | 2 | no | — |
| 67 | C2×C4⋊Dic5 | — | 2 | 1 | no | — |
| 68 | #4070 | — | 2 | 2 | no | — |
| 69 | #4055 | — | 2 | 8 | no | — |
| 70 | #4055 | — | 2 | 16 | no | — |
| 71 | C2×Dic20 | — | 2 | 2 | no | — |
| 72 | C2×Dic20 | — | 2 | 1 | no | — |
| 73 | C2×Dic20 | — | 2 | 2 | no | — |
| 74 | C2×Dic20 | — | 2 | 4 | no | — |
| 75 | C2×Dic20 | — | 2 | 4 | no | — |
| 76 | C2×Dic20 | D4 | 1 | 4 | yes | complemented |
| 77 | C2×Dic20 | C23 | 1 | 1 | yes | characteristic |
| 78 | C2×Dic20 | C23 | 1 | 2 | yes | — |
| 79 | C2×Dic20 | C23 | 1 | 1 | yes | characteristic |
| 80 | #4050 | — | 2 | 2 | no | — |
| 81 | #4050 | — | 2 | 4 | no | — |
| 82 | #4050 | — | 2 | 4 | no | — |
| 83 | #4050 | — | 2 | 2 | no | — |
| 84 | #4050 | — | 2 | 2 | no | — |
| 85 | #4050 | D4 | 1 | 4 | yes | complemented |
| 86 | C2×D40 | C23 | 1 | 1 | yes | characteristic |
| 87 | C2×D40 | C23 | 1 | 1 | yes | characteristic |
| 88 | C2×#677 | — | 2 | 2 | no | — |
| 89 | C2×#677 | — | 2 | 1 | no | — |
| 90 | C2×#677 | — | 2 | 1 | no | — |
| 91 | C5×M32 | — | 2 | 2 | no | — |
| 92 | C2×C5×C16 | — | 2 | 2 | no | — |
| 93 | C2×C5×C16 | C23 | 1 | 1 | yes | characteristic |
| 94 | C2×C5×C16 | C23 | 1 | 1 | yes | characteristic |
| 95 | C2×C5×C16 | C23 | 1 | 2 | yes | — |
| 96 | #3953 | — | 2 | 2 | no | — |
| 97 | #3950 | — | 2 | 1 | no | — |
| 98 | #3950 | C23 | 1 | 2 | yes | — |
| 99 | #3948 | — | 2 | 2 | no | — |
| 100 | Dic40 | — | 2 | 2 | no | — |
| 101 | Dic40 | — | 2 | 4 | no | — |
| 102 | #3932 | — | 2 | 2 | no | — |
| 103 | #3932 | — | 2 | 4 | no | — |
| 104 | #3932 | — | 2 | 2 | no | — |
| 105 | D80 | — | 2 | 2 | no | — |
| 106 | C2×#578 | — | 5 | 1 | no | — |
| 107 | C2×#510 | — | 5 | 1 | no | — |
| 108 | C2×#508 | — | 5 | 1 | no | — |
| 109 | #3061 | — | 5 | 1 | no | — |
| 110 | #2189 | — | 5 | 2 | no | — |
| 111 | #2188 | — | 5 | 2 | no | — |
| 112 | #2186 | — | 5 | 2 | no | — |
| 113 | #2185 | — | 5 | 2 | no | — |
| 114 | #2139 | — | 5 | 1 | no | — |
| 115 | C2×#358 | — | 5 | 1 | no | — |
| 116 | #2113 | D5 | 1 | 1 | yes | characteristic, complemented |
| 117 | C5×#41 | — | 2 | 2 | no | — |
| 118 | C5×#41 | — | 2 | 2 | no | — |
| 119 | C2×C5×Q8 | D8 | 1 | 1 | yes | characteristic |
| 120 | C2×C5×D4 | D8 | 1 | 1 | yes | characteristic |
| 121 | C2×C5×D4 | D8 | 1 | 2 | yes | — |
| 122 | C22×C4×C5 | C2×D4 | 1 | 2 | yes | — |
| 123 | C22×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 124 | C2×C22⋊D5 | — | 4 | 2 | no | — |
| 125 | C2×C22⋊D5 | — | 4 | 1 | no | — |
| 126 | C2×C22⋊D5 | — | 4 | 1 | no | — |
| 127 | C2×C22⋊D5 | — | 4 | 2 | no | — |
| 128 | C22×Dic5 | — | 4 | 2 | no | — |
| 129 | C22×Dic5 | — | 4 | 1 | no | — |
| 130 | C22×Dic5 | — | 4 | 1 | no | — |
| 131 | Q8×D5 | — | 4 | 8 | no | — |
| 132 | #711 | — | 4 | 16 | no | — |
| 133 | #711 | — | 4 | 8 | no | — |
| 134 | #709 | — | 2 | 8 | no | — |
| 135 | #709 | — | 2 | 4 | no | — |
| 136 | #709 | — | 4 | 4 | no | — |
| 137 | #709 | — | 4 | 2 | no | — |
| 138 | #709 | — | 4 | 2 | no | — |
| 139 | #709 | — | 4 | 2 | no | — |
| 140 | C2×D20 | — | 2 | 1 | no | — |
| 141 | C2×D20 | — | 2 | 1 | no | — |
| 142 | C2×C4×D5 | — | 4 | 2 | no | — |
| 143 | C2×C4×D5 | — | 4 | 1 | no | — |
| 144 | C2×C4×D5 | — | 4 | 1 | no | — |
| 145 | C2×Dic10 | — | 2 | 8 | no | — |
| 146 | C2×Dic10 | — | 2 | 4 | no | — |
| 147 | C2×Dic10 | — | 2 | 2 | no | — |
| 148 | C2×Dic10 | — | 2 | 1 | no | — |
| 149 | C2×Dic10 | — | 2 | 1 | no | — |
| 150 | C2×Dic10 | — | 4 | 4 | no | — |
| 151 | C2×Dic10 | — | 4 | 2 | no | — |
| 152 | C2×Dic10 | — | 4 | 1 | no | — |
| 153 | C2×Dic10 | — | 4 | 2 | no | — |
| 154 | C5×M16 | — | 2 | 2 | no | — |
| 155 | C5×M16 | — | 2 | 4 | no | — |
| 156 | C2×C5×C8 | — | 2 | 2 | no | — |
| 157 | C2×C5×C8 | — | 2 | 2 | no | — |
| 158 | C2×C5×C8 | C2×D4 | 1 | 2 | yes | — |
| 159 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 160 | C2×C5×C8 | C2×D4 | 1 | 2 | yes | — |
| 161 | C2×C5×C8 | C2×D4 | 1 | 2 | yes | — |
| 162 | C2×C5×C8 | C24 | 1 | 1 | yes | characteristic |
| 163 | C22⋊Dic5 | — | 4 | 2 | no | — |
| 164 | #685 | — | 4 | 2 | no | — |
| 165 | C4⋊Dic5 | — | 2 | 2 | no | — |
| 166 | C4⋊Dic5 | — | 4 | 1 | no | — |
| 167 | #683 | — | 4 | 2 | no | — |
| 168 | Dic20 | — | 2 | 8 | no | — |
| 169 | Dic20 | — | 2 | 4 | no | — |
| 170 | Dic20 | — | 2 | 1 | no | — |
| 171 | Dic20 | — | 2 | 2 | no | — |
| 172 | Dic20 | — | 2 | 1 | no | — |
| 173 | Dic20 | — | 2 | 1 | no | — |
| 174 | Dic20 | C2×D4 | 1 | 4 | yes | — |
| 175 | Dic20 | C2×D4 | 1 | 2 | yes | — |
| 176 | D40 | — | 2 | 1 | no | — |
| 177 | D40 | — | 2 | 1 | no | — |
| 178 | D40 | — | 2 | 1 | no | — |
| 179 | D40 | C2×D4 | 1 | 2 | yes | — |
| 180 | #677 | — | 2 | 8 | no | — |
| 181 | #677 | — | 2 | 4 | no | — |
| 182 | #677 | — | 4 | 2 | no | — |
| 183 | C5×C16 | — | 2 | 1 | no | — |
| 184 | C5×C16 | — | 2 | 1 | no | — |
| 185 | C5×C16 | — | 2 | 2 | no | — |
| 186 | C2×2−1+4 | — | 10 | 1 | no | — |
| 187 | #578 | — | 10 | 4 | no | — |
| 188 | #578 | — | 10 | 4 | no | — |
| 189 | C2×#137 | — | 10 | 1 | no | — |
| 190 | C2×#137 | — | 10 | 2 | no | — |
| 191 | C2×#135 | — | 5 | 1 | no | — |
| 192 | C2×#135 | — | 5 | 1 | no | — |
| 193 | C2×#135 | — | 5 | 2 | no | — |
| 194 | C22×Q16 | — | 5 | 1 | no | — |
| 195 | C22×Q16 | — | 5 | 2 | no | — |
| 196 | C2×#131 | C2×D5 | 1 | 1 | yes | characteristic |
| 197 | #537 | — | 10 | 1 | no | — |
| 198 | #510 | — | 10 | 4 | no | — |
| 199 | #508 | — | 10 | 4 | no | — |
| 200 | C2×Q32 | — | 5 | 1 | no | — |
| 201 | C2×Q32 | — | 5 | 2 | no | — |
| 202 | C2×SD32 | — | 5 | 1 | no | — |
| 203 | C2×SD32 | — | 5 | 1 | no | — |
| 204 | C2×SD32 | — | 5 | 2 | no | — |
| 205 | C2×D16 | — | 5 | 1 | no | — |
| 206 | C2×M32 | C2×D5 | 1 | 1 | yes | characteristic |
| 207 | C22×C16 | C2×D5 | 1 | 1 | yes | characteristic |
| 208 | #468 | — | 10 | 2 | no | — |
| 209 | #467 | — | 5 | 2 | no | — |
| 210 | #466 | — | 5 | 2 | no | — |
| 211 | C2×#107 | — | 5 | 1 | no | — |
| 212 | #417 | — | 10 | 1 | no | — |
| 213 | #358 | — | 5 | 2 | no | — |
| 214 | #358 | — | 5 | 2 | no | — |
| 215 | #358 | — | 5 | 2 | no | — |
| 216 | #357 | — | 5 | 2 | no | — |
| 217 | C22⋊C16 | C2×D5 | 1 | 2 | yes | — |
| 218 | C22⋊C16 | C2×D5 | 1 | 2 | yes | — |
| 219 | C23×C5 | C2×D8 | 1 | 2 | yes | — |
| 220 | C23×C5 | C2×D8 | 1 | 1 | yes | characteristic |
| 221 | C22×D5 | — | 4 | 1 | no | — |
| 222 | C22×D5 | — | 4 | 1 | no | — |
| 223 | C5×Q8 | — | 2 | 2 | no | — |
| 224 | C5×D4 | — | 2 | 4 | no | — |
| 225 | C5×D4 | — | 2 | 2 | no | — |
| 226 | C2×C4×C5 | — | 2 | 2 | no | — |
| 227 | C2×C4×C5 | — | 2 | 2 | no | — |
| 228 | C2×C4×C5 | #120 | 1 | 2 | yes | — |
| 229 | C2×C4×C5 | C2×D8 | 1 | 2 | yes | — |
| 230 | C2×C4×C5 | C2×D8 | 1 | 1 | yes | characteristic |
| 231 | C2×C4×C5 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 232 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 233 | C22⋊D5 | — | 4 | 8 | no | — |
| 234 | C22⋊D5 | — | 4 | 4 | no | — |
| 235 | C22⋊D5 | — | 8 | 2 | no | — |
| 236 | C22⋊D5 | — | 16 | 2 | no | — |
| 237 | C2×Dic5 | — | 4 | 8 | no | — |
| 238 | C2×Dic5 | — | 4 | 1 | no | — |
| 239 | C2×Dic5 | — | 4 | 2 | no | — |
| 240 | C2×Dic5 | — | 4 | 4 | no | — |
| 241 | C2×Dic5 | — | 4 | 1 | no | — |
| 242 | C2×Dic5 | — | 4 | 2 | no | — |
| 243 | C2×Dic5 | — | 16 | 1 | no | — |
| 244 | D20 | — | 2 | 2 | no | — |
| 245 | D20 | — | 4 | 1 | no | — |
| 246 | D20 | — | 4 | 1 | no | — |
| 247 | D20 | — | 4 | 1 | no | — |
| 248 | C4×D5 | — | 4 | 8 | no | — |
| 249 | C4×D5 | — | 4 | 4 | no | — |
| 250 | C4×D5 | — | 8 | 2 | no | — |
| 251 | Dic10 | — | 2 | 4 | no | — |
| 252 | Dic10 | — | 2 | 2 | no | — |
| 253 | Dic10 | — | 4 | 8 | no | — |
| 254 | Dic10 | — | 4 | 1 | no | — |
| 255 | Dic10 | — | 4 | 2 | no | — |
| 256 | Dic10 | — | 4 | 4 | no | — |
| 257 | Dic10 | — | 4 | 1 | no | — |
| 258 | Dic10 | — | 4 | 1 | no | — |
| 259 | C5×C8 | — | 2 | 2 | no | — |
| 260 | C5×C8 | #120 | 1 | 2 | yes | — |
| 261 | C5×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 262 | C5×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 263 | 2−1+4 | — | 10 | 8 | no | — |
| 264 | 2−1+4 | — | 20 | 4 | no | — |
| 265 | C2×#41 | — | 10 | 2 | no | — |
| 266 | C2×#41 | — | 10 | 1 | no | — |
| 267 | C2×#41 | — | 10 | 1 | no | — |
| 268 | C2×#41 | — | 20 | 1 | no | — |
| 269 | C2×#41 | — | 20 | 2 | no | — |
| 270 | C2×#41 | D20 | 1 | 1 | yes | characteristic |
| 271 | C22×Q8 | — | 10 | 2 | no | — |
| 272 | C22×Q8 | — | 10 | 1 | no | — |
| 273 | C22×Q8 | — | 20 | 1 | no | — |
| 274 | #137 | — | 10 | 8 | no | — |
| 275 | #137 | — | 10 | 16 | no | — |
| 276 | #135 | — | 5 | 4 | no | — |
| 277 | #135 | — | 10 | 4 | no | — |
| 278 | #135 | — | 10 | 4 | no | — |
| 279 | #135 | — | 10 | 2 | no | — |
| 280 | #135 | — | 10 | 2 | no | — |
| 281 | #135 | — | 10 | 2 | no | — |
| 282 | C2×Q16 | — | 5 | 4 | no | — |
| 283 | C2×Q16 | — | 5 | 2 | no | — |
| 284 | C2×Q16 | — | 5 | 1 | no | — |
| 285 | C2×Q16 | — | 5 | 1 | no | — |
| 286 | C2×Q16 | — | 10 | 4 | no | — |
| 287 | C2×Q16 | — | 10 | 4 | no | — |
| 288 | C2×Q16 | — | 10 | 2 | no | — |
| 289 | C2×Q16 | — | 10 | 1 | no | — |
| 290 | C2×Q16 | — | 10 | 2 | no | — |
| 291 | C2×SD16 | — | 10 | 2 | no | — |
| 292 | C2×SD16 | — | 10 | 1 | no | — |
| 293 | C2×SD16 | — | 10 | 1 | no | — |
| 294 | C2×D8 | — | 5 | 1 | no | — |
| 295 | C2×D8 | — | 5 | 1 | no | — |
| 296 | #131 | — | 2 | 2 | no | — |
| 297 | #131 | — | 2 | 2 | no | — |
| 298 | C2×M16 | D20 | 1 | 1 | yes | characteristic |
| 299 | C2×M16 | D20 | 1 | 2 | yes | — |
| 300 | C22×C8 | C22×D5 | 1 | 2 | yes | — |
| 301 | C22×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 302 | C22⋊Q8 | — | 10 | 2 | no | — |
| 303 | C22⋊Q8 | — | 20 | 1 | no | — |
| 304 | #121 | — | 10 | 2 | no | — |
| 305 | #121 | — | 20 | 1 | no | — |
| 306 | #121 | — | 20 | 2 | no | — |
| 307 | C2×C4⋊C4 | — | 10 | 1 | no | — |
| 308 | Q32 | — | 10 | 2 | no | — |
| 309 | Q32 | — | 10 | 4 | no | — |
| 310 | SD32 | — | 10 | 2 | no | — |
| 311 | SD32 | — | 10 | 2 | no | — |
| 312 | SD32 | — | 10 | 4 | no | — |
| 313 | D16 | — | 10 | 2 | no | — |
| 314 | M32 | — | 2 | 2 | no | — |
| 315 | C2×C16 | — | 2 | 2 | no | — |
| 316 | C2×C16 | C22×D5 | 1 | 2 | yes | — |
| 317 | C2×C16 | C22×D5 | 1 | 1 | yes | characteristic |
| 318 | C2×C16 | C22×D5 | 1 | 1 | yes | characteristic |
| 319 | #107 | — | 5 | 2 | no | — |
| 320 | #107 | — | 10 | 1 | no | — |
| 321 | #103 | — | 10 | 2 | no | — |
| 322 | #102 | — | 10 | 2 | no | — |
| 323 | C22×C5 | — | 2 | 1 | no | — |
| 324 | C22×C5 | — | 2 | 1 | no | — |
| 325 | C22×C5 | — | 2 | 2 | no | — |
| 326 | C22×C5 | — | 2 | 2 | no | — |
| 327 | C22×C5 | — | 2 | 2 | no | — |
| 328 | C22×C5 | #447 | 1 | 2 | yes | — |
| 329 | C22×C5 | C22×D8 | 1 | 1 | yes | characteristic |
| 330 | C2×D5 | — | 4 | 2 | no | — |
| 331 | C2×D5 | — | 8 | 1 | no | — |
| 332 | C2×D5 | — | 8 | 1 | no | — |
| 333 | C2×D5 | — | 8 | 1 | no | — |
| 334 | C2×D5 | — | 8 | 1 | no | — |
| 335 | C2×D5 | — | 8 | 1 | no | — |
| 336 | C4×C5 | — | 2 | 2 | no | — |
| 337 | C4×C5 | #447 | 1 | 2 | yes | — |
| 338 | C4×C5 | C2×#120 | 1 | 1 | yes | characteristic |
| 339 | C4×C5 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 340 | Dic5 | — | 4 | 2 | no | — |
| 341 | Dic5 | — | 4 | 4 | no | — |
| 342 | Dic5 | — | 8 | 2 | no | — |
| 343 | Dic5 | — | 8 | 1 | no | — |
| 344 | #41 | — | 2 | 2 | no | — |
| 345 | #41 | — | 2 | 2 | no | — |
| 346 | #41 | — | 10 | 8 | no | — |
| 347 | #41 | — | 10 | 4 | no | — |
| 348 | #41 | — | 20 | 4 | no | — |
| 349 | #41 | — | 20 | 16 | no | — |
| 350 | #41 | — | 20 | 8 | no | — |
| 351 | #41 | — | 20 | 2 | no | — |
| 352 | #41 | — | 20 | 2 | no | — |
| 353 | #41 | — | 20 | 2 | no | — |
| 354 | C2×Q8 | — | 10 | 8 | no | — |
| 355 | C2×Q8 | — | 10 | 2 | no | — |
| 356 | C2×Q8 | — | 10 | 1 | no | — |
| 357 | C2×Q8 | — | 10 | 1 | no | — |
| 358 | C2×Q8 | — | 10 | 4 | no | — |
| 359 | C2×Q8 | — | 20 | 4 | no | — |
| 360 | C2×Q8 | — | 20 | 8 | no | — |
| 361 | C2×Q8 | — | 20 | 2 | no | — |
| 362 | C2×Q8 | — | 20 | 1 | no | — |
| 363 | C2×Q8 | — | 20 | 2 | no | — |
| 364 | C2×Q8 | D40 | 1 | 1 | yes | characteristic |
| 365 | C2×D4 | — | 10 | 1 | no | — |
| 366 | C2×D4 | — | 10 | 1 | no | — |
| 367 | C2×D4 | — | 20 | 2 | no | — |
| 368 | C2×D4 | — | 20 | 1 | no | — |
| 369 | C2×D4 | — | 20 | 1 | no | — |
| 370 | C2×D4 | — | 20 | 2 | no | — |
| 371 | C2×D4 | D40 | 1 | 2 | yes | — |
| 372 | C2×D4 | D40 | 1 | 1 | yes | characteristic |
| 373 | C22×C4 | — | 20 | 2 | no | — |
| 374 | C22×C4 | — | 20 | 1 | no | — |
| 375 | C22×C4 | — | 20 | 2 | no | — |
| 376 | C22×C4 | — | 20 | 1 | no | — |
| 377 | C22×C4 | — | 20 | 1 | no | — |
| 378 | C22×C4 | — | 20 | 1 | no | — |
| 379 | C22×C4 | C2×D20 | 1 | 2 | yes | — |
| 380 | C22×C4 | C2×D20 | 1 | 1 | yes | characteristic |
| 381 | Q16 | — | 5 | 4 | no | — |
| 382 | Q16 | — | 5 | 2 | no | — |
| 383 | Q16 | — | 10 | 8 | no | — |
| 384 | Q16 | — | 10 | 2 | no | — |
| 385 | Q16 | — | 10 | 1 | no | — |
| 386 | Q16 | — | 10 | 1 | no | — |
| 387 | Q16 | — | 10 | 1 | no | — |
| 388 | Q16 | — | 10 | 4 | no | — |
| 389 | SD16 | — | 10 | 8 | no | — |
| 390 | SD16 | — | 10 | 4 | no | — |
| 391 | SD16 | — | 20 | 2 | no | — |
| 392 | D8 | — | 5 | 2 | no | — |
| 393 | D8 | — | 10 | 1 | no | — |
| 394 | D8 | — | 10 | 1 | no | — |
| 395 | D8 | — | 10 | 1 | no | — |
| 396 | M16 | — | 2 | 2 | no | — |
| 397 | M16 | — | 2 | 4 | no | — |
| 398 | C2×C8 | — | 2 | 2 | no | — |
| 399 | C2×C8 | — | 2 | 2 | no | — |
| 400 | C2×C8 | C2×D20 | 1 | 2 | yes | — |
| 401 | C2×C8 | C2×D20 | 1 | 1 | yes | characteristic |
| 402 | C2×C8 | D4×D5 | 1 | 2 | yes | — |
| 403 | C2×C8 | D4×D5 | 1 | 2 | yes | — |
| 404 | C2×C8 | C23×D5 | 1 | 1 | yes | characteristic |
| 405 | C4⋊C4 | — | 10 | 2 | no | — |
| 406 | C4⋊C4 | — | 20 | 1 | no | — |
| 407 | C4⋊C4 | — | 20 | 2 | no | — |
| 408 | C22⋊C4 | — | 20 | 2 | no | — |
| 409 | C22⋊C4 | — | 20 | 2 | no | — |
| 410 | C16 | — | 2 | 1 | no | — |
| 411 | C16 | — | 2 | 1 | no | — |
| 412 | C16 | — | 2 | 2 | no | — |
| 413 | C2×C5 | — | 2 | 2 | no | — |
| 414 | C2×C5 | — | 4 | 2 | no | — |
| 415 | C2×C5 | C2×#447 | 1 | 1 | yes | characteristic |
| 416 | C2×C5 | #3416 | 1 | 1 | yes | characteristic |
| 417 | C2×C5 | #3417 | 1 | 1 | yes | characteristic |
| 418 | D5 | — | 8 | 2 | no | — |
| 419 | D5 | — | 16 | 1 | no | — |
| 420 | C23 | — | 20 | 1 | no | — |
| 421 | C23 | — | 20 | 1 | no | — |
| 422 | C23 | C2×D40 | 1 | 2 | yes | — |
| 423 | C23 | C2×D40 | 1 | 1 | yes | characteristic |
| 424 | Q8 | — | 2 | 2 | no | — |
| 425 | Q8 | — | 10 | 4 | no | — |
| 426 | Q8 | — | 10 | 2 | no | — |
| 427 | Q8 | — | 20 | 8 | no | — |
| 428 | Q8 | — | 20 | 1 | no | — |
| 429 | Q8 | — | 20 | 2 | no | — |
| 430 | Q8 | — | 20 | 4 | no | — |
| 431 | Q8 | — | 20 | 1 | no | — |
| 432 | Q8 | — | 20 | 1 | no | — |
| 433 | D4 | — | 2 | 4 | no | — |
| 434 | D4 | — | 2 | 2 | no | — |
| 435 | D4 | — | 10 | 2 | no | — |
| 436 | D4 | — | 20 | 8 | no | — |
| 437 | D4 | — | 20 | 4 | no | — |
| 438 | D4 | — | 20 | 1 | no | — |
| 439 | D4 | — | 20 | 1 | no | — |
| 440 | D4 | — | 20 | 1 | no | — |
| 441 | D4 | — | 40 | 2 | no | — |
| 442 | D4 | — | 80 | 2 | no | — |
| 443 | C2×C4 | — | 2 | 2 | no | — |
| 444 | C2×C4 | — | 2 | 2 | no | — |
| 445 | C2×C4 | — | 20 | 8 | no | — |
| 446 | C2×C4 | — | 20 | 8 | no | — |
| 447 | C2×C4 | — | 20 | 2 | no | — |
| 448 | C2×C4 | — | 20 | 1 | no | — |
| 449 | C2×C4 | — | 20 | 4 | no | — |
| 450 | C2×C4 | — | 20 | 4 | no | — |
| 451 | C2×C4 | — | 20 | 2 | no | — |
| 452 | C2×C4 | — | 20 | 1 | no | — |
| 453 | C2×C4 | — | 40 | 2 | no | — |
| 454 | C2×C4 | — | 80 | 1 | no | — |
| 455 | C2×C4 | #4028 | 1 | 2 | yes | — |
| 456 | C2×C4 | C2×D40 | 1 | 2 | yes | — |
| 457 | C2×C4 | C2×D40 | 1 | 1 | yes | characteristic |
| 458 | C2×C4 | #4054 | 1 | 2 | yes | — |
| 459 | C2×C4 | C22×D20 | 1 | 1 | yes | characteristic |
| 460 | C8 | — | 2 | 2 | no | — |
| 461 | C8 | #4028 | 1 | 2 | yes | — |
| 462 | C8 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 463 | C8 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 464 | C5 | #33527 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 465 | C22 | — | 2 | 1 | no | — |
| 466 | C22 | — | 2 | 1 | no | — |
| 467 | C22 | — | 2 | 2 | no | — |
| 468 | C22 | — | 2 | 2 | no | — |
| 469 | C22 | — | 2 | 2 | no | — |
| 470 | C22 | — | 20 | 2 | no | — |
| 471 | C22 | — | 40 | 1 | no | — |
| 472 | C22 | — | 40 | 1 | no | — |
| 473 | C22 | — | 40 | 1 | no | — |
| 474 | C22 | — | 40 | 1 | no | — |
| 475 | C22 | — | 40 | 1 | no | — |
| 476 | C22 | #65021 | 1 | 2 | yes | — |
| 477 | C22 | C22×D40 | 1 | 1 | yes | characteristic |
| 478 | C4 | — | 2 | 2 | no | — |
| 479 | C4 | — | 20 | 4 | no | — |
| 480 | C4 | — | 20 | 2 | no | — |
| 481 | C4 | — | 40 | 1 | no | — |
| 482 | C4 | — | 40 | 2 | no | — |
| 483 | C4 | #65021 | 1 | 2 | yes | — |
| 484 | C4 | C2×#4028 | 1 | 1 | yes | characteristic |
| 485 | C4 | C2×#4054 | 1 | 1 | yes | characteristic |
| 486 | C2 | — | 2 | 2 | no | — |
| 487 | C2 | — | 4 | 2 | no | — |
| 488 | C2 | — | 40 | 2 | no | — |
| 489 | C2 | — | 80 | 1 | no | — |
| 490 | C2 | C2×#65021 | 1 | 1 | yes | characteristic |
| 491 | C2 | #10613745 | 1 | 1 | yes | characteristic |
| 492 | C2 | #10613746 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#66087 | C2 | semidirect |
| 2. #10615532 | C2 | semidirect |
| 3. C2×#65198 | C2 | semidirect |
| 4. C2×#65193 | C2 | semidirect |
| 5. C5×#2113 | C2 | semidirect |
| 6. #10602232 | C2 | semidirect |
| 7. C2×#64723 | C2 | semidirect |
| 8. #10599906 | C2 | semidirect |
| 9. #10599905 | C2 | semidirect |
| 10. #10599904 | C2 | semidirect |
| 11. #10599902 | C2 | semidirect |
| 76. C2×Dic20 | D4 | semidirect |
| 85. #4050 | D4 | semidirect |
| 116. #2113 | D5 | semidirect |
| 464. C5 | #33527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66087 | 2 |
| #10615532 | 2 |
| C2×#65198 | 2 |
| C2×#65193 | 2 |
| C5×#2113 | 2 |
| #10602232 | 2 |
| C2×#64723 | 2 |
| #10599906 | 2 |
| #10599905 | 2 |
| #10599904 | 2 |
| #10599902 | 2 |
| #33527 | 5 |