Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1770 conjugacy classes of subgroups.
The subgroup lattice has 504 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C5×#2659 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10614565 | C2 | 1 | 2 | yes | maximal |
| 3 | #10614476 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10609724 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #10609720 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #10608997 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #10608996 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #10605658 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #10605640 | C2 | 1 | 4 | yes | maximal |
| 10 | C2×#64953 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | #10605091 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C23×C4×D5 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×C5×C22⋊Q8 | C22 | 1 | 2 | yes | — |
| 14 | C2×#4092 | C22 | 1 | 2 | yes | — |
| 15 | C2×#4092 | C22 | 1 | 2 | yes | — |
| 16 | C22×#685 | C22 | 1 | 2 | yes | — |
| 17 | C2×#4044 | C22 | 1 | 4 | yes | — |
| 18 | C5×#398 | C22 | 1 | 4 | yes | complemented |
| 19 | C5×#395 | C22 | 1 | 4 | yes | complemented |
| 20 | C5×#380 | C22 | 1 | 4 | yes | — |
| 21 | C2×C5×#95 | C22 | 1 | 1 | yes | characteristic |
| 22 | #65519 | C22 | 1 | 4 | yes | complemented |
| 23 | #65501 | C22 | 1 | 2 | yes | — |
| 24 | #65499 | C22 | 1 | 4 | yes | — |
| 25 | C2×#3963 | C22 | 1 | 2 | yes | — |
| 26 | C2×#3963 | C22 | 1 | 1 | yes | characteristic |
| 27 | #65283 | C22 | 1 | 4 | yes | — |
| 28 | #65282 | C22 | 1 | 4 | yes | — |
| 29 | #65279 | C22 | 1 | 4 | yes | — |
| 30 | #65278 | C22 | 1 | 4 | yes | — |
| 31 | #65278 | C22 | 1 | 4 | yes | — |
| 32 | #65276 | C22 | 1 | 2 | yes | — |
| 33 | #65276 | C22 | 1 | 2 | yes | — |
| 34 | #65274 | C22 | 1 | 4 | yes | complemented |
| 35 | #65273 | C22 | 1 | 4 | yes | complemented |
| 36 | #65271 | C22 | 1 | 4 | yes | complemented |
| 37 | #65270 | C22 | 1 | 4 | yes | complemented |
| 38 | #65270 | C22 | 1 | 4 | yes | complemented |
| 39 | #65270 | C22 | 1 | 4 | yes | complemented |
| 40 | #65261 | C22 | 1 | 4 | yes | complemented |
| 41 | #65244 | C22 | 1 | 4 | yes | — |
| 42 | #65239 | C22 | 1 | 4 | yes | — |
| 43 | #65235 | C22 | 1 | 4 | yes | — |
| 44 | C22⋊C4×Dic5 | C22 | 1 | 4 | yes | — |
| 45 | #64964 | C22 | 1 | 4 | yes | — |
| 46 | #64963 | C22 | 1 | 4 | yes | — |
| 47 | #64959 | C22 | 1 | 4 | yes | — |
| 48 | #64958 | C22 | 1 | 4 | yes | — |
| 49 | #64953 | C22 | 1 | 4 | yes | — |
| 50 | #64953 | C22 | 1 | 4 | yes | — |
| 51 | #64949 | C22 | 1 | 4 | yes | complemented |
| 52 | #64948 | C22 | 1 | 4 | yes | complemented |
| 53 | #64947 | C22 | 1 | 4 | yes | complemented |
| 54 | #64946 | C22 | 1 | 4 | yes | complemented |
| 55 | #64942 | C22 | 1 | 4 | yes | complemented |
| 56 | #64939 | C22 | 1 | 4 | yes | complemented |
| 57 | #36732 | — | 5 | 1 | no | maximal, Sylow |
| 58 | C24×D5 | C23 | 1 | 1 | yes | characteristic |
| 59 | C22×C5×Q8 | C23 | 1 | 2 | yes | — |
| 60 | C23×C4×C5 | C23 | 1 | 2 | yes | — |
| 61 | C23×C4×C5 | C23 | 1 | 1 | yes | characteristic |
| 62 | C23×Dic5 | C23 | 1 | 2 | yes | — |
| 63 | C23×Dic5 | C23 | 1 | 1 | yes | characteristic |
| 64 | C22×C4×D5 | — | 2 | 4 | no | — |
| 65 | C22×C4×D5 | — | 4 | 4 | no | — |
| 66 | C22×C4×D5 | C23 | 1 | 2 | yes | — |
| 67 | C22×C4×D5 | C23 | 1 | 2 | yes | — |
| 68 | C5×C22⋊Q8 | — | 2 | 8 | no | — |
| 69 | C2×C5×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 70 | C2×C5×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 71 | C2×C5×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 72 | C2×C5×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 73 | C2×C5×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 74 | C2×C22⋊Dic5 | C23 | 1 | 4 | yes | — |
| 75 | #4092 | — | 4 | 4 | no | — |
| 76 | #4092 | — | 4 | 4 | no | — |
| 77 | C2×#685 | — | 4 | 4 | no | — |
| 78 | C2×#685 | C23 | 1 | 4 | yes | — |
| 79 | C2×#685 | C23 | 1 | 4 | yes | — |
| 80 | C2×#685 | C23 | 1 | 4 | yes | — |
| 81 | C2×#685 | C23 | 1 | 4 | yes | — |
| 82 | C2×#685 | C23 | 1 | 4 | yes | — |
| 83 | C2×#685 | C23 | 1 | 4 | yes | — |
| 84 | C2×C4⋊Dic5 | C23 | 1 | 4 | yes | — |
| 85 | C2×C4⋊Dic5 | C23 | 1 | 4 | yes | — |
| 86 | C2×C4⋊Dic5 | C23 | 1 | 2 | yes | — |
| 87 | C2×C4⋊Dic5 | C23 | 1 | 2 | yes | — |
| 88 | C2×#683 | C23 | 1 | 4 | yes | — |
| 89 | C2×#683 | C23 | 1 | 4 | yes | — |
| 90 | C2×#683 | C23 | 1 | 4 | yes | — |
| 91 | C2×#683 | C23 | 1 | 4 | yes | — |
| 92 | C2×C4×Dic5 | C23 | 1 | 4 | yes | — |
| 93 | C2×C4×Dic5 | C23 | 1 | 4 | yes | — |
| 94 | #4044 | — | 4 | 8 | no | — |
| 95 | C5×#95 | C23 | 1 | 4 | yes | — |
| 96 | C5×#95 | C23 | 1 | 4 | yes | — |
| 97 | C5×#95 | C23 | 1 | 4 | yes | — |
| 98 | #3963 | C23 | 1 | 4 | yes | — |
| 99 | #3963 | C23 | 1 | 4 | yes | — |
| 100 | #3963 | C23 | 1 | 4 | yes | — |
| 101 | #3963 | C23 | 1 | 4 | yes | — |
| 102 | #3963 | C23 | 1 | 4 | yes | — |
| 103 | #3963 | C23 | 1 | 4 | yes | — |
| 104 | #3963 | C23 | 1 | 4 | yes | — |
| 105 | #3963 | C23 | 1 | 4 | yes | — |
| 106 | #3963 | C23 | 1 | 4 | yes | — |
| 107 | #3963 | C23 | 1 | 4 | yes | — |
| 108 | #3963 | C23 | 1 | 4 | yes | — |
| 109 | #3963 | C23 | 1 | 4 | yes | — |
| 110 | #2848 | — | 5 | 2 | no | — |
| 111 | #2744 | — | 5 | 4 | no | — |
| 112 | #2739 | — | 5 | 4 | no | — |
| 113 | #2698 | — | 5 | 4 | no | — |
| 114 | #2689 | — | 5 | 4 | no | — |
| 115 | #2659 | D5 | 1 | 1 | yes | characteristic, complemented |
| 116 | #2646 | — | 5 | 1 | no | — |
| 117 | #2505 | — | 5 | 4 | no | — |
| 118 | #2480 | — | 5 | 4 | no | — |
| 119 | #2329 | — | 5 | 2 | no | — |
| 120 | C2×#381 | — | 5 | 1 | no | — |
| 121 | C24×C5 | C24 | 1 | 1 | yes | characteristic |
| 122 | C23×D5 | — | 2 | 2 | no | — |
| 123 | C23×D5 | — | 2 | 4 | no | — |
| 124 | C23×D5 | — | 2 | 4 | no | — |
| 125 | C23×D5 | — | 4 | 1 | no | — |
| 126 | C23×D5 | — | 4 | 1 | no | — |
| 127 | C23×D5 | C24 | 1 | 2 | yes | — |
| 128 | C2×C5×Q8 | — | 2 | 4 | no | — |
| 129 | C2×C5×Q8 | — | 4 | 2 | no | — |
| 130 | C2×C5×Q8 | — | 4 | 2 | no | — |
| 131 | C22×C4×C5 | — | 2 | 4 | no | — |
| 132 | C22×C4×C5 | — | 4 | 2 | no | — |
| 133 | C22×C4×C5 | — | 4 | 2 | no | — |
| 134 | C22×C4×C5 | — | 4 | 2 | no | — |
| 135 | C22×C4×C5 | #41 | 1 | 4 | yes | — |
| 136 | C22×C4×C5 | C24 | 1 | 4 | yes | — |
| 137 | C22×C4×C5 | C24 | 1 | 4 | yes | — |
| 138 | C22×C4×C5 | C24 | 1 | 4 | yes | — |
| 139 | C22×C4×C5 | C24 | 1 | 2 | yes | — |
| 140 | C22×Dic5 | — | 2 | 2 | no | — |
| 141 | C22×Dic5 | — | 2 | 4 | no | — |
| 142 | C22×Dic5 | — | 4 | 2 | no | — |
| 143 | C22×Dic5 | — | 4 | 2 | no | — |
| 144 | C22×Dic5 | — | 4 | 2 | no | — |
| 145 | C22×Dic5 | C24 | 1 | 4 | yes | — |
| 146 | C22×Dic5 | C24 | 1 | 4 | yes | — |
| 147 | C22×Dic5 | C24 | 1 | 1 | yes | characteristic |
| 148 | C22×Dic5 | C24 | 1 | 1 | yes | characteristic |
| 149 | C22×Dic5 | C24 | 1 | 4 | yes | — |
| 150 | C2×C4×D5 | — | 2 | 4 | no | — |
| 151 | C2×C4×D5 | — | 2 | 4 | no | — |
| 152 | C2×C4×D5 | — | 2 | 4 | no | — |
| 153 | C2×C4×D5 | — | 2 | 4 | no | — |
| 154 | C2×C4×D5 | — | 4 | 2 | no | — |
| 155 | C2×C4×D5 | — | 4 | 2 | no | — |
| 156 | C2×C4×D5 | — | 4 | 16 | no | — |
| 157 | C5×C4⋊C4 | — | 2 | 4 | no | — |
| 158 | C5×C4⋊C4 | — | 2 | 8 | no | — |
| 159 | C5×C4⋊C4 | — | 4 | 4 | no | — |
| 160 | C5×C4⋊C4 | — | 4 | 4 | no | — |
| 161 | C5×C22⋊C4 | — | 2 | 8 | no | — |
| 162 | C22⋊Dic5 | — | 2 | 8 | no | — |
| 163 | #685 | — | 2 | 8 | no | — |
| 164 | #685 | — | 2 | 8 | no | — |
| 165 | #685 | — | 2 | 8 | no | — |
| 166 | #685 | — | 4 | 4 | no | — |
| 167 | #685 | — | 4 | 4 | no | — |
| 168 | #685 | — | 4 | 4 | no | — |
| 169 | C4⋊Dic5 | — | 4 | 4 | no | — |
| 170 | C4⋊Dic5 | — | 4 | 4 | no | — |
| 171 | C4⋊Dic5 | — | 4 | 2 | no | — |
| 172 | C4⋊Dic5 | — | 4 | 2 | no | — |
| 173 | #683 | — | 4 | 4 | no | — |
| 174 | #683 | — | 4 | 4 | no | — |
| 175 | #683 | — | 4 | 4 | no | — |
| 176 | #683 | — | 4 | 4 | no | — |
| 177 | C4×Dic5 | — | 4 | 4 | no | — |
| 178 | C4×Dic5 | — | 4 | 4 | no | — |
| 179 | C24×C4 | — | 5 | 1 | no | — |
| 180 | C2×#126 | — | 5 | 4 | no | — |
| 181 | C2×C22⋊Q8 | — | 5 | 2 | no | — |
| 182 | C2×C22⋊Q8 | — | 5 | 2 | no | — |
| 183 | C2×C22⋊Q8 | C2×D5 | 1 | 2 | yes | — |
| 184 | C22×C22⋊C4 | — | 5 | 2 | no | — |
| 185 | #400 | — | 5 | 4 | no | — |
| 186 | #400 | — | 5 | 4 | no | — |
| 187 | #400 | — | 5 | 4 | no | — |
| 188 | #400 | — | 5 | 4 | no | — |
| 189 | #398 | — | 5 | 4 | no | — |
| 190 | #398 | — | 5 | 4 | no | — |
| 191 | #398 | C2×D5 | 1 | 4 | yes | complemented |
| 192 | #397 | — | 5 | 4 | no | — |
| 193 | #397 | — | 5 | 4 | no | — |
| 194 | #397 | — | 5 | 4 | no | — |
| 195 | #396 | — | 5 | 4 | no | — |
| 196 | #395 | C2×D5 | 1 | 4 | yes | complemented |
| 197 | #391 | — | 5 | 4 | no | — |
| 198 | #389 | — | 5 | 4 | no | — |
| 199 | #389 | — | 5 | 4 | no | — |
| 200 | #388 | — | 5 | 4 | no | — |
| 201 | #388 | — | 5 | 4 | no | — |
| 202 | #388 | — | 5 | 4 | no | — |
| 203 | #387 | — | 5 | 4 | no | — |
| 204 | #387 | — | 5 | 4 | no | — |
| 205 | #387 | — | 5 | 4 | no | — |
| 206 | #387 | — | 5 | 4 | no | — |
| 207 | #385 | — | 5 | 4 | no | — |
| 208 | #385 | — | 5 | 4 | no | — |
| 209 | #385 | — | 5 | 4 | no | — |
| 210 | #385 | — | 5 | 4 | no | — |
| 211 | #385 | — | 5 | 4 | no | — |
| 212 | #382 | — | 5 | 4 | no | — |
| 213 | #381 | — | 5 | 4 | no | — |
| 214 | #381 | — | 5 | 4 | no | — |
| 215 | #380 | — | 5 | 2 | no | — |
| 216 | #380 | — | 5 | 2 | no | — |
| 217 | #380 | — | 5 | 2 | no | — |
| 218 | #380 | C2×D5 | 1 | 4 | yes | — |
| 219 | #379 | — | 5 | 4 | no | — |
| 220 | C4×C22⋊C4 | — | 5 | 4 | no | — |
| 221 | C2×#95 | — | 5 | 1 | no | — |
| 222 | C2×#95 | — | 5 | 2 | no | — |
| 223 | C2×#95 | C2×D5 | 1 | 1 | yes | characteristic |
| 224 | C23×C5 | — | 2 | 2 | no | — |
| 225 | C23×C5 | — | 2 | 1 | no | — |
| 226 | C23×C5 | — | 2 | 1 | no | — |
| 227 | C23×C5 | C2×#41 | 1 | 2 | yes | — |
| 228 | C23×C5 | 2−1+4 | 1 | 4 | yes | — |
| 229 | C23×C5 | C25 | 1 | 1 | yes | characteristic |
| 230 | C22×D5 | — | 2 | 8 | no | — |
| 231 | C22×D5 | — | 2 | 2 | no | — |
| 232 | C22×D5 | — | 2 | 2 | no | — |
| 233 | C22×D5 | — | 2 | 2 | no | — |
| 234 | C22×D5 | — | 2 | 2 | no | — |
| 235 | C22×D5 | — | 2 | 2 | no | — |
| 236 | C22×D5 | — | 2 | 2 | no | — |
| 237 | C22×D5 | — | 4 | 8 | no | — |
| 238 | C22×D5 | — | 4 | 8 | no | — |
| 239 | C22×D5 | — | 4 | 4 | no | — |
| 240 | C22×D5 | — | 4 | 4 | no | — |
| 241 | C22×D5 | H(5,𝔽2) | 1 | 4 | yes | — |
| 242 | C5×Q8 | — | 8 | 4 | no | — |
| 243 | C2×C4×C5 | — | 2 | 2 | no | — |
| 244 | C2×C4×C5 | — | 2 | 2 | no | — |
| 245 | C2×C4×C5 | — | 2 | 4 | no | — |
| 246 | C2×C4×C5 | — | 2 | 4 | no | — |
| 247 | C2×C4×C5 | — | 2 | 4 | no | — |
| 248 | C2×C4×C5 | — | 2 | 4 | no | — |
| 249 | C2×C4×C5 | — | 2 | 4 | no | — |
| 250 | C2×C4×C5 | — | 2 | 4 | no | — |
| 251 | C2×C4×C5 | — | 2 | 4 | no | — |
| 252 | C2×C4×C5 | — | 2 | 4 | no | — |
| 253 | C2×C4×C5 | — | 2 | 4 | no | — |
| 254 | C2×C4×C5 | — | 4 | 4 | no | — |
| 255 | C2×C4×C5 | — | 8 | 4 | no | — |
| 256 | C2×C4×C5 | C2×#41 | 1 | 4 | yes | — |
| 257 | C2×Dic5 | — | 2 | 1 | no | — |
| 258 | C2×Dic5 | — | 2 | 1 | no | — |
| 259 | C2×Dic5 | — | 2 | 4 | no | — |
| 260 | C2×Dic5 | — | 2 | 4 | no | — |
| 261 | C2×Dic5 | — | 2 | 4 | no | — |
| 262 | C2×Dic5 | — | 2 | 2 | no | — |
| 263 | C2×Dic5 | — | 2 | 2 | no | — |
| 264 | C2×Dic5 | — | 2 | 4 | no | — |
| 265 | C2×Dic5 | — | 2 | 4 | no | — |
| 266 | C2×Dic5 | — | 2 | 4 | no | — |
| 267 | C2×Dic5 | — | 2 | 4 | no | — |
| 268 | C2×Dic5 | — | 2 | 4 | no | — |
| 269 | C2×Dic5 | — | 2 | 4 | no | — |
| 270 | C2×Dic5 | — | 4 | 4 | no | — |
| 271 | C2×Dic5 | — | 8 | 4 | no | — |
| 272 | C4×D5 | — | 4 | 8 | no | — |
| 273 | C4×D5 | — | 4 | 8 | no | — |
| 274 | C25 | — | 5 | 1 | no | — |
| 275 | C22×Q8 | C22×D5 | 1 | 2 | yes | — |
| 276 | C23×C4 | — | 5 | 2 | no | — |
| 277 | C23×C4 | — | 5 | 1 | no | — |
| 278 | C23×C4 | — | 5 | 2 | no | — |
| 279 | C23×C4 | — | 5 | 2 | no | — |
| 280 | C23×C4 | — | 10 | 4 | no | — |
| 281 | C23×C4 | — | 20 | 4 | no | — |
| 282 | C23×C4 | C22×D5 | 1 | 2 | yes | — |
| 283 | C23×C4 | C22×D5 | 1 | 1 | yes | characteristic |
| 284 | #126 | — | 20 | 8 | no | — |
| 285 | C22⋊Q8 | — | 2 | 8 | no | — |
| 286 | C22⋊Q8 | — | 20 | 4 | no | — |
| 287 | C22⋊Q8 | — | 20 | 4 | no | — |
| 288 | C2×C4⋊C4 | — | 5 | 2 | no | — |
| 289 | C2×C4⋊C4 | — | 5 | 2 | no | — |
| 290 | C2×C4⋊C4 | — | 5 | 4 | no | — |
| 291 | C2×C4⋊C4 | — | 5 | 4 | no | — |
| 292 | C2×C4⋊C4 | — | 5 | 4 | no | — |
| 293 | C2×C4⋊C4 | — | 5 | 4 | no | — |
| 294 | C2×C4⋊C4 | — | 5 | 4 | no | — |
| 295 | C2×C4⋊C4 | — | 5 | 4 | no | — |
| 296 | C2×C4⋊C4 | C22×D5 | 1 | 2 | yes | — |
| 297 | C2×C4⋊C4 | C22×D5 | 1 | 4 | yes | — |
| 298 | C2×C4⋊C4 | C22×D5 | 1 | 4 | yes | — |
| 299 | C2×C4⋊C4 | C22×D5 | 1 | 4 | yes | — |
| 300 | C2×C22⋊C4 | — | 5 | 4 | no | — |
| 301 | C2×C22⋊C4 | — | 5 | 4 | no | — |
| 302 | C2×C22⋊C4 | — | 5 | 4 | no | — |
| 303 | C2×C22⋊C4 | — | 5 | 4 | no | — |
| 304 | C2×C22⋊C4 | — | 5 | 4 | no | — |
| 305 | C2×C22⋊C4 | — | 5 | 4 | no | — |
| 306 | C2×C22⋊C4 | — | 5 | 4 | no | — |
| 307 | C2×C22⋊C4 | — | 20 | 4 | no | — |
| 308 | C2×C22⋊C4 | C22×D5 | 1 | 4 | yes | — |
| 309 | C2×C42 | — | 5 | 4 | no | — |
| 310 | C2×C42 | — | 5 | 4 | no | — |
| 311 | #95 | — | 5 | 4 | no | — |
| 312 | #95 | — | 5 | 4 | no | — |
| 313 | #95 | — | 5 | 4 | no | — |
| 314 | #95 | — | 5 | 4 | no | — |
| 315 | #95 | — | 5 | 4 | no | — |
| 316 | #95 | — | 5 | 4 | no | — |
| 317 | #95 | — | 5 | 4 | no | — |
| 318 | #95 | — | 5 | 4 | no | — |
| 319 | #95 | — | 5 | 4 | no | — |
| 320 | #95 | — | 5 | 4 | no | — |
| 321 | #95 | — | 5 | 4 | no | — |
| 322 | #95 | — | 5 | 4 | no | — |
| 323 | #95 | C22×D5 | 1 | 4 | yes | — |
| 324 | #95 | C22×D5 | 1 | 4 | yes | — |
| 325 | #95 | C22×D5 | 1 | 4 | yes | — |
| 326 | C22×C5 | — | 2 | 2 | no | — |
| 327 | C22×C5 | — | 2 | 2 | no | — |
| 328 | C22×C5 | — | 2 | 4 | no | — |
| 329 | C22×C5 | — | 2 | 4 | no | — |
| 330 | C22×C5 | #541 | 1 | 4 | yes | — |
| 331 | C22×C5 | C22×#41 | 1 | 1 | yes | characteristic |
| 332 | C22×C5 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 333 | C22×C5 | C2×2−1+4 | 1 | 2 | yes | — |
| 334 | C22×C5 | #585 | 1 | 1 | yes | characteristic |
| 335 | C22×C5 | #585 | 1 | 1 | yes | characteristic |
| 336 | C2×D5 | — | 2 | 4 | no | — |
| 337 | C2×D5 | — | 2 | 4 | no | — |
| 338 | C2×D5 | — | 2 | 4 | no | — |
| 339 | C2×D5 | — | 4 | 16 | no | — |
| 340 | C2×D5 | — | 4 | 2 | no | — |
| 341 | C2×D5 | — | 4 | 2 | no | — |
| 342 | C2×D5 | — | 4 | 2 | no | — |
| 343 | C2×D5 | — | 4 | 2 | no | — |
| 344 | C4×C5 | — | 2 | 4 | no | — |
| 345 | C4×C5 | — | 4 | 4 | no | — |
| 346 | C4×C5 | — | 4 | 4 | no | — |
| 347 | C4×C5 | — | 4 | 4 | no | — |
| 348 | Dic5 | — | 4 | 1 | no | — |
| 349 | Dic5 | — | 4 | 1 | no | — |
| 350 | Dic5 | — | 4 | 4 | no | — |
| 351 | Dic5 | — | 4 | 4 | no | — |
| 352 | Dic5 | — | 4 | 4 | no | — |
| 353 | C24 | — | 5 | 2 | no | — |
| 354 | C24 | — | 10 | 4 | no | — |
| 355 | C24 | — | 10 | 2 | no | — |
| 356 | C24 | — | 10 | 4 | no | — |
| 357 | C24 | — | 20 | 1 | no | — |
| 358 | C24 | — | 20 | 1 | no | — |
| 359 | C24 | C23×D5 | 1 | 1 | yes | characteristic |
| 360 | C2×Q8 | — | 2 | 4 | no | — |
| 361 | C2×Q8 | — | 4 | 2 | no | — |
| 362 | C2×Q8 | — | 4 | 2 | no | — |
| 363 | C22×C4 | — | 2 | 4 | no | — |
| 364 | C22×C4 | — | 4 | 2 | no | — |
| 365 | C22×C4 | — | 4 | 2 | no | — |
| 366 | C22×C4 | — | 4 | 2 | no | — |
| 367 | C22×C4 | — | 5 | 4 | no | — |
| 368 | C22×C4 | — | 5 | 1 | no | — |
| 369 | C22×C4 | — | 5 | 1 | no | — |
| 370 | C22×C4 | — | 5 | 4 | no | — |
| 371 | C22×C4 | — | 5 | 4 | no | — |
| 372 | C22×C4 | — | 10 | 4 | no | — |
| 373 | C22×C4 | — | 10 | 4 | no | — |
| 374 | C22×C4 | — | 10 | 2 | no | — |
| 375 | C22×C4 | — | 10 | 4 | no | — |
| 376 | C22×C4 | — | 10 | 4 | no | — |
| 377 | C22×C4 | — | 10 | 4 | no | — |
| 378 | C22×C4 | — | 20 | 2 | no | — |
| 379 | C22×C4 | — | 20 | 2 | no | — |
| 380 | C22×C4 | — | 20 | 16 | no | — |
| 381 | C22×C4 | — | 20 | 2 | no | — |
| 382 | C22×C4 | — | 20 | 2 | no | — |
| 383 | C22×C4 | — | 20 | 2 | no | — |
| 384 | C22×C4 | #711 | 1 | 4 | yes | — |
| 385 | C22×C4 | C23×D5 | 1 | 4 | yes | — |
| 386 | C22×C4 | C23×D5 | 1 | 4 | yes | — |
| 387 | C22×C4 | C23×D5 | 1 | 4 | yes | — |
| 388 | C22×C4 | C23×D5 | 1 | 2 | yes | — |
| 389 | C4⋊C4 | — | 2 | 4 | no | — |
| 390 | C4⋊C4 | — | 2 | 8 | no | — |
| 391 | C4⋊C4 | — | 4 | 4 | no | — |
| 392 | C4⋊C4 | — | 4 | 4 | no | — |
| 393 | C4⋊C4 | — | 20 | 4 | no | — |
| 394 | C4⋊C4 | — | 20 | 4 | no | — |
| 395 | C4⋊C4 | — | 20 | 2 | no | — |
| 396 | C4⋊C4 | — | 20 | 2 | no | — |
| 397 | C4⋊C4 | — | 20 | 4 | no | — |
| 398 | C4⋊C4 | — | 20 | 4 | no | — |
| 399 | C4⋊C4 | — | 20 | 4 | no | — |
| 400 | C4⋊C4 | — | 20 | 4 | no | — |
| 401 | C22⋊C4 | — | 2 | 8 | no | — |
| 402 | C22⋊C4 | — | 10 | 8 | no | — |
| 403 | C22⋊C4 | — | 10 | 8 | no | — |
| 404 | C22⋊C4 | — | 10 | 8 | no | — |
| 405 | C22⋊C4 | — | 10 | 8 | no | — |
| 406 | C22⋊C4 | — | 20 | 4 | no | — |
| 407 | C22⋊C4 | — | 20 | 4 | no | — |
| 408 | C22⋊C4 | — | 20 | 4 | no | — |
| 409 | C42 | — | 20 | 4 | no | — |
| 410 | C42 | — | 20 | 4 | no | — |
| 411 | C2×C5 | — | 2 | 4 | no | — |
| 412 | C2×C5 | C2×#541 | 1 | 1 | yes | characteristic |
| 413 | C2×C5 | #3490 | 1 | 1 | yes | characteristic |
| 414 | C2×C5 | #3493 | 1 | 1 | yes | characteristic |
| 415 | C2×C5 | #3535 | 1 | 2 | yes | — |
| 416 | C2×C5 | #3535 | 1 | 2 | yes | — |
| 417 | D5 | — | 4 | 4 | no | — |
| 418 | C23 | — | 2 | 2 | no | — |
| 419 | C23 | — | 2 | 1 | no | — |
| 420 | C23 | — | 2 | 1 | no | — |
| 421 | C23 | — | 5 | 4 | no | — |
| 422 | C23 | — | 10 | 8 | no | — |
| 423 | C23 | — | 10 | 2 | no | — |
| 424 | C23 | — | 10 | 2 | no | — |
| 425 | C23 | — | 10 | 2 | no | — |
| 426 | C23 | — | 10 | 2 | no | — |
| 427 | C23 | — | 10 | 2 | no | — |
| 428 | C23 | — | 10 | 2 | no | — |
| 429 | C23 | — | 20 | 8 | no | — |
| 430 | C23 | — | 20 | 8 | no | — |
| 431 | C23 | — | 20 | 4 | no | — |
| 432 | C23 | — | 20 | 4 | no | — |
| 433 | C23 | C2×#711 | 1 | 2 | yes | — |
| 434 | C23 | #4147 | 1 | 4 | yes | — |
| 435 | C23 | C24×D5 | 1 | 1 | yes | characteristic |
| 436 | Q8 | — | 8 | 4 | no | — |
| 437 | C2×C4 | — | 2 | 2 | no | — |
| 438 | C2×C4 | — | 2 | 2 | no | — |
| 439 | C2×C4 | — | 2 | 4 | no | — |
| 440 | C2×C4 | — | 2 | 4 | no | — |
| 441 | C2×C4 | — | 2 | 4 | no | — |
| 442 | C2×C4 | — | 2 | 4 | no | — |
| 443 | C2×C4 | — | 2 | 4 | no | — |
| 444 | C2×C4 | — | 2 | 4 | no | — |
| 445 | C2×C4 | — | 2 | 4 | no | — |
| 446 | C2×C4 | — | 2 | 4 | no | — |
| 447 | C2×C4 | — | 2 | 4 | no | — |
| 448 | C2×C4 | — | 4 | 4 | no | — |
| 449 | C2×C4 | — | 8 | 4 | no | — |
| 450 | C2×C4 | — | 10 | 1 | no | — |
| 451 | C2×C4 | — | 10 | 1 | no | — |
| 452 | C2×C4 | — | 10 | 4 | no | — |
| 453 | C2×C4 | — | 10 | 4 | no | — |
| 454 | C2×C4 | — | 10 | 4 | no | — |
| 455 | C2×C4 | — | 10 | 4 | no | — |
| 456 | C2×C4 | — | 10 | 4 | no | — |
| 457 | C2×C4 | — | 10 | 4 | no | — |
| 458 | C2×C4 | — | 10 | 2 | no | — |
| 459 | C2×C4 | — | 10 | 2 | no | — |
| 460 | C2×C4 | — | 10 | 4 | no | — |
| 461 | C2×C4 | — | 10 | 4 | no | — |
| 462 | C2×C4 | — | 10 | 4 | no | — |
| 463 | C2×C4 | — | 20 | 8 | no | — |
| 464 | C2×C4 | — | 20 | 8 | no | — |
| 465 | C2×C4 | — | 20 | 4 | no | — |
| 466 | C2×C4 | — | 40 | 4 | no | — |
| 467 | C2×C4 | C2×#711 | 1 | 4 | yes | — |
| 468 | C5 | #36732 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 469 | C22 | — | 2 | 2 | no | — |
| 470 | C22 | — | 2 | 4 | no | — |
| 471 | C22 | — | 2 | 4 | no | — |
| 472 | C22 | — | 2 | 2 | no | — |
| 473 | C22 | — | 10 | 4 | no | — |
| 474 | C22 | — | 10 | 4 | no | — |
| 475 | C22 | — | 10 | 4 | no | — |
| 476 | C22 | — | 20 | 16 | no | — |
| 477 | C22 | — | 20 | 2 | no | — |
| 478 | C22 | — | 20 | 2 | no | — |
| 479 | C22 | — | 20 | 2 | no | — |
| 480 | C22 | — | 20 | 2 | no | — |
| 481 | C22 | #66065 | 1 | 4 | yes | — |
| 482 | C22 | C22×#711 | 1 | 1 | yes | characteristic |
| 483 | C22 | C2×#4147 | 1 | 2 | yes | — |
| 484 | C22 | D5×H(5,𝔽2) | 1 | 2 | yes | — |
| 485 | C22 | #66285 | 1 | 1 | yes | characteristic |
| 486 | C22 | #66287 | 1 | 1 | yes | characteristic |
| 487 | C4 | — | 2 | 4 | no | — |
| 488 | C4 | — | 4 | 4 | no | — |
| 489 | C4 | — | 4 | 4 | no | — |
| 490 | C4 | — | 4 | 4 | no | — |
| 491 | C4 | — | 20 | 1 | no | — |
| 492 | C4 | — | 20 | 1 | no | — |
| 493 | C4 | — | 20 | 4 | no | — |
| 494 | C4 | — | 20 | 4 | no | — |
| 495 | C4 | — | 20 | 4 | no | — |
| 496 | C2 | — | 2 | 4 | no | — |
| 497 | C2 | — | 20 | 4 | no | — |
| 498 | C2 | C2×#66065 | 1 | 1 | yes | characteristic |
| 499 | C2 | #10618210 | 1 | 1 | yes | characteristic |
| 500 | C2 | #10618267 | 1 | 1 | yes | characteristic |
| 501 | C2 | #10618481 | 1 | 2 | yes | — |
| 502 | C2 | #10618501 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D5 |
| commutator, socle, cosocle | C23×C5 | C25 |
| Fitting | C5×#2659 | C2 |
| prime radical | C24×D5 | C23 |
| hypercenter | #2659 | D5 |
| hypocenter | C5 | #36732 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ #2659 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#2659 | C2 | semidirect |
| 3. #10614476 | C2 | semidirect |
| 4. #10609724 | C2 | semidirect |
| 5. #10609720 | C2 | semidirect |
| 6. #10608997 | C2 | semidirect |
| 7. #10608996 | C2 | semidirect |
| 8. #10605658 | C2 | semidirect |
| 11. #10605091 | C2 | semidirect |
| 18. C5×#398 | C22 | semidirect |
| 19. C5×#395 | C22 | semidirect |
| 22. #65519 | C22 | semidirect |
| 34. #65274 | C22 | semidirect |
| 35. #65273 | C22 | semidirect |
| 36. #65271 | C22 | semidirect |
| 37. #65270 | C22 | semidirect |
| 38. #65270 | C22 | semidirect |
| 39. #65270 | C22 | semidirect |
| 40. #65261 | C22 | semidirect |
| 51. #64949 | C22 | semidirect |
| 52. #64948 | C22 | semidirect |
| 53. #64947 | C22 | semidirect |
| 54. #64946 | C22 | semidirect |
| 55. #64942 | C22 | semidirect |
| 56. #64939 | C22 | semidirect |
| 115. #2659 | D5 | semidirect |
| 191. #398 | C2×D5 | semidirect |
| 196. #395 | C2×D5 | semidirect |
| 468. C5 | #36732 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2659 | 2 |
| #10614565 | 2 |
| #10614476 | 2 |
| #10609724 | 2 |
| #10609720 | 2 |
| #10608997 | 2 |
| #10608996 | 2 |
| #10605658 | 2 |
| #10605640 | 2 |
| C2×#64953 | 2 |
| #10605091 | 2 |
| #36732 | 5 |