Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1474 conjugacy classes of subgroups.
The subgroup lattice has 434 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C5×#2845 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10609747 | C2 | 1 | 4 | yes | maximal |
| 3 | #10609746 | C2 | 1 | 4 | yes | maximal |
| 4 | #10609674 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #10609472 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #10609471 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #10609470 | C2 | 1 | 4 | yes | maximal |
| 8 | #10605950 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #10605949 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #10605879 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | #10605878 | C2 | 1 | 2 | yes | maximal |
| 12 | C2×#4038 | C22 | 1 | 2 | yes | — |
| 13 | C2×#4033 | C22 | 1 | 4 | yes | — |
| 14 | C2×C42×D5 | C22 | 1 | 1 | yes | characteristic |
| 15 | C5×#398 | C22 | 1 | 4 | yes | — |
| 16 | C5×#398 | C22 | 1 | 4 | yes | — |
| 17 | C5×#398 | C22 | 1 | 4 | yes | — |
| 18 | C5×#382 | C22 | 1 | 2 | yes | — |
| 19 | C5×#382 | C22 | 1 | 1 | yes | characteristic |
| 20 | #65283 | C22 | 1 | 4 | yes | — |
| 21 | #65283 | C22 | 1 | 4 | yes | — |
| 22 | #65281 | C22 | 1 | 4 | yes | — |
| 23 | #65276 | C22 | 1 | 2 | yes | — |
| 24 | #65276 | C22 | 1 | 2 | yes | — |
| 25 | #65275 | C22 | 1 | 4 | yes | — |
| 26 | #65273 | C22 | 1 | 4 | yes | — |
| 27 | #65273 | C22 | 1 | 4 | yes | — |
| 28 | #65272 | C22 | 1 | 4 | yes | — |
| 29 | #65271 | C22 | 1 | 4 | yes | — |
| 30 | #65269 | C22 | 1 | 4 | yes | — |
| 31 | #65268 | C22 | 1 | 4 | yes | — |
| 32 | #65268 | C22 | 1 | 4 | yes | — |
| 33 | #65268 | C22 | 1 | 4 | yes | — |
| 34 | #65265 | C22 | 1 | 2 | yes | — |
| 35 | C4⋊C4×Dic5 | C22 | 1 | 2 | yes | — |
| 36 | C4⋊C4×Dic5 | C22 | 1 | 2 | yes | — |
| 37 | C4⋊C4×Dic5 | C22 | 1 | 4 | yes | — |
| 38 | C4⋊C4×Dic5 | C22 | 1 | 4 | yes | — |
| 39 | #65225 | C22 | 1 | 2 | yes | — |
| 40 | #65225 | C22 | 1 | 1 | yes | characteristic |
| 41 | #64962 | C22 | 1 | 4 | yes | — |
| 42 | #64956 | C22 | 1 | 4 | yes | — |
| 43 | #64955 | C22 | 1 | 4 | yes | — |
| 44 | #64953 | C22 | 1 | 4 | yes | — |
| 45 | #64950 | C22 | 1 | 4 | yes | — |
| 46 | #64949 | C22 | 1 | 4 | yes | — |
| 47 | #64949 | C22 | 1 | 4 | yes | — |
| 48 | #64948 | C22 | 1 | 4 | yes | — |
| 49 | #64946 | C22 | 1 | 4 | yes | — |
| 50 | #64946 | C22 | 1 | 4 | yes | — |
| 51 | #64945 | C22 | 1 | 4 | yes | — |
| 52 | #64945 | C22 | 1 | 4 | yes | — |
| 53 | #64940 | C22 | 1 | 4 | yes | — |
| 54 | #64938 | C22 | 1 | 4 | yes | — |
| 55 | #64938 | C22 | 1 | 4 | yes | — |
| 56 | #64937 | C22 | 1 | 4 | yes | — |
| 57 | #36691 | — | 5 | 1 | no | maximal, Sylow |
| 58 | C22×C4×D5 | C23 | 1 | 1 | yes | characteristic |
| 59 | C22×C4×D5 | C23 | 1 | 2 | yes | — |
| 60 | C22×Dic10 | C23 | 1 | 4 | yes | — |
| 61 | C2×C5×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 62 | C2×C5×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 63 | C2×C5×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 64 | C2×C5×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 65 | C2×C5×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 66 | C2×C5×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 67 | C2×C42×C5 | C23 | 1 | 1 | yes | characteristic |
| 68 | C2×#685 | C23 | 1 | 4 | yes | — |
| 69 | C2×#685 | C23 | 1 | 4 | yes | — |
| 70 | C2×#685 | C23 | 1 | 4 | yes | — |
| 71 | C2×C4⋊Dic5 | C23 | 1 | 4 | yes | — |
| 72 | C2×C4⋊Dic5 | C23 | 1 | 4 | yes | — |
| 73 | C2×C4⋊Dic5 | C23 | 1 | 2 | yes | — |
| 74 | C2×C4⋊Dic5 | C23 | 1 | 2 | yes | — |
| 75 | C2×C4⋊Dic5 | C23 | 1 | 2 | yes | — |
| 76 | C2×#683 | C23 | 1 | 4 | yes | — |
| 77 | C2×#683 | C23 | 1 | 4 | yes | — |
| 78 | C2×#683 | C23 | 1 | 4 | yes | — |
| 79 | C2×#683 | C23 | 1 | 4 | yes | — |
| 80 | C2×#683 | C23 | 1 | 4 | yes | — |
| 81 | C2×#683 | C23 | 1 | 4 | yes | — |
| 82 | C2×C4×Dic5 | C23 | 1 | 4 | yes | — |
| 83 | C2×C4×Dic5 | C23 | 1 | 4 | yes | — |
| 84 | C2×C4×Dic5 | C23 | 1 | 4 | yes | — |
| 85 | C2×C4×Dic5 | C23 | 1 | 2 | yes | — |
| 86 | C2×C4×Dic5 | C23 | 1 | 1 | yes | characteristic |
| 87 | #4038 | — | 4 | 4 | no | — |
| 88 | #4033 | — | 4 | 8 | no | — |
| 89 | C42×D5 | Q8 | 1 | 8 | yes | complemented |
| 90 | C5×#95 | C23 | 1 | 4 | yes | — |
| 91 | C5×#95 | C23 | 1 | 4 | yes | — |
| 92 | C5×#95 | C23 | 1 | 4 | yes | — |
| 93 | C5×#95 | C23 | 1 | 4 | yes | — |
| 94 | #3963 | C23 | 1 | 4 | yes | — |
| 95 | #3963 | C23 | 1 | 4 | yes | — |
| 96 | #3963 | C23 | 1 | 4 | yes | — |
| 97 | #3963 | 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 | #2845 | — | 5 | 1 | no | — |
| 107 | #2845 | D5 | 1 | 1 | yes | characteristic, complemented |
| 108 | #2844 | — | 5 | 2 | no | — |
| 109 | #2843 | — | 5 | 4 | no | — |
| 110 | #2841 | — | 5 | 4 | no | — |
| 111 | #2841 | — | 5 | 4 | no | — |
| 112 | #2402 | — | 5 | 4 | no | — |
| 113 | #2399 | — | 5 | 4 | no | — |
| 114 | #2396 | — | 5 | 4 | no | — |
| 115 | #2285 | — | 5 | 1 | no | — |
| 116 | #2283 | — | 5 | 2 | no | — |
| 117 | C23×D5 | C24 | 1 | 1 | yes | characteristic |
| 118 | C22×C4×C5 | C24 | 1 | 4 | yes | — |
| 119 | C22×C4×C5 | C24 | 1 | 4 | yes | — |
| 120 | C22×C4×C5 | C24 | 1 | 4 | yes | — |
| 121 | C22×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 122 | C22×C4×C5 | C24 | 1 | 2 | yes | — |
| 123 | C22×Dic5 | C24 | 1 | 4 | yes | — |
| 124 | C22×Dic5 | C24 | 1 | 4 | yes | — |
| 125 | C22×Dic5 | C24 | 1 | 4 | yes | — |
| 126 | C22×Dic5 | C24 | 1 | 2 | yes | — |
| 127 | C22×Dic5 | C24 | 1 | 1 | yes | characteristic |
| 128 | C2×C4×D5 | — | 2 | 2 | no | — |
| 129 | C2×C4×D5 | — | 2 | 2 | no | — |
| 130 | C2×C4×D5 | — | 4 | 2 | no | — |
| 131 | C2×C4×D5 | — | 4 | 2 | no | — |
| 132 | C2×C4×D5 | C2×Q8 | 1 | 4 | yes | — |
| 133 | C2×C4×D5 | C2×Q8 | 1 | 8 | yes | — |
| 134 | C2×Dic10 | — | 4 | 4 | no | — |
| 135 | C2×Dic10 | — | 4 | 4 | no | — |
| 136 | C2×Dic10 | — | 4 | 4 | no | — |
| 137 | C5×C4⋊C4 | — | 4 | 2 | no | — |
| 138 | C5×C4⋊C4 | — | 4 | 2 | no | — |
| 139 | C5×C4⋊C4 | — | 4 | 4 | no | — |
| 140 | C5×C4⋊C4 | — | 4 | 4 | no | — |
| 141 | C5×C4⋊C4 | — | 4 | 4 | no | — |
| 142 | C5×C4⋊C4 | — | 4 | 2 | no | — |
| 143 | C42×C5 | C2×Q8 | 1 | 4 | yes | — |
| 144 | #685 | — | 4 | 4 | no | — |
| 145 | #685 | — | 4 | 4 | no | — |
| 146 | #685 | — | 4 | 4 | no | — |
| 147 | C4⋊Dic5 | — | 4 | 2 | no | — |
| 148 | C4⋊Dic5 | — | 4 | 2 | no | — |
| 149 | C4⋊Dic5 | — | 4 | 4 | no | — |
| 150 | C4⋊Dic5 | — | 4 | 2 | no | — |
| 151 | C4⋊Dic5 | — | 4 | 4 | no | — |
| 152 | #683 | — | 4 | 4 | no | — |
| 153 | #683 | — | 4 | 4 | no | — |
| 154 | #683 | — | 4 | 4 | no | — |
| 155 | #683 | — | 4 | 4 | no | — |
| 156 | #683 | — | 4 | 4 | no | — |
| 157 | #683 | — | 4 | 4 | no | — |
| 158 | C4×Dic5 | — | 2 | 8 | no | — |
| 159 | C4×Dic5 | — | 2 | 8 | no | — |
| 160 | C4×Dic5 | — | 2 | 8 | no | — |
| 161 | C4×Dic5 | C2×Q8 | 1 | 4 | yes | — |
| 162 | C4×Dic5 | C2×Q8 | 1 | 8 | yes | — |
| 163 | C2×C4×Q8 | — | 5 | 4 | no | — |
| 164 | C2×#117 | — | 5 | 2 | no | — |
| 165 | C22×C42 | — | 5 | 1 | no | — |
| 166 | #400 | — | 5 | 4 | no | — |
| 167 | #400 | — | 5 | 4 | no | — |
| 168 | #400 | — | 5 | 4 | no | — |
| 169 | #400 | — | 5 | 4 | no | — |
| 170 | #400 | — | 5 | 4 | no | — |
| 171 | #399 | — | 5 | 4 | no | — |
| 172 | #398 | — | 5 | 4 | no | — |
| 173 | #398 | — | 5 | 4 | no | — |
| 174 | #398 | — | 5 | 4 | no | — |
| 175 | #398 | — | 5 | 4 | no | — |
| 176 | #398 | — | 5 | 4 | no | — |
| 177 | #398 | — | 5 | 4 | no | — |
| 178 | #398 | — | 5 | 4 | no | — |
| 179 | #398 | C2×D5 | 1 | 4 | yes | — |
| 180 | #398 | C2×D5 | 1 | 4 | yes | — |
| 181 | #398 | C2×D5 | 1 | 4 | yes | — |
| 182 | #396 | — | 5 | 4 | no | — |
| 183 | #396 | — | 5 | 4 | no | — |
| 184 | #395 | — | 5 | 4 | no | — |
| 185 | #395 | — | 5 | 4 | no | — |
| 186 | #395 | — | 5 | 4 | no | — |
| 187 | #395 | — | 5 | 4 | no | — |
| 188 | #395 | — | 5 | 4 | no | — |
| 189 | #393 | — | 5 | 4 | no | — |
| 190 | #384 | — | 5 | 2 | no | — |
| 191 | #383 | — | 5 | 4 | no | — |
| 192 | #382 | — | 5 | 1 | no | — |
| 193 | #382 | — | 5 | 2 | no | — |
| 194 | #382 | C2×D5 | 1 | 2 | yes | — |
| 195 | #382 | C2×D5 | 1 | 1 | yes | characteristic |
| 196 | #381 | — | 5 | 4 | no | — |
| 197 | #380 | — | 5 | 2 | no | — |
| 198 | #380 | — | 5 | 2 | no | — |
| 199 | #380 | — | 5 | 4 | no | — |
| 200 | C4×C4⋊C4 | — | 5 | 4 | no | — |
| 201 | C4×C4⋊C4 | — | 5 | 4 | no | — |
| 202 | C4×C4⋊C4 | — | 5 | 2 | no | — |
| 203 | C4×C4⋊C4 | — | 5 | 2 | no | — |
| 204 | C4×C4⋊C4 | — | 5 | 4 | no | — |
| 205 | C4×C4⋊C4 | — | 5 | 4 | no | — |
| 206 | C4×C22⋊C4 | — | 5 | 4 | no | — |
| 207 | #376 | — | 5 | 4 | no | — |
| 208 | C23×C5 | C25 | 1 | 1 | yes | characteristic |
| 209 | C22×D5 | — | 2 | 1 | no | — |
| 210 | C22×D5 | — | 2 | 1 | no | — |
| 211 | C22×D5 | — | 2 | 2 | no | — |
| 212 | C22×D5 | — | 2 | 2 | no | — |
| 213 | C22×D5 | C22×Q8 | 1 | 2 | yes | — |
| 214 | C2×C4×C5 | — | 2 | 1 | no | — |
| 215 | C2×C4×C5 | — | 2 | 1 | no | — |
| 216 | C2×C4×C5 | — | 2 | 2 | no | — |
| 217 | C2×C4×C5 | — | 2 | 2 | no | — |
| 218 | C2×C4×C5 | — | 2 | 4 | no | — |
| 219 | C2×C4×C5 | — | 2 | 4 | no | — |
| 220 | C2×C4×C5 | — | 2 | 4 | no | — |
| 221 | C2×C4×C5 | — | 2 | 4 | no | — |
| 222 | C2×C4×C5 | — | 2 | 4 | no | — |
| 223 | C2×C4×C5 | — | 2 | 4 | no | — |
| 224 | C2×C4×C5 | — | 2 | 4 | no | — |
| 225 | C2×C4×C5 | — | 2 | 4 | no | — |
| 226 | C2×C4×C5 | — | 2 | 4 | no | — |
| 227 | C2×C4×C5 | C22×Q8 | 1 | 2 | yes | — |
| 228 | C2×C4×C5 | C22×Q8 | 1 | 4 | yes | — |
| 229 | C2×Dic5 | — | 2 | 2 | no | — |
| 230 | C2×Dic5 | — | 2 | 2 | no | — |
| 231 | C2×Dic5 | — | 2 | 4 | no | — |
| 232 | C2×Dic5 | — | 2 | 4 | no | — |
| 233 | C2×Dic5 | — | 2 | 4 | no | — |
| 234 | C2×Dic5 | — | 2 | 4 | no | — |
| 235 | C2×Dic5 | — | 2 | 4 | no | — |
| 236 | C2×Dic5 | — | 2 | 4 | no | — |
| 237 | C2×Dic5 | — | 2 | 4 | no | — |
| 238 | C2×Dic5 | — | 2 | 4 | no | — |
| 239 | C2×Dic5 | — | 2 | 4 | no | — |
| 240 | C2×Dic5 | C22×Q8 | 1 | 4 | yes | — |
| 241 | C2×Dic5 | C22×Q8 | 1 | 2 | yes | — |
| 242 | C2×Dic5 | H(5,𝔽2) | 1 | 2 | yes | — |
| 243 | C2×Dic5 | 2−1+4 | 1 | 2 | yes | — |
| 244 | C4×D5 | — | 2 | 8 | no | — |
| 245 | C4×D5 | — | 4 | 8 | no | — |
| 246 | Dic10 | — | 4 | 16 | no | — |
| 247 | C22×Q8 | — | 5 | 4 | no | — |
| 248 | C23×C4 | — | 5 | 1 | no | — |
| 249 | C23×C4 | — | 5 | 2 | no | — |
| 250 | C4×Q8 | — | 20 | 8 | no | — |
| 251 | #117 | — | 20 | 4 | no | — |
| 252 | C2×C4⋊C4 | — | 5 | 2 | no | — |
| 253 | C2×C4⋊C4 | — | 5 | 4 | no | — |
| 254 | C2×C4⋊C4 | — | 5 | 4 | no | — |
| 255 | C2×C4⋊C4 | — | 5 | 2 | no | — |
| 256 | C2×C4⋊C4 | — | 5 | 2 | no | — |
| 257 | C2×C4⋊C4 | — | 5 | 4 | no | — |
| 258 | C2×C4⋊C4 | — | 5 | 4 | no | — |
| 259 | C2×C4⋊C4 | — | 5 | 4 | no | — |
| 260 | C2×C4⋊C4 | — | 5 | 4 | no | — |
| 261 | C2×C4⋊C4 | — | 5 | 4 | no | — |
| 262 | C2×C4⋊C4 | — | 5 | 4 | no | — |
| 263 | C2×C4⋊C4 | C22×D5 | 1 | 2 | yes | — |
| 264 | C2×C4⋊C4 | C22×D5 | 1 | 4 | yes | — |
| 265 | C2×C4⋊C4 | C22×D5 | 1 | 2 | yes | — |
| 266 | C2×C4⋊C4 | C22×D5 | 1 | 2 | yes | — |
| 267 | C2×C4⋊C4 | C22×D5 | 1 | 4 | yes | — |
| 268 | C2×C4⋊C4 | C22×D5 | 1 | 4 | yes | — |
| 269 | C2×C22⋊C4 | — | 5 | 4 | no | — |
| 270 | C2×C22⋊C4 | — | 5 | 4 | no | — |
| 271 | C2×C22⋊C4 | — | 5 | 4 | no | — |
| 272 | C2×C42 | — | 5 | 2 | no | — |
| 273 | C2×C42 | — | 5 | 1 | no | — |
| 274 | C2×C42 | — | 5 | 8 | no | — |
| 275 | C2×C42 | — | 5 | 4 | no | — |
| 276 | C2×C42 | — | 5 | 4 | no | — |
| 277 | C2×C42 | — | 5 | 4 | no | — |
| 278 | C2×C42 | C22×D5 | 1 | 1 | yes | characteristic |
| 279 | #95 | — | 5 | 4 | no | — |
| 280 | #95 | — | 5 | 4 | no | — |
| 281 | #95 | — | 5 | 4 | no | — |
| 282 | #95 | — | 5 | 4 | no | — |
| 283 | #95 | — | 5 | 4 | no | — |
| 284 | #95 | — | 5 | 4 | no | — |
| 285 | #95 | — | 5 | 4 | no | — |
| 286 | #95 | — | 5 | 4 | no | — |
| 287 | #95 | — | 5 | 4 | no | — |
| 288 | #95 | — | 5 | 4 | no | — |
| 289 | #95 | — | 5 | 4 | no | — |
| 290 | #95 | — | 5 | 4 | no | — |
| 291 | #95 | C22×D5 | 1 | 4 | yes | — |
| 292 | #95 | C22×D5 | 1 | 4 | yes | — |
| 293 | #95 | C22×D5 | 1 | 4 | yes | — |
| 294 | #95 | C22×D5 | 1 | 4 | yes | — |
| 295 | C22×C5 | C23×Q8 | 1 | 1 | yes | characteristic |
| 296 | C22×C5 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 297 | C22×C5 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 298 | C22×C5 | #585 | 1 | 2 | yes | — |
| 299 | C22×C5 | #585 | 1 | 2 | yes | — |
| 300 | C2×D5 | — | 2 | 2 | no | — |
| 301 | C2×D5 | — | 2 | 4 | no | — |
| 302 | C2×D5 | — | 4 | 2 | no | — |
| 303 | C2×D5 | — | 4 | 1 | no | — |
| 304 | C2×D5 | — | 4 | 1 | no | — |
| 305 | C4×C5 | — | 2 | 2 | no | — |
| 306 | C4×C5 | — | 2 | 4 | no | — |
| 307 | C4×C5 | — | 4 | 4 | no | — |
| 308 | C4×C5 | — | 4 | 4 | no | — |
| 309 | C4×C5 | — | 4 | 4 | no | — |
| 310 | Dic5 | — | 2 | 4 | no | — |
| 311 | Dic5 | — | 4 | 4 | no | — |
| 312 | Dic5 | — | 4 | 4 | no | — |
| 313 | Dic5 | — | 4 | 4 | no | — |
| 314 | Dic5 | #544 | 1 | 4 | yes | — |
| 315 | C24 | — | 5 | 1 | no | — |
| 316 | C2×Q8 | — | 20 | 4 | no | — |
| 317 | C2×Q8 | — | 20 | 4 | no | — |
| 318 | C2×Q8 | — | 20 | 4 | no | — |
| 319 | C22×C4 | — | 5 | 1 | no | — |
| 320 | C22×C4 | — | 5 | 2 | no | — |
| 321 | C22×C4 | — | 5 | 4 | no | — |
| 322 | C22×C4 | — | 5 | 8 | no | — |
| 323 | C22×C4 | — | 5 | 4 | no | — |
| 324 | C22×C4 | — | 5 | 4 | no | — |
| 325 | C22×C4 | — | 5 | 4 | no | — |
| 326 | C22×C4 | — | 10 | 2 | no | — |
| 327 | C22×C4 | — | 10 | 2 | no | — |
| 328 | C22×C4 | — | 20 | 2 | no | — |
| 329 | C22×C4 | — | 20 | 2 | no | — |
| 330 | C22×C4 | C23×D5 | 1 | 4 | yes | — |
| 331 | C22×C4 | C23×D5 | 1 | 4 | yes | — |
| 332 | C22×C4 | C23×D5 | 1 | 4 | yes | — |
| 333 | C22×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 334 | C22×C4 | C23×D5 | 1 | 2 | yes | — |
| 335 | C4⋊C4 | — | 4 | 2 | no | — |
| 336 | C4⋊C4 | — | 4 | 4 | no | — |
| 337 | C4⋊C4 | — | 4 | 2 | no | — |
| 338 | C4⋊C4 | — | 4 | 2 | no | — |
| 339 | C4⋊C4 | — | 4 | 4 | no | — |
| 340 | C4⋊C4 | — | 4 | 4 | no | — |
| 341 | C4⋊C4 | — | 20 | 2 | no | — |
| 342 | C4⋊C4 | — | 20 | 4 | no | — |
| 343 | C4⋊C4 | — | 20 | 4 | no | — |
| 344 | C4⋊C4 | — | 20 | 4 | no | — |
| 345 | C4⋊C4 | — | 20 | 4 | no | — |
| 346 | C4⋊C4 | — | 20 | 4 | no | — |
| 347 | C4⋊C4 | — | 20 | 4 | no | — |
| 348 | C4⋊C4 | — | 20 | 2 | no | — |
| 349 | C4⋊C4 | — | 20 | 2 | no | — |
| 350 | C4⋊C4 | — | 20 | 4 | no | — |
| 351 | C4⋊C4 | — | 20 | 4 | no | — |
| 352 | C22⋊C4 | — | 20 | 4 | no | — |
| 353 | C22⋊C4 | — | 20 | 4 | no | — |
| 354 | C22⋊C4 | — | 20 | 4 | no | — |
| 355 | C42 | — | 5 | 8 | no | — |
| 356 | C42 | — | 5 | 4 | no | — |
| 357 | C42 | — | 10 | 8 | no | — |
| 358 | C42 | — | 10 | 8 | no | — |
| 359 | C42 | — | 10 | 8 | no | — |
| 360 | C42 | Q8×D5 | 1 | 4 | yes | — |
| 361 | C2×C5 | C2×#544 | 1 | 1 | yes | characteristic |
| 362 | C2×C5 | #3458 | 1 | 2 | yes | — |
| 363 | C2×C5 | #3529 | 1 | 2 | yes | — |
| 364 | C2×C5 | #3531 | 1 | 1 | yes | characteristic |
| 365 | C2×C5 | #3531 | 1 | 1 | yes | characteristic |
| 366 | D5 | — | 4 | 2 | no | — |
| 367 | C23 | — | 5 | 2 | no | — |
| 368 | C23 | — | 10 | 1 | no | — |
| 369 | C23 | — | 10 | 2 | no | — |
| 370 | C23 | — | 10 | 1 | no | — |
| 371 | C23 | — | 10 | 2 | no | — |
| 372 | C23 | C24×D5 | 1 | 1 | yes | characteristic |
| 373 | Q8 | — | 20 | 16 | no | — |
| 374 | C2×C4 | — | 2 | 1 | no | — |
| 375 | C2×C4 | — | 2 | 2 | no | — |
| 376 | C2×C4 | — | 2 | 1 | no | — |
| 377 | C2×C4 | — | 2 | 2 | no | — |
| 378 | C2×C4 | — | 2 | 4 | no | — |
| 379 | C2×C4 | — | 2 | 4 | no | — |
| 380 | C2×C4 | — | 2 | 4 | no | — |
| 381 | C2×C4 | — | 2 | 4 | no | — |
| 382 | C2×C4 | — | 2 | 4 | no | — |
| 383 | C2×C4 | — | 2 | 4 | no | — |
| 384 | C2×C4 | — | 2 | 4 | no | — |
| 385 | C2×C4 | — | 2 | 4 | no | — |
| 386 | C2×C4 | — | 2 | 4 | no | — |
| 387 | C2×C4 | — | 5 | 2 | no | — |
| 388 | C2×C4 | — | 5 | 2 | no | — |
| 389 | C2×C4 | — | 5 | 2 | no | — |
| 390 | C2×C4 | — | 5 | 4 | no | — |
| 391 | C2×C4 | — | 10 | 8 | no | — |
| 392 | C2×C4 | — | 10 | 2 | no | — |
| 393 | C2×C4 | — | 10 | 2 | no | — |
| 394 | C2×C4 | — | 10 | 4 | no | — |
| 395 | C2×C4 | — | 10 | 4 | no | — |
| 396 | C2×C4 | — | 10 | 4 | no | — |
| 397 | C2×C4 | — | 10 | 4 | no | — |
| 398 | C2×C4 | — | 10 | 4 | no | — |
| 399 | C2×C4 | — | 10 | 4 | no | — |
| 400 | C2×C4 | — | 10 | 4 | no | — |
| 401 | C2×C4 | — | 10 | 4 | no | — |
| 402 | C2×C4 | — | 10 | 4 | no | — |
| 403 | C2×C4 | — | 20 | 8 | no | — |
| 404 | C2×C4 | C2×Q8×D5 | 1 | 4 | yes | — |
| 405 | C2×C4 | C2×Q8×D5 | 1 | 2 | yes | — |
| 406 | C5 | #36691 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 407 | C22 | — | 10 | 4 | no | — |
| 408 | C22 | — | 10 | 2 | no | — |
| 409 | C22 | — | 20 | 2 | no | — |
| 410 | C22 | — | 20 | 1 | no | — |
| 411 | C22 | — | 20 | 1 | no | — |
| 412 | C22 | C22×Q8×D5 | 1 | 1 | yes | characteristic |
| 413 | C22 | D5×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 414 | C22 | #66285 | 1 | 2 | yes | — |
| 415 | C22 | D5×2−1+4 | 1 | 1 | yes | characteristic |
| 416 | C22 | #66287 | 1 | 2 | yes | — |
| 417 | C4 | — | 2 | 4 | no | — |
| 418 | C4 | — | 2 | 2 | no | — |
| 419 | C4 | — | 4 | 4 | no | — |
| 420 | C4 | — | 4 | 4 | no | — |
| 421 | C4 | — | 4 | 4 | no | — |
| 422 | C4 | — | 5 | 4 | no | — |
| 423 | C4 | — | 10 | 4 | no | — |
| 424 | C4 | — | 20 | 4 | no | — |
| 425 | C4 | — | 20 | 4 | no | — |
| 426 | C4 | — | 20 | 4 | no | — |
| 427 | C2 | — | 20 | 2 | no | — |
| 428 | C2 | #10618482 | 1 | 2 | yes | — |
| 429 | C2 | D5×#544 | 1 | 1 | yes | characteristic |
| 430 | C2 | #10618994 | 1 | 2 | yes | — |
| 431 | C2 | #10618995 | 1 | 1 | yes | characteristic |
| 432 | C2 | #10619040 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D5 |
| commutator, socle, cosocle | C23×C5 | C25 |
| Fitting | C5×#2845 | C2 |
| prime radical | C23×D5 | C24 |
| hypercenter | #2845 | D5 |
| hypocenter | C5 | #36691 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ #2845 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#2845 | C2 | semidirect |
| 4. #10609674 | C2 | semidirect |
| 5. #10609472 | C2 | semidirect |
| 6. #10609471 | C2 | semidirect |
| 8. #10605950 | C2 | semidirect |
| 9. #10605949 | C2 | semidirect |
| 89. C42×D5 | Q8 | semidirect |
| 107. #2845 | D5 | semidirect |
| 406. C5 | #36691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2845 | 2 |
| #10609747 | 2 |
| #10609746 | 2 |
| #10609674 | 2 |
| #10609472 | 2 |
| #10609471 | 2 |
| #10609470 | 2 |
| #10605950 | 2 |
| #10605949 | 2 |
| #10605879 | 2 |
| #10605878 | 2 |
| #36691 | 5 |