Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1664 conjugacy classes of subgroups.
The subgroup lattice has 460 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C5×#2819 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10614723 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | Dic5×#124 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10608833 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #10608623 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #10608587 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #10608509 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #10608482 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #10608397 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #10605950 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #10605881 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×C5×#124 | C22 | 1 | 2 | yes | — |
| 13 | C2×Q8×Dic5 | C22 | 1 | 2 | yes | — |
| 14 | C2×D4×Dic5 | C22 | 1 | 2 | yes | — |
| 15 | C2×D4×Dic5 | C22 | 1 | 4 | yes | — |
| 16 | C2×#4023 | C22 | 1 | 4 | yes | — |
| 17 | C2×#4016 | C22 | 1 | 1 | yes | characteristic |
| 18 | C5×#394 | C22 | 1 | 4 | yes | — |
| 19 | C5×#393 | C22 | 1 | 4 | yes | — |
| 20 | C5×#392 | C22 | 1 | 4 | yes | — |
| 21 | C5×#382 | C22 | 1 | 1 | yes | characteristic |
| 22 | #65519 | C22 | 1 | 2 | yes | — |
| 23 | #65518 | C22 | 1 | 4 | yes | — |
| 24 | #65511 | C22 | 1 | 4 | yes | — |
| 25 | #65511 | C22 | 1 | 4 | yes | — |
| 26 | #65511 | C22 | 1 | 4 | yes | — |
| 27 | #65511 | C22 | 1 | 4 | yes | — |
| 28 | #65510 | C22 | 1 | 2 | yes | — |
| 29 | #65273 | C22 | 1 | 4 | yes | — |
| 30 | C4⋊C4×Dic5 | C22 | 1 | 2 | yes | — |
| 31 | #65262 | C22 | 1 | 2 | yes | — |
| 32 | #65242 | C22 | 1 | 4 | yes | — |
| 33 | #65242 | C22 | 1 | 4 | yes | — |
| 34 | #65241 | C22 | 1 | 4 | yes | — |
| 35 | #65241 | C22 | 1 | 4 | yes | — |
| 36 | #65240 | C22 | 1 | 4 | yes | — |
| 37 | #65240 | C22 | 1 | 4 | yes | — |
| 38 | #65238 | C22 | 1 | 4 | yes | — |
| 39 | #65238 | C22 | 1 | 4 | yes | — |
| 40 | #65237 | C22 | 1 | 4 | yes | — |
| 41 | #65237 | C22 | 1 | 4 | yes | — |
| 42 | #65237 | C22 | 1 | 4 | yes | — |
| 43 | #65237 | C22 | 1 | 4 | yes | — |
| 44 | C22⋊C4×Dic5 | C22 | 1 | 4 | yes | — |
| 45 | C22⋊C4×Dic5 | C22 | 1 | 4 | yes | — |
| 46 | C22⋊C4×Dic5 | C22 | 1 | 4 | yes | — |
| 47 | #65225 | C22 | 1 | 2 | yes | — |
| 48 | C42×Dic5 | C22 | 1 | 1 | yes | characteristic |
| 49 | #64950 | C22 | 1 | 4 | yes | — |
| 50 | #64949 | C22 | 1 | 4 | yes | — |
| 51 | #64948 | C22 | 1 | 4 | yes | — |
| 52 | #64946 | C22 | 1 | 4 | yes | — |
| 53 | #64946 | C22 | 1 | 4 | yes | — |
| 54 | #64941 | C22 | 1 | 4 | yes | — |
| 55 | #64938 | C22 | 1 | 4 | yes | — |
| 56 | #64938 | C22 | 1 | 4 | yes | — |
| 57 | #36695 | — | 5 | 1 | no | maximal, Sylow |
| 58 | C22×C5×Q8 | C23 | 1 | 2 | yes | — |
| 59 | C22×C5×D4 | C23 | 1 | 2 | yes | — |
| 60 | C22×C5×D4 | C23 | 1 | 4 | yes | — |
| 61 | C23×Dic5 | C23 | 1 | 4 | yes | — |
| 62 | C5×#124 | — | 2 | 8 | no | — |
| 63 | C2×C5×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 64 | C2×C5×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 65 | C2×C5×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 66 | C2×C5×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 67 | C2×C5×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 68 | C2×C42×C5 | C23 | 1 | 1 | yes | characteristic |
| 69 | C2×C22⋊Dic5 | C23 | 1 | 4 | yes | — |
| 70 | C2×C22⋊Dic5 | C23 | 1 | 4 | yes | — |
| 71 | C2×C22⋊Dic5 | C23 | 1 | 4 | yes | — |
| 72 | C2×C22⋊Dic5 | C23 | 1 | 4 | yes | — |
| 73 | C2×C22⋊Dic5 | C23 | 1 | 4 | yes | — |
| 74 | C2×C22⋊Dic5 | C23 | 1 | 4 | yes | — |
| 75 | C2×C22⋊Dic5 | C23 | 1 | 4 | yes | — |
| 76 | Q8×Dic5 | — | 4 | 4 | no | — |
| 77 | D4×Dic5 | — | 4 | 8 | no | — |
| 78 | D4×Dic5 | — | 4 | 4 | no | — |
| 79 | C2×C4⋊Dic5 | C23 | 1 | 2 | yes | — |
| 80 | C2×C4⋊Dic5 | C23 | 1 | 4 | yes | — |
| 81 | C2×C4⋊Dic5 | C23 | 1 | 2 | yes | — |
| 82 | C2×C4⋊Dic5 | C23 | 1 | 2 | yes | — |
| 83 | C2×C4⋊Dic5 | C23 | 1 | 4 | yes | — |
| 84 | C2×#683 | C23 | 1 | 4 | yes | — |
| 85 | C2×#683 | C23 | 1 | 4 | yes | — |
| 86 | C2×#683 | C23 | 1 | 4 | yes | — |
| 87 | C2×#683 | C23 | 1 | 4 | yes | — |
| 88 | C2×#683 | C23 | 1 | 4 | yes | — |
| 89 | C2×#683 | C23 | 1 | 4 | yes | — |
| 90 | C2×C4×Dic5 | C23 | 1 | 4 | yes | — |
| 91 | C2×C4×Dic5 | C23 | 1 | 4 | yes | — |
| 92 | C2×C4×Dic5 | C23 | 1 | 2 | yes | — |
| 93 | C2×C4×Dic5 | C23 | 1 | 1 | yes | characteristic |
| 94 | C2×C4×Dic5 | C23 | 1 | 2 | yes | — |
| 95 | C2×C4×Dic5 | C23 | 1 | 1 | yes | characteristic |
| 96 | #4023 | — | 4 | 8 | no | — |
| 97 | #4016 | — | 2 | 4 | no | — |
| 98 | C5×#95 | C23 | 1 | 4 | yes | — |
| 99 | C5×#95 | 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 | #2845 | — | 5 | 1 | no | — |
| 110 | #2837 | — | 5 | 4 | no | — |
| 111 | #2831 | — | 5 | 4 | no | — |
| 112 | #2829 | — | 5 | 4 | no | — |
| 113 | #2820 | — | 5 | 2 | no | — |
| 114 | #2819 | D5 | 1 | 1 | yes | characteristic |
| 115 | #2396 | — | 5 | 4 | no | — |
| 116 | #2395 | — | 5 | 4 | no | — |
| 117 | #2392 | — | 5 | 4 | no | — |
| 118 | C4×#125 | — | 5 | 1 | no | — |
| 119 | C4×#124 | — | 5 | 2 | no | — |
| 120 | C24×C5 | C24 | 1 | 4 | yes | — |
| 121 | C2×C5×Q8 | — | 2 | 4 | no | — |
| 122 | C2×C5×Q8 | — | 4 | 2 | no | — |
| 123 | C2×C5×Q8 | — | 4 | 2 | no | — |
| 124 | C2×C5×D4 | — | 2 | 4 | no | — |
| 125 | C2×C5×D4 | — | 4 | 2 | no | — |
| 126 | C2×C5×D4 | — | 4 | 4 | no | — |
| 127 | C2×C5×D4 | — | 4 | 4 | no | — |
| 128 | C2×C5×D4 | — | 4 | 2 | no | — |
| 129 | C2×C5×D4 | — | 4 | 4 | no | — |
| 130 | C22×C4×C5 | C24 | 1 | 4 | yes | — |
| 131 | C22×C4×C5 | C24 | 1 | 4 | yes | — |
| 132 | C22×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 133 | C22×C4×C5 | C24 | 1 | 2 | yes | — |
| 134 | C22×Dic5 | — | 2 | 8 | no | — |
| 135 | C22×Dic5 | — | 2 | 8 | no | — |
| 136 | C22×Dic5 | — | 2 | 8 | no | — |
| 137 | C22×Dic5 | C24 | 1 | 1 | yes | characteristic |
| 138 | C22×Dic5 | C24 | 1 | 2 | yes | — |
| 139 | C22×Dic5 | C24 | 1 | 4 | yes | — |
| 140 | C22×Dic5 | C24 | 1 | 4 | yes | — |
| 141 | C22×Dic5 | C24 | 1 | 4 | yes | — |
| 142 | C22×Dic5 | C24 | 1 | 1 | yes | characteristic |
| 143 | C5×C4⋊C4 | — | 4 | 2 | no | — |
| 144 | C5×C22⋊C4 | — | 2 | 8 | no | — |
| 145 | C5×C22⋊C4 | — | 2 | 8 | no | — |
| 146 | C5×C22⋊C4 | — | 4 | 4 | no | — |
| 147 | C5×C22⋊C4 | — | 4 | 4 | no | — |
| 148 | C42×C5 | #41 | 1 | 4 | yes | — |
| 149 | C22⋊Dic5 | — | 4 | 4 | no | — |
| 150 | C22⋊Dic5 | — | 4 | 4 | no | — |
| 151 | C22⋊Dic5 | — | 4 | 4 | no | — |
| 152 | C22⋊Dic5 | — | 4 | 4 | no | — |
| 153 | C22⋊Dic5 | — | 4 | 4 | no | — |
| 154 | C22⋊Dic5 | — | 4 | 4 | no | — |
| 155 | C22⋊Dic5 | — | 4 | 4 | no | — |
| 156 | C4⋊Dic5 | — | 2 | 4 | no | — |
| 157 | C4⋊Dic5 | — | 4 | 4 | no | — |
| 158 | C4⋊Dic5 | — | 4 | 2 | no | — |
| 159 | C4⋊Dic5 | — | 4 | 2 | no | — |
| 160 | C4⋊Dic5 | — | 4 | 4 | no | — |
| 161 | #683 | — | 2 | 8 | no | — |
| 162 | #683 | — | 4 | 4 | no | — |
| 163 | #683 | — | 4 | 4 | no | — |
| 164 | #683 | — | 4 | 4 | no | — |
| 165 | #683 | — | 4 | 4 | no | — |
| 166 | #683 | — | 4 | 4 | no | — |
| 167 | C4×Dic5 | — | 2 | 8 | no | — |
| 168 | C4×Dic5 | — | 2 | 8 | no | — |
| 169 | C4×Dic5 | — | 2 | 4 | no | — |
| 170 | C4×Dic5 | — | 2 | 2 | no | — |
| 171 | C4×Dic5 | — | 4 | 2 | no | — |
| 172 | C4×Dic5 | — | 4 | 1 | no | — |
| 173 | C2×#125 | — | 5 | 1 | no | — |
| 174 | C2×#124 | C2×D5 | 1 | 2 | yes | — |
| 175 | C2×C4×Q8 | — | 5 | 2 | no | — |
| 176 | C2×C4×D4 | — | 5 | 4 | no | — |
| 177 | C2×C4×D4 | — | 5 | 2 | no | — |
| 178 | C2×#117 | — | 5 | 4 | no | — |
| 179 | #400 | — | 5 | 4 | no | — |
| 180 | #400 | — | 5 | 4 | no | — |
| 181 | #399 | — | 5 | 4 | no | — |
| 182 | #399 | — | 5 | 4 | no | — |
| 183 | #398 | — | 5 | 4 | no | — |
| 184 | #398 | — | 5 | 4 | no | — |
| 185 | #398 | — | 5 | 4 | no | — |
| 186 | #398 | — | 5 | 4 | no | — |
| 187 | #397 | — | 5 | 4 | no | — |
| 188 | #397 | — | 5 | 4 | no | — |
| 189 | #397 | — | 5 | 4 | no | — |
| 190 | #397 | — | 5 | 4 | no | — |
| 191 | #396 | — | 5 | 4 | no | — |
| 192 | #396 | — | 5 | 4 | no | — |
| 193 | #396 | — | 5 | 4 | no | — |
| 194 | #396 | — | 5 | 4 | no | — |
| 195 | #395 | — | 5 | 4 | no | — |
| 196 | #394 | — | 5 | 4 | no | — |
| 197 | #394 | — | 5 | 4 | no | — |
| 198 | #394 | — | 5 | 4 | no | — |
| 199 | #394 | — | 5 | 4 | no | — |
| 200 | #394 | C2×D5 | 1 | 4 | yes | — |
| 201 | #393 | C2×D5 | 1 | 4 | yes | — |
| 202 | #392 | C2×D5 | 1 | 4 | yes | — |
| 203 | #391 | — | 5 | 2 | no | — |
| 204 | #390 | — | 5 | 2 | no | — |
| 205 | #389 | — | 5 | 2 | no | — |
| 206 | #388 | — | 5 | 4 | no | — |
| 207 | #388 | — | 5 | 4 | no | — |
| 208 | #387 | — | 5 | 4 | no | — |
| 209 | #382 | — | 5 | 2 | no | — |
| 210 | #382 | C2×D5 | 1 | 1 | yes | characteristic |
| 211 | C4×C4⋊C4 | — | 5 | 2 | no | — |
| 212 | C4×C4⋊C4 | — | 5 | 4 | no | — |
| 213 | C4×C4⋊C4 | — | 5 | 4 | no | — |
| 214 | C4×C22⋊C4 | — | 5 | 4 | no | — |
| 215 | C4×C22⋊C4 | — | 5 | 4 | no | — |
| 216 | C4×C22⋊C4 | — | 5 | 4 | no | — |
| 217 | C43 | — | 5 | 1 | no | — |
| 218 | C23×C5 | — | 2 | 4 | no | — |
| 219 | C23×C5 | — | 2 | 4 | no | — |
| 220 | C23×C5 | — | 2 | 4 | no | — |
| 221 | C23×C5 | — | 2 | 4 | no | — |
| 222 | C23×C5 | — | 2 | 4 | no | — |
| 223 | C23×C5 | — | 2 | 4 | no | — |
| 224 | C23×C5 | — | 2 | 4 | no | — |
| 225 | C23×C5 | C25 | 1 | 1 | yes | characteristic |
| 226 | C5×Q8 | — | 4 | 8 | no | — |
| 227 | C5×D4 | — | 4 | 8 | no | — |
| 228 | C5×D4 | — | 4 | 16 | no | — |
| 229 | C2×C4×C5 | — | 2 | 2 | no | — |
| 230 | C2×C4×C5 | — | 2 | 1 | no | — |
| 231 | C2×C4×C5 | — | 2 | 1 | no | — |
| 232 | C2×C4×C5 | — | 2 | 2 | no | — |
| 233 | C2×C4×C5 | — | 2 | 4 | no | — |
| 234 | C2×C4×C5 | — | 2 | 4 | no | — |
| 235 | C2×C4×C5 | — | 2 | 4 | no | — |
| 236 | C2×C4×C5 | — | 2 | 4 | no | — |
| 237 | C2×C4×C5 | — | 2 | 4 | no | — |
| 238 | C2×C4×C5 | — | 2 | 4 | no | — |
| 239 | C2×C4×C5 | C2×#41 | 1 | 4 | yes | — |
| 240 | C2×C4×C5 | C2×#41 | 1 | 2 | yes | — |
| 241 | C2×Dic5 | — | 2 | 4 | no | — |
| 242 | C2×Dic5 | — | 2 | 4 | no | — |
| 243 | C2×Dic5 | — | 2 | 4 | no | — |
| 244 | C2×Dic5 | — | 2 | 2 | no | — |
| 245 | C2×Dic5 | — | 2 | 4 | no | — |
| 246 | C2×Dic5 | — | 2 | 4 | no | — |
| 247 | C2×Dic5 | — | 2 | 1 | no | — |
| 248 | C2×Dic5 | — | 2 | 4 | no | — |
| 249 | C2×Dic5 | — | 2 | 2 | no | — |
| 250 | C2×Dic5 | — | 2 | 2 | no | — |
| 251 | C2×Dic5 | — | 2 | 2 | no | — |
| 252 | C2×Dic5 | — | 2 | 4 | no | — |
| 253 | C2×Dic5 | — | 2 | 4 | no | — |
| 254 | C2×Dic5 | — | 2 | 4 | no | — |
| 255 | C2×Dic5 | — | 4 | 16 | no | — |
| 256 | C2×Dic5 | H(5,𝔽2) | 1 | 4 | yes | — |
| 257 | C2×Dic5 | 2−1+4 | 1 | 2 | yes | — |
| 258 | C22×Q8 | C22×D5 | 1 | 2 | yes | — |
| 259 | C22×D4 | C22×D5 | 1 | 2 | yes | — |
| 260 | C22×D4 | C22×D5 | 1 | 4 | yes | — |
| 261 | C23×C4 | — | 5 | 4 | no | — |
| 262 | #125 | — | 10 | 4 | no | — |
| 263 | #124 | — | 2 | 8 | no | — |
| 264 | C4×Q8 | — | 20 | 4 | no | — |
| 265 | C4×D4 | — | 20 | 8 | no | — |
| 266 | C4×D4 | — | 20 | 4 | no | — |
| 267 | #117 | — | 20 | 8 | no | — |
| 268 | C2×C4⋊C4 | — | 5 | 4 | no | — |
| 269 | C2×C4⋊C4 | — | 5 | 2 | no | — |
| 270 | C2×C4⋊C4 | — | 5 | 4 | no | — |
| 271 | C2×C4⋊C4 | — | 5 | 4 | no | — |
| 272 | C2×C4⋊C4 | — | 5 | 2 | no | — |
| 273 | C2×C4⋊C4 | — | 5 | 4 | no | — |
| 274 | C2×C4⋊C4 | — | 5 | 2 | no | — |
| 275 | C2×C4⋊C4 | — | 5 | 4 | no | — |
| 276 | C2×C4⋊C4 | — | 5 | 4 | no | — |
| 277 | C2×C4⋊C4 | — | 5 | 4 | no | — |
| 278 | C2×C4⋊C4 | — | 5 | 4 | no | — |
| 279 | C2×C4⋊C4 | C22×D5 | 1 | 2 | yes | — |
| 280 | C2×C22⋊C4 | — | 5 | 4 | no | — |
| 281 | C2×C22⋊C4 | — | 5 | 4 | no | — |
| 282 | C2×C22⋊C4 | — | 5 | 4 | no | — |
| 283 | C2×C22⋊C4 | — | 5 | 4 | no | — |
| 284 | C2×C22⋊C4 | — | 5 | 4 | no | — |
| 285 | C2×C22⋊C4 | — | 5 | 4 | no | — |
| 286 | C2×C22⋊C4 | — | 5 | 4 | no | — |
| 287 | C2×C22⋊C4 | C22×D5 | 1 | 4 | yes | — |
| 288 | C2×C22⋊C4 | C22×D5 | 1 | 4 | yes | — |
| 289 | C2×C22⋊C4 | C22×D5 | 1 | 4 | yes | — |
| 290 | C2×C22⋊C4 | C22×D5 | 1 | 4 | yes | — |
| 291 | C2×C42 | — | 5 | 4 | no | — |
| 292 | C2×C42 | — | 5 | 4 | no | — |
| 293 | C2×C42 | — | 5 | 2 | no | — |
| 294 | C2×C42 | — | 5 | 1 | no | — |
| 295 | C2×C42 | — | 5 | 2 | no | — |
| 296 | C2×C42 | — | 5 | 1 | no | — |
| 297 | C2×C42 | C22×D5 | 1 | 1 | yes | characteristic |
| 298 | #95 | — | 5 | 4 | no | — |
| 299 | #95 | — | 5 | 4 | no | — |
| 300 | #95 | — | 5 | 4 | no | — |
| 301 | #95 | — | 5 | 4 | no | — |
| 302 | #95 | — | 5 | 4 | no | — |
| 303 | #95 | — | 5 | 4 | no | — |
| 304 | #95 | — | 5 | 4 | no | — |
| 305 | #95 | — | 5 | 4 | no | — |
| 306 | #95 | — | 5 | 4 | no | — |
| 307 | #95 | C22×D5 | 1 | 4 | yes | — |
| 308 | #95 | C22×D5 | 1 | 4 | yes | — |
| 309 | C22×C5 | — | 4 | 4 | no | — |
| 310 | C22×C5 | — | 4 | 4 | no | — |
| 311 | C22×C5 | — | 4 | 4 | no | — |
| 312 | C22×C5 | — | 4 | 4 | no | — |
| 313 | C22×C5 | — | 4 | 4 | no | — |
| 314 | C22×C5 | — | 4 | 4 | no | — |
| 315 | C22×C5 | — | 4 | 4 | no | — |
| 316 | C22×C5 | C22×#41 | 1 | 1 | yes | characteristic |
| 317 | C22×C5 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 318 | C22×C5 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 319 | C22×C5 | #585 | 1 | 2 | yes | — |
| 320 | C22×C5 | #585 | 1 | 1 | yes | characteristic |
| 321 | C4×C5 | — | 2 | 4 | no | — |
| 322 | C4×C5 | — | 2 | 2 | no | — |
| 323 | C4×C5 | — | 4 | 4 | no | — |
| 324 | C4×C5 | — | 4 | 4 | no | — |
| 325 | Dic5 | — | 4 | 4 | no | — |
| 326 | Dic5 | — | 4 | 4 | no | — |
| 327 | Dic5 | — | 4 | 4 | no | — |
| 328 | Dic5 | — | 4 | 2 | no | — |
| 329 | Dic5 | — | 4 | 1 | no | — |
| 330 | Dic5 | #562 | 1 | 4 | yes | — |
| 331 | C24 | C23×D5 | 1 | 4 | yes | — |
| 332 | C2×Q8 | — | 2 | 4 | no | — |
| 333 | C2×Q8 | — | 4 | 2 | no | — |
| 334 | C2×Q8 | — | 4 | 2 | no | — |
| 335 | C2×D4 | — | 2 | 4 | no | — |
| 336 | C2×D4 | — | 4 | 2 | no | — |
| 337 | C2×D4 | — | 4 | 4 | no | — |
| 338 | C2×D4 | — | 4 | 2 | no | — |
| 339 | C2×D4 | — | 4 | 4 | no | — |
| 340 | C2×D4 | — | 4 | 4 | no | — |
| 341 | C22×C4 | — | 5 | 1 | no | — |
| 342 | C22×C4 | — | 5 | 1 | no | — |
| 343 | C22×C4 | — | 5 | 4 | no | — |
| 344 | C22×C4 | — | 5 | 2 | no | — |
| 345 | C22×C4 | — | 5 | 4 | no | — |
| 346 | C22×C4 | — | 5 | 4 | no | — |
| 347 | C22×C4 | — | 10 | 8 | no | — |
| 348 | C22×C4 | — | 10 | 8 | no | — |
| 349 | C22×C4 | — | 10 | 8 | no | — |
| 350 | C22×C4 | C23×D5 | 1 | 4 | yes | — |
| 351 | C22×C4 | C23×D5 | 1 | 4 | yes | — |
| 352 | C22×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 353 | C22×C4 | C23×D5 | 1 | 2 | yes | — |
| 354 | C4⋊C4 | — | 4 | 2 | no | — |
| 355 | C4⋊C4 | — | 10 | 8 | no | — |
| 356 | C4⋊C4 | — | 10 | 4 | no | — |
| 357 | C4⋊C4 | — | 20 | 4 | no | — |
| 358 | C4⋊C4 | — | 20 | 4 | no | — |
| 359 | C4⋊C4 | — | 20 | 2 | no | — |
| 360 | C4⋊C4 | — | 20 | 4 | no | — |
| 361 | C4⋊C4 | — | 20 | 2 | no | — |
| 362 | C4⋊C4 | — | 20 | 4 | no | — |
| 363 | C4⋊C4 | — | 20 | 4 | no | — |
| 364 | C4⋊C4 | — | 20 | 4 | no | — |
| 365 | C4⋊C4 | — | 20 | 4 | no | — |
| 366 | C22⋊C4 | — | 2 | 8 | no | — |
| 367 | C22⋊C4 | — | 2 | 8 | no | — |
| 368 | C22⋊C4 | — | 4 | 4 | no | — |
| 369 | C22⋊C4 | — | 4 | 4 | no | — |
| 370 | C22⋊C4 | — | 20 | 4 | no | — |
| 371 | C22⋊C4 | — | 20 | 4 | no | — |
| 372 | C22⋊C4 | — | 20 | 4 | no | — |
| 373 | C22⋊C4 | — | 20 | 4 | no | — |
| 374 | C22⋊C4 | — | 20 | 4 | no | — |
| 375 | C22⋊C4 | — | 20 | 4 | no | — |
| 376 | C22⋊C4 | — | 20 | 4 | no | — |
| 377 | C42 | — | 10 | 8 | no | — |
| 378 | C42 | — | 10 | 8 | no | — |
| 379 | C42 | — | 10 | 4 | no | — |
| 380 | C42 | — | 10 | 2 | no | — |
| 381 | C42 | — | 20 | 1 | no | — |
| 382 | C42 | — | 20 | 2 | no | — |
| 383 | C42 | #711 | 1 | 4 | yes | — |
| 384 | C2×C5 | — | 8 | 4 | no | — |
| 385 | C2×C5 | #3460 | 1 | 2 | yes | — |
| 386 | C2×C5 | #3461 | 1 | 1 | yes | characteristic |
| 387 | C2×C5 | C2×#562 | 1 | 1 | yes | characteristic |
| 388 | C2×C5 | #3529 | 1 | 2 | yes | — |
| 389 | C2×C5 | #3531 | 1 | 1 | yes | characteristic |
| 390 | C23 | — | 2 | 4 | no | — |
| 391 | C23 | — | 2 | 4 | no | — |
| 392 | C23 | — | 2 | 4 | no | — |
| 393 | C23 | — | 2 | 4 | no | — |
| 394 | C23 | — | 2 | 4 | no | — |
| 395 | C23 | — | 2 | 4 | no | — |
| 396 | C23 | — | 2 | 4 | no | — |
| 397 | C23 | C24×D5 | 1 | 1 | yes | characteristic |
| 398 | Q8 | — | 4 | 8 | no | — |
| 399 | D4 | — | 4 | 8 | no | — |
| 400 | D4 | — | 4 | 16 | no | — |
| 401 | C2×C4 | — | 2 | 2 | no | — |
| 402 | C2×C4 | — | 2 | 1 | no | — |
| 403 | C2×C4 | — | 2 | 2 | no | — |
| 404 | C2×C4 | — | 2 | 1 | no | — |
| 405 | C2×C4 | — | 2 | 4 | no | — |
| 406 | C2×C4 | — | 2 | 4 | no | — |
| 407 | C2×C4 | — | 2 | 4 | no | — |
| 408 | C2×C4 | — | 2 | 4 | no | — |
| 409 | C2×C4 | — | 2 | 4 | no | — |
| 410 | C2×C4 | — | 2 | 4 | no | — |
| 411 | C2×C4 | — | 5 | 4 | no | — |
| 412 | C2×C4 | — | 5 | 2 | no | — |
| 413 | C2×C4 | — | 10 | 4 | no | — |
| 414 | C2×C4 | — | 10 | 4 | no | — |
| 415 | C2×C4 | — | 10 | 2 | no | — |
| 416 | C2×C4 | — | 10 | 4 | no | — |
| 417 | C2×C4 | — | 10 | 4 | no | — |
| 418 | C2×C4 | — | 10 | 4 | no | — |
| 419 | C2×C4 | — | 10 | 2 | no | — |
| 420 | C2×C4 | — | 10 | 2 | no | — |
| 421 | C2×C4 | — | 10 | 2 | no | — |
| 422 | C2×C4 | — | 10 | 4 | no | — |
| 423 | C2×C4 | — | 10 | 4 | no | — |
| 424 | C2×C4 | — | 10 | 4 | no | — |
| 425 | C2×C4 | — | 10 | 1 | no | — |
| 426 | C2×C4 | — | 10 | 4 | no | — |
| 427 | C2×C4 | — | 20 | 16 | no | — |
| 428 | C2×C4 | C2×#711 | 1 | 2 | yes | — |
| 429 | C2×C4 | C2×#711 | 1 | 4 | yes | — |
| 430 | C5 | #36695 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 431 | C22 | — | 4 | 4 | no | — |
| 432 | C22 | — | 4 | 4 | no | — |
| 433 | C22 | — | 4 | 4 | no | — |
| 434 | C22 | — | 4 | 4 | no | — |
| 435 | C22 | — | 4 | 4 | no | — |
| 436 | C22 | — | 4 | 4 | no | — |
| 437 | C22 | — | 4 | 4 | no | — |
| 438 | C22 | C22×#711 | 1 | 1 | yes | characteristic |
| 439 | C22 | D5×H(5,𝔽2) | 1 | 2 | yes | — |
| 440 | C22 | #66285 | 1 | 2 | yes | — |
| 441 | C22 | #66285 | 1 | 1 | yes | characteristic |
| 442 | C22 | D5×2−1+4 | 1 | 1 | yes | characteristic |
| 443 | C4 | — | 2 | 4 | no | — |
| 444 | C4 | — | 2 | 2 | no | — |
| 445 | C4 | — | 4 | 4 | no | — |
| 446 | C4 | — | 4 | 4 | no | — |
| 447 | C4 | — | 5 | 4 | no | — |
| 448 | C4 | — | 20 | 4 | no | — |
| 449 | C4 | — | 20 | 2 | no | — |
| 450 | C4 | — | 20 | 4 | no | — |
| 451 | C4 | — | 20 | 1 | no | — |
| 452 | C4 | — | 20 | 4 | no | — |
| 453 | C2 | — | 8 | 4 | no | — |
| 454 | C2 | #10618215 | 1 | 2 | yes | — |
| 455 | C2 | #10618266 | 1 | 1 | yes | characteristic |
| 456 | C2 | #10618986 | 1 | 2 | yes | — |
| 457 | C2 | #10618995 | 1 | 1 | yes | characteristic |
| 458 | C2 | D5×#562 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D5 |
| commutator, socle, cosocle | C23×C5 | C25 |
| Fitting, prime radical | C5×#2819 | C2 |
| hypercenter | #2819 | D5 |
| hypocenter | C5 | #36695 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ #2819 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10614723 | C2 | semidirect |
| 3. Dic5×#124 | C2 | semidirect |
| 4. #10608833 | C2 | semidirect |
| 5. #10608623 | C2 | semidirect |
| 6. #10608587 | C2 | semidirect |
| 7. #10608509 | C2 | semidirect |
| 8. #10608482 | C2 | semidirect |
| 9. #10608397 | C2 | semidirect |
| 10. #10605950 | C2 | semidirect |
| 11. #10605881 | C2 | semidirect |
| 430. C5 | #36695 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2819 | 2 |
| #10614723 | 2 |
| Dic5×#124 | 2 |
| #10608833 | 2 |
| #10608623 | 2 |
| #10608587 | 2 |
| #10608509 | 2 |
| #10608482 | 2 |
| #10608397 | 2 |
| #10605950 | 2 |
| #10605881 | 2 |
| #36695 | 5 |