Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1738 conjugacy classes of subgroups.
The subgroup lattice has 374 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C5×#2644 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10609419 | C2 | 1 | 6 | yes | maximal, complemented |
| 3 | #10609192 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | #10609156 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10609014 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #10608106 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #10608021 | C2 | 1 | 3 | yes | maximal |
| 8 | #10607834 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #10607694 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | D5×#376 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #10605139 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C22×#711 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#4038 | C22 | 1 | 3 | yes | — |
| 14 | C2×C42×D5 | C22 | 1 | 3 | yes | — |
| 15 | C5×#397 | C22 | 1 | 6 | yes | — |
| 16 | C5×#396 | C22 | 1 | 2 | yes | — |
| 17 | C5×#390 | C22 | 1 | 3 | yes | — |
| 18 | C5×#389 | C22 | 1 | 3 | yes | — |
| 19 | C5×#376 | C22 | 1 | 1 | yes | characteristic |
| 20 | #65510 | C22 | 1 | 3 | yes | — |
| 21 | #65278 | C22 | 1 | 6 | yes | — |
| 22 | #65275 | C22 | 1 | 6 | yes | — |
| 23 | #65274 | C22 | 1 | 3 | yes | — |
| 24 | #65271 | C22 | 1 | 6 | yes | — |
| 25 | C4⋊C4×Dic5 | C22 | 1 | 6 | yes | — |
| 26 | #65263 | C22 | 1 | 3 | yes | — |
| 27 | #65262 | C22 | 1 | 3 | yes | — |
| 28 | #65245 | C22 | 1 | 6 | yes | — |
| 29 | #65245 | C22 | 1 | 6 | yes | — |
| 30 | #65242 | C22 | 1 | 6 | yes | — |
| 31 | #65241 | C22 | 1 | 6 | yes | — |
| 32 | #65241 | C22 | 1 | 6 | yes | — |
| 33 | #65237 | C22 | 1 | 6 | yes | — |
| 34 | C22⋊C4×Dic5 | C22 | 1 | 6 | yes | — |
| 35 | C22⋊C4×Dic5 | C22 | 1 | 6 | yes | — |
| 36 | #65221 | C22 | 1 | 3 | yes | — |
| 37 | #65218 | C22 | 1 | 3 | yes | — |
| 38 | #65217 | C22 | 1 | 3 | yes | — |
| 39 | #64957 | C22 | 1 | 6 | yes | — |
| 40 | D5×#95 | C22 | 1 | 1 | yes | characteristic |
| 41 | D5×#95 | C22 | 1 | 3 | yes | — |
| 42 | C5⋊#401 | C22 | 1 | 2 | yes | — |
| 43 | C5⋊#401 | C22 | 1 | 6 | yes | — |
| 44 | #64949 | C22 | 1 | 6 | yes | — |
| 45 | #64947 | C22 | 1 | 6 | yes | — |
| 46 | #64938 | C22 | 1 | 6 | yes | — |
| 47 | #64937 | C22 | 1 | 3 | yes | — |
| 48 | #64937 | C22 | 1 | 1 | yes | characteristic |
| 49 | #34639 | — | 5 | 1 | no | maximal, Sylow |
| 50 | C22×C5×D4 | C23 | 1 | 1 | yes | characteristic |
| 51 | C22×C22⋊D5 | C23 | 1 | 2 | yes | — |
| 52 | C23×Dic5 | C23 | 1 | 2 | yes | — |
| 53 | C2×#711 | — | 2 | 12 | no | — |
| 54 | C22×C4×D5 | C23 | 1 | 3 | yes | — |
| 55 | C22×C4×D5 | C23 | 1 | 3 | yes | — |
| 56 | C22×C4×D5 | C23 | 1 | 1 | yes | characteristic |
| 57 | C22×Dic10 | C23 | 1 | 1 | yes | characteristic |
| 58 | C2×C5×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 59 | C2×C5×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 60 | C2×C5×C22⋊C4 | C23 | 1 | 6 | yes | — |
| 61 | C2×C5×C22⋊C4 | C23 | 1 | 6 | yes | — |
| 62 | C2×C42×C5 | C23 | 1 | 3 | yes | — |
| 63 | C2×C22⋊Dic5 | C23 | 1 | 6 | yes | — |
| 64 | C2×C22⋊Dic5 | C23 | 1 | 6 | yes | — |
| 65 | C2×#685 | C23 | 1 | 6 | yes | — |
| 66 | C2×C4⋊Dic5 | C23 | 1 | 3 | yes | — |
| 67 | C2×C4⋊Dic5 | C23 | 1 | 6 | yes | — |
| 68 | C2×#683 | C23 | 1 | 6 | yes | — |
| 69 | C2×#683 | C23 | 1 | 6 | yes | — |
| 70 | C2×C4×Dic5 | C23 | 1 | 3 | yes | — |
| 71 | C2×C4×Dic5 | C23 | 1 | 3 | yes | — |
| 72 | C2×C4×Dic5 | C23 | 1 | 3 | yes | — |
| 73 | C2×C4×Dic5 | C23 | 1 | 6 | yes | — |
| 74 | #4038 | — | 2 | 12 | no | — |
| 75 | C42×D5 | — | 2 | 12 | no | — |
| 76 | C5×#95 | C23 | 1 | 1 | yes | characteristic |
| 77 | C5×#95 | C23 | 1 | 3 | yes | — |
| 78 | C5×#95 | C23 | 1 | 6 | yes | — |
| 79 | #3963 | C23 | 1 | 3 | yes | — |
| 80 | #3963 | C23 | 1 | 3 | yes | — |
| 81 | #3963 | C23 | 1 | 3 | yes | — |
| 82 | #3963 | C23 | 1 | 3 | yes | — |
| 83 | #3963 | C23 | 1 | 6 | yes | — |
| 84 | #3963 | C23 | 1 | 6 | yes | — |
| 85 | #3963 | C23 | 1 | 6 | yes | — |
| 86 | #3963 | C23 | 1 | 6 | yes | — |
| 87 | #3963 | C23 | 1 | 6 | yes | — |
| 88 | #3963 | C23 | 1 | 6 | yes | — |
| 89 | #3963 | C23 | 1 | 6 | yes | — |
| 90 | #2645 | — | 5 | 3 | no | — |
| 91 | #2645 | — | 5 | 1 | no | — |
| 92 | #2644 | — | 5 | 3 | no | — |
| 93 | #2644 | D5 | 1 | 1 | yes | characteristic, complemented |
| 94 | #2643 | — | 5 | 6 | no | — |
| 95 | #2643 | — | 5 | 2 | no | — |
| 96 | #2401 | — | 5 | 6 | no | — |
| 97 | #2401 | — | 5 | 2 | no | — |
| 98 | #2297 | — | 5 | 3 | no | — |
| 99 | #2296 | — | 5 | 3 | no | — |
| 100 | C2×#376 | — | 5 | 1 | no | — |
| 101 | C24×C5 | C24 | 1 | 2 | yes | — |
| 102 | C23×D5 | C24 | 1 | 1 | yes | characteristic |
| 103 | C2×C5×D4 | — | 2 | 6 | no | — |
| 104 | C22×C4×C5 | C24 | 1 | 3 | yes | — |
| 105 | C22×C4×C5 | C24 | 1 | 3 | yes | — |
| 106 | C22×C4×C5 | C24 | 1 | 6 | yes | — |
| 107 | C22×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 108 | C2×C22⋊D5 | — | 2 | 12 | no | — |
| 109 | C22×Dic5 | — | 2 | 12 | no | — |
| 110 | C22×Dic5 | C24 | 1 | 3 | yes | — |
| 111 | C22×Dic5 | C24 | 1 | 3 | yes | — |
| 112 | C22×Dic5 | C24 | 1 | 6 | yes | — |
| 113 | C22×Dic5 | C24 | 1 | 2 | yes | — |
| 114 | C22×Dic5 | C24 | 1 | 1 | yes | characteristic |
| 115 | #711 | — | 4 | 16 | no | — |
| 116 | C2×C4×D5 | — | 2 | 6 | no | — |
| 117 | C2×C4×D5 | — | 2 | 6 | no | — |
| 118 | C2×C4×D5 | — | 4 | 3 | no | — |
| 119 | C2×C4×D5 | — | 4 | 3 | no | — |
| 120 | C2×C4×D5 | — | 4 | 3 | no | — |
| 121 | C2×C4×D5 | — | 4 | 3 | no | — |
| 122 | C2×C4×D5 | #41 | 1 | 12 | yes | — |
| 123 | C2×Dic10 | — | 2 | 6 | no | — |
| 124 | C5×C4⋊C4 | — | 2 | 6 | no | — |
| 125 | C5×C4⋊C4 | — | 4 | 6 | no | — |
| 126 | C5×C22⋊C4 | — | 4 | 6 | no | — |
| 127 | C5×C22⋊C4 | — | 4 | 6 | no | — |
| 128 | C42×C5 | — | 2 | 6 | no | — |
| 129 | C22⋊Dic5 | — | 4 | 6 | no | — |
| 130 | C22⋊Dic5 | — | 4 | 6 | no | — |
| 131 | #685 | — | 2 | 12 | no | — |
| 132 | C4⋊Dic5 | — | 2 | 6 | no | — |
| 133 | C4⋊Dic5 | — | 4 | 6 | no | — |
| 134 | #683 | — | 4 | 6 | no | — |
| 135 | #683 | — | 4 | 6 | no | — |
| 136 | C4×Dic5 | — | 2 | 6 | no | — |
| 137 | C4×Dic5 | — | 2 | 6 | no | — |
| 138 | C4×Dic5 | — | 2 | 6 | no | — |
| 139 | C4×Dic5 | — | 2 | 12 | no | — |
| 140 | C22×#41 | — | 5 | 1 | no | — |
| 141 | C2×#117 | — | 5 | 3 | no | — |
| 142 | C22×C42 | — | 5 | 3 | no | — |
| 143 | #401 | — | 5 | 6 | no | — |
| 144 | #401 | — | 5 | 2 | no | — |
| 145 | #400 | — | 5 | 6 | no | — |
| 146 | #400 | — | 5 | 6 | no | — |
| 147 | #400 | — | 5 | 6 | no | — |
| 148 | #400 | — | 5 | 6 | no | — |
| 149 | #397 | — | 5 | 6 | no | — |
| 150 | #397 | — | 5 | 6 | no | — |
| 151 | #397 | — | 5 | 6 | no | — |
| 152 | #397 | C2×D5 | 1 | 6 | yes | — |
| 153 | #396 | — | 5 | 6 | no | — |
| 154 | #396 | C2×D5 | 1 | 2 | yes | — |
| 155 | #391 | — | 5 | 3 | no | — |
| 156 | #391 | — | 5 | 3 | no | — |
| 157 | #390 | — | 5 | 3 | no | — |
| 158 | #390 | C2×D5 | 1 | 3 | yes | — |
| 159 | #389 | — | 5 | 3 | no | — |
| 160 | #389 | — | 5 | 3 | no | — |
| 161 | #389 | — | 5 | 3 | no | — |
| 162 | #389 | C2×D5 | 1 | 3 | yes | — |
| 163 | #386 | — | 5 | 6 | no | — |
| 164 | #386 | — | 5 | 6 | no | — |
| 165 | #385 | — | 5 | 6 | no | — |
| 166 | #385 | — | 5 | 6 | no | — |
| 167 | C4×C4⋊C4 | — | 5 | 6 | no | — |
| 168 | C4×C4⋊C4 | — | 5 | 6 | no | — |
| 169 | C4×C22⋊C4 | — | 5 | 6 | no | — |
| 170 | C4×C22⋊C4 | — | 5 | 6 | no | — |
| 171 | #376 | — | 5 | 3 | no | — |
| 172 | #376 | — | 5 | 3 | no | — |
| 173 | #376 | — | 5 | 1 | no | — |
| 174 | #376 | C2×D5 | 1 | 1 | yes | characteristic |
| 175 | C2×#95 | — | 5 | 3 | no | — |
| 176 | C2×#95 | — | 5 | 1 | no | — |
| 177 | C23×C5 | — | 2 | 6 | no | — |
| 178 | C23×C5 | — | 2 | 2 | no | — |
| 179 | C23×C5 | — | 2 | 6 | no | — |
| 180 | C23×C5 | C25 | 1 | 1 | yes | characteristic |
| 181 | C22×D5 | — | 2 | 3 | no | — |
| 182 | C22×D5 | — | 2 | 1 | no | — |
| 183 | C22×D5 | C2×#41 | 1 | 6 | yes | — |
| 184 | C5×D4 | — | 4 | 4 | no | — |
| 185 | C2×C4×C5 | — | 2 | 6 | no | — |
| 186 | C2×C4×C5 | — | 2 | 3 | no | — |
| 187 | C2×C4×C5 | — | 2 | 3 | no | — |
| 188 | C2×C4×C5 | — | 2 | 3 | no | — |
| 189 | C2×C4×C5 | — | 2 | 6 | no | — |
| 190 | C2×C4×C5 | — | 2 | 6 | no | — |
| 191 | C2×C4×C5 | — | 2 | 3 | no | — |
| 192 | C2×C4×C5 | — | 2 | 3 | no | — |
| 193 | C2×C4×C5 | — | 2 | 3 | no | — |
| 194 | C2×C4×C5 | C2×#41 | 1 | 6 | yes | — |
| 195 | C22⋊D5 | — | 4 | 8 | no | — |
| 196 | C2×Dic5 | — | 2 | 3 | no | — |
| 197 | C2×Dic5 | — | 2 | 3 | no | — |
| 198 | C2×Dic5 | — | 2 | 6 | no | — |
| 199 | C2×Dic5 | — | 2 | 6 | no | — |
| 200 | C2×Dic5 | — | 2 | 6 | no | — |
| 201 | C2×Dic5 | — | 2 | 3 | no | — |
| 202 | C2×Dic5 | — | 2 | 6 | no | — |
| 203 | C2×Dic5 | — | 2 | 3 | no | — |
| 204 | C2×Dic5 | — | 2 | 3 | no | — |
| 205 | C2×Dic5 | — | 2 | 3 | no | — |
| 206 | C2×Dic5 | — | 4 | 8 | no | — |
| 207 | C2×Dic5 | C2×#41 | 1 | 6 | yes | — |
| 208 | C4×D5 | — | 4 | 12 | no | — |
| 209 | C4×D5 | — | 4 | 12 | no | — |
| 210 | C4×D5 | #126 | 1 | 16 | yes | — |
| 211 | Dic10 | — | 4 | 4 | no | — |
| 212 | C2×#41 | — | 10 | 12 | no | — |
| 213 | C22×Q8 | — | 5 | 1 | no | — |
| 214 | C22×D4 | — | 5 | 2 | no | — |
| 215 | C22×D4 | C22×D5 | 1 | 1 | yes | characteristic |
| 216 | C23×C4 | — | 5 | 1 | no | — |
| 217 | C23×C4 | — | 5 | 2 | no | — |
| 218 | C23×C4 | — | 5 | 3 | no | — |
| 219 | C23×C4 | — | 5 | 3 | no | — |
| 220 | #117 | — | 10 | 12 | no | — |
| 221 | C2×C4⋊C4 | — | 5 | 3 | no | — |
| 222 | C2×C4⋊C4 | — | 5 | 6 | no | — |
| 223 | C2×C4⋊C4 | — | 5 | 6 | no | — |
| 224 | C2×C4⋊C4 | — | 5 | 6 | no | — |
| 225 | C2×C4⋊C4 | C22×D5 | 1 | 3 | yes | — |
| 226 | C2×C4⋊C4 | C22×D5 | 1 | 6 | yes | — |
| 227 | C2×C22⋊C4 | — | 5 | 6 | no | — |
| 228 | C2×C22⋊C4 | — | 5 | 6 | no | — |
| 229 | C2×C22⋊C4 | — | 5 | 6 | no | — |
| 230 | C2×C22⋊C4 | C22×D5 | 1 | 6 | yes | — |
| 231 | C2×C22⋊C4 | C22×D5 | 1 | 6 | yes | — |
| 232 | C2×C42 | — | 5 | 6 | no | — |
| 233 | C2×C42 | — | 5 | 3 | no | — |
| 234 | C2×C42 | — | 5 | 3 | no | — |
| 235 | C2×C42 | — | 5 | 3 | no | — |
| 236 | C2×C42 | — | 10 | 12 | no | — |
| 237 | C2×C42 | C22×D5 | 1 | 3 | yes | — |
| 238 | #95 | — | 5 | 3 | no | — |
| 239 | #95 | — | 5 | 3 | no | — |
| 240 | #95 | — | 5 | 3 | no | — |
| 241 | #95 | — | 5 | 3 | no | — |
| 242 | #95 | — | 5 | 6 | no | — |
| 243 | #95 | — | 5 | 6 | no | — |
| 244 | #95 | — | 5 | 6 | no | — |
| 245 | #95 | — | 5 | 6 | no | — |
| 246 | #95 | — | 5 | 6 | no | — |
| 247 | #95 | — | 5 | 6 | no | — |
| 248 | #95 | — | 5 | 6 | no | — |
| 249 | #95 | C22×D5 | 1 | 1 | yes | characteristic |
| 250 | #95 | C22×D5 | 1 | 3 | yes | — |
| 251 | #95 | C22×D5 | 1 | 6 | yes | — |
| 252 | C22×C5 | — | 4 | 2 | no | — |
| 253 | C22×C5 | — | 4 | 6 | no | — |
| 254 | C22×C5 | — | 4 | 6 | no | — |
| 255 | C22×C5 | C22×#41 | 1 | 3 | yes | — |
| 256 | C22×C5 | #585 | 1 | 3 | yes | — |
| 257 | C22×C5 | #585 | 1 | 1 | yes | characteristic |
| 258 | C2×D5 | — | 2 | 6 | no | — |
| 259 | C2×D5 | — | 2 | 6 | no | — |
| 260 | C2×D5 | C2×#126 | 1 | 4 | yes | — |
| 261 | C4×C5 | — | 4 | 3 | no | — |
| 262 | C4×C5 | — | 4 | 3 | no | — |
| 263 | C4×C5 | — | 4 | 6 | no | — |
| 264 | C4×C5 | C2×#126 | 1 | 4 | yes | — |
| 265 | Dic5 | — | 4 | 2 | no | — |
| 266 | Dic5 | — | 4 | 3 | no | — |
| 267 | Dic5 | — | 4 | 3 | no | — |
| 268 | Dic5 | — | 4 | 6 | no | — |
| 269 | Dic5 | C2×#126 | 1 | 4 | yes | — |
| 270 | C24 | — | 5 | 1 | no | — |
| 271 | C24 | C23×D5 | 1 | 2 | yes | — |
| 272 | #41 | — | 20 | 16 | no | — |
| 273 | C2×Q8 | — | 10 | 6 | no | — |
| 274 | C2×D4 | — | 2 | 6 | no | — |
| 275 | C2×D4 | — | 10 | 12 | no | — |
| 276 | C22×C4 | — | 5 | 1 | no | — |
| 277 | C22×C4 | — | 5 | 12 | no | — |
| 278 | C22×C4 | — | 5 | 2 | no | — |
| 279 | C22×C4 | — | 5 | 3 | no | — |
| 280 | C22×C4 | — | 5 | 3 | no | — |
| 281 | C22×C4 | — | 5 | 6 | no | — |
| 282 | C22×C4 | — | 10 | 6 | no | — |
| 283 | C22×C4 | — | 10 | 6 | no | — |
| 284 | C22×C4 | — | 10 | 12 | no | — |
| 285 | C22×C4 | — | 20 | 3 | no | — |
| 286 | C22×C4 | — | 20 | 3 | no | — |
| 287 | C22×C4 | — | 20 | 3 | no | — |
| 288 | C22×C4 | — | 20 | 3 | no | — |
| 289 | C22×C4 | C23×D5 | 1 | 3 | yes | — |
| 290 | C22×C4 | C23×D5 | 1 | 3 | yes | — |
| 291 | C22×C4 | C23×D5 | 1 | 6 | yes | — |
| 292 | C22×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 293 | C4⋊C4 | — | 2 | 6 | no | — |
| 294 | C4⋊C4 | — | 4 | 6 | no | — |
| 295 | C4⋊C4 | — | 10 | 6 | no | — |
| 296 | C4⋊C4 | — | 20 | 6 | no | — |
| 297 | C4⋊C4 | — | 20 | 6 | no | — |
| 298 | C4⋊C4 | — | 20 | 6 | no | — |
| 299 | C22⋊C4 | — | 4 | 6 | no | — |
| 300 | C22⋊C4 | — | 4 | 6 | no | — |
| 301 | C22⋊C4 | — | 10 | 12 | no | — |
| 302 | C22⋊C4 | — | 20 | 6 | no | — |
| 303 | C22⋊C4 | — | 20 | 6 | no | — |
| 304 | C42 | — | 2 | 6 | no | — |
| 305 | C42 | — | 10 | 6 | no | — |
| 306 | C42 | — | 10 | 6 | no | — |
| 307 | C42 | — | 10 | 12 | no | — |
| 308 | C42 | — | 10 | 6 | no | — |
| 309 | C2×C5 | — | 8 | 2 | no | — |
| 310 | C2×C5 | C22×#126 | 1 | 1 | yes | characteristic |
| 311 | C2×C5 | #3455 | 1 | 3 | yes | — |
| 312 | C2×C5 | #3455 | 1 | 3 | yes | — |
| 313 | D5 | — | 2 | 4 | no | — |
| 314 | C23 | — | 2 | 6 | no | — |
| 315 | C23 | — | 2 | 6 | no | — |
| 316 | C23 | — | 2 | 2 | no | — |
| 317 | C23 | — | 5 | 6 | no | — |
| 318 | C23 | — | 10 | 3 | no | — |
| 319 | C23 | — | 10 | 1 | no | — |
| 320 | C23 | C24×D5 | 1 | 1 | yes | characteristic |
| 321 | Q8 | — | 20 | 4 | no | — |
| 322 | D4 | — | 4 | 4 | no | — |
| 323 | D4 | — | 20 | 8 | no | — |
| 324 | C2×C4 | — | 2 | 3 | no | — |
| 325 | C2×C4 | — | 2 | 3 | no | — |
| 326 | C2×C4 | — | 2 | 6 | no | — |
| 327 | C2×C4 | — | 2 | 3 | no | — |
| 328 | C2×C4 | — | 2 | 3 | no | — |
| 329 | C2×C4 | — | 2 | 6 | no | — |
| 330 | C2×C4 | — | 2 | 6 | no | — |
| 331 | C2×C4 | — | 2 | 3 | no | — |
| 332 | C2×C4 | — | 2 | 3 | no | — |
| 333 | C2×C4 | — | 5 | 6 | no | — |
| 334 | C2×C4 | — | 5 | 16 | no | — |
| 335 | C2×C4 | — | 10 | 3 | no | — |
| 336 | C2×C4 | — | 10 | 3 | no | — |
| 337 | C2×C4 | — | 10 | 6 | no | — |
| 338 | C2×C4 | — | 10 | 6 | no | — |
| 339 | C2×C4 | — | 10 | 3 | no | — |
| 340 | C2×C4 | — | 10 | 6 | no | — |
| 341 | C2×C4 | — | 10 | 3 | no | — |
| 342 | C2×C4 | — | 10 | 3 | no | — |
| 343 | C2×C4 | — | 10 | 3 | no | — |
| 344 | C2×C4 | — | 10 | 6 | no | — |
| 345 | C2×C4 | — | 20 | 12 | no | — |
| 346 | C2×C4 | — | 20 | 12 | no | — |
| 347 | C2×C4 | — | 20 | 8 | no | — |
| 348 | C2×C4 | D5×#41 | 1 | 6 | yes | — |
| 349 | C5 | #34639 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 350 | C22 | — | 4 | 6 | no | — |
| 351 | C22 | — | 4 | 6 | no | — |
| 352 | C22 | — | 4 | 2 | no | — |
| 353 | C22 | — | 5 | 4 | no | — |
| 354 | C22 | — | 10 | 6 | no | — |
| 355 | C22 | — | 10 | 6 | no | — |
| 356 | C22 | C2×D5×#41 | 1 | 3 | yes | — |
| 357 | C22 | #66285 | 1 | 3 | yes | — |
| 358 | C22 | #66287 | 1 | 1 | yes | characteristic |
| 359 | C4 | — | 4 | 3 | no | — |
| 360 | C4 | — | 4 | 6 | no | — |
| 361 | C4 | — | 4 | 3 | no | — |
| 362 | C4 | — | 5 | 4 | no | — |
| 363 | C4 | — | 20 | 3 | no | — |
| 364 | C4 | — | 20 | 3 | no | — |
| 365 | C4 | — | 20 | 6 | no | — |
| 366 | C4 | — | 20 | 2 | no | — |
| 367 | C4 | D5×#126 | 1 | 4 | yes | — |
| 368 | C2 | — | 8 | 2 | no | — |
| 369 | C2 | — | 10 | 4 | no | — |
| 370 | C2 | C2×D5×#126 | 1 | 1 | yes | characteristic |
| 371 | C2 | #10618368 | 1 | 3 | yes | — |
| 372 | C2 | #10618424 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D5 |
| commutator, socle, cosocle | C23×C5 | C25 |
| Fitting | C5×#2644 | C2 |
| prime radical | C22×#711 | C22 |
| hypercenter | #2644 | D5 |
| hypocenter | C5 | #34639 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ #2644 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#2644 | C2 | semidirect |
| 2. #10609419 | C2 | semidirect |
| 3. #10609192 | C2 | semidirect |
| 4. #10609156 | C2 | semidirect |
| 5. #10609014 | C2 | semidirect |
| 6. #10608106 | C2 | semidirect |
| 8. #10607834 | C2 | semidirect |
| 9. #10607694 | C2 | semidirect |
| 10. D5×#376 | C2 | semidirect |
| 11. #10605139 | C2 | semidirect |
| 93. #2644 | D5 | semidirect |
| 349. C5 | #34639 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2644 | 2 |
| #10609419 | 2 |
| #10609192 | 2 |
| #10609156 | 2 |
| #10609014 | 2 |
| #10608106 | 2 |
| #10608021 | 2 |
| #10607834 | 2 |
| #10607694 | 2 |
| D5×#376 | 2 |
| #10605139 | 2 |
| #34639 | 5 |