← #13107825
Subgroups — #13107825
Order 1600.
1784 conjugacy classes of subgroups.
The subgroup lattice has 315 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#87902 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C5×#4144 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #11717495 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | C2×#87880 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #11717478 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | D5×#711 | C2 | 1 | 8 | yes | maximal, complemented |
| 7 | #11717474 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #11717471 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11717463 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | C2×C52×D4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | C2×C22⋊(C5⋊D5) | C22 | 1 | 2 | yes | complemented |
| 12 | C22×#1039 | C22 | 1 | 2 | yes | complemented |
| 13 | #87902 | C22 | 1 | 4 | yes | complemented |
| 14 | #87902 | C22 | 1 | 4 | yes | complemented |
| 15 | C2×C4×C5⋊D5 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | C2×#6045 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | C2×C5×C22⋊D5 | C22 | 1 | 8 | yes | complemented |
| 18 | C5×#711 | C22 | 1 | 8 | yes | complemented |
| 19 | C5×D4×D5 | C22 | 1 | 8 | yes | complemented |
| 20 | C5×#709 | C22 | 1 | 4 | yes | complemented |
| 21 | #87886 | C22 | 1 | 4 | yes | complemented |
| 22 | D5×C22⋊D5 | C22 | 1 | 16 | yes | complemented |
| 23 | C2×#6039 | C22 | 1 | 4 | yes | complemented |
| 24 | C2×#6037 | C22 | 1 | 4 | yes | complemented |
| 25 | #87880 | C22 | 1 | 8 | yes | complemented |
| 26 | #87880 | C22 | 1 | 4 | yes | complemented |
| 27 | #87880 | C22 | 1 | 8 | yes | complemented |
| 28 | #87880 | C22 | 1 | 8 | yes | complemented |
| 29 | #87879 | C22 | 1 | 16 | yes | complemented |
| 30 | C2×D5×Dic5 | C22 | 1 | 8 | yes | complemented |
| 31 | #87877 | C22 | 1 | 2 | yes | complemented |
| 32 | C4×D52 | C22 | 1 | 4 | yes | complemented |
| 33 | #87873 | C22 | 1 | 4 | yes | complemented |
| 34 | #87872 | C22 | 1 | 2 | yes | complemented |
| 35 | #87871 | C22 | 1 | 4 | yes | complemented |
| 36 | #87870 | C22 | 1 | 8 | yes | complemented |
| 37 | D5×Dic10 | C22 | 1 | 8 | yes | complemented |
| 38 | #66285 | — | 5 | 2 | no | maximal |
| 39 | C23×C52 | C23 | 1 | 2 | yes | — |
| 40 | C22×C5⋊D5 | C23 | 1 | 1 | yes | characteristic |
| 41 | C22×C5×D5 | C23 | 1 | 8 | yes | — |
| 42 | C2×D52 | C23 | 1 | 4 | yes | — |
| 43 | C52×D4 | C23 | 1 | 4 | yes | — |
| 44 | C2×C4×C52 | C23 | 1 | 1 | yes | characteristic |
| 45 | C22⋊(C5⋊D5) | C23 | 1 | 8 | yes | — |
| 46 | C2×#1039 | C23 | 1 | 4 | yes | — |
| 47 | C2×#1039 | C23 | 1 | 2 | yes | — |
| 48 | C2×#1039 | C23 | 1 | 1 | yes | characteristic |
| 49 | C2×#1039 | C23 | 1 | 4 | yes | — |
| 50 | C4×C5⋊D5 | C23 | 1 | 2 | yes | — |
| 51 | C4×C5⋊D5 | C23 | 1 | 2 | yes | — |
| 52 | #6045 | C23 | 1 | 4 | yes | — |
| 53 | C5×C22⋊D5 | C23 | 1 | 16 | yes | — |
| 54 | C5×C22⋊D5 | C23 | 1 | 8 | yes | — |
| 55 | C2×C5×Dic5 | C23 | 1 | 8 | yes | — |
| 56 | C5×D20 | C23 | 1 | 4 | yes | — |
| 57 | C4×C5×D5 | C23 | 1 | 8 | yes | — |
| 58 | C5×Dic10 | C23 | 1 | 4 | yes | — |
| 59 | #6039 | C23 | 1 | 8 | yes | — |
| 60 | #6039 | C23 | 1 | 4 | yes | — |
| 61 | #6038 | C23 | 1 | 8 | yes | — |
| 62 | #6037 | C23 | 1 | 8 | yes | — |
| 63 | #6037 | C23 | 1 | 4 | yes | — |
| 64 | #6036 | C23 | 1 | 4 | yes | — |
| 65 | D5×Dic5 | C23 | 1 | 16 | yes | — |
| 66 | D5×Dic5 | C23 | 1 | 8 | yes | — |
| 67 | C5×H(5,𝔽2) | — | 5 | 2 | no | — |
| 68 | #4150 | — | 5 | 8 | no | — |
| 69 | #4150 | — | 5 | 4 | no | — |
| 70 | D5×#41 | — | 5 | 8 | no | — |
| 71 | D5×#41 | — | 5 | 4 | no | — |
| 72 | #4144 | — | 5 | 8 | no | — |
| 73 | #4144 | — | 5 | 8 | no | — |
| 74 | #4144 | D5 | 1 | 2 | yes | complemented |
| 75 | C2×#711 | — | 5 | 2 | no | — |
| 76 | C2×#711 | — | 5 | 8 | no | — |
| 77 | C2×#711 | — | 5 | 8 | no | — |
| 78 | C2×#711 | — | 10 | 2 | no | — |
| 79 | C22×C52 | — | 4 | 2 | no | — |
| 80 | C22×C52 | C24 | 1 | 4 | yes | — |
| 81 | C22×C52 | C24 | 1 | 1 | yes | characteristic |
| 82 | C2×C5⋊D5 | — | 4 | 1 | no | — |
| 83 | C2×C5⋊D5 | C24 | 1 | 2 | yes | — |
| 84 | C2×C5×D5 | — | 4 | 8 | no | — |
| 85 | C2×C5×D5 | C24 | 1 | 8 | yes | — |
| 86 | D52 | — | 4 | 4 | no | — |
| 87 | C4×C52 | C24 | 1 | 2 | yes | — |
| 88 | #1039 | C24 | 1 | 1 | yes | characteristic |
| 89 | #1039 | C24 | 1 | 4 | yes | — |
| 90 | #1039 | C24 | 1 | 1 | yes | characteristic |
| 91 | C5×Dic5 | C24 | 1 | 8 | yes | — |
| 92 | C5×#41 | — | 5 | 8 | no | — |
| 93 | C5×#41 | — | 5 | 4 | no | — |
| 94 | C2×C5×D4 | — | 2 | 2 | no | — |
| 95 | C2×C5×D4 | — | 5 | 8 | no | — |
| 96 | C2×C5×D4 | — | 5 | 8 | no | — |
| 97 | C2×C5×D4 | C2×D5 | 1 | 2 | yes | complemented |
| 98 | C2×C22⋊D5 | — | 5 | 4 | no | — |
| 99 | C2×C22⋊D5 | — | 5 | 8 | no | — |
| 100 | C2×C22⋊D5 | — | 5 | 16 | no | — |
| 101 | C2×C22⋊D5 | — | 10 | 4 | no | — |
| 102 | C2×C22⋊D5 | C2×D5 | 1 | 8 | yes | complemented |
| 103 | C22×Dic5 | — | 5 | 4 | no | — |
| 104 | C22×Dic5 | — | 5 | 8 | no | — |
| 105 | C22×Dic5 | — | 10 | 4 | no | — |
| 106 | #713 | — | 5 | 4 | no | — |
| 107 | Q8×D5 | — | 5 | 8 | no | — |
| 108 | Q8×D5 | — | 5 | 4 | no | — |
| 109 | #711 | — | 5 | 8 | no | — |
| 110 | #711 | — | 5 | 8 | no | — |
| 111 | #711 | — | 5 | 16 | no | — |
| 112 | #711 | — | 5 | 8 | no | — |
| 113 | #711 | — | 5 | 16 | no | — |
| 114 | #711 | — | 5 | 16 | no | — |
| 115 | #711 | — | 5 | 16 | no | — |
| 116 | #711 | — | 5 | 8 | no | — |
| 117 | #711 | — | 5 | 4 | no | — |
| 118 | #711 | — | 10 | 8 | no | — |
| 119 | #711 | — | 10 | 8 | no | — |
| 120 | #711 | C2×D5 | 1 | 8 | yes | complemented |
| 121 | D4×D5 | — | 5 | 16 | no | — |
| 122 | D4×D5 | — | 5 | 8 | no | — |
| 123 | D4×D5 | — | 5 | 4 | no | — |
| 124 | D4×D5 | C2×D5 | 1 | 8 | yes | complemented |
| 125 | #709 | — | 5 | 16 | no | — |
| 126 | #709 | — | 5 | 8 | no | — |
| 127 | #709 | — | 5 | 8 | no | — |
| 128 | #709 | C2×D5 | 1 | 4 | yes | complemented |
| 129 | C2×C4×D5 | — | 5 | 8 | no | — |
| 130 | C2×C4×D5 | — | 5 | 2 | no | — |
| 131 | C2×C4×D5 | — | 5 | 8 | no | — |
| 132 | C2×C4×D5 | — | 10 | 2 | no | — |
| 133 | C2×Dic10 | — | 5 | 2 | no | — |
| 134 | C2×Dic10 | — | 5 | 8 | no | — |
| 135 | C2×Dic10 | — | 5 | 8 | no | — |
| 136 | C2×Dic10 | — | 10 | 2 | no | — |
| 137 | #585 | — | 25 | 1 | no | Sylow |
| 138 | C2×C52 | — | 2 | 1 | no | — |
| 139 | C2×C52 | — | 2 | 4 | no | — |
| 140 | C2×C52 | C25 | 1 | 1 | yes | characteristic |
| 141 | C5⋊D5 | — | 2 | 2 | no | — |
| 142 | C5×D5 | — | 2 | 8 | no | — |
| 143 | C23×C5 | — | 2 | 4 | no | — |
| 144 | C23×C5 | — | 5 | 8 | no | — |
| 145 | C23×C5 | C22×D5 | 1 | 4 | yes | — |
| 146 | C22×D5 | — | 5 | 2 | no | — |
| 147 | C22×D5 | — | 5 | 8 | no | — |
| 148 | C22×D5 | — | 10 | 2 | no | — |
| 149 | C22×D5 | C22×D5 | 1 | 8 | yes | — |
| 150 | C5×Q8 | — | 5 | 4 | no | — |
| 151 | C5×D4 | — | 2 | 8 | no | — |
| 152 | C5×D4 | — | 5 | 8 | no | — |
| 153 | C5×D4 | — | 5 | 16 | no | — |
| 154 | C5×D4 | — | 5 | 4 | no | — |
| 155 | C5×D4 | C22×D5 | 1 | 8 | yes | — |
| 156 | C2×C4×C5 | — | 2 | 2 | no | — |
| 157 | C2×C4×C5 | — | 5 | 8 | no | — |
| 158 | C2×C4×C5 | — | 5 | 8 | no | — |
| 159 | C2×C4×C5 | C22×D5 | 1 | 2 | yes | — |
| 160 | C22⋊D5 | — | 5 | 16 | no | — |
| 161 | C22⋊D5 | — | 5 | 16 | no | — |
| 162 | C22⋊D5 | — | 5 | 8 | no | — |
| 163 | C22⋊D5 | — | 5 | 8 | no | — |
| 164 | C22⋊D5 | — | 10 | 16 | no | — |
| 165 | C22⋊D5 | C22×D5 | 1 | 16 | yes | — |
| 166 | C22⋊D5 | C22×D5 | 1 | 8 | yes | — |
| 167 | C2×Dic5 | — | 5 | 4 | no | — |
| 168 | C2×Dic5 | — | 5 | 8 | no | — |
| 169 | C2×Dic5 | — | 5 | 2 | no | — |
| 170 | C2×Dic5 | — | 5 | 8 | no | — |
| 171 | C2×Dic5 | — | 5 | 16 | no | — |
| 172 | C2×Dic5 | — | 5 | 8 | no | — |
| 173 | C2×Dic5 | — | 10 | 4 | no | — |
| 174 | C2×Dic5 | — | 10 | 2 | no | — |
| 175 | C2×Dic5 | — | 10 | 8 | no | — |
| 176 | C2×Dic5 | — | 10 | 8 | no | — |
| 177 | C2×Dic5 | C22×D5 | 1 | 8 | yes | — |
| 178 | D20 | — | 5 | 8 | no | — |
| 179 | D20 | C22×D5 | 1 | 4 | yes | — |
| 180 | C4×D5 | — | 5 | 8 | no | — |
| 181 | C4×D5 | — | 5 | 16 | no | — |
| 182 | C4×D5 | — | 5 | 4 | no | — |
| 183 | C4×D5 | — | 5 | 4 | no | — |
| 184 | C4×D5 | — | 5 | 8 | no | — |
| 185 | C4×D5 | — | 10 | 4 | no | — |
| 186 | C4×D5 | — | 10 | 4 | no | — |
| 187 | C4×D5 | C22×D5 | 1 | 8 | yes | — |
| 188 | Dic10 | — | 5 | 8 | no | — |
| 189 | Dic10 | — | 5 | 16 | no | — |
| 190 | Dic10 | — | 5 | 8 | no | — |
| 191 | Dic10 | — | 10 | 8 | no | — |
| 192 | Dic10 | C22×D5 | 1 | 4 | yes | — |
| 193 | 2−1+4 | — | 25 | 4 | no | — |
| 194 | 2−1+4 | — | 25 | 2 | no | — |
| 195 | H(5,𝔽2) | — | 5 | 2 | no | — |
| 196 | H(5,𝔽2) | — | 25 | 4 | no | — |
| 197 | H(5,𝔽2) | — | 25 | 4 | no | — |
| 198 | C2×#41 | — | 25 | 4 | no | — |
| 199 | C2×#41 | — | 25 | 8 | no | — |
| 200 | C2×#41 | — | 25 | 2 | no | — |
| 201 | C2×#41 | — | 25 | 1 | no | — |
| 202 | C52 | #585 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 203 | C22×C5 | — | 2 | 2 | no | — |
| 204 | C22×C5 | — | 2 | 8 | no | — |
| 205 | C22×C5 | — | 4 | 4 | no | — |
| 206 | C22×C5 | — | 4 | 8 | no | — |
| 207 | C22×C5 | — | 5 | 8 | no | — |
| 208 | C22×C5 | — | 20 | 8 | no | — |
| 209 | C22×C5 | C23×D5 | 1 | 2 | yes | — |
| 210 | C22×C5 | C23×D5 | 1 | 8 | yes | — |
| 211 | C2×D5 | — | 4 | 8 | no | — |
| 212 | C2×D5 | — | 5 | 4 | no | — |
| 213 | C2×D5 | — | 10 | 4 | no | — |
| 214 | C2×D5 | — | 20 | 8 | no | — |
| 215 | C2×D5 | — | 20 | 2 | no | — |
| 216 | C2×D5 | — | 20 | 4 | no | — |
| 217 | C2×D5 | C23×D5 | 1 | 8 | yes | — |
| 218 | C4×C5 | — | 2 | 4 | no | — |
| 219 | C4×C5 | — | 5 | 8 | no | — |
| 220 | C4×C5 | C23×D5 | 1 | 4 | yes | — |
| 221 | Dic5 | — | 5 | 8 | no | — |
| 222 | Dic5 | — | 5 | 2 | no | — |
| 223 | Dic5 | — | 5 | 2 | no | — |
| 224 | Dic5 | — | 10 | 8 | no | — |
| 225 | Dic5 | — | 10 | 2 | no | — |
| 226 | Dic5 | — | 10 | 2 | no | — |
| 227 | Dic5 | C23×D5 | 1 | 8 | yes | — |
| 228 | #41 | — | 5 | 8 | no | — |
| 229 | #41 | — | 5 | 4 | no | — |
| 230 | #41 | — | 25 | 4 | no | — |
| 231 | #41 | — | 25 | 16 | no | — |
| 232 | #41 | — | 25 | 8 | no | — |
| 233 | #41 | — | 25 | 4 | no | — |
| 234 | #41 | — | 25 | 8 | no | — |
| 235 | #41 | — | 25 | 8 | no | — |
| 236 | #41 | — | 25 | 8 | no | — |
| 237 | #41 | — | 25 | 4 | no | — |
| 238 | #41 | — | 25 | 4 | no | — |
| 239 | #41 | — | 25 | 4 | no | — |
| 240 | C2×Q8 | — | 25 | 4 | no | — |
| 241 | C2×Q8 | — | 25 | 8 | no | — |
| 242 | C2×Q8 | — | 25 | 2 | no | — |
| 243 | C2×Q8 | — | 25 | 1 | no | — |
| 244 | C2×D4 | — | 5 | 8 | no | — |
| 245 | C2×D4 | — | 5 | 8 | no | — |
| 246 | C2×D4 | — | 25 | 4 | no | — |
| 247 | C2×D4 | — | 25 | 2 | no | — |
| 248 | C2×D4 | — | 25 | 16 | no | — |
| 249 | C2×D4 | — | 25 | 4 | no | — |
| 250 | C2×D4 | — | 25 | 2 | no | — |
| 251 | C2×D4 | D52 | 1 | 1 | yes | characteristic, complemented |
| 252 | C22×C4 | — | 25 | 4 | no | — |
| 253 | C22×C4 | — | 25 | 8 | no | — |
| 254 | C22×C4 | — | 25 | 2 | no | — |
| 255 | C22×C4 | — | 25 | 1 | no | — |
| 256 | C2×C5 | — | 2 | 4 | no | — |
| 257 | C2×C5 | — | 2 | 8 | no | — |
| 258 | C2×C5 | — | 2 | 2 | no | — |
| 259 | C2×C5 | — | 2 | 2 | no | — |
| 260 | C2×C5 | — | 4 | 8 | no | — |
| 261 | C2×C5 | — | 10 | 8 | no | — |
| 262 | C2×C5 | C24×D5 | 1 | 2 | yes | — |
| 263 | D5 | — | 2 | 8 | no | — |
| 264 | D5 | — | 10 | 4 | no | — |
| 265 | D5 | — | 20 | 4 | no | — |
| 266 | C23 | — | 5 | 8 | no | — |
| 267 | C23 | — | 25 | 4 | no | — |
| 268 | C23 | — | 25 | 1 | no | — |
| 269 | C23 | C2×D52 | 1 | 2 | yes | — |
| 270 | Q8 | — | 5 | 4 | no | — |
| 271 | Q8 | — | 25 | 4 | no | — |
| 272 | Q8 | — | 25 | 8 | no | — |
| 273 | Q8 | — | 25 | 4 | no | — |
| 274 | D4 | — | 5 | 16 | no | — |
| 275 | D4 | — | 5 | 8 | no | — |
| 276 | D4 | — | 5 | 4 | no | — |
| 277 | D4 | — | 25 | 8 | no | — |
| 278 | D4 | — | 25 | 4 | no | — |
| 279 | D4 | — | 25 | 8 | no | — |
| 280 | D4 | — | 25 | 8 | no | — |
| 281 | D4 | C2×D52 | 1 | 4 | yes | — |
| 282 | C2×C4 | — | 5 | 8 | no | — |
| 283 | C2×C4 | — | 5 | 8 | no | — |
| 284 | C2×C4 | — | 25 | 4 | no | — |
| 285 | C2×C4 | — | 25 | 8 | no | — |
| 286 | C2×C4 | — | 25 | 16 | no | — |
| 287 | C2×C4 | — | 25 | 4 | no | — |
| 288 | C2×C4 | — | 25 | 1 | no | — |
| 289 | C2×C4 | — | 25 | 4 | no | — |
| 290 | C2×C4 | — | 25 | 2 | no | — |
| 291 | C2×C4 | — | 25 | 2 | no | — |
| 292 | C2×C4 | — | 25 | 2 | no | — |
| 293 | C2×C4 | C2×D52 | 1 | 1 | yes | characteristic |
| 294 | C5 | — | 2 | 2 | no | — |
| 295 | C5 | #66285 | 1 | 2 | yes | complemented |
| 296 | C22 | — | 4 | 2 | no | — |
| 297 | C22 | — | 5 | 8 | no | — |
| 298 | C22 | — | 20 | 8 | no | — |
| 299 | C22 | — | 25 | 2 | no | — |
| 300 | C22 | — | 100 | 1 | no | — |
| 301 | C22 | — | 100 | 4 | no | — |
| 302 | C22 | C22×D52 | 1 | 4 | yes | — |
| 303 | C22 | C22×D52 | 1 | 1 | yes | characteristic |
| 304 | C4 | — | 5 | 8 | no | — |
| 305 | C4 | — | 25 | 1 | no | — |
| 306 | C4 | — | 25 | 4 | no | — |
| 307 | C4 | — | 25 | 1 | no | — |
| 308 | C4 | C22×D52 | 1 | 2 | yes | — |
| 309 | C2 | — | 2 | 1 | no | — |
| 310 | C2 | — | 2 | 4 | no | — |
| 311 | C2 | — | 10 | 8 | no | — |
| 312 | C2 | — | 50 | 2 | no | — |
| 313 | C2 | C23×D52 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta