← #13043138
Subgroups — #13043138
Order 1280.
716 conjugacy classes of subgroups.
The subgroup lattice has 270 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #10617415 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10617413 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #10613743 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #10604115 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #10604114 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #10604101 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C2×#64845 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #41×AGL(1,𝔽5) | C4 | 1 | 1 | yes | characteristic |
| 9 | D5⋊#131 | C4 | 1 | 1 | yes | characteristic |
| 10 | D5×#131 | C22 | 1 | 1 | yes | characteristic |
| 11 | #65791 | C4 | 1 | 2 | yes | complemented |
| 12 | #65728 | C4 | 1 | 3 | yes | — |
| 13 | M16×AGL(1,𝔽5) | C4 | 1 | 3 | yes | — |
| 14 | #65725 | C4 | 1 | 6 | yes | complemented |
| 15 | #65718 | C22 | 1 | 3 | yes | — |
| 16 | C2×#3992 | C22 | 1 | 3 | yes | — |
| 17 | D5⋊M32 | C22 | 1 | 3 | yes | — |
| 18 | C2×#3990 | C22 | 1 | 3 | yes | — |
| 19 | C5×#504 | C4 | 1 | 1 | yes | characteristic, complemented |
| 20 | #65429 | C4 | 1 | 1 | yes | characteristic, complemented |
| 21 | #65196 | C4 | 1 | 3 | yes | complemented |
| 22 | D5×M32 | C22 | 1 | 3 | yes | — |
| 23 | #65190 | C4 | 1 | 3 | yes | complemented |
| 24 | C2×#3930 | C22 | 1 | 3 | yes | — |
| 25 | #64846 | C22 | 1 | 6 | yes | — |
| 26 | #64845 | C22 | 1 | 1 | yes | characteristic |
| 27 | #64845 | C22 | 1 | 3 | yes | — |
| 28 | #64845 | C22 | 1 | 3 | yes | — |
| 29 | #64845 | C22 | 1 | 3 | yes | — |
| 30 | #33329 | — | 5 | 1 | no | maximal, Sylow |
| 31 | D5×#41 | C2×C4 | 1 | 1 | yes | characteristic |
| 32 | Q8×AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 33 | #4133 | — | 2 | 1 | no | — |
| 34 | D4×AGL(1,𝔽5) | — | 2 | 3 | no | — |
| 35 | #4131 | — | 2 | 3 | no | — |
| 36 | #4130 | C2×C4 | 1 | 3 | yes | — |
| 37 | C2×C4×AGL(1,𝔽5) | C2×C4 | 1 | 3 | yes | — |
| 38 | D5⋊M16 | C2×C4 | 1 | 3 | yes | — |
| 39 | C2×D5⋊C8 | C2×C4 | 1 | 3 | yes | — |
| 40 | C5×#131 | C2×C4 | 1 | 1 | yes | characteristic |
| 41 | #4094 | C2×C4 | 1 | 1 | yes | characteristic |
| 42 | #4053 | C2×C4 | 1 | 3 | yes | — |
| 43 | D5×M16 | C2×C4 | 1 | 3 | yes | — |
| 44 | #4047 | C2×C4 | 1 | 3 | yes | — |
| 45 | C2×C8×D5 | C23 | 1 | 3 | yes | — |
| 46 | #3998 | C2×C4 | 1 | 6 | yes | complemented |
| 47 | C2×#674 | C2×C4 | 1 | 6 | yes | complemented |
| 48 | #3992 | C2×C4 | 1 | 3 | yes | — |
| 49 | #3992 | C2×C4 | 1 | 3 | yes | — |
| 50 | #3992 | C23 | 1 | 1 | yes | characteristic |
| 51 | #3992 | C23 | 1 | 3 | yes | — |
| 52 | C8×AGL(1,𝔽5) | C2×C4 | 1 | 6 | yes | — |
| 53 | #3990 | C2×C4 | 1 | 6 | yes | complemented |
| 54 | #3990 | C23 | 1 | 1 | yes | characteristic |
| 55 | #3990 | C23 | 1 | 3 | yes | — |
| 56 | D5⋊C16 | C2×C4 | 1 | 6 | yes | complemented |
| 57 | C5×M32 | C2×C4 | 1 | 3 | yes | complemented |
| 58 | C2×C5×C16 | C2×C4 | 1 | 3 | yes | complemented |
| 59 | #3944 | C2×C4 | 1 | 3 | yes | complemented |
| 60 | C2×#672 | C2×C4 | 1 | 3 | yes | complemented |
| 61 | #3930 | C2×C4 | 1 | 3 | yes | complemented |
| 62 | #3930 | C2×C4 | 1 | 3 | yes | complemented |
| 63 | #3930 | C23 | 1 | 1 | yes | characteristic |
| 64 | #3930 | C23 | 1 | 3 | yes | — |
| 65 | D5×C16 | C2×C4 | 1 | 6 | yes | complemented |
| 66 | #3407 | — | 5 | 1 | no | — |
| 67 | #3407 | — | 5 | 1 | no | — |
| 68 | #2875 | — | 5 | 1 | no | — |
| 69 | #2110 | — | 5 | 3 | no | — |
| 70 | #2110 | — | 5 | 3 | no | — |
| 71 | C2×#347 | — | 5 | 3 | no | — |
| 72 | C2×#347 | — | 5 | 3 | no | — |
| 73 | C22×AGL(1,𝔽5) | — | 2 | 3 | no | — |
| 74 | C5×#41 | C42 | 1 | 1 | yes | characteristic |
| 75 | #713 | M16 | 1 | 1 | yes | characteristic |
| 76 | Q8×D5 | M16 | 1 | 1 | yes | characteristic |
| 77 | #711 | M16 | 1 | 3 | yes | — |
| 78 | D4×D5 | M16 | 1 | 3 | yes | — |
| 79 | #709 | C42 | 1 | 3 | yes | — |
| 80 | C2×C4×D5 | C22×C4 | 1 | 3 | yes | — |
| 81 | C22⋊AGL(1,𝔽5) | — | 2 | 3 | no | — |
| 82 | #704 | — | 2 | 3 | no | — |
| 83 | C2×#170 | — | 2 | 3 | no | — |
| 84 | C4⋊AGL(1,𝔽5) | — | 2 | 3 | no | — |
| 85 | C4×AGL(1,𝔽5) | — | 2 | 3 | no | — |
| 86 | C4×AGL(1,𝔽5) | C22×C4 | 1 | 1 | yes | characteristic |
| 87 | C4×AGL(1,𝔽5) | C22×C4 | 1 | 3 | yes | — |
| 88 | #700 | — | 2 | 3 | no | — |
| 89 | D5⋊C8 | — | 2 | 3 | no | — |
| 90 | D5⋊C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 91 | D5⋊C8 | C22×C4 | 1 | 3 | yes | — |
| 92 | C5×M16 | C42 | 1 | 3 | yes | — |
| 93 | C2×C5×C8 | C22×C4 | 1 | 3 | yes | — |
| 94 | #681 | C42 | 1 | 3 | yes | — |
| 95 | C2×#168 | C22×C4 | 1 | 3 | yes | — |
| 96 | #676 | C42 | 1 | 6 | yes | — |
| 97 | C8×D5 | C22×C4 | 1 | 3 | yes | — |
| 98 | C8×D5 | C22×C4 | 1 | 3 | yes | — |
| 99 | C8×D5 | C22×C4 | 1 | 3 | yes | — |
| 100 | C8×D5 | C24 | 1 | 1 | yes | characteristic |
| 101 | #674 | C22×C4 | 1 | 6 | yes | — |
| 102 | #674 | C22×C4 | 1 | 2 | yes | — |
| 103 | C5×C16 | C22×C4 | 1 | 3 | yes | — |
| 104 | C5×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 105 | #672 | C22×C4 | 1 | 3 | yes | — |
| 106 | #672 | C22×C4 | 1 | 1 | yes | characteristic |
| 107 | C2×#131 | — | 5 | 1 | no | — |
| 108 | C2×#131 | — | 5 | 1 | no | — |
| 109 | C4×#41 | — | 5 | 1 | no | — |
| 110 | #504 | — | 5 | 6 | no | — |
| 111 | #504 | — | 5 | 2 | no | — |
| 112 | #504 | — | 5 | 1 | no | — |
| 113 | #504 | — | 5 | 3 | no | — |
| 114 | #504 | — | 5 | 3 | no | — |
| 115 | #504 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 116 | C2×M32 | — | 5 | 3 | no | — |
| 117 | C2×M32 | — | 5 | 3 | no | — |
| 118 | C2×M32 | — | 5 | 3 | no | — |
| 119 | C2×M32 | — | 5 | 3 | no | — |
| 120 | #405 | — | 5 | 3 | no | — |
| 121 | #405 | — | 5 | 3 | no | — |
| 122 | C4×M16 | — | 5 | 3 | no | — |
| 123 | C2×#97 | — | 5 | 3 | no | — |
| 124 | #347 | — | 5 | 1 | no | — |
| 125 | #347 | — | 5 | 3 | no | — |
| 126 | #347 | — | 5 | 3 | no | — |
| 127 | #347 | — | 5 | 3 | no | — |
| 128 | #347 | — | 5 | 6 | no | — |
| 129 | C22×D5 | C2×M16 | 1 | 3 | yes | — |
| 130 | C2×AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 131 | C2×AGL(1,𝔽5) | — | 2 | 3 | no | — |
| 132 | C2×AGL(1,𝔽5) | — | 8 | 3 | no | — |
| 133 | C5×Q8 | #97 | 1 | 1 | yes | characteristic |
| 134 | C5×D4 | #97 | 1 | 3 | yes | — |
| 135 | C2×C4×C5 | C2×C42 | 1 | 3 | yes | — |
| 136 | C22⋊D5 | #97 | 1 | 6 | yes | — |
| 137 | C2×Dic5 | C2×M16 | 1 | 3 | yes | — |
| 138 | D20 | #97 | 1 | 3 | yes | — |
| 139 | C4×D5 | C2×C42 | 1 | 3 | yes | — |
| 140 | C4×D5 | C2×M16 | 1 | 3 | yes | — |
| 141 | C4×D5 | C2×M16 | 1 | 3 | yes | — |
| 142 | C4×D5 | C23×C4 | 1 | 1 | yes | characteristic |
| 143 | Dic10 | #97 | 1 | 3 | yes | — |
| 144 | #170 | — | 2 | 1 | no | — |
| 145 | #170 | — | 2 | 3 | no | — |
| 146 | C5×C8 | C2×C42 | 1 | 3 | yes | — |
| 147 | C5×C8 | C23×C4 | 1 | 1 | yes | characteristic |
| 148 | #168 | C2×C42 | 1 | 3 | yes | — |
| 149 | #168 | C23×C4 | 1 | 1 | yes | characteristic |
| 150 | C2×#41 | — | 5 | 1 | no | — |
| 151 | #131 | — | 5 | 1 | no | — |
| 152 | #131 | — | 5 | 3 | no | — |
| 153 | #131 | — | 5 | 3 | no | — |
| 154 | #131 | — | 10 | 3 | no | — |
| 155 | #131 | — | 10 | 1 | no | — |
| 156 | #131 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 157 | C2×M16 | — | 5 | 3 | no | — |
| 158 | C2×M16 | — | 5 | 3 | no | — |
| 159 | C22×C8 | — | 5 | 3 | no | — |
| 160 | C22×C8 | — | 5 | 3 | no | — |
| 161 | C4×Q8 | — | 10 | 1 | no | — |
| 162 | C4×D4 | — | 10 | 3 | no | — |
| 163 | #117 | — | 5 | 3 | no | — |
| 164 | C2×C42 | — | 5 | 3 | no | — |
| 165 | M32 | — | 5 | 1 | no | — |
| 166 | M32 | — | 5 | 3 | no | — |
| 167 | M32 | — | 5 | 6 | no | — |
| 168 | M32 | — | 5 | 6 | no | — |
| 169 | M32 | — | 5 | 3 | no | — |
| 170 | M32 | — | 5 | 3 | no | — |
| 171 | M32 | — | 5 | 3 | no | — |
| 172 | M32 | — | 5 | 3 | no | — |
| 173 | M32 | — | 5 | 1 | no | — |
| 174 | M32 | C2×AGL(1,𝔽5) | 1 | 3 | yes | complemented |
| 175 | C2×C16 | — | 5 | 6 | no | — |
| 176 | C2×C16 | — | 5 | 6 | no | — |
| 177 | C2×C16 | — | 5 | 3 | no | — |
| 178 | C2×C16 | — | 5 | 6 | no | — |
| 179 | C2×C16 | C2×AGL(1,𝔽5) | 1 | 3 | yes | complemented |
| 180 | #97 | — | 5 | 1 | no | — |
| 181 | #97 | — | 5 | 3 | no | — |
| 182 | #97 | — | 5 | 3 | no | — |
| 183 | #97 | — | 5 | 3 | no | — |
| 184 | C4×C8 | — | 5 | 6 | no | — |
| 185 | C22×C5 | C2×#97 | 1 | 3 | yes | — |
| 186 | C2×D5 | — | 4 | 3 | no | — |
| 187 | C2×D5 | C2×#97 | 1 | 3 | yes | — |
| 188 | C2×D5 | C22×M16 | 1 | 1 | yes | characteristic |
| 189 | AGL(1,𝔽5) | — | 4 | 3 | no | — |
| 190 | AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 191 | C4×C5 | C2×#97 | 1 | 3 | yes | — |
| 192 | C4×C5 | C22×C42 | 1 | 1 | yes | characteristic |
| 193 | Dic5 | C2×#97 | 1 | 3 | yes | — |
| 194 | Dic5 | C22×M16 | 1 | 1 | yes | characteristic |
| 195 | #41 | — | 5 | 1 | no | — |
| 196 | #41 | — | 5 | 3 | no | — |
| 197 | #41 | — | 5 | 3 | no | — |
| 198 | #41 | C4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 199 | C2×Q8 | — | 5 | 1 | no | — |
| 200 | C2×D4 | — | 5 | 3 | no | — |
| 201 | C22×C4 | — | 5 | 3 | no | — |
| 202 | C22×C4 | — | 10 | 3 | no | — |
| 203 | M16 | — | 5 | 3 | no | — |
| 204 | M16 | — | 5 | 6 | no | — |
| 205 | M16 | — | 10 | 3 | no | — |
| 206 | M16 | — | 10 | 3 | no | — |
| 207 | M16 | C4×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 208 | C2×C8 | — | 5 | 3 | no | — |
| 209 | C2×C8 | — | 5 | 3 | no | — |
| 210 | C2×C8 | — | 5 | 3 | no | — |
| 211 | C2×C8 | — | 5 | 1 | no | — |
| 212 | C2×C8 | — | 5 | 3 | no | — |
| 213 | C2×C8 | — | 5 | 3 | no | — |
| 214 | C2×C8 | — | 5 | 1 | no | — |
| 215 | C2×C8 | — | 10 | 3 | no | — |
| 216 | C2×C8 | — | 10 | 3 | no | — |
| 217 | C2×C8 | C22×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 218 | C4⋊C4 | — | 10 | 3 | no | — |
| 219 | C22⋊C4 | — | 10 | 3 | no | — |
| 220 | C42 | — | 5 | 3 | no | — |
| 221 | C42 | — | 5 | 1 | no | — |
| 222 | C42 | — | 10 | 3 | no | — |
| 223 | C16 | — | 5 | 6 | no | — |
| 224 | C16 | — | 5 | 2 | no | — |
| 225 | C16 | — | 5 | 1 | no | — |
| 226 | C16 | — | 5 | 3 | no | — |
| 227 | C16 | C22×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 228 | C16 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 229 | C2×C5 | — | 2 | 3 | no | — |
| 230 | C2×C5 | C22×#97 | 1 | 1 | yes | characteristic |
| 231 | D5 | — | 2 | 1 | no | — |
| 232 | D5 | — | 2 | 3 | no | — |
| 233 | C23 | — | 5 | 3 | no | — |
| 234 | Q8 | — | 5 | 3 | no | — |
| 235 | Q8 | #3992 | 1 | 1 | yes | characteristic |
| 236 | D4 | — | 5 | 6 | no | — |
| 237 | D4 | — | 5 | 3 | no | — |
| 238 | D4 | #3992 | 1 | 3 | yes | — |
| 239 | C2×C4 | — | 5 | 3 | no | — |
| 240 | C2×C4 | — | 5 | 3 | no | — |
| 241 | C2×C4 | — | 5 | 3 | no | — |
| 242 | C2×C4 | — | 5 | 1 | no | — |
| 243 | C2×C4 | — | 5 | 3 | no | — |
| 244 | C2×C4 | — | 10 | 1 | no | — |
| 245 | C2×C4 | — | 10 | 3 | no | — |
| 246 | C2×C4 | — | 40 | 3 | no | — |
| 247 | C2×C4 | C2×C4×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 248 | C8 | — | 5 | 1 | no | — |
| 249 | C8 | — | 5 | 3 | no | — |
| 250 | C8 | — | 10 | 1 | no | — |
| 251 | C8 | — | 10 | 3 | no | — |
| 252 | C8 | C2×C4×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 253 | C8 | C23×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 254 | C5 | #33329 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 255 | C22 | — | 5 | 1 | no | — |
| 256 | C22 | — | 5 | 3 | no | — |
| 257 | C22 | — | 20 | 3 | no | — |
| 258 | C22 | C2×#3992 | 1 | 3 | yes | — |
| 259 | C4 | — | 5 | 1 | no | — |
| 260 | C4 | — | 5 | 3 | no | — |
| 261 | C4 | — | 20 | 1 | no | — |
| 262 | C4 | — | 20 | 3 | no | — |
| 263 | C4 | C2×#3992 | 1 | 3 | yes | — |
| 264 | C4 | C22×C4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 265 | C2 | — | 2 | 3 | no | — |
| 266 | C2 | — | 10 | 1 | no | — |
| 267 | C2 | — | 10 | 3 | no | — |
| 268 | C2 | C22×#3992 | 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