← #13043405
Subgroups — #13043405
Order 1280.
636 conjugacy classes of subgroups.
The subgroup lattice has 256 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #10617418 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10617416 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #10613743 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #10604117 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | D5⋊#365 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #10604104 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C2×#64847 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #66266 | — | 2 | 1 | no | — |
| 9 | #66264 | — | 2 | 1 | no | — |
| 10 | D5×#131 | C22 | 1 | 1 | yes | characteristic |
| 11 | #65729 | — | 2 | 3 | no | — |
| 12 | #65727 | — | 2 | 3 | no | — |
| 13 | D5⋊#108 | C22 | 1 | 3 | yes | — |
| 14 | C2×#3995 | C22 | 1 | 3 | yes | — |
| 15 | #65721 | C22 | 1 | 3 | yes | — |
| 16 | C2×#3993 | C22 | 1 | 3 | yes | — |
| 17 | C5×#504 | C4 | 1 | 1 | yes | characteristic, complemented |
| 18 | #65429 | C4 | 1 | 1 | yes | characteristic, complemented |
| 19 | #65196 | C4 | 1 | 3 | yes | complemented |
| 20 | D5×M32 | C22 | 1 | 3 | yes | — |
| 21 | #65190 | C4 | 1 | 3 | yes | complemented |
| 22 | C2×#3930 | C22 | 1 | 3 | yes | — |
| 23 | ΓL(1,𝔽81) | C22 | 1 | 3 | yes | — |
| 24 | ΓL(1,𝔽81) | C22 | 1 | 3 | yes | — |
| 25 | #64847 | C22 | 1 | 3 | yes | — |
| 26 | #64847 | C22 | 1 | 6 | yes | — |
| 27 | #64847 | C22 | 1 | 1 | yes | characteristic |
| 28 | #33404 | — | 5 | 1 | no | maximal, Sylow |
| 29 | D5×#41 | D4 | 1 | 1 | yes | characteristic |
| 30 | Q8×AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 31 | #4133 | — | 4 | 1 | no | — |
| 32 | D4×AGL(1,𝔽5) | — | 4 | 3 | no | — |
| 33 | #4131 | — | 4 | 3 | no | — |
| 34 | #4130 | — | 2 | 3 | no | — |
| 35 | C2×C4⋊AGL(1,𝔽5) | — | 2 | 3 | no | — |
| 36 | D5⋊M16 | — | 2 | 3 | no | — |
| 37 | C2×#700 | — | 2 | 3 | no | — |
| 38 | C5×#131 | C2×C4 | 1 | 1 | yes | characteristic |
| 39 | #4094 | Q8 | 1 | 1 | yes | characteristic |
| 40 | #4053 | Q8 | 1 | 3 | yes | — |
| 41 | D5×M16 | D4 | 1 | 3 | yes | — |
| 42 | #4047 | C2×C4 | 1 | 3 | yes | — |
| 43 | C2×C8×D5 | C23 | 1 | 3 | yes | — |
| 44 | #3996 | — | 2 | 3 | no | — |
| 45 | #3995 | — | 2 | 3 | no | — |
| 46 | #3995 | C23 | 1 | 3 | yes | — |
| 47 | #3995 | C23 | 1 | 1 | yes | characteristic |
| 48 | #3994 | — | 2 | 3 | no | — |
| 49 | #3993 | — | 2 | 3 | no | — |
| 50 | #3993 | C23 | 1 | 3 | yes | — |
| 51 | #3993 | C23 | 1 | 1 | yes | characteristic |
| 52 | C5×M32 | C2×C4 | 1 | 3 | yes | complemented |
| 53 | C2×C5×C16 | C2×C4 | 1 | 3 | yes | complemented |
| 54 | #3944 | C2×C4 | 1 | 3 | yes | complemented |
| 55 | C2×#672 | C2×C4 | 1 | 3 | yes | complemented |
| 56 | #3930 | C2×C4 | 1 | 3 | yes | complemented |
| 57 | #3930 | C2×C4 | 1 | 3 | yes | complemented |
| 58 | #3930 | C23 | 1 | 1 | yes | characteristic |
| 59 | #3930 | C23 | 1 | 3 | yes | — |
| 60 | D5×C16 | C2×C4 | 1 | 6 | yes | complemented |
| 61 | #3407 | — | 5 | 1 | no | — |
| 62 | #2916 | — | 5 | 1 | no | — |
| 63 | #2912 | — | 5 | 1 | no | — |
| 64 | #2155 | — | 5 | 3 | no | — |
| 65 | #2155 | — | 5 | 3 | no | — |
| 66 | C2×#365 | — | 5 | 3 | no | — |
| 67 | C2×#365 | — | 5 | 3 | no | — |
| 68 | C22×AGL(1,𝔽5) | — | 4 | 3 | no | — |
| 69 | C5×#41 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 70 | #713 | SD16 | 1 | 1 | yes | characteristic |
| 71 | Q8×D5 | SD16 | 1 | 1 | yes | characteristic |
| 72 | #711 | SD16 | 1 | 3 | yes | — |
| 73 | D4×D5 | SD16 | 1 | 3 | yes | — |
| 74 | #709 | C4⋊C4 | 1 | 3 | yes | — |
| 75 | C2×C4×D5 | C2×D4 | 1 | 3 | yes | — |
| 76 | C22⋊AGL(1,𝔽5) | — | 4 | 3 | no | — |
| 77 | #704 | — | 4 | 3 | no | — |
| 78 | C2×#170 | — | 4 | 3 | no | — |
| 79 | C4⋊AGL(1,𝔽5) | — | 2 | 3 | no | — |
| 80 | C4⋊AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 81 | C4⋊AGL(1,𝔽5) | — | 4 | 3 | no | — |
| 82 | C4×AGL(1,𝔽5) | — | 4 | 3 | no | — |
| 83 | #700 | — | 2 | 3 | no | — |
| 84 | #700 | — | 2 | 1 | no | — |
| 85 | #700 | — | 4 | 3 | no | — |
| 86 | D5⋊C8 | — | 4 | 3 | no | — |
| 87 | C5×M16 | C4⋊C4 | 1 | 3 | yes | — |
| 88 | C2×C5×C8 | C22×C4 | 1 | 3 | yes | — |
| 89 | #681 | C4⋊C4 | 1 | 3 | yes | — |
| 90 | C2×#168 | C2×Q8 | 1 | 3 | yes | — |
| 91 | #676 | C4⋊C4 | 1 | 6 | yes | — |
| 92 | C8×D5 | C22×C4 | 1 | 3 | yes | — |
| 93 | C8×D5 | C2×D4 | 1 | 3 | yes | — |
| 94 | C8×D5 | C2×Q8 | 1 | 3 | yes | — |
| 95 | C8×D5 | C24 | 1 | 1 | yes | characteristic |
| 96 | C5×C16 | C22×C4 | 1 | 3 | yes | — |
| 97 | C5×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 98 | #672 | C22×C4 | 1 | 3 | yes | — |
| 99 | #672 | C22×C4 | 1 | 1 | yes | characteristic |
| 100 | #568 | — | 10 | 1 | no | — |
| 101 | C2×#131 | — | 5 | 1 | no | — |
| 102 | #520 | — | 10 | 1 | no | — |
| 103 | #504 | — | 5 | 1 | no | — |
| 104 | #504 | — | 5 | 3 | no | — |
| 105 | #504 | — | 5 | 3 | no | — |
| 106 | #504 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 107 | C2×M32 | — | 5 | 3 | no | — |
| 108 | C2×M32 | — | 5 | 3 | no | — |
| 109 | #430 | — | 10 | 3 | no | — |
| 110 | C2×#108 | — | 5 | 3 | no | — |
| 111 | C2×#108 | — | 5 | 3 | no | — |
| 112 | #428 | — | 10 | 3 | no | — |
| 113 | #427 | — | 5 | 3 | no | — |
| 114 | C2×#106 | — | 5 | 3 | no | — |
| 115 | #365 | — | 5 | 3 | no | — |
| 116 | #365 | — | 5 | 6 | no | — |
| 117 | #365 | — | 5 | 1 | no | — |
| 118 | #365 | — | 5 | 3 | no | — |
| 119 | #365 | — | 5 | 3 | no | — |
| 120 | C22×D5 | C2×SD16 | 1 | 3 | yes | — |
| 121 | C2×AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 122 | C2×AGL(1,𝔽5) | — | 4 | 3 | no | — |
| 123 | C2×AGL(1,𝔽5) | — | 16 | 3 | no | — |
| 124 | C5×Q8 | #106 | 1 | 1 | yes | characteristic |
| 125 | C5×D4 | #106 | 1 | 3 | yes | — |
| 126 | C2×C4×C5 | C2×C4⋊C4 | 1 | 3 | yes | — |
| 127 | C22⋊D5 | #106 | 1 | 6 | yes | — |
| 128 | C2×Dic5 | C2×SD16 | 1 | 3 | yes | — |
| 129 | D20 | #106 | 1 | 3 | yes | — |
| 130 | C4×D5 | C2×C4⋊C4 | 1 | 3 | yes | — |
| 131 | C4×D5 | C2×SD16 | 1 | 3 | yes | — |
| 132 | C4×D5 | C2×SD16 | 1 | 3 | yes | — |
| 133 | C4×D5 | C22×D4 | 1 | 1 | yes | characteristic |
| 134 | Dic10 | #106 | 1 | 3 | yes | — |
| 135 | #170 | — | 4 | 1 | no | — |
| 136 | #170 | — | 4 | 3 | no | — |
| 137 | C5×C8 | C2×C4⋊C4 | 1 | 3 | yes | — |
| 138 | C5×C8 | C23×C4 | 1 | 1 | yes | characteristic |
| 139 | #168 | C2×C4⋊C4 | 1 | 3 | yes | — |
| 140 | #168 | C22×Q8 | 1 | 1 | yes | characteristic |
| 141 | C2×#41 | — | 5 | 1 | no | — |
| 142 | #131 | — | 5 | 1 | no | — |
| 143 | #131 | — | 5 | 3 | no | — |
| 144 | #131 | — | 5 | 3 | no | — |
| 145 | #131 | — | 20 | 3 | no | — |
| 146 | #131 | — | 20 | 1 | no | — |
| 147 | #131 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 148 | C2×M16 | — | 5 | 3 | no | — |
| 149 | C2×M16 | — | 10 | 3 | no | — |
| 150 | C2×M16 | — | 10 | 3 | no | — |
| 151 | C22×C8 | — | 5 | 3 | no | — |
| 152 | C4×Q8 | — | 20 | 1 | no | — |
| 153 | C4×D4 | — | 20 | 3 | no | — |
| 154 | #117 | — | 10 | 3 | no | — |
| 155 | C2×C4⋊C4 | — | 10 | 3 | no | — |
| 156 | M32 | — | 5 | 3 | no | — |
| 157 | M32 | — | 5 | 3 | no | — |
| 158 | M32 | — | 5 | 3 | no | — |
| 159 | M32 | — | 5 | 3 | no | — |
| 160 | M32 | — | 5 | 1 | no | — |
| 161 | M32 | C2×AGL(1,𝔽5) | 1 | 3 | yes | complemented |
| 162 | C2×C16 | — | 5 | 3 | no | — |
| 163 | C2×C16 | — | 5 | 6 | no | — |
| 164 | C2×C16 | C2×AGL(1,𝔽5) | 1 | 3 | yes | complemented |
| 165 | #108 | — | 5 | 3 | no | — |
| 166 | #108 | — | 5 | 1 | no | — |
| 167 | #108 | — | 10 | 3 | no | — |
| 168 | #108 | — | 10 | 3 | no | — |
| 169 | #107 | — | 10 | 3 | no | — |
| 170 | #106 | — | 5 | 3 | no | — |
| 171 | #106 | — | 5 | 1 | no | — |
| 172 | #106 | — | 10 | 3 | no | — |
| 173 | C22×C5 | C2×#106 | 1 | 3 | yes | — |
| 174 | C2×D5 | — | 4 | 3 | no | — |
| 175 | C2×D5 | C2×#106 | 1 | 3 | yes | — |
| 176 | C2×D5 | C22×SD16 | 1 | 1 | yes | characteristic |
| 177 | AGL(1,𝔽5) | — | 8 | 1 | no | — |
| 178 | AGL(1,𝔽5) | — | 8 | 3 | no | — |
| 179 | C4×C5 | C2×#106 | 1 | 3 | yes | — |
| 180 | C4×C5 | C22×C4⋊C4 | 1 | 1 | yes | characteristic |
| 181 | Dic5 | C2×#106 | 1 | 3 | yes | — |
| 182 | Dic5 | C22×SD16 | 1 | 1 | yes | characteristic |
| 183 | #41 | — | 5 | 1 | no | — |
| 184 | #41 | — | 5 | 3 | no | — |
| 185 | #41 | — | 5 | 3 | no | — |
| 186 | #41 | C4⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 187 | C2×Q8 | — | 5 | 1 | no | — |
| 188 | C2×D4 | — | 5 | 3 | no | — |
| 189 | C22×C4 | — | 5 | 3 | no | — |
| 190 | C22×C4 | — | 20 | 3 | no | — |
| 191 | M16 | — | 5 | 3 | no | — |
| 192 | M16 | — | 5 | 6 | no | — |
| 193 | M16 | — | 10 | 3 | no | — |
| 194 | M16 | — | 10 | 1 | no | — |
| 195 | M16 | — | 20 | 3 | no | — |
| 196 | M16 | — | 20 | 3 | no | — |
| 197 | M16 | C4⋊AGL(1,𝔽5) | 1 | 3 | yes | — |
| 198 | C2×C8 | — | 5 | 3 | no | — |
| 199 | C2×C8 | — | 5 | 3 | no | — |
| 200 | C2×C8 | — | 5 | 3 | no | — |
| 201 | C2×C8 | — | 5 | 1 | no | — |
| 202 | C2×C8 | — | 5 | 3 | no | — |
| 203 | C2×C8 | — | 20 | 3 | no | — |
| 204 | C2×C8 | — | 20 | 3 | no | — |
| 205 | C2×C8 | C22×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 206 | C4⋊C4 | — | 10 | 3 | no | — |
| 207 | C4⋊C4 | — | 10 | 1 | no | — |
| 208 | C4⋊C4 | — | 20 | 3 | no | — |
| 209 | C22⋊C4 | — | 20 | 3 | no | — |
| 210 | C42 | — | 20 | 3 | no | — |
| 211 | C16 | — | 5 | 1 | no | — |
| 212 | C16 | — | 5 | 3 | no | — |
| 213 | C16 | C22×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 214 | C16 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 215 | C2×C5 | — | 2 | 3 | no | — |
| 216 | C2×C5 | C22×#106 | 1 | 1 | yes | characteristic |
| 217 | D5 | — | 2 | 1 | no | — |
| 218 | D5 | — | 2 | 3 | no | — |
| 219 | C23 | — | 5 | 3 | no | — |
| 220 | Q8 | — | 5 | 3 | no | — |
| 221 | Q8 | #3993 | 1 | 1 | yes | characteristic |
| 222 | D4 | — | 5 | 6 | no | — |
| 223 | D4 | — | 5 | 3 | no | — |
| 224 | D4 | #3993 | 1 | 3 | yes | — |
| 225 | C2×C4 | — | 5 | 3 | no | — |
| 226 | C2×C4 | — | 5 | 3 | no | — |
| 227 | C2×C4 | — | 5 | 3 | no | — |
| 228 | C2×C4 | — | 5 | 1 | no | — |
| 229 | C2×C4 | — | 5 | 3 | no | — |
| 230 | C2×C4 | — | 20 | 1 | no | — |
| 231 | C2×C4 | — | 20 | 3 | no | — |
| 232 | C2×C4 | — | 80 | 3 | no | — |
| 233 | C2×C4 | C2×C4⋊AGL(1,𝔽5) | 1 | 3 | yes | — |
| 234 | C8 | — | 5 | 1 | no | — |
| 235 | C8 | — | 5 | 3 | no | — |
| 236 | C8 | — | 20 | 1 | no | — |
| 237 | C8 | — | 20 | 3 | no | — |
| 238 | C8 | C2×C4⋊AGL(1,𝔽5) | 1 | 3 | yes | — |
| 239 | C8 | C23×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 240 | C5 | #33404 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 241 | C22 | — | 5 | 1 | no | — |
| 242 | C22 | — | 5 | 3 | no | — |
| 243 | C22 | — | 20 | 3 | no | — |
| 244 | C22 | C2×#3993 | 1 | 3 | yes | — |
| 245 | C4 | — | 5 | 1 | no | — |
| 246 | C4 | — | 5 | 3 | no | — |
| 247 | C4 | — | 40 | 3 | no | — |
| 248 | C4 | — | 40 | 1 | no | — |
| 249 | C4 | C2×#3993 | 1 | 3 | yes | — |
| 250 | C4 | C22×C4⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 251 | C2 | — | 2 | 3 | no | — |
| 252 | C2 | — | 10 | 1 | no | — |
| 253 | C2 | — | 10 | 3 | no | — |
| 254 | C2 | C22×#3993 | 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