← #13044369
Subgroups — #13044369
Order 1280.
1800 conjugacy classes of subgroups.
The subgroup lattice has 222 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | D5×#564 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10617348 | C2 | 1 | 3 | yes | maximal |
| 3 | #10617346 | C2 | 1 | 12 | yes | maximal |
| 4 | #10617345 | C2 | 1 | 12 | yes | maximal |
| 5 | AGL(1,𝔽5)×#125 | C2 | 1 | 3 | yes | maximal |
| 6 | C5×#564 | C4 | 1 | 1 | yes | characteristic, complemented |
| 7 | D5×#125 | C22 | 1 | 12 | yes | — |
| 8 | D5×#125 | C22 | 1 | 3 | yes | — |
| 9 | C5⋊#564 | C4 | 1 | 12 | yes | complemented |
| 10 | C5⋊#564 | C4 | 1 | 3 | yes | complemented |
| 11 | #65712 | C22 | 1 | 12 | yes | — |
| 12 | #65712 | C22 | 1 | 12 | yes | — |
| 13 | #65712 | C22 | 1 | 6 | yes | — |
| 14 | #65711 | C22 | 1 | 12 | yes | — |
| 15 | #65711 | C22 | 1 | 12 | yes | — |
| 16 | #65711 | C22 | 1 | 12 | yes | — |
| 17 | #65711 | C22 | 1 | 12 | yes | — |
| 18 | #65711 | C22 | 1 | 12 | yes | — |
| 19 | C4⋊C4×AGL(1,𝔽5) | C22 | 1 | 6 | yes | — |
| 20 | C4⋊C4×AGL(1,𝔽5) | C22 | 1 | 12 | yes | — |
| 21 | C4⋊C4×AGL(1,𝔽5) | C22 | 1 | 12 | yes | — |
| 22 | #65690 | C22 | 1 | 4 | yes | — |
| 23 | #65689 | C22 | 1 | 3 | yes | — |
| 24 | C4×C4⋊AGL(1,𝔽5) | C22 | 1 | 12 | yes | — |
| 25 | C42×AGL(1,𝔽5) | C22 | 1 | 1 | yes | characteristic |
| 26 | #34526 | — | 5 | 1 | no | maximal, Sylow |
| 27 | C2×C4⋊AGL(1,𝔽5) | C23 | 1 | 12 | yes | — |
| 28 | C2×C4⋊AGL(1,𝔽5) | C23 | 1 | 12 | yes | — |
| 29 | C2×C4⋊AGL(1,𝔽5) | C23 | 1 | 6 | yes | — |
| 30 | C2×C4×AGL(1,𝔽5) | C23 | 1 | 3 | yes | — |
| 31 | C2×C4×AGL(1,𝔽5) | C23 | 1 | 3 | yes | — |
| 32 | C2×C4×AGL(1,𝔽5) | C23 | 1 | 12 | yes | — |
| 33 | C2×C4×AGL(1,𝔽5) | C23 | 1 | 12 | yes | — |
| 34 | C5×#125 | C2×C4 | 1 | 12 | yes | — |
| 35 | C5×#125 | C2×C4 | 1 | 3 | yes | — |
| 36 | D5×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 37 | D5×C4⋊C4 | C23 | 1 | 12 | yes | — |
| 38 | D5×C4⋊C4 | C23 | 1 | 12 | yes | — |
| 39 | #4036 | C2×C4 | 1 | 12 | yes | — |
| 40 | #4036 | C2×C4 | 1 | 12 | yes | — |
| 41 | #4036 | C2×C4 | 1 | 6 | yes | — |
| 42 | #4035 | C2×C4 | 1 | 12 | yes | — |
| 43 | #4035 | C2×C4 | 1 | 12 | yes | — |
| 44 | #4035 | C2×C4 | 1 | 12 | yes | — |
| 45 | #4035 | C2×C4 | 1 | 12 | yes | — |
| 46 | #4035 | C2×C4 | 1 | 12 | yes | — |
| 47 | C42×D5 | C23 | 1 | 1 | yes | characteristic |
| 48 | C42×D5 | C23 | 1 | 4 | yes | — |
| 49 | #4016 | C2×C4 | 1 | 12 | yes | — |
| 50 | #4016 | C2×C4 | 1 | 3 | yes | — |
| 51 | (C2×AGL(1,𝔽5))⋊C4 | C23 | 1 | 12 | yes | — |
| 52 | (C2×AGL(1,𝔽5))⋊C4 | C23 | 1 | 12 | yes | — |
| 53 | (C2×AGL(1,𝔽5))⋊C4 | C23 | 1 | 12 | yes | — |
| 54 | (C2×AGL(1,𝔽5))⋊C4 | C23 | 1 | 12 | yes | — |
| 55 | (C2×AGL(1,𝔽5))⋊C4 | C23 | 1 | 12 | yes | — |
| 56 | C2×#564 | — | 5 | 1 | no | — |
| 57 | #2382 | — | 5 | 3 | no | — |
| 58 | #2370 | — | 5 | 12 | no | — |
| 59 | #2336 | — | 5 | 12 | no | — |
| 60 | C4×#125 | — | 5 | 3 | no | — |
| 61 | C22×AGL(1,𝔽5) | C24 | 1 | 12 | yes | — |
| 62 | C22×AGL(1,𝔽5) | C24 | 1 | 1 | yes | characteristic |
| 63 | C22×AGL(1,𝔽5) | C24 | 1 | 3 | yes | — |
| 64 | C2×C4×D5 | C24 | 1 | 3 | yes | — |
| 65 | C2×C4×D5 | C24 | 1 | 12 | yes | — |
| 66 | C4⋊AGL(1,𝔽5) | — | 2 | 24 | no | — |
| 67 | C4⋊AGL(1,𝔽5) | — | 4 | 12 | no | — |
| 68 | C4⋊AGL(1,𝔽5) | — | 4 | 6 | no | — |
| 69 | C4×AGL(1,𝔽5) | — | 2 | 6 | no | — |
| 70 | C4×AGL(1,𝔽5) | — | 4 | 12 | no | — |
| 71 | C4×AGL(1,𝔽5) | — | 4 | 12 | no | — |
| 72 | C4×AGL(1,𝔽5) | — | 4 | 3 | no | — |
| 73 | C5×C4⋊C4 | C22×C4 | 1 | 12 | yes | — |
| 74 | C5×C4⋊C4 | C22×C4 | 1 | 6 | yes | — |
| 75 | C5×C4⋊C4 | C22×C4 | 1 | 12 | yes | — |
| 76 | C42×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 77 | C42×C5 | C22×C4 | 1 | 4 | yes | — |
| 78 | C4⋊Dic5 | C22×C4 | 1 | 12 | yes | — |
| 79 | C4⋊Dic5 | C22×C4 | 1 | 12 | yes | — |
| 80 | C4⋊Dic5 | C22×C4 | 1 | 6 | yes | — |
| 81 | #683 | C22×C4 | 1 | 12 | yes | — |
| 82 | #683 | C22×C4 | 1 | 12 | yes | — |
| 83 | #683 | C22×C4 | 1 | 12 | yes | — |
| 84 | #683 | C22×C4 | 1 | 12 | yes | — |
| 85 | #683 | C22×C4 | 1 | 12 | yes | — |
| 86 | C4×Dic5 | C22×C4 | 1 | 3 | yes | — |
| 87 | C4×Dic5 | C22×C4 | 1 | 12 | yes | — |
| 88 | #564 | — | 5 | 12 | no | — |
| 89 | #564 | — | 5 | 3 | no | — |
| 90 | #564 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 91 | C2×#125 | — | 5 | 3 | no | — |
| 92 | C2×#125 | — | 5 | 12 | no | — |
| 93 | #389 | — | 5 | 6 | no | — |
| 94 | #389 | — | 5 | 12 | no | — |
| 95 | #389 | — | 5 | 12 | no | — |
| 96 | #387 | — | 5 | 12 | no | — |
| 97 | #387 | — | 5 | 12 | no | — |
| 98 | #387 | — | 5 | 12 | no | — |
| 99 | #387 | — | 5 | 12 | no | — |
| 100 | #387 | — | 5 | 12 | no | — |
| 101 | #383 | — | 5 | 4 | no | — |
| 102 | #382 | — | 5 | 3 | no | — |
| 103 | C4×C4⋊C4 | — | 5 | 6 | no | — |
| 104 | C4×C4⋊C4 | — | 5 | 12 | no | — |
| 105 | C4×C4⋊C4 | — | 5 | 12 | no | — |
| 106 | C4×C4⋊C4 | — | 5 | 12 | no | — |
| 107 | C43 | — | 5 | 1 | no | — |
| 108 | C22×D5 | C25 | 1 | 1 | yes | characteristic |
| 109 | C2×AGL(1,𝔽5) | — | 2 | 6 | no | — |
| 110 | C2×AGL(1,𝔽5) | — | 2 | 3 | no | — |
| 111 | C2×AGL(1,𝔽5) | — | 2 | 12 | no | — |
| 112 | C2×AGL(1,𝔽5) | — | 2 | 12 | no | — |
| 113 | C2×AGL(1,𝔽5) | — | 2 | 12 | no | — |
| 114 | C2×AGL(1,𝔽5) | 2−1+4 | 1 | 6 | yes | — |
| 115 | C2×C4×C5 | C23×C4 | 1 | 3 | yes | — |
| 116 | C2×C4×C5 | C23×C4 | 1 | 12 | yes | — |
| 117 | C2×Dic5 | C23×C4 | 1 | 3 | yes | — |
| 118 | C2×Dic5 | C23×C4 | 1 | 12 | yes | — |
| 119 | C4×D5 | — | 2 | 3 | no | — |
| 120 | C4×D5 | — | 2 | 12 | no | — |
| 121 | C4×D5 | — | 2 | 12 | no | — |
| 122 | C4×D5 | — | 2 | 3 | no | — |
| 123 | #125 | — | 5 | 12 | no | — |
| 124 | #125 | — | 5 | 12 | no | — |
| 125 | #125 | — | 5 | 12 | no | — |
| 126 | #125 | — | 5 | 12 | no | — |
| 127 | #125 | — | 5 | 12 | no | — |
| 128 | #125 | — | 5 | 6 | no | — |
| 129 | #125 | — | 5 | 12 | no | — |
| 130 | #125 | — | 5 | 12 | no | — |
| 131 | #125 | — | 5 | 3 | no | — |
| 132 | #125 | — | 5 | 12 | no | — |
| 133 | #125 | C2×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 134 | #125 | C2×AGL(1,𝔽5) | 1 | 12 | yes | — |
| 135 | C2×C4⋊C4 | — | 5 | 6 | no | — |
| 136 | C2×C4⋊C4 | — | 5 | 12 | no | — |
| 137 | C2×C4⋊C4 | — | 5 | 12 | no | — |
| 138 | C2×C4⋊C4 | — | 5 | 12 | no | — |
| 139 | C2×C4⋊C4 | — | 5 | 6 | no | — |
| 140 | C2×C4⋊C4 | — | 5 | 12 | no | — |
| 141 | C2×C42 | — | 5 | 1 | no | — |
| 142 | C2×C42 | — | 5 | 4 | no | — |
| 143 | C2×C42 | — | 5 | 3 | no | — |
| 144 | C2×C42 | — | 5 | 3 | no | — |
| 145 | C2×C42 | — | 5 | 12 | no | — |
| 146 | C2×C42 | — | 5 | 12 | no | — |
| 147 | #95 | — | 5 | 12 | no | — |
| 148 | #95 | — | 5 | 12 | no | — |
| 149 | #95 | — | 5 | 12 | no | — |
| 150 | #95 | — | 5 | 12 | no | — |
| 151 | #95 | — | 5 | 12 | no | — |
| 152 | C22×C5 | C24×C4 | 1 | 1 | yes | characteristic |
| 153 | C2×D5 | C2×2−1+4 | 1 | 3 | yes | — |
| 154 | C2×D5 | #585 | 1 | 3 | yes | — |
| 155 | AGL(1,𝔽5) | — | 2 | 6 | no | — |
| 156 | AGL(1,𝔽5) | — | 4 | 12 | no | — |
| 157 | AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 158 | C4×C5 | — | 2 | 3 | no | — |
| 159 | C4×C5 | — | 2 | 12 | no | — |
| 160 | Dic5 | — | 2 | 3 | no | — |
| 161 | Dic5 | — | 2 | 12 | no | — |
| 162 | C22×C4 | — | 5 | 3 | no | — |
| 163 | C22×C4 | — | 5 | 3 | no | — |
| 164 | C22×C4 | — | 5 | 12 | no | — |
| 165 | C22×C4 | — | 5 | 1 | no | — |
| 166 | C22×C4 | — | 5 | 12 | no | — |
| 167 | C4⋊C4 | — | 5 | 12 | no | — |
| 168 | C4⋊C4 | — | 5 | 12 | no | — |
| 169 | C4⋊C4 | — | 5 | 12 | no | — |
| 170 | C4⋊C4 | — | 5 | 12 | no | — |
| 171 | C4⋊C4 | — | 5 | 12 | no | — |
| 172 | C4⋊C4 | — | 5 | 6 | no | — |
| 173 | C4⋊C4 | — | 5 | 12 | no | — |
| 174 | C4⋊C4 | — | 5 | 12 | no | — |
| 175 | C4⋊C4 | — | 10 | 24 | no | — |
| 176 | C4⋊C4 | — | 20 | 12 | no | — |
| 177 | C4⋊C4 | — | 20 | 6 | no | — |
| 178 | C4⋊C4 | C22×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 179 | C4⋊C4 | C22×AGL(1,𝔽5) | 1 | 12 | yes | — |
| 180 | C4⋊C4 | C22×AGL(1,𝔽5) | 1 | 12 | yes | — |
| 181 | C42 | — | 5 | 3 | no | — |
| 182 | C42 | — | 5 | 12 | no | — |
| 183 | C42 | — | 10 | 6 | no | — |
| 184 | C42 | — | 20 | 12 | no | — |
| 185 | C42 | — | 20 | 12 | no | — |
| 186 | C42 | — | 20 | 3 | no | — |
| 187 | C42 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 188 | C42 | C22×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 189 | C2×C5 | C4×2−1+4 | 1 | 3 | yes | — |
| 190 | D5 | #3553 | 1 | 3 | yes | — |
| 191 | D5 | #3556 | 1 | 1 | yes | characteristic |
| 192 | C23 | — | 5 | 1 | no | — |
| 193 | C2×C4 | — | 5 | 6 | no | — |
| 194 | C2×C4 | — | 5 | 3 | no | — |
| 195 | C2×C4 | — | 5 | 12 | no | — |
| 196 | C2×C4 | — | 10 | 3 | no | — |
| 197 | C2×C4 | — | 10 | 12 | no | — |
| 198 | C2×C4 | — | 10 | 3 | no | — |
| 199 | C2×C4 | — | 10 | 12 | no | — |
| 200 | C2×C4 | — | 10 | 6 | no | — |
| 201 | C2×C4 | — | 10 | 3 | no | — |
| 202 | C2×C4 | — | 10 | 12 | no | — |
| 203 | C2×C4 | — | 10 | 12 | no | — |
| 204 | C2×C4 | — | 10 | 12 | no | — |
| 205 | C2×C4 | C23×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 206 | C2×C4 | C23×AGL(1,𝔽5) | 1 | 12 | yes | — |
| 207 | C5 | #34526 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 208 | C22 | — | 5 | 3 | no | — |
| 209 | C22 | — | 5 | 3 | no | — |
| 210 | C22 | C24×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 211 | C4 | — | 2 | 3 | no | — |
| 212 | C4 | — | 2 | 12 | no | — |
| 213 | C4 | — | 10 | 6 | no | — |
| 214 | C4 | — | 10 | 3 | no | — |
| 215 | C4 | — | 10 | 12 | no | — |
| 216 | C4 | — | 20 | 12 | no | — |
| 217 | C4 | — | 20 | 1 | no | — |
| 218 | C2 | — | 5 | 3 | no | — |
| 219 | C2 | — | 5 | 1 | no | — |
| 220 | C2 | AGL(1,𝔽5)×2−1+4 | 1 | 3 | yes | — |
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