← #13046020
Subgroups — #13046020
Order 1280.
10930 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 | C2×D5×2−1+4 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | AGL(1,𝔽5)×2−1+4 | C2 | 1 | 32 | yes | maximal, complemented |
| 3 | #10619412 | C2 | 1 | 20 | yes | maximal, complemented |
| 4 | C2×#66262 | C2 | 1 | 10 | yes | maximal, complemented |
| 5 | C2×C5×2−1+4 | C4 | 1 | 1 | yes | characteristic, complemented |
| 6 | D5×2−1+4 | C4 | 1 | 16 | yes | complemented |
| 7 | D5×2−1+4 | C22 | 1 | 16 | yes | — |
| 8 | C2×#4150 | C4 | 1 | 10 | yes | complemented |
| 9 | C2×D5×#41 | C22 | 1 | 10 | yes | — |
| 10 | C2×#4147 | C4 | 1 | 5 | yes | complemented |
| 11 | C22×Q8×D5 | C22 | 1 | 5 | yes | — |
| 12 | #66266 | C22 | 1 | 160 | yes | complemented |
| 13 | #41×AGL(1,𝔽5) | C22 | 1 | 160 | yes | complemented |
| 14 | #66262 | C22 | 1 | 40 | yes | — |
| 15 | #66262 | C22 | 1 | 80 | yes | complemented |
| 16 | C2×Q8×AGL(1,𝔽5) | C22 | 1 | 80 | yes | complemented |
| 17 | #66258 | C22 | 1 | 40 | yes | — |
| 18 | C2×#4130 | C22 | 1 | 60 | yes | — |
| 19 | #62653 | — | 5 | 1 | no | maximal, Sylow |
| 20 | C5×2−1+4 | C2×C4 | 1 | 16 | yes | complemented |
| 21 | C2×C5×#41 | C2×C4 | 1 | 10 | yes | complemented |
| 22 | C22×C5×Q8 | C2×C4 | 1 | 5 | yes | complemented |
| 23 | #4150 | C2×C4 | 1 | 160 | yes | complemented |
| 24 | D5×#41 | C2×C4 | 1 | 80 | yes | complemented |
| 25 | D5×#41 | C23 | 1 | 80 | yes | — |
| 26 | #4147 | C2×C4 | 1 | 80 | yes | complemented |
| 27 | C2×#713 | C2×C4 | 1 | 10 | yes | complemented |
| 28 | C2×Q8×D5 | C2×C4 | 1 | 20 | yes | complemented |
| 29 | C2×Q8×D5 | C2×C4 | 1 | 40 | yes | complemented |
| 30 | C2×Q8×D5 | C23 | 1 | 40 | yes | — |
| 31 | C2×Q8×D5 | C23 | 1 | 10 | yes | — |
| 32 | C2×#711 | C2×C4 | 1 | 30 | yes | complemented |
| 33 | C2×D4×D5 | C23 | 1 | 10 | yes | — |
| 34 | C2×#709 | C2×C4 | 1 | 30 | yes | complemented |
| 35 | C22×C4×D5 | C23 | 1 | 15 | yes | — |
| 36 | C22×Dic10 | C2×C4 | 1 | 15 | yes | complemented |
| 37 | C2×C22⋊AGL(1,𝔽5) | C23 | 1 | 40 | yes | — |
| 38 | Q8×AGL(1,𝔽5) | C23 | 1 | 320 | yes | — |
| 39 | D4×AGL(1,𝔽5) | C23 | 1 | 320 | yes | — |
| 40 | #4130 | C23 | 1 | 80 | yes | — |
| 41 | #4130 | C23 | 1 | 240 | yes | — |
| 42 | C2×C4⋊AGL(1,𝔽5) | C23 | 1 | 120 | yes | — |
| 43 | C2×C4×AGL(1,𝔽5) | C23 | 1 | 120 | yes | — |
| 44 | C22×2−1+4 | — | 5 | 1 | no | — |
| 45 | C4×2−1+4 | — | 5 | 32 | no | — |
| 46 | #3428 | — | 5 | 20 | no | — |
| 47 | C2×#519 | — | 5 | 10 | no | — |
| 48 | C23×D5 | C24 | 1 | 5 | yes | — |
| 49 | C22×AGL(1,𝔽5) | C24 | 1 | 80 | yes | — |
| 50 | C5×#41 | C22×C4 | 1 | 80 | yes | — |
| 51 | C2×C5×Q8 | C22×C4 | 1 | 10 | yes | — |
| 52 | C2×C5×Q8 | C22×C4 | 1 | 40 | yes | — |
| 53 | C2×C5×D4 | C22×C4 | 1 | 10 | yes | — |
| 54 | C22×C4×C5 | C22×C4 | 1 | 15 | yes | — |
| 55 | C2×C22⋊D5 | C22×C4 | 1 | 20 | yes | — |
| 56 | C22×Dic5 | C22×C4 | 1 | 15 | yes | — |
| 57 | #713 | C22×C4 | 1 | 80 | yes | — |
| 58 | Q8×D5 | C22×C4 | 1 | 40 | yes | — |
| 59 | Q8×D5 | C22×C4 | 1 | 160 | yes | — |
| 60 | Q8×D5 | C24 | 1 | 40 | yes | — |
| 61 | #711 | C22×C4 | 1 | 240 | yes | — |
| 62 | D4×D5 | C22×C4 | 1 | 40 | yes | — |
| 63 | D4×D5 | C24 | 1 | 40 | yes | — |
| 64 | #709 | C22×C4 | 1 | 240 | yes | — |
| 65 | C2×D20 | C22×C4 | 1 | 10 | yes | — |
| 66 | C2×C4×D5 | C22×C4 | 1 | 30 | yes | — |
| 67 | C2×C4×D5 | C22×C4 | 1 | 60 | yes | — |
| 68 | C2×C4×D5 | C24 | 1 | 60 | yes | — |
| 69 | C2×C4×D5 | C24 | 1 | 10 | yes | — |
| 70 | C2×Dic10 | C22×C4 | 1 | 30 | yes | — |
| 71 | C2×Dic10 | C22×C4 | 1 | 120 | yes | — |
| 72 | C22⋊AGL(1,𝔽5) | C24 | 1 | 16 | yes | — |
| 73 | C22⋊AGL(1,𝔽5) | C24 | 1 | 80 | yes | — |
| 74 | C4⋊AGL(1,𝔽5) | C24 | 1 | 160 | yes | — |
| 75 | C4×AGL(1,𝔽5) | C24 | 1 | 160 | yes | — |
| 76 | C2×2−1+4 | — | 5 | 16 | no | — |
| 77 | C2×2−1+4 | — | 5 | 16 | no | — |
| 78 | C2×2−1+4 | — | 5 | 10 | no | — |
| 79 | C2×2−1+4 | — | 5 | 5 | no | — |
| 80 | C2×2−1+4 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 81 | C22×#41 | — | 5 | 10 | no | — |
| 82 | C23×Q8 | — | 5 | 5 | no | — |
| 83 | #520 | — | 5 | 160 | no | — |
| 84 | #519 | — | 5 | 40 | no | — |
| 85 | #519 | — | 5 | 80 | no | — |
| 86 | #518 | — | 5 | 40 | no | — |
| 87 | C4×#41 | — | 5 | 160 | no | — |
| 88 | C2×C4×Q8 | — | 5 | 80 | no | — |
| 89 | C2×#117 | — | 5 | 60 | no | — |
| 90 | C23×C5 | C23×C4 | 1 | 5 | yes | — |
| 91 | C22×D5 | — | 4 | 10 | no | — |
| 92 | C22×D5 | C23×C4 | 1 | 5 | yes | — |
| 93 | C22×D5 | C23×C4 | 1 | 10 | yes | — |
| 94 | C22×D5 | C25 | 1 | 1 | yes | characteristic |
| 95 | C22×D5 | C25 | 1 | 10 | yes | — |
| 96 | C2×AGL(1,𝔽5) | — | 4 | 80 | no | — |
| 97 | C2×AGL(1,𝔽5) | C25 | 1 | 32 | yes | — |
| 98 | C5×Q8 | C23×C4 | 1 | 40 | yes | — |
| 99 | C5×D4 | C23×C4 | 1 | 40 | yes | — |
| 100 | C2×C4×C5 | C23×C4 | 1 | 10 | yes | — |
| 101 | C2×C4×C5 | C23×C4 | 1 | 60 | yes | — |
| 102 | C22⋊D5 | C23×C4 | 1 | 80 | yes | — |
| 103 | C2×Dic5 | C23×C4 | 1 | 10 | yes | — |
| 104 | C2×Dic5 | C23×C4 | 1 | 60 | yes | — |
| 105 | D20 | C23×C4 | 1 | 40 | yes | — |
| 106 | C4×D5 | C23×C4 | 1 | 20 | yes | — |
| 107 | C4×D5 | C23×C4 | 1 | 120 | yes | — |
| 108 | C4×D5 | C25 | 1 | 20 | yes | — |
| 109 | Dic10 | C23×C4 | 1 | 120 | yes | — |
| 110 | 2−1+4 | — | 5 | 160 | no | — |
| 111 | 2−1+4 | — | 5 | 80 | no | — |
| 112 | 2−1+4 | C2×AGL(1,𝔽5) | 1 | 16 | yes | complemented |
| 113 | C2×#41 | — | 5 | 80 | no | — |
| 114 | C2×#41 | — | 5 | 80 | no | — |
| 115 | C2×#41 | — | 5 | 10 | no | — |
| 116 | C2×#41 | — | 5 | 30 | no | — |
| 117 | C2×#41 | — | 5 | 30 | no | — |
| 118 | C2×#41 | C2×AGL(1,𝔽5) | 1 | 10 | yes | complemented |
| 119 | C22×Q8 | — | 5 | 40 | no | — |
| 120 | C22×Q8 | — | 5 | 10 | no | — |
| 121 | C22×Q8 | — | 5 | 40 | no | — |
| 122 | C22×Q8 | — | 5 | 20 | no | — |
| 123 | C22×Q8 | — | 5 | 15 | no | — |
| 124 | C22×Q8 | C2×AGL(1,𝔽5) | 1 | 5 | yes | complemented |
| 125 | C22×D4 | — | 5 | 10 | no | — |
| 126 | C23×C4 | — | 5 | 15 | no | — |
| 127 | C4×Q8 | — | 5 | 320 | no | — |
| 128 | C4×D4 | — | 5 | 320 | no | — |
| 129 | #117 | — | 5 | 80 | no | — |
| 130 | #117 | — | 5 | 240 | no | — |
| 131 | C2×C4⋊C4 | — | 5 | 120 | no | — |
| 132 | C2×C22⋊C4 | — | 5 | 40 | no | — |
| 133 | C2×C42 | — | 5 | 120 | no | — |
| 134 | C22×C5 | — | 4 | 5 | no | — |
| 135 | C22×C5 | C24×C4 | 1 | 1 | yes | characteristic |
| 136 | C22×C5 | C24×C4 | 1 | 10 | yes | — |
| 137 | C2×D5 | — | 2 | 20 | no | — |
| 138 | C2×D5 | — | 2 | 2 | no | — |
| 139 | C2×D5 | — | 4 | 10 | no | — |
| 140 | C2×D5 | — | 4 | 5 | no | — |
| 141 | C2×D5 | C24×C4 | 1 | 1 | yes | characteristic |
| 142 | C2×D5 | C24×C4 | 1 | 10 | yes | — |
| 143 | C2×D5 | C26 | 1 | 1 | yes | characteristic |
| 144 | AGL(1,𝔽5) | — | 2 | 32 | no | — |
| 145 | C4×C5 | C24×C4 | 1 | 20 | yes | — |
| 146 | Dic5 | C24×C4 | 1 | 20 | yes | — |
| 147 | C24 | — | 5 | 5 | no | — |
| 148 | #41 | — | 5 | 80 | no | — |
| 149 | #41 | — | 5 | 240 | no | — |
| 150 | #41 | — | 5 | 240 | no | — |
| 151 | #41 | C22×AGL(1,𝔽5) | 1 | 80 | yes | — |
| 152 | C2×Q8 | — | 5 | 40 | no | — |
| 153 | C2×Q8 | — | 5 | 40 | no | — |
| 154 | C2×Q8 | — | 5 | 160 | no | — |
| 155 | C2×Q8 | — | 5 | 30 | no | — |
| 156 | C2×Q8 | — | 5 | 120 | no | — |
| 157 | C2×Q8 | C22×AGL(1,𝔽5) | 1 | 10 | yes | — |
| 158 | C2×Q8 | C22×AGL(1,𝔽5) | 1 | 40 | yes | — |
| 159 | C2×D4 | — | 5 | 20 | no | — |
| 160 | C2×D4 | — | 5 | 40 | no | — |
| 161 | C2×D4 | — | 5 | 40 | no | — |
| 162 | C2×D4 | — | 5 | 10 | no | — |
| 163 | C2×D4 | C22×AGL(1,𝔽5) | 1 | 10 | yes | — |
| 164 | C22×C4 | — | 5 | 15 | no | — |
| 165 | C22×C4 | — | 5 | 60 | no | — |
| 166 | C22×C4 | — | 5 | 10 | no | — |
| 167 | C22×C4 | — | 5 | 30 | no | — |
| 168 | C22×C4 | — | 5 | 60 | no | — |
| 169 | C22×C4 | — | 5 | 80 | no | — |
| 170 | C22×C4 | C22×AGL(1,𝔽5) | 1 | 15 | yes | — |
| 171 | C4⋊C4 | — | 5 | 160 | no | — |
| 172 | C22⋊C4 | — | 5 | 16 | no | — |
| 173 | C22⋊C4 | — | 5 | 80 | no | — |
| 174 | C42 | — | 5 | 160 | no | — |
| 175 | C2×C5 | — | 2 | 1 | no | — |
| 176 | C2×C5 | — | 2 | 10 | no | — |
| 177 | C2×C5 | C25×C4 | 1 | 1 | yes | characteristic |
| 178 | D5 | — | 2 | 1 | no | — |
| 179 | D5 | — | 2 | 10 | no | — |
| 180 | D5 | 2−1+6 | 1 | 2 | yes | — |
| 181 | C23 | — | 5 | 1 | no | — |
| 182 | C23 | — | 5 | 10 | no | — |
| 183 | C23 | — | 5 | 10 | no | — |
| 184 | C23 | — | 5 | 5 | no | — |
| 185 | C23 | — | 20 | 10 | no | — |
| 186 | C23 | C23×AGL(1,𝔽5) | 1 | 5 | yes | — |
| 187 | Q8 | — | 5 | 120 | no | — |
| 188 | Q8 | C23×AGL(1,𝔽5) | 1 | 40 | yes | — |
| 189 | D4 | — | 5 | 80 | no | — |
| 190 | D4 | — | 5 | 40 | no | — |
| 191 | D4 | C23×AGL(1,𝔽5) | 1 | 40 | yes | — |
| 192 | C2×C4 | — | 5 | 10 | no | — |
| 193 | C2×C4 | — | 5 | 60 | no | — |
| 194 | C2×C4 | — | 5 | 20 | no | — |
| 195 | C2×C4 | — | 5 | 20 | no | — |
| 196 | C2×C4 | — | 5 | 120 | no | — |
| 197 | C2×C4 | — | 5 | 32 | no | — |
| 198 | C2×C4 | — | 20 | 80 | no | — |
| 199 | C2×C4 | C23×AGL(1,𝔽5) | 1 | 10 | yes | — |
| 200 | C2×C4 | C23×AGL(1,𝔽5) | 1 | 60 | yes | — |
| 201 | C5 | #62653 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 202 | C22 | — | 4 | 5 | no | — |
| 203 | C22 | — | 5 | 1 | no | — |
| 204 | C22 | — | 5 | 1 | no | — |
| 205 | C22 | — | 5 | 10 | no | — |
| 206 | C22 | — | 10 | 20 | no | — |
| 207 | C22 | — | 10 | 2 | no | — |
| 208 | C22 | — | 20 | 5 | no | — |
| 209 | C22 | — | 20 | 10 | no | — |
| 210 | C22 | C24×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 211 | C22 | C24×AGL(1,𝔽5) | 1 | 10 | yes | — |
| 212 | C4 | — | 5 | 20 | no | — |
| 213 | C4 | — | 10 | 32 | no | — |
| 214 | C4 | C24×AGL(1,𝔽5) | 1 | 20 | yes | — |
| 215 | C2 | — | 2 | 1 | no | — |
| 216 | C2 | — | 2 | 10 | no | — |
| 217 | C2 | — | 5 | 2 | no | — |
| 218 | C2 | — | 10 | 1 | no | — |
| 219 | C2 | — | 10 | 10 | no | — |
| 220 | C2 | C25×AGL(1,𝔽5) | 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