Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
412 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10615018 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10604155 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #10598757 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10598750 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C5×#532 | C4 | 1 | 1 | yes | characteristic |
| 6 | C2×#4095 | — | 2 | 2 | no | — |
| 7 | C2×#4020 | C4 | 1 | 1 | yes | characteristic |
| 8 | #65374 | C4 | 1 | 1 | yes | characteristic |
| 9 | #65374 | C22 | 1 | 1 | yes | characteristic |
| 10 | #65362 | C4 | 1 | 1 | yes | characteristic |
| 11 | #65362 | C22 | 1 | 1 | yes | characteristic |
| 12 | #65347 | — | 2 | 2 | no | — |
| 13 | C4×#681 | C22 | 1 | 1 | yes | characteristic |
| 14 | #64912 | — | 2 | 2 | no | — |
| 15 | #64861 | C22 | 1 | 4 | yes | complemented |
| 16 | #64860 | — | 2 | 2 | no | — |
| 17 | #11992 | — | 5 | 1 | no | maximal, Sylow |
| 18 | C2×C5×#41 | — | 2 | 1 | no | — |
| 19 | C22×D20 | — | 2 | 1 | no | — |
| 20 | C22×D20 | — | 4 | 1 | no | — |
| 21 | C5×C4⋊Q8 | C2×C4 | 1 | 1 | yes | characteristic |
| 22 | C5×#127 | C2×C4 | 1 | 1 | yes | characteristic |
| 23 | C5×#124 | — | 2 | 1 | no | — |
| 24 | C5×#121 | — | 4 | 1 | no | — |
| 25 | C4×C5×D4 | — | 4 | 1 | no | — |
| 26 | C2×C42×C5 | C2×C4 | 1 | 1 | yes | characteristic |
| 27 | #4095 | — | 4 | 8 | no | — |
| 28 | C2×#688 | — | 2 | 2 | no | — |
| 29 | C2×#688 | — | 2 | 2 | no | — |
| 30 | C2×#686 | — | 2 | 2 | no | — |
| 31 | C2×#686 | — | 2 | 2 | no | — |
| 32 | C2×#681 | D4 | 1 | 2 | yes | — |
| 33 | #4020 | — | 2 | 1 | no | — |
| 34 | #4020 | — | 4 | 1 | no | — |
| 35 | #4020 | C2×C4 | 1 | 1 | yes | characteristic |
| 36 | #4020 | C2×C4 | 1 | 1 | yes | characteristic |
| 37 | #3998 | — | 2 | 4 | no | — |
| 38 | #3935 | D4 | 1 | 2 | yes | — |
| 39 | C4×#168 | C2×C4 | 1 | 1 | yes | characteristic |
| 40 | C4×#168 | C23 | 1 | 1 | yes | characteristic |
| 41 | #3151 | — | 5 | 1 | no | — |
| 42 | #2165 | — | 5 | 2 | no | — |
| 43 | #1359 | — | 5 | 2 | no | — |
| 44 | #1357 | — | 5 | 2 | no | — |
| 45 | C23×D5 | — | 4 | 1 | no | — |
| 46 | C5×#41 | — | 4 | 4 | no | — |
| 47 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 48 | C2×C5×D4 | — | 2 | 1 | no | — |
| 49 | C2×C5×D4 | — | 4 | 1 | no | — |
| 50 | C2×C5×D4 | — | 4 | 1 | no | — |
| 51 | C22×C4×C5 | — | 2 | 1 | no | — |
| 52 | C22×C4×C5 | — | 4 | 1 | no | — |
| 53 | C22×C4×C5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 54 | C2×D20 | — | 2 | 1 | no | — |
| 55 | C2×D20 | — | 2 | 1 | no | — |
| 56 | C2×D20 | — | 4 | 4 | no | — |
| 57 | C2×D20 | — | 4 | 1 | no | — |
| 58 | C2×D20 | — | 4 | 1 | no | — |
| 59 | C2×D20 | — | 4 | 2 | no | — |
| 60 | C2×D20 | — | 4 | 1 | no | — |
| 61 | C2×D20 | — | 8 | 4 | no | — |
| 62 | C5×C4⋊C4 | — | 4 | 1 | no | — |
| 63 | C5×C22⋊C4 | — | 4 | 2 | no | — |
| 64 | C42×C5 | — | 2 | 1 | no | — |
| 65 | C42×C5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 66 | C42×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 67 | #688 | — | 4 | 4 | no | — |
| 68 | #688 | — | 4 | 4 | no | — |
| 69 | #686 | — | 4 | 4 | no | — |
| 70 | #686 | — | 4 | 4 | no | — |
| 71 | #681 | — | 2 | 4 | no | — |
| 72 | C2×#168 | C22⋊C4 | 1 | 2 | yes | — |
| 73 | C2×#168 | C2×D4 | 1 | 2 | yes | — |
| 74 | #674 | — | 4 | 4 | no | — |
| 75 | C2×AGL(1,ℤ/8) | — | 10 | 2 | no | — |
| 76 | #532 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 77 | C2×#127 | — | 5 | 1 | no | — |
| 78 | #496 | — | 10 | 2 | no | — |
| 79 | #493 | — | 5 | 1 | no | — |
| 80 | #493 | — | 5 | 1 | no | — |
| 81 | #492 | — | 5 | 1 | no | — |
| 82 | #492 | — | 5 | 1 | no | — |
| 83 | C4×M16 | — | 5 | 1 | no | — |
| 84 | #364 | — | 5 | 4 | no | — |
| 85 | #349 | — | 10 | 2 | no | — |
| 86 | #347 | — | 10 | 2 | no | — |
| 87 | C23×C5 | — | 4 | 1 | no | — |
| 88 | C23×C5 | #100 | 1 | 1 | yes | characteristic |
| 89 | C22×D5 | — | 4 | 1 | no | — |
| 90 | C22×D5 | — | 4 | 1 | no | — |
| 91 | C22×D5 | — | 8 | 2 | no | — |
| 92 | C22×D5 | — | 8 | 4 | no | — |
| 93 | C5×Q8 | — | 4 | 2 | no | — |
| 94 | C5×D4 | — | 4 | 2 | no | — |
| 95 | C5×D4 | — | 8 | 2 | no | — |
| 96 | C5×D4 | — | 8 | 2 | no | — |
| 97 | C2×C4×C5 | — | 2 | 1 | no | — |
| 98 | C2×C4×C5 | — | 2 | 2 | no | — |
| 99 | C2×C4×C5 | — | 2 | 1 | no | — |
| 100 | C2×C4×C5 | — | 4 | 2 | no | — |
| 101 | C2×C4×C5 | — | 4 | 1 | no | — |
| 102 | C2×C4×C5 | — | 8 | 2 | no | — |
| 103 | C2×C4×C5 | #100 | 1 | 1 | yes | characteristic |
| 104 | C2×C4×C5 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 105 | D20 | — | 4 | 2 | no | — |
| 106 | D20 | — | 4 | 2 | no | — |
| 107 | D20 | — | 8 | 2 | no | — |
| 108 | D20 | — | 8 | 2 | no | — |
| 109 | D20 | — | 8 | 2 | no | — |
| 110 | D20 | — | 8 | 4 | no | — |
| 111 | #168 | — | 2 | 2 | no | — |
| 112 | #168 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 113 | C2×#41 | — | 2 | 1 | no | — |
| 114 | C22×D4 | — | 10 | 1 | no | — |
| 115 | C22×D4 | — | 20 | 1 | no | — |
| 116 | AGL(1,ℤ/8) | — | 20 | 8 | no | — |
| 117 | C2×SD16 | — | 10 | 2 | no | — |
| 118 | C2×SD16 | — | 10 | 2 | no | — |
| 119 | C2×D8 | — | 10 | 2 | no | — |
| 120 | C2×D8 | — | 10 | 2 | no | — |
| 121 | C2×M16 | — | 5 | 2 | no | — |
| 122 | C4⋊Q8 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 123 | #127 | — | 5 | 1 | no | — |
| 124 | #127 | — | 5 | 1 | no | — |
| 125 | #127 | — | 10 | 1 | no | — |
| 126 | #127 | — | 20 | 1 | no | — |
| 127 | #127 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 128 | #124 | — | 2 | 1 | no | — |
| 129 | #121 | — | 4 | 1 | no | — |
| 130 | C4×D4 | — | 4 | 1 | no | — |
| 131 | C2×C42 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 132 | M32 | — | 10 | 4 | no | — |
| 133 | #97 | — | 5 | 2 | no | — |
| 134 | C4×C8 | — | 5 | 1 | no | — |
| 135 | C4×C8 | — | 5 | 1 | no | — |
| 136 | C22×C5 | — | 2 | 1 | no | — |
| 137 | C22×C5 | — | 4 | 1 | no | — |
| 138 | C22×C5 | — | 8 | 2 | no | — |
| 139 | C22×C5 | — | 8 | 1 | no | — |
| 140 | C22×C5 | C2×#100 | 1 | 1 | yes | characteristic |
| 141 | C2×D5 | — | 8 | 2 | no | — |
| 142 | C2×D5 | — | 8 | 2 | no | — |
| 143 | C2×D5 | — | 8 | 1 | no | — |
| 144 | C2×D5 | — | 8 | 1 | no | — |
| 145 | C2×D5 | — | 16 | 4 | no | — |
| 146 | C4×C5 | — | 2 | 2 | no | — |
| 147 | C4×C5 | — | 2 | 1 | no | — |
| 148 | C4×C5 | — | 4 | 1 | no | — |
| 149 | C4×C5 | — | 8 | 1 | no | — |
| 150 | C4×C5 | #418 | 1 | 2 | yes | — |
| 151 | C24 | — | 20 | 1 | no | — |
| 152 | #41 | — | 4 | 4 | no | — |
| 153 | C2×Q8 | — | 2 | 1 | no | — |
| 154 | C2×D4 | — | 2 | 1 | no | — |
| 155 | C2×D4 | — | 4 | 1 | no | — |
| 156 | C2×D4 | — | 4 | 1 | no | — |
| 157 | C2×D4 | — | 10 | 1 | no | — |
| 158 | C2×D4 | — | 10 | 1 | no | — |
| 159 | C2×D4 | — | 20 | 4 | no | — |
| 160 | C2×D4 | — | 20 | 1 | no | — |
| 161 | C2×D4 | — | 20 | 1 | no | — |
| 162 | C2×D4 | — | 20 | 2 | no | — |
| 163 | C2×D4 | — | 20 | 1 | no | — |
| 164 | C2×D4 | — | 40 | 4 | no | — |
| 165 | C22×C4 | — | 2 | 1 | no | — |
| 166 | C22×C4 | — | 4 | 1 | no | — |
| 167 | C22×C4 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 168 | SD16 | — | 20 | 4 | no | — |
| 169 | SD16 | — | 20 | 4 | no | — |
| 170 | D8 | — | 20 | 4 | no | — |
| 171 | D8 | — | 20 | 4 | no | — |
| 172 | M16 | — | 10 | 4 | no | — |
| 173 | C2×C8 | — | 5 | 2 | no | — |
| 174 | C2×C8 | — | 5 | 2 | no | — |
| 175 | C4⋊C4 | — | 4 | 1 | no | — |
| 176 | C22⋊C4 | — | 4 | 2 | no | — |
| 177 | C42 | — | 2 | 1 | no | — |
| 178 | C42 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 179 | C42 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 180 | C16 | — | 20 | 4 | no | — |
| 181 | C2×C5 | — | 2 | 1 | no | — |
| 182 | C2×C5 | — | 4 | 1 | no | — |
| 183 | C2×C5 | — | 16 | 1 | no | — |
| 184 | C2×C5 | #1555 | 1 | 1 | yes | characteristic |
| 185 | D5 | — | 16 | 1 | no | — |
| 186 | D5 | — | 16 | 1 | no | — |
| 187 | C23 | — | 4 | 1 | no | — |
| 188 | C23 | — | 20 | 1 | no | — |
| 189 | C23 | — | 20 | 1 | no | — |
| 190 | C23 | — | 40 | 2 | no | — |
| 191 | C23 | — | 40 | 4 | no | — |
| 192 | C23 | #4013 | 1 | 1 | yes | characteristic |
| 193 | Q8 | — | 4 | 2 | no | — |
| 194 | D4 | — | 4 | 2 | no | — |
| 195 | D4 | — | 8 | 2 | no | — |
| 196 | D4 | — | 8 | 2 | no | — |
| 197 | D4 | — | 20 | 2 | no | — |
| 198 | D4 | — | 20 | 2 | no | — |
| 199 | D4 | — | 40 | 2 | no | — |
| 200 | D4 | — | 40 | 2 | no | — |
| 201 | D4 | — | 40 | 2 | no | — |
| 202 | D4 | — | 40 | 4 | no | — |
| 203 | C2×C4 | — | 2 | 1 | no | — |
| 204 | C2×C4 | — | 2 | 2 | no | — |
| 205 | C2×C4 | — | 2 | 1 | no | — |
| 206 | C2×C4 | — | 4 | 2 | no | — |
| 207 | C2×C4 | — | 4 | 1 | no | — |
| 208 | C2×C4 | — | 8 | 2 | no | — |
| 209 | C2×C4 | #4013 | 1 | 1 | yes | characteristic |
| 210 | C2×C4 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 211 | C8 | — | 5 | 4 | no | — |
| 212 | C8 | — | 10 | 2 | no | — |
| 213 | C5 | #11992 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 214 | C22 | — | 2 | 1 | no | — |
| 215 | C22 | — | 4 | 1 | no | — |
| 216 | C22 | — | 8 | 2 | no | — |
| 217 | C22 | — | 8 | 1 | no | — |
| 218 | C22 | — | 40 | 2 | no | — |
| 219 | C22 | — | 40 | 2 | no | — |
| 220 | C22 | — | 40 | 1 | no | — |
| 221 | C22 | — | 40 | 1 | no | — |
| 222 | C22 | — | 80 | 4 | no | — |
| 223 | C22 | C2×#4013 | 1 | 1 | yes | characteristic |
| 224 | C4 | — | 2 | 2 | no | — |
| 225 | C4 | — | 2 | 1 | no | — |
| 226 | C4 | — | 4 | 1 | no | — |
| 227 | C4 | — | 8 | 1 | no | — |
| 228 | C4 | #65767 | 1 | 2 | yes | — |
| 229 | C2 | — | 2 | 1 | no | — |
| 230 | C2 | — | 4 | 1 | no | — |
| 231 | C2 | — | 16 | 1 | no | — |
| 232 | C2 | — | 80 | 1 | no | — |
| 233 | C2 | — | 80 | 1 | no | — |
| 234 | C2 | #10604927 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10604155 | C2 | semidirect |
| 3. #10598757 | C2 | semidirect |
| 4. #10598750 | C2 | semidirect |
| 15. #64861 | C22 | semidirect |
| 213. C5 | #11992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615018 | 2 |
| #10604155 | 2 |
| #10598757 | 2 |
| #10598750 | 2 |
| #11992 | 5 |