Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
794 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#3036 | C2 | semidirect |
| 2. #10615033 | C2 | semidirect |
| 3. #10614109 | C2 | semidirect |
| 4. #10602604 | C2 | semidirect |
| 5. #10602390 | C2 | semidirect |
| 6. #10601295 | C2 | semidirect |
| 7. #10598206 | C2 | semidirect |
| 44. C5×C4⋊Q8 | D4 | semidirect |
| 45. C5×#127 | D4 | semidirect |
| 70. C5×C4⋊C8 | D4 | semidirect |
| 78. C4⋊#168 | D4 | semidirect |
| 82. #3036 | D5 | semidirect |
| 104. C2×C5×D4 | D8 | semidirect |
| 247. C4⋊Q8 | C22⋊D5 | semidirect |
| 254. #127 | C22⋊D5 | semidirect |
| 274. C4⋊C8 | C22⋊D5 | semidirect |
| 343. C2×D4 | #686 | semidirect |
| 443. C5 | #10238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3036 | 2 |
| #10615033 | 2 |
| #10614109 | 2 |
| #10602604 | 2 |
| #10602390 | 2 |
| #10601295 | 2 |
| #10598206 | 2 |
| #10238 | 5 |