Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
908 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 171 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×#4086 |
| commutator, cosocle | C42×C5 | C24 |
| Frattini | C42 | C23×D5 |
| Fitting | C5×#3138 | C2 |
| socle | C22×C5 | C2×#127 |
| hypercenter | #3138 | D5 |
| hypocenter | C5 | #19747 |
| LCS | G ▷ C42×C5 ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #3138 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#3138 | C2 | semidirect |
| 2. #10615078 | C2 | semidirect |
| 3. #10614894 | C2 | semidirect |
| 4. #10610266 | C2 | semidirect |
| 5. #10601987 | C2 | semidirect |
| 6. #10601980 | C2 | semidirect |
| 7. #10601977 | C2 | semidirect |
| 8. #10601973 | C2 | semidirect |
| 9. #10600642 | C2 | semidirect |
| 20. #65377 | C22 | semidirect |
| 21. #65374 | C22 | semidirect |
| 22. #65370 | C22 | semidirect |
| 23. #65367 | C22 | semidirect |
| 33. #64984 | C22 | semidirect |
| 34. #64983 | C22 | semidirect |
| 35. #64969 | C22 | semidirect |
| 36. #64675 | C22 | semidirect |
| 37. #64674 | C22 | semidirect |
| 38. C8×#168 | C22 | semidirect |
| 84. #3138 | D5 | semidirect |
| 189. #168 | AGL(1,ℤ/8) | semidirect |
| 323. C5 | #19747 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3138 | 2 |
| #10615078 | 2 |
| #10614894 | 2 |
| #10610266 | 2 |
| #10601987 | 2 |
| #10601980 | 2 |
| #10601977 | 2 |
| #10601973 | 2 |
| #10600642 | 2 |
| #19747 | 5 |