Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
10894 conjugacy classes of subgroups; only the 3815 normal subgroups are shown.
This group has 10894 conjugacy classes of subgroups — too many to draw. Only its 3815 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C24×D20 |
| commutator, cosocle | C4×C5 | C26 |
| Frattini | C4 | C25×D5 |
| Fitting | C5×#3573 | C2 |
| socle | C2×C5 | C24×D4 |
| hypercenter | #3573 | D5 |
| hypocenter | C5 | #63091 |
| LCS | G ▷ C4×C5 ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C2 ◁ #585 ◁ #3573 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10619442 | C2 | semidirect |
| 2. C5×#3573 | C2 | semidirect |
| 3. #10619068 | C2 | semidirect |
| 4. #10619064 | C2 | semidirect |
| 5. C2×#66086 | C2 | semidirect |
| 9. #66283 | C22 | semidirect |
| 10. C2×#4149 | C22 | semidirect |
| 11. C5×#568 | C22 | semidirect |
| 12. C2×C5×#131 | C22 | semidirect |
| 13. #66087 | C22 | semidirect |
| 14. #66086 | C22 | semidirect |
| 15. #66086 | C22 | semidirect |
| 16. #66085 | C22 | semidirect |
| 17. #66082 | C22 | semidirect |
| 18. C2×#4054 | C22 | semidirect |
| 19. C2×#4050 | C22 | semidirect |
| 20. C22×D40 | C22 | semidirect |
| 25. #4150 | C23 | semidirect |
| 27. #4149 | C23 | semidirect |
| 33. C2×#709 | C23 | semidirect |
| 34. C22×D20 | C23 | semidirect |
| 35. C5×#131 | C23 | semidirect |
| 36. C5×#131 | C23 | semidirect |
| 37. C2×C5×M16 | C23 | semidirect |
| 38. C22×C5×C8 | C23 | semidirect |
| 39. #4055 | C23 | semidirect |
| 40. #4054 | C23 | semidirect |
| 41. C2×Dic20 | C23 | semidirect |
| 42. #4050 | C23 | semidirect |
| 43. #4050 | C23 | semidirect |
| 44. C2×D40 | C23 | semidirect |
| 45. C2×D40 | C23 | semidirect |
| 46. C2×#677 | C23 | semidirect |
| 51. #3573 | D5 | semidirect |
| 90. #568 | C2×D5 | semidirect |
| 91. C2×#131 | C2×D5 | semidirect |
| 129. #131 | C22×D5 | semidirect |
| 130. #131 | C22×D5 | semidirect |
| 131. C2×M16 | C22×D5 | semidirect |
| 132. C22×C8 | C22×D5 | semidirect |
| 184. C5 | #63091 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10619442 | 2 |
| C5×#3573 | 2 |
| #10619068 | 2 |
| #10619064 | 2 |
| C2×#66086 | 2 |
| #63091 | 5 |