Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
2070 conjugacy classes of subgroups; only the 501 normal subgroups are shown.
This group has 2070 conjugacy classes of subgroups — too many to draw. Only its 501 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D5 |
| commutator, socle, cosocle | C23×C5 | C25 |
| Fitting | C5×#2840 | C2 |
| hypercenter | #2840 | D5 |
| hypocenter | C5 | #36675 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ #2840 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#2840 | C2 | semidirect |
| 2. #10608617 | C2 | semidirect |
| 3. #10608590 | C2 | semidirect |
| 4. #10608510 | C2 | semidirect |
| 5. #10608508 | C2 | semidirect |
| 6. #10605591 | C2 | semidirect |
| 7. #10605549 | C2 | semidirect |
| 9. C22×#713 | C22 | semidirect |
| 11. C2×Q8×Dic5 | C22 | semidirect |
| 16. #65520 | C22 | semidirect |
| 17. #65518 | C22 | semidirect |
| 24. #64963 | C22 | semidirect |
| 25. #64961 | C22 | semidirect |
| 26. #64955 | C22 | semidirect |
| 27. #64949 | C22 | semidirect |
| 28. #64937 | C22 | semidirect |
| 56. #2840 | D5 | semidirect |
| 65. C24×C5 | #41 | semidirect |
| 183. C24 | #713 | semidirect |
| 240. C5 | #36675 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2840 | 2 |
| #10608617 | 2 |
| #10608590 | 2 |
| #10608510 | 2 |
| #10608508 | 2 |
| #10605591 | 2 |
| #10605549 | 2 |
| #36675 | 5 |