Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
712 conjugacy classes of subgroups; only the 323 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 323 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C23×D5 |
| commutator, socle | C22×C5 | C22×C42 |
| Fitting | C5×#1454 | C2 |
| prime radical | C23×D5 | C42 |
| cosocle | C42×C5 | C24 |
| hypercenter | #1454 | D5 |
| hypocenter | C5 | #17339 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C42 ◁ #1454 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#1454 | C2 | semidirect |
| 3. #10601537 | C2 | semidirect |
| 4. #10598868 | C2 | semidirect |
| 5. #10598867 | C2 | semidirect |
| 6. #10598843 | C2 | semidirect |
| 7. #10598842 | C2 | semidirect |
| 19. C5×#322 | C22 | semidirect |
| 20. C5×C82 | C22 | semidirect |
| 21. #64675 | C22 | semidirect |
| 22. #64674 | C22 | semidirect |
| 23. #64674 | C22 | semidirect |
| 24. C8×#168 | C22 | semidirect |
| 55. #1454 | D5 | semidirect |
| 89. #322 | C2×D5 | semidirect |
| 91. C82 | C2×D5 | semidirect |
| 183. C5 | #17339 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611013 | 2 |
| C5×#1454 | 2 |
| #10601537 | 2 |
| #10598868 | 2 |
| #10598867 | 2 |
| #10598843 | 2 |
| #10598842 | 2 |
| #17339 | 5 |