Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
3666 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 3666 conjugacy classes of subgroups — too many to draw. Only its 667 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C23×D5 |
| commutator, cosocle | C23×C5 | C25 |
| Frattini | C23 | C24×D5 |
| Fitting | C2×C5×#383 | C2 |
| socle | C24×C5 | C24 |
| hypercenter | C2×#383 | D5 |
| hypocenter | C5 | C2×#2818 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C24 ◁ C2×#383 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#4020 | C2 | semidirect |
| 2. C22×#4022 | C2 | semidirect |
| 3. C2×C5×#383 | C2 | semidirect |
| 4. #10606047 | C2 | direct (N × H) |
| 5. C2×#64960 | C2 | semidirect |
| 6. C2×#64961 | C2 | semidirect |
| 14. C2×#4022 | C22 | semidirect |
| 16. C2×#4020 | C22 | semidirect |
| 17. C5×#383 | C22 | semidirect |
| 19. #64961 | C22 | semidirect |
| 20. #64960 | C22 | semidirect |
| 32. C2×C42×C5 | D4 | semidirect |
| 48. C2×#383 | D5 | semidirect |
| 70. C42×C5 | C2×D4 | semidirect |
| 86. #383 | C2×D5 | semidirect |
| 129. C2×C42 | D20 | semidirect |
| 170. C42 | C2×D20 | semidirect |
| 171. C2×C5 | #2818 | semidirect |
| 199. C5 | C2×#2818 | semidirect |
| 216. C2 | #10606047 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4020 | 2 |
| C22×#4022 | 2 |
| C2×C5×#383 | 2 |
| #10606047 | 2 |
| C2×#64960 | 2 |
| C2×#64961 | 2 |
| C2×#2818 | 5 |