Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
438 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 204 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C5 | C23×D9 |
| commutator, cosocle | C2×C9 | C24×C5 |
| Frattini | C2×C3 | C23×C5×D3 |
| Fitting | C5×C9×#41 | C2 |
| socle | C2×C3×C5 | C23×D3 |
| hypercenter | C5×#41 | D9 |
| hypocenter | C9 | C5×2−1+4 |
| LCS | G ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C2×C5 ◁ C5×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×C9×#41 | C2 | semidirect |
| 2. C5×Q8×D9 | C2 | semidirect |
| 3. C5×#3699 | C2 | semidirect |
| 4. C5×#3697 | C2 | semidirect |
| 5. C2×C5×Dic18 | C2 | semidirect |
| 16. #63716 | C5 | direct (N × H) |
| 28. C9×#41 | C2×C5 | semidirect |
| 29. Q8×D9 | C2×C5 | semidirect |
| 30. #3699 | C2×C5 | semidirect |
| 31. #3697 | C2×C5 | semidirect |
| 32. C2×Dic18 | C2×C5 | semidirect |
| 48. C5×#41 | D9 | semidirect |
| 70. C5×C9 | 2−1+4 | semidirect |
| 108. #41 | C5×D9 | semidirect |
| 120. C9 | C5×2−1+4 | semidirect |
| 133. C5 | #63716 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C9×#41 | 2 |
| C5×Q8×D9 | 2 |
| C5×#3699 | 2 |
| C5×#3697 | 2 |
| C2×C5×Dic18 | 2 |
| C5×#1010 | 3 |
| #63716 | 5 |