Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
876 conjugacy classes of subgroups; only the 510 normal subgroups are shown.
This group has 876 conjugacy classes of subgroups — too many to draw. Only its 510 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C32 | C23×D5 |
| commutator, cosocle | C2×C5 | C24×C32 |
| Frattini | C2 | C23×C32×D5 |
| Fitting | C32×C5×#41 | C2 |
| socle | C2×C32×C5 | C24 |
| hypercenter | C32×#41 | D5 |
| hypocenter | C5 | C32×2−1+4 |
| LCS | G ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C2×C32 ◁ C32×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×C5×#41 | C2 | semidirect |
| 2. C32×Q8×D5 | C2 | semidirect |
| 3. C32×#711 | C2 | semidirect |
| 4. C32×#709 | C2 | semidirect |
| 5. C2×C32×Dic10 | C2 | semidirect |
| 6. C3×#4150 | C3 | direct (N × H) |
| 17. C3×C5×#41 | C2×C3 | semidirect |
| 18. C3×Q8×D5 | C2×C3 | semidirect |
| 19. C3×#711 | C2×C3 | semidirect |
| 20. C3×#709 | C2×C3 | semidirect |
| 21. C2×C3×Dic10 | C2×C3 | semidirect |
| 27. #4150 | C32 | direct (N × H) |
| 30. C32×#41 | D5 | semidirect |
| 46. C5×#41 | C2×C32 | semidirect |
| 47. Q8×D5 | C2×C32 | semidirect |
| 48. #711 | C2×C32 | semidirect |
| 49. #709 | C2×C32 | semidirect |
| 50. C2×Dic10 | C2×C32 | semidirect |
| 67. C3×#41 | C3×D5 | semidirect |
| 70. C32×C5 | 2−1+4 | semidirect |
| 108. #41 | C32×D5 | semidirect |
| 111. C3×C5 | C3×2−1+4 | semidirect |
| 120. C32 | #4150 | direct (N × H) |
| 133. C5 | C32×2−1+4 | semidirect |
| 139. C3 | C3×#4150 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C5×#41 | 2 |
| C32×Q8×D5 | 2 |
| C32×#711 | 2 |
| C32×#709 | 2 |
| C2×C32×Dic10 | 2 |
| C3×#4150 | 3 |
| C32×2−1+4 | 5 |