Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
492 conjugacy classes of subgroups; only the 208 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 208 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C5 | C22×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 | C2×C5×#41 |
| LCS | G ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C4×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×#3701 | C2 | semidirect |
| 3. C5×Q8×D9 | C2 | semidirect |
| 4. C5×#3699 | C2 | semidirect |
| 5. C5×D4×D9 | C2 | semidirect |
| 6. C5×#3697 | C2 | semidirect |
| 7. C2×C4×C5×D9 | C2 | semidirect |
| 10. C5×Q8×C9 | C22 | semidirect |
| 11. C5×D4×C9 | C22 | semidirect |
| 12. C2×C4×C5×C9 | C22 | semidirect |
| 13. C5×#611 | C22 | semidirect |
| 14. C2×C5×Dic9 | C22 | semidirect |
| 15. C5×D36 | C22 | semidirect |
| 18. C4×C5×D9 | C22 | semidirect |
| 19. C4×C5×D9 | C22 | semidirect |
| 20. C5×Dic18 | C22 | semidirect |
| 21. #41×D9 | C5 | direct (N × H) |
| 38. C9×#41 | C2×C5 | semidirect |
| 39. #3701 | C2×C5 | semidirect |
| 40. Q8×D9 | C2×C5 | semidirect |
| 41. #3699 | C2×C5 | semidirect |
| 42. D4×D9 | C2×C5 | semidirect |
| 43. #3697 | C2×C5 | semidirect |
| 44. C2×C4×D9 | C2×C5 | semidirect |
| 61. C5×D9 | #41 | direct (N × H) |
| 65. C5×#41 | D9 | direct (N × H) |
| 70. Q8×C9 | C22×C5 | semidirect |
| 71. D4×C9 | C22×C5 | semidirect |
| 72. C2×C4×C9 | C22×C5 | semidirect |
| 73. #611 | C22×C5 | semidirect |
| 74. C2×Dic9 | C22×C5 | semidirect |
| 75. D36 | C22×C5 | semidirect |
| 78. C4×D9 | C22×C5 | semidirect |
| 79. C4×D9 | C22×C5 | semidirect |
| 80. Dic18 | C22×C5 | semidirect |
| 96. C5×C9 | C2×#41 | semidirect |
| 99. C5×Q8 | C2×D9 | semidirect |
| 102. C5×D4 | C2×D9 | semidirect |
| 108. C2×C4×C5 | C2×D9 | semidirect |
| 145. D9 | C5×#41 | direct (N × H) |
| 149. #41 | C5×D9 | direct (N × H) |
| 166. C9 | C2×C5×#41 | semidirect |
| 169. Q8 | C2×C5×D9 | semidirect |
| 172. D4 | C2×C5×D9 | semidirect |
| 178. C2×C4 | C2×C5×D9 | semidirect |
| 183. C5 | #41×D9 | 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×#3701 | 2 |
| C5×Q8×D9 | 2 |
| C5×#3699 | 2 |
| C5×D4×D9 | 2 |
| C5×#3697 | 2 |
| C2×C4×C5×D9 | 2 |
| C5×D3×#41 | 3 |
| #41×D9 | 5 |