Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
132 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C42×C5×C9 | C2 | semidirect |
| 3. C5×#3667 | C2 | semidirect |
| 8. C5×D36 | C4 | semidirect |
| 10. C5×Dic18 | C4 | semidirect |
| 12. #63364 | C5 | direct (N × H) |
| 24. C42×C9 | C2×C5 | semidirect |
| 25. #3667 | C2×C5 | semidirect |
| 39. C42×C5 | D9 | semidirect |
| 43. D36 | C4×C5 | semidirect |
| 45. Dic18 | C4×C5 | semidirect |
| 56. C5×C9 | #104 | semidirect |
| 92. C42 | C5×D9 | semidirect |
| 103. C9 | C5×#104 | semidirect |
| 114. C5 | #63364 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3697 | 2 |
| C42×C5×C9 | 2 |
| C5×#3667 | 2 |
| C5×#805 | 3 |
| #63364 | 5 |