Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
126 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 9. C5×Dic18 | C4 | semidirect |
| 11. #63376 | C5 | direct (N × H) |
| 41. Dic18 | C4×C5 | semidirect |
| 51. C5×C9 | #103 | semidirect |
| 93. C9 | C5×#103 | semidirect |
| 103. C5 | #63376 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Dic18 | 2 |
| C2×C5×C8×C9 | 2 |
| C5×C4⋊Dic9 | 2 |
| C5×#816 | 3 |
| #63376 | 5 |