Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
200 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 32 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. C5×#3792 | C2 | semidirect |
| 8. #63788 | C5 | direct (N × H) |
| 18. #3792 | C2×C5 | semidirect |
| 41. C32×C5 | #100 | semidirect |
| 85. C32 | C5×#100 | semidirect |
| 95. C5 | #63788 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#638 | 2 |
| C5×#3792 | 2 |
| #63788 | 5 |
| C5×#100 | 9 |