Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
270 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 1. C5×#3796 | C2 | semidirect |
| 2. C5×C8×C3⋊D3 | C2 | semidirect |
| 3. C3×C5×#204 | C2 | semidirect |
| 4. C5×#3718 | C2 | semidirect |
| 5. C5×#3713 | C2 | semidirect |
| 14. #63809 | C5 | direct (N × H) |
| 20. C5×#204 | D3 | semidirect |
| 29. #3796 | C2×C5 | semidirect |
| 30. C8×C3⋊D3 | C2×C5 | semidirect |
| 31. C3×#204 | C2×C5 | semidirect |
| 32. #3718 | C2×C5 | semidirect |
| 33. #3713 | C2×C5 | semidirect |
| 79. #204 | C5×D3 | semidirect |
| 82. C32×C5 | #135 | semidirect |
| 130. C3×C5 | #916 | semidirect |
| 144. C32 | C5×#135 | semidirect |
| 158. C5 | #63809 | direct (N × H) |
| 165. C3 | C5×#916 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3796 | 2 |
| C5×C8×C3⋊D3 | 2 |
| C3×C5×#204 | 2 |
| C5×#3718 | 2 |
| C5×#3713 | 2 |
| C5×#916 | 3 |
| #63809 | 5 |