Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
208 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 36 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×C4⋊#157 | C2 | semidirect |
| 3. C5×#3787 | C2 | semidirect |
| 6. C32×C5×D4 | C4 | semidirect |
| 8. C5×C4⋊(C3⋊D3) | C4 | semidirect |
| 11. #63782 | C5 | direct (N × H) |
| 23. C4⋊#157 | C2×C5 | semidirect |
| 24. #3787 | C2×C5 | semidirect |
| 40. C32×D4 | C4×C5 | semidirect |
| 42. C4⋊(C3⋊D3) | C4×C5 | semidirect |
| 53. C32×C5 | #102 | semidirect |
| 57. C5×D4 | #157 | semidirect |
| 109. C32 | C5×#102 | semidirect |
| 113. D4 | C5×#157 | semidirect |
| 122. C5 | #63782 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D4×C3⋊D3 | 2 |
| C5×C4⋊#157 | 2 |
| C5×#3787 | 2 |
| #63782 | 5 |
| C5×#102 | 9 |