Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
372 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 110 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×#3832 | C2 | semidirect |
| 2. C32×C5×Q16 | C2 | semidirect |
| 3. C5×#3755 | C2 | semidirect |
| 4. C5×#3745 | C2 | semidirect |
| 5. C5×C8×C3⋊D3 | C2 | semidirect |
| 14. #64128 | C5 | direct (N × H) |
| 16. C3×C5×Q16 | D3 | semidirect |
| 26. #3832 | C2×C5 | semidirect |
| 27. C32×Q16 | C2×C5 | semidirect |
| 28. #3755 | C2×C5 | semidirect |
| 29. #3745 | C2×C5 | semidirect |
| 30. C8×C3⋊D3 | C2×C5 | semidirect |
| 43. C5×Q16 | C3⋊D3 | semidirect |
| 60. C3×Q16 | C5×D3 | semidirect |
| 64. C32×C5 | #135 | semidirect |
| 97. Q16 | C5×C3⋊D3 | semidirect |
| 101. C3×C5 | #919 | semidirect |
| 110. C32 | C5×#135 | semidirect |
| 121. C5 | #64128 | direct (N × H) |
| 127. C3 | C5×#919 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3832 | 2 |
| C32×C5×Q16 | 2 |
| C5×#3755 | 2 |
| C5×#3745 | 2 |
| C5×C8×C3⋊D3 | 2 |
| C5×#919 | 3 |
| #64128 | 5 |