Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
168 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 168 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. C4×C5×#157 | C2 | semidirect |
| 3. C5×#3788 | C2 | semidirect |
| 5. C32×C5×Q8 | C4 | semidirect |
| 7. C5×C4⋊(C3⋊D3) | C4 | semidirect |
| 11. #63785 | C5 | direct (N × H) |
| 21. C4×#157 | C2×C5 | semidirect |
| 22. #3788 | C2×C5 | semidirect |
| 35. C32×Q8 | C4×C5 | semidirect |
| 37. C4⋊(C3⋊D3) | C4×C5 | semidirect |
| 47. C32×C5 | #104 | semidirect |
| 48. C5×Q8 | #157 | semidirect |
| 91. C32 | C5×#104 | semidirect |
| 92. Q8 | C5×#157 | semidirect |
| 102. C5 | #63785 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3832 | 2 |
| C4×C5×#157 | 2 |
| C5×#3788 | 2 |
| #63785 | 5 |
| C5×#104 | 9 |