Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
472 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 198 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. C3×C5×C4⋊Q8 | C2 | semidirect |
| 2. C5×#947 | C2 | semidirect |
| 3. C5×#895 | C2 | semidirect |
| 4. C5×#892 | C2 | semidirect |
| 5. C4×C5×D12 | C2 | semidirect |
| 17. #5734 | C5 | direct (N × H) |
| 18. C5×C4⋊Q8 | D3 | semidirect |
| 32. C3×C4⋊Q8 | C2×C5 | semidirect |
| 33. #947 | C2×C5 | semidirect |
| 34. #895 | C2×C5 | semidirect |
| 35. #892 | C2×C5 | semidirect |
| 36. C4×D12 | C2×C5 | semidirect |
| 75. C4⋊Q8 | C5×D3 | semidirect |
| 110. C3×C5 | #555 | semidirect |
| 134. C5 | #5734 | direct (N × H) |
| 143. C3 | C5×#555 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×C4⋊Q8 | 2 |
| C5×#947 | 2 |
| C5×#895 | 2 |
| C5×#892 | 2 |
| C4×C5×D12 | 2 |
| C5×#555 | 3 |
| #5734 | 5 |