Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
228 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 228 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 |
|---|---|---|
| 3. C3×C5×#107 | C2 | semidirect |
| 4. C5×#818 | C2 | semidirect |
| 5. C5×#808 | C2 | semidirect |
| 14. C5×D3×C8 | C4 | semidirect |
| 15. #4880 | C5 | direct (N × H) |
| 19. C5×#107 | D3 | semidirect |
| 32. C3×#107 | C2×C5 | semidirect |
| 33. #818 | C2×C5 | semidirect |
| 34. #808 | C2×C5 | semidirect |
| 60. D3×C8 | C4×C5 | semidirect |
| 73. #107 | C5×D3 | semidirect |
| 105. C3×C5 | #427 | semidirect |
| 132. C5 | #4880 | direct (N × H) |
| 142. C3 | C5×#427 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D3×C8 | 2 |
| C5×#892 | 2 |
| C3×C5×#107 | 2 |
| C5×#818 | 2 |
| C5×#808 | 2 |
| C5×#427 | 3 |
| #4880 | 5 |