Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
496 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 214 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×#4150 | C2 | semidirect |
| 2. C3×C5×#131 | C2 | semidirect |
| 3. C3×#4055 | C2 | semidirect |
| 4. C2×C3×Dic20 | C2 | semidirect |
| 5. C3×#4050 | C2 | semidirect |
| 6. #66087 | C3 | direct (N × H) |
| 19. #4150 | C2×C3 | semidirect |
| 20. C5×#131 | C2×C3 | semidirect |
| 21. #4055 | C2×C3 | semidirect |
| 22. C2×Dic20 | C2×C3 | semidirect |
| 23. #4050 | C2×C3 | semidirect |
| 39. C3×#131 | D5 | semidirect |
| 83. #131 | C3×D5 | semidirect |
| 114. C3×C5 | #578 | semidirect |
| 137. C5 | C3×#578 | semidirect |
| 143. C3 | #66087 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4150 | 2 |
| C3×C5×#131 | 2 |
| C3×#4055 | 2 |
| C2×C3×Dic20 | 2 |
| C3×#4050 | 2 |
| #66087 | 3 |
| C3×#578 | 5 |