Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
288 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 86 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×#124 | C2 | semidirect |
| 2. C2×C3×#688 | C2 | semidirect |
| 3. C2×C3×#686 | C2 | semidirect |
| 4. C3×#4020 | C2 | semidirect |
| 5. C3×#3935 | C2 | semidirect |
| 6. #65347 | C3 | direct (N × H) |
| 17. C5×#124 | C2×C3 | semidirect |
| 18. C2×#688 | C2×C3 | semidirect |
| 19. C2×#686 | C2×C3 | semidirect |
| 20. #4020 | C2×C3 | semidirect |
| 21. #3935 | C2×C3 | semidirect |
| 32. C3×#168 | D4 | semidirect |
| 36. C3×#124 | D5 | semidirect |
| 75. #168 | C3×D4 | semidirect |
| 79. #124 | C3×D5 | semidirect |
| 113. C3×C5 | #496 | semidirect |
| 141. C5 | C3×#496 | semidirect |
| 150. C3 | #65347 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#124 | 2 |
| C2×C3×#688 | 2 |
| C2×C3×#686 | 2 |
| C3×#4020 | 2 |
| C3×#3935 | 2 |
| #65347 | 3 |
| C3×#496 | 5 |