Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
124 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 58 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×#41 | C2 | semidirect |
| 2. C3×#709 | C2 | semidirect |
| 3. C3×#689 | C2 | semidirect |
| 4. C3×#688 | C2 | semidirect |
| 5. C3×#687 | C2 | semidirect |
| 6. C3×#686 | C2 | semidirect |
| 7. C2×C3×#168 | C2 | semidirect |
| 8. #4096 | C3 | direct (N × H) |
| 21. C5×#41 | C2×C3 | semidirect |
| 22. #709 | C2×C3 | semidirect |
| 23. #689 | C2×C3 | semidirect |
| 24. #688 | C2×C3 | semidirect |
| 25. #687 | C2×C3 | semidirect |
| 26. #686 | C2×C3 | semidirect |
| 27. C2×#168 | C2×C3 | semidirect |
| 36. C3×#41 | D5 | semidirect |
| 77. #41 | C3×D5 | semidirect |
| 83. C3×C5 | #135 | semidirect |
| 110. C5 | C3×#135 | semidirect |
| 118. C3 | #4096 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#41 | 2 |
| C3×#709 | 2 |
| C3×#689 | 2 |
| C3×#688 | 2 |
| C3×#687 | 2 |
| C3×#686 | 2 |
| C2×C3×#168 | 2 |
| #4096 | 3 |
| C3×#135 | 5 |