Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
120 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 120 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. C2×C3×C5×Q8 | C2 | semidirect |
| 3. C3×#689 | C2 | semidirect |
| 4. C3×#688 | C2 | semidirect |
| 5. C3×#681 | C2 | semidirect |
| 6. #4088 | C3 | direct (N × H) |
| 17. C2×C5×Q8 | C2×C3 | semidirect |
| 19. #689 | C2×C3 | semidirect |
| 20. #688 | C2×C3 | semidirect |
| 21. #681 | C2×C3 | semidirect |
| 29. C2×C3×Q8 | D5 | semidirect |
| 62. C2×Q8 | C3×D5 | semidirect |
| 66. C3×C5 | #137 | semidirect |
| 88. C5 | C3×#137 | semidirect |
| 95. C3 | #4088 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×Q8 | 2 |
| C3×#709 | 2 |
| C3×#689 | 2 |
| C3×#688 | 2 |
| C3×#681 | 2 |
| #4088 | 3 |
| C3×#137 | 5 |