Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
120 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 54 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 |
|---|---|---|
| 2. C3×Q8×D5 | C2 | semidirect |
| 3. C3×C5×Q16 | C2 | semidirect |
| 4. C3×#689 | C2 | semidirect |
| 5. C3×#688 | C2 | semidirect |
| 6. C3×#677 | C2 | semidirect |
| 7. C3×#676 | C2 | semidirect |
| 8. #4064 | C3 | direct (N × H) |
| 22. Q8×D5 | C2×C3 | semidirect |
| 23. C5×Q16 | C2×C3 | semidirect |
| 24. #689 | C2×C3 | semidirect |
| 25. #688 | C2×C3 | semidirect |
| 26. #677 | C2×C3 | semidirect |
| 27. #676 | C2×C3 | semidirect |
| 38. C3×Q16 | D5 | semidirect |
| 78. Q16 | C3×D5 | semidirect |
| 82. C3×C5 | #137 | semidirect |
| 107. C5 | C3×#137 | semidirect |
| 115. C3 | #4064 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#713 | 2 |
| C3×Q8×D5 | 2 |
| C3×C5×Q16 | 2 |
| C3×#689 | 2 |
| C3×#688 | 2 |
| C3×#677 | 2 |
| C3×#676 | 2 |
| #4064 | 3 |
| C3×#137 | 5 |