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. C3×C5×C4⋊C4 | C2 | semidirect |
| 5. C3×C4⋊Dic5 | C2 | semidirect |
| 6. C3×#683 | C2 | semidirect |
| 7. C3×C4×Dic5 | C2 | semidirect |
| 8. #4044 | C3 | direct (N × H) |
| 17. C5×C4⋊C4 | C2×C3 | semidirect |
| 21. C4⋊Dic5 | C2×C3 | semidirect |
| 22. #683 | C2×C3 | semidirect |
| 23. C4×Dic5 | C2×C3 | semidirect |
| 36. C3×C4⋊C4 | D5 | semidirect |
| 72. C4⋊C4 | C3×D5 | semidirect |
| 77. C3×C5 | #126 | semidirect |
| 103. C5 | C3×#126 | semidirect |
| 114. C3 | #4044 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×C4⋊C4 | 2 |
| C3×#685 | 2 |
| C3×C4⋊Dic5 | 2 |
| C3×#683 | 2 |
| C3×C4×Dic5 | 2 |
| #4044 | 3 |
| C3×#126 | 5 |