Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
152 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 82 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×C5×C4⋊C4 | C2 | semidirect |
| 4. C3×C4⋊Dic5 | C2 | semidirect |
| 5. C3×C4×Dic5 | C2 | semidirect |
| 6. #4038 | C3 | direct (N × H) |
| 12. C3×C4×D5 | C4 | semidirect |
| 15. C5×C4⋊C4 | C2×C3 | semidirect |
| 17. C4⋊Dic5 | C2×C3 | semidirect |
| 18. C4×Dic5 | C2×C3 | semidirect |
| 29. C3×C4⋊C4 | D5 | semidirect |
| 37. C4×D5 | C3×C4 | semidirect |
| 59. C4⋊C4 | C3×D5 | semidirect |
| 62. C3×C5 | #117 | semidirect |
| 85. C5 | C3×#117 | semidirect |
| 94. C3 | #4038 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D5 | 2 |
| C3×C5×C4⋊C4 | 2 |
| C3×#685 | 2 |
| C3×C4⋊Dic5 | 2 |
| C3×C4×Dic5 | 2 |
| #4038 | 3 |
| C3×#117 | 5 |