Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
152 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 52 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×C5×D12 | C2 | semidirect |
| 2. C2×C3×D20 | C2 | semidirect |
| 3. C2×C3⋊#168 | C2 | semidirect |
| 4. #6652 | C2 | direct (N × H) |
| 10. C5×D12 | C22 | semidirect |
| 12. C3×D20 | C22 | semidirect |
| 13. C3⋊#168 | C22 | semidirect |
| 16. C2×D20 | D3 | semidirect |
| 27. C2×D12 | D5 | semidirect |
| 36. D20 | C2×D3 | semidirect |
| 39. C2×C3×C5 | D8 | semidirect |
| 49. D12 | C2×D5 | semidirect |
| 62. C3×C5 | C2×D8 | semidirect |
| 71. C2×C5 | #213 | semidirect |
| 83. C2×C3 | #686 | semidirect |
| 86. C5 | C2×#213 | semidirect |
| 94. C3 | C2×#686 | semidirect |
| 97. C2 | #6652 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D12 | 2 |
| C2×C3×D20 | 2 |
| C2×C3⋊#168 | 2 |
| #6652 | 2 |
| C2×#686 | 3 |
| C2×#213 | 5 |