Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
312 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 132 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×Dic30 | C2 | semidirect |
| 3. C2×C3×Dic10 | C2 | semidirect |
| 4. C2×#1204 | C2 | semidirect |
| 6. D3×Dic10 | C2 | direct (N × H) |
| 11. Dic30 | C22 | semidirect |
| 15. C3×Dic10 | C22 | semidirect |
| 16. #1204 | C22 | semidirect |
| 24. C2×Dic10 | D3 | direct (N × H) |
| 26. C2×C5×D3 | Q8 | semidirect |
| 47. Dic10 | C2×D3 | direct (N × H) |
| 49. C2×C3×C5 | C2×Q8 | semidirect |
| 51. C5×D3 | C2×Q8 | semidirect |
| 75. C3×C5 | C22×Q8 | semidirect |
| 77. C2×D3 | Dic10 | direct (N × H) |
| 84. C2×C5 | D3×Q8 | semidirect |
| 96. C2×C3 | C2×Dic10 | semidirect |
| 98. D3 | C2×Dic10 | direct (N × H) |
| 99. C5 | C2×D3×Q8 | semidirect |
| 107. C3 | C22×Dic10 | semidirect |
| 109. C2 | D3×Dic10 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic30 | 2 |
| C2×C4×C5×D3 | 2 |
| C2×C3×Dic10 | 2 |
| C2×#1204 | 2 |
| C2×D3×Dic5 | 2 |
| D3×Dic10 | 2 |
| C22×Dic10 | 3 |
| C2×D3×Q8 | 5 |