Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
188 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 66 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×C4×C5×D3 | C2 | semidirect |
| 2. C2×C3×C4×D5 | C2 | semidirect |
| 4. C4×Dic15 | C2 | semidirect |
| 5. #6669 | C2 | semidirect |
| 6. (C2×D3)⋊Dic5 | C2 | semidirect |
| 7. #6665 | C2 | semidirect |
| 18. #1201 | C4 | direct (N × H) |
| 22. C2×C4×D5 | D3 | semidirect |
| 30. C2×C5×D3 | C2×C4 | semidirect |
| 33. C2×C3×D5 | C2×C4 | semidirect |
| 34. C3×C4×C5 | D4 | semidirect |
| 36. Dic15 | C2×C4 | semidirect |
| 41. C2×C4×D3 | D5 | semidirect |
| 78. C2×D5 | C4×D3 | semidirect |
| 80. C4×C5 | #67 | semidirect |
| 91. C3×C5 | C4×D4 | semidirect |
| 98. C2×D3 | C4×D5 | semidirect |
| 100. C3×C4 | C22⋊D5 | semidirect |
| 124. C5 | C4×#67 | semidirect |
| 136. C4 | #1201 | direct (N × H) |
| 137. C3 | C4×C22⋊D5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×D3 | 2 |
| C2×C3×C4×D5 | 2 |
| C2×#1201 | 2 |
| C4×Dic15 | 2 |
| #6669 | 2 |
| (C2×D3)⋊Dic5 | 2 |
| #6665 | 2 |
| C4×C22⋊D5 | 3 |
| C4×#67 | 5 |