Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
148 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 50 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×#1204 | C2 | semidirect |
| 3. #6712 | C2 | semidirect |
| 4. C5×C4⋊Dic3 | C2 | semidirect |
| 6. #6669 | C2 | semidirect |
| 29. C2×C3×D5 | Q8 | semidirect |
| 40. C4⋊Dic3 | D5 | semidirect |
| 69. C2×D5 | Dic6 | semidirect |
| 83. C3×C5 | C22⋊Q8 | semidirect |
| 111. C5 | #878 | semidirect |
| 122. C3 | #4042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1204 | 2 |
| C2×D5×Dic3 | 2 |
| #6712 | 2 |
| C5×C4⋊Dic3 | 2 |
| C3×#685 | 2 |
| #6669 | 2 |
| #6665 | 2 |
| #4042 | 3 |
| #878 | 5 |