Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
124 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 47 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. C3×C5×#41 | C2 | semidirect |
| 2. #6817 | C2 | semidirect |
| 3. #6718 | C2 | semidirect |
| 4. #6717 | C2 | semidirect |
| 5. #6716 | C2 | semidirect |
| 6. #6715 | C2 | semidirect |
| 7. C2×C3⋊#168 | C2 | semidirect |
| 21. C5×#41 | D3 | semidirect |
| 35. C3×#41 | D5 | semidirect |
| 77. #41 | D15 | semidirect |
| 83. C3×C5 | #135 | semidirect |
| 110. C5 | #950 | semidirect |
| 118. C3 | #4096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#41 | 2 |
| #6817 | 2 |
| #6718 | 2 |
| #6717 | 2 |
| #6716 | 2 |
| #6715 | 2 |
| C2×C3⋊#168 | 2 |
| #4096 | 3 |
| #950 | 5 |