Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
136 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 40 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×#713 | C2 | semidirect |
| 2. D5×D12 | C2 | semidirect |
| 3. #6717 | C2 | semidirect |
| 4. C5×#215 | C2 | semidirect |
| 5. #6653 | C2 | semidirect |
| 6. #6652 | C2 | semidirect |
| 7. #6649 | C2 | semidirect |
| 10. C3×C5×Q8 | C22 | semidirect |
| 14. C3×D20 | C22 | semidirect |
| 18. C3⋊#168 | C22 | semidirect |
| 19. C5×C3⋊C8 | C22 | semidirect |
| 21. #713 | D3 | semidirect |
| 39. #215 | D5 | semidirect |
| 44. C5×Q8 | C2×D3 | semidirect |
| 49. D20 | C2×D3 | semidirect |
| 61. C3×Q8 | C2×D5 | semidirect |
| 70. C3⋊C8 | C2×D5 | semidirect |
| 86. C3×C5 | AGL(1,ℤ/8) | semidirect |
| 101. Q8 | D3×D5 | semidirect |
| 116. C5 | #949 | semidirect |
| 125. C3 | #4060 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#713 | 2 |
| D5×D12 | 2 |
| #6717 | 2 |
| C5×#215 | 2 |
| #6653 | 2 |
| #6652 | 2 |
| #6649 | 2 |
| #4060 | 3 |
| #949 | 5 |