Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
136 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 38 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. #6821 | C2 | semidirect |
| 2. #6777 | C2 | semidirect |
| 3. C5×#215 | C2 | semidirect |
| 4. C3×#688 | C2 | semidirect |
| 5. #6654 | C2 | semidirect |
| 6. #6653 | C2 | semidirect |
| 7. #6651 | C2 | semidirect |
| 10. C3×C5×Q8 | C22 | semidirect |
| 12. D60 | C22 | semidirect |
| 18. C3×#168 | C22 | semidirect |
| 19. C5×C3⋊C8 | C22 | semidirect |
| 24. #688 | D3 | semidirect |
| 39. #215 | D5 | semidirect |
| 44. C5×Q8 | C2×D3 | semidirect |
| 53. #168 | 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 | #914 | semidirect |
| 125. C3 | #4060 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #6821 | 2 |
| #6777 | 2 |
| C5×#215 | 2 |
| C3×#688 | 2 |
| #6654 | 2 |
| #6653 | 2 |
| #6651 | 2 |
| #4060 | 3 |
| #914 | 5 |