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. C5×#239 | C2 | semidirect |
| 2. D3×D20 | C2 | semidirect |
| 3. #6717 | C2 | semidirect |
| 4. C3×#688 | C2 | semidirect |
| 5. #6654 | C2 | semidirect |
| 6. #6652 | C2 | semidirect |
| 7. #6650 | C2 | semidirect |
| 10. C3×C5×Q8 | C22 | semidirect |
| 13. C5×D12 | C22 | semidirect |
| 18. C3⋊#168 | C22 | semidirect |
| 19. C3×#168 | C22 | semidirect |
| 24. #688 | D3 | semidirect |
| 36. #239 | D5 | semidirect |
| 44. C5×Q8 | C2×D3 | semidirect |
| 53. #168 | C2×D3 | semidirect |
| 61. C3×Q8 | C2×D5 | semidirect |
| 66. D12 | C2×D5 | semidirect |
| 86. C3×C5 | AGL(1,ℤ/8) | semidirect |
| 101. Q8 | D3×D5 | semidirect |
| 116. C5 | #914 | semidirect |
| 125. C3 | #4095 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#239 | 2 |
| D3×D20 | 2 |
| #6717 | 2 |
| C3×#688 | 2 |
| #6654 | 2 |
| #6652 | 2 |
| #6650 | 2 |
| #4095 | 3 |
| #914 | 5 |