Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
136 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 44 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×D3×Q8 | C2 | semidirect |
| 3. #6717 | C2 | semidirect |
| 4. C3×#688 | C2 | semidirect |
| 5. #6660 | C2 | semidirect |
| 6. #6655 | C2 | semidirect |
| 7. D3×#168 | C2 | semidirect |
| 10. C3×C5×Q8 | C22 | semidirect |
| 15. C5×Dic6 | C22 | semidirect |
| 18. C3⋊#168 | C22 | semidirect |
| 19. C3×#168 | C22 | semidirect |
| 26. #688 | D3 | direct (N × H) |
| 36. D3×Q8 | D5 | semidirect |
| 46. C5×Q8 | C2×D3 | semidirect |
| 53. #168 | C2×D3 | semidirect |
| 58. C5×D3 | SD16 | semidirect |
| 60. C3×Q8 | C2×D5 | semidirect |
| 67. Dic6 | C2×D5 | semidirect |
| 85. C3×C5 | C2×SD16 | semidirect |
| 101. Q8 | D3×D5 | semidirect |
| 112. D3 | #688 | direct (N × H) |
| 113. C5 | D3×SD16 | semidirect |
| 122. C3 | C2×#688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D3×Q8 | 2 |
| D3×D20 | 2 |
| #6717 | 2 |
| C3×#688 | 2 |
| #6660 | 2 |
| #6655 | 2 |
| D3×#168 | 2 |
| C2×#688 | 3 |
| D3×SD16 | 5 |