Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
136 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 43 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. Q8×D15 | C2 | semidirect |
| 3. C3×C5×SD16 | C2 | semidirect |
| 4. #6717 | C2 | semidirect |
| 5. #6716 | C2 | semidirect |
| 6. #6706 | C2 | semidirect |
| 7. C8×D15 | C2 | semidirect |
| 10. C3×C5×Q8 | C22 | semidirect |
| 17. Dic30 | C22 | semidirect |
| 18. C3×C5×C8 | C22 | semidirect |
| 19. C3⋊#168 | C22 | semidirect |
| 23. C5×SD16 | D3 | semidirect |
| 38. C3×SD16 | D5 | semidirect |
| 44. C5×Q8 | C2×D3 | semidirect |
| 52. C5×C8 | C2×D3 | semidirect |
| 58. D15 | SD16 | direct (N × H) |
| 60. C3×Q8 | C2×D5 | semidirect |
| 68. C3×C8 | C2×D5 | semidirect |
| 83. SD16 | D15 | direct (N × H) |
| 85. C3×C5 | C2×SD16 | semidirect |
| 101. Q8 | C2×D15 | semidirect |
| 108. C8 | C2×D15 | semidirect |
| 113. C5 | D3×SD16 | semidirect |
| 122. C3 | D5×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D15 | 2 |
| D4×D15 | 2 |
| C3×C5×SD16 | 2 |
| #6717 | 2 |
| #6716 | 2 |
| #6706 | 2 |
| C8×D15 | 2 |
| D5×SD16 | 3 |
| D3×SD16 | 5 |