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. C3×Q8×D5 | C2 | semidirect |
| 3. #6717 | C2 | semidirect |
| 4. C5×#215 | C2 | semidirect |
| 5. #6658 | C2 | semidirect |
| 6. #6656 | C2 | semidirect |
| 7. D5×C3⋊C8 | C2 | semidirect |
| 10. C3×C5×Q8 | C22 | semidirect |
| 16. C3×Dic10 | C22 | semidirect |
| 18. C3⋊#168 | C22 | semidirect |
| 19. C5×C3⋊C8 | C22 | semidirect |
| 21. Q8×D5 | D3 | semidirect |
| 41. #215 | D5 | direct (N × H) |
| 44. C5×Q8 | C2×D3 | semidirect |
| 51. Dic10 | C2×D3 | semidirect |
| 57. C3×D5 | SD16 | semidirect |
| 62. C3×Q8 | C2×D5 | semidirect |
| 69. C3⋊C8 | C2×D5 | semidirect |
| 85. C3×C5 | C2×SD16 | semidirect |
| 97. D5 | #215 | direct (N × H) |
| 101. Q8 | D3×D5 | semidirect |
| 113. C5 | C2×#215 | 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 |
|---|---|
| C3×Q8×D5 | 2 |
| D5×D12 | 2 |
| #6717 | 2 |
| C5×#215 | 2 |
| #6658 | 2 |
| #6656 | 2 |
| D5×C3⋊C8 | 2 |
| D5×SD16 | 3 |
| C2×#215 | 5 |