Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
136 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 58 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. C3×C5×SD16 | C2 | semidirect |
| 4. C3×#688 | C2 | semidirect |
| 5. C3×#687 | C2 | semidirect |
| 6. C3×#677 | C2 | semidirect |
| 7. C3×C8×D5 | C2 | semidirect |
| 8. D5×SD16 | C3 | direct (N × H) |
| 10. C3×C5×Q8 | C22 | semidirect |
| 17. C3×Dic10 | C22 | semidirect |
| 18. C3×C5×C8 | C22 | semidirect |
| 19. C3×#168 | C22 | semidirect |
| 21. Q8×D5 | C2×C3 | semidirect |
| 23. C5×SD16 | C2×C3 | semidirect |
| 24. #688 | C2×C3 | semidirect |
| 25. #687 | C2×C3 | semidirect |
| 26. #677 | C2×C3 | semidirect |
| 27. C8×D5 | C2×C3 | semidirect |
| 41. C3×SD16 | D5 | direct (N × H) |
| 44. C5×Q8 | C22×C3 | semidirect |
| 51. Dic10 | C22×C3 | semidirect |
| 52. C5×C8 | C22×C3 | semidirect |
| 53. #168 | C22×C3 | semidirect |
| 58. C3×D5 | SD16 | direct (N × H) |
| 62. C3×Q8 | C2×D5 | semidirect |
| 69. C3×C8 | C2×D5 | semidirect |
| 83. SD16 | C3×D5 | direct (N × H) |
| 85. C3×C5 | C2×SD16 | semidirect |
| 97. D5 | C3×SD16 | direct (N × H) |
| 101. Q8 | C2×C3×D5 | semidirect |
| 108. C8 | C2×C3×D5 | semidirect |
| 113. C5 | C2×C3×SD16 | semidirect |
| 122. C3 | D5×SD16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×D5 | 2 |
| C3×D4×D5 | 2 |
| C3×C5×SD16 | 2 |
| C3×#688 | 2 |
| C3×#687 | 2 |
| C3×#677 | 2 |
| C3×C8×D5 | 2 |
| D5×SD16 | 3 |
| C2×C3×SD16 | 5 |