Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
152 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 66 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. C2×C3×C5×D4 | C2 | semidirect |
| 2. C2×C3×D20 | C2 | semidirect |
| 3. C3×#686 | C2 | direct (N × H) |
| 4. C2×C3×#168 | C2 | semidirect |
| 5. C2×#686 | C3 | direct (N × H) |
| 9. C3×C5×D4 | C22 | semidirect |
| 12. C3×D20 | C22 | semidirect |
| 13. C3×#168 | C22 | semidirect |
| 15. C2×C5×D4 | C2×C3 | semidirect |
| 16. C2×D20 | C2×C3 | semidirect |
| 17. #686 | C2×C3 | direct (N × H) |
| 18. C2×#168 | C2×C3 | semidirect |
| 27. C2×C3×D4 | D5 | semidirect |
| 33. C5×D4 | C22×C3 | semidirect |
| 36. D20 | C22×C3 | semidirect |
| 37. #168 | C22×C3 | semidirect |
| 40. C2×C3×C5 | D8 | semidirect |
| 48. C3×D4 | C2×D5 | semidirect |
| 59. C2×D4 | C3×D5 | semidirect |
| 62. C3×C5 | C2×D8 | semidirect |
| 71. C2×C5 | C3×D8 | semidirect |
| 79. D4 | C2×C3×D5 | semidirect |
| 84. C2×C3 | #686 | direct (N × H) |
| 86. C5 | C2×C3×D8 | semidirect |
| 94. C3 | C2×#686 | direct (N × H) |
| 97. C2 | C3×#686 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×D4 | 2 |
| C2×C3×D20 | 2 |
| C3×#686 | 2 |
| C2×C3×#168 | 2 |
| C2×#686 | 3 |
| C2×C3×D8 | 5 |