Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
260 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 74 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. C23×C3×D5 | C2 | semidirect |
| 2. C2×C3×C22⋊D5 | C2 | semidirect |
| 3. C2×C3×D20 | C2 | semidirect |
| 4. C3×C5×C22⋊C4 | C2 | semidirect |
| 5. C3×#685 | C2 | semidirect |
| 6. #4028 | C3 | direct (N × H) |
| 11. C22×C3×D5 | C22 | semidirect |
| 12. C2×C3×C4×C5 | C22 | semidirect |
| 14. C2×C3×Dic5 | C22 | semidirect |
| 17. C23×D5 | C2×C3 | semidirect |
| 18. C2×C22⋊D5 | C2×C3 | semidirect |
| 19. C2×D20 | C2×C3 | semidirect |
| 20. C5×C22⋊C4 | C2×C3 | semidirect |
| 21. #685 | C2×C3 | semidirect |
| 23. C22×C3×C5 | D4 | semidirect |
| 30. C2×C3×D5 | D4 | semidirect |
| 37. C3×C22⋊C4 | D5 | semidirect |
| 42. C22×D5 | C22×C3 | semidirect |
| 43. C2×C4×C5 | C22×C3 | semidirect |
| 45. C2×Dic5 | C22×C3 | semidirect |
| 61. C2×C3×C4 | C2×D5 | semidirect |
| 63. C22×C5 | C3×D4 | semidirect |
| 70. C2×D5 | C3×D4 | semidirect |
| 77. C22⋊C4 | C3×D5 | semidirect |
| 78. C3×C5 | #120 | semidirect |
| 86. C22×C3 | D20 | semidirect |
| 103. C2×C4 | C2×C3×D5 | semidirect |
| 109. C5 | C3×#120 | semidirect |
| 117. C22 | C3×D20 | semidirect |
| 121. C3 | #4028 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×D5 | 2 |
| C2×C3×C22⋊D5 | 2 |
| C2×C3×D20 | 2 |
| C3×C5×C22⋊C4 | 2 |
| C3×#685 | 2 |
| #4028 | 3 |
| C3×#120 | 5 |