Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
188 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 188 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. C22×C3×C4×C5 | C2 | semidirect |
| 2. C2×C3×C22⋊D5 | C2 | semidirect |
| 3. C2×C3×D20 | C2 | semidirect |
| 4. C3×#685 | C2 | semidirect |
| 5. C3×C4⋊Dic5 | C2 | semidirect |
| 6. #4076 | C3 | direct (N × H) |
| 16. C22×C4×C5 | C2×C3 | semidirect |
| 17. C2×C22⋊D5 | C2×C3 | semidirect |
| 18. C2×D20 | C2×C3 | semidirect |
| 19. #685 | C2×C3 | semidirect |
| 20. C4⋊Dic5 | C2×C3 | semidirect |
| 23. C22×C3×C5 | D4 | semidirect |
| 29. C3×C4×C5 | D4 | semidirect |
| 33. C22×C3×C4 | D5 | semidirect |
| 60. C22×C5 | C3×D4 | semidirect |
| 66. C4×C5 | C3×D4 | semidirect |
| 70. C22×C4 | C3×D5 | semidirect |
| 73. C3×C5 | #121 | semidirect |
| 79. C22×C3 | D20 | semidirect |
| 83. C3×C4 | C22⋊D5 | semidirect |
| 102. C5 | C3×#121 | semidirect |
| 108. C22 | C3×D20 | semidirect |
| 112. C4 | C3×C22⋊D5 | semidirect |
| 113. C3 | #4076 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4×C5 | 2 |
| C2×C3×C22⋊D5 | 2 |
| C2×C3×D20 | 2 |
| C3×#685 | 2 |
| C3×C4⋊Dic5 | 2 |
| #4076 | 3 |
| C3×#121 | 5 |