Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
136 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 40 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. D3×D20 | C2 | semidirect |
| 2. #6769 | C2 | semidirect |
| 3. D120 | C2 | semidirect |
| 4. C5×ΓL(1,𝔽25) | C2 | semidirect |
| 5. C3×#677 | C2 | semidirect |
| 6. #6658 | C2 | semidirect |
| 7. #6653 | C2 | semidirect |
| 11. D60 | C22 | semidirect |
| 14. C3×Dic10 | C22 | semidirect |
| 18. C3×C5×C8 | C22 | semidirect |
| 19. C5×C3⋊C8 | C22 | semidirect |
| 27. #677 | D3 | semidirect |
| 42. ΓL(1,𝔽25) | D5 | semidirect |
| 51. Dic10 | C2×D3 | semidirect |
| 53. C5×C8 | C2×D3 | semidirect |
| 69. C3×C8 | C2×D5 | semidirect |
| 70. C3⋊C8 | C2×D5 | semidirect |
| 86. C3×C5 | AGL(1,ℤ/8) | semidirect |
| 110. C8 | D3×D5 | semidirect |
| 116. C5 | #914 | semidirect |
| 125. C3 | #4054 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×D20 | 2 |
| #6769 | 2 |
| D120 | 2 |
| C5×ΓL(1,𝔽25) | 2 |
| C3×#677 | 2 |
| #6658 | 2 |
| #6653 | 2 |
| #4054 | 3 |
| #914 | 5 |