Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
328 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D3×D5 |
| commutator, socle, cosocle | C2×C3×C5 | C24 |
| Fitting | C3×C5×D4 | C22 |
| hypercenter | D4 | D3×D5 |
| hypocenter | C3×C5 | C2×#41 |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C2 ◁ D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #6819 | C2 | semidirect |
| 2. C5×D3×D4 | C2 | semidirect |
| 3. C3×#711 | C2 | semidirect |
| 4. D3×C22⋊D5 | C2 | semidirect |
| 5. #6782 | C2 | semidirect |
| 6. C2×D3×Dic5 | C2 | semidirect |
| 7. #6780 | C2 | semidirect |
| 8. C4×D3×D5 | C2 | semidirect |
| 9. #6772 | C2 | semidirect |
| 10. #6768 | C2 | semidirect |
| 11. D3×Dic10 | C2 | semidirect |
| 15. C3×C5×D4 | C22 | semidirect |
| 16. #1220 | C22 | semidirect |
| 17. C2×Dic15 | C22 | semidirect |
| 18. C4×D15 | C22 | semidirect |
| 19. Dic30 | C22 | semidirect |
| 20. C5×#67 | C22 | semidirect |
| 21. C5×D12 | C22 | semidirect |
| 23. C3×C22⋊D5 | C22 | semidirect |
| 24. C2×C3×Dic5 | C22 | semidirect |
| 25. C3×C4×D5 | C22 | semidirect |
| 26. C3×Dic10 | C22 | semidirect |
| 27. #1204 | C22 | semidirect |
| 28. #1203 | C22 | semidirect |
| 29. #1201 | C22 | semidirect |
| 30. #1200 | C22 | semidirect |
| 33. D3×Dic5 | C22 | semidirect |
| 34. D3×Dic5 | C22 | semidirect |
| 35. D5×Dic3 | C22 | semidirect |
| 45. #711 | D3 | direct (N × H) |
| 67. D3×D4 | D5 | semidirect |
| 76. C5×D4 | C2×D3 | semidirect |
| 81. C22⋊D5 | C2×D3 | semidirect |
| 87. C2×Dic5 | C2×D3 | semidirect |
| 91. C4×D5 | C2×D3 | semidirect |
| 94. Dic10 | C2×D3 | semidirect |
| 101. C5×D3 | #41 | semidirect |
| 106. C3×D4 | C2×D5 | semidirect |
| 111. #67 | C2×D5 | semidirect |
| 115. D12 | C2×D5 | semidirect |
| 149. C3×C5 | C2×#41 | semidirect |
| 180. D4 | D3×D5 | semidirect |
| 197. D3 | #711 | direct (N × H) |
| 198. C5 | D3×#41 | semidirect |
| 212. C3 | C2×#711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #6819 | 2 |
| C5×D3×D4 | 2 |
| C3×#711 | 2 |
| D3×C22⋊D5 | 2 |
| #6782 | 2 |
| C2×D3×Dic5 | 2 |
| #6780 | 2 |
| C4×D3×D5 | 2 |
| #6772 | 2 |
| #6768 | 2 |
| D3×Dic10 | 2 |
| C2×#711 | 3 |
| D3×#41 | 5 |