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 | C4 | C2×D3×D5 |
| commutator, socle, cosocle | C2×C3×C5 | C24 |
| Frattini | C2 | C22×D3×D5 |
| Fitting | C2×C3×C4×C5 | C22 |
| hypercenter | C2×C4 | D3×D5 |
| hypocenter | C3×C5 | C2×#41 |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #6817 | C2 | semidirect |
| 2. C5×#235 | C2 | semidirect |
| 3. C2×C3×C4×D5 | C2 | semidirect |
| 4. D5×#67 | C2 | semidirect |
| 5. #6782 | C2 | semidirect |
| 6. D5×D12 | C2 | semidirect |
| 7. C4×D3×D5 | C2 | semidirect |
| 8. #6773 | C2 | semidirect |
| 9. #6772 | C2 | semidirect |
| 10. #6771 | C2 | semidirect |
| 11. D5×Dic6 | C2 | semidirect |
| 15. C2×C3×C4×C5 | C22 | semidirect |
| 16. #1220 | C22 | semidirect |
| 17. D60 | C22 | semidirect |
| 18. C4×D15 | C22 | semidirect |
| 19. Dic30 | C22 | semidirect |
| 20. C5×#67 | C22 | semidirect |
| 21. C5×D12 | C22 | semidirect |
| 22. C4×C5×D3 | C22 | semidirect |
| 23. C5×Dic6 | C22 | semidirect |
| 24. C2×C3×Dic5 | C22 | semidirect |
| 27. C3×C4×D5 | C22 | semidirect |
| 28. C3×C4×D5 | C22 | semidirect |
| 29. #1204 | C22 | semidirect |
| 30. #1203 | C22 | semidirect |
| 31. #1202 | C22 | semidirect |
| 32. #1201 | C22 | semidirect |
| 33. #1200 | C22 | semidirect |
| 34. D3×Dic5 | C22 | semidirect |
| 47. C2×C4×D5 | D3 | semidirect |
| 68. #235 | D5 | direct (N × H) |
| 78. C2×C4×C5 | C2×D3 | semidirect |
| 83. C2×Dic5 | C2×D3 | semidirect |
| 91. C4×D5 | C2×D3 | semidirect |
| 92. C4×D5 | C2×D3 | semidirect |
| 100. C3×D5 | #41 | semidirect |
| 109. C2×C3×C4 | C2×D5 | semidirect |
| 113. #67 | C2×D5 | semidirect |
| 117. D12 | C2×D5 | semidirect |
| 121. C4×D3 | C2×D5 | semidirect |
| 124. Dic6 | C2×D5 | semidirect |
| 149. C3×C5 | C2×#41 | semidirect |
| 168. D5 | #235 | direct (N × H) |
| 191. C2×C4 | D3×D5 | semidirect |
| 198. C5 | C2×#235 | semidirect |
| 212. C3 | D5×#41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #6817 | 2 |
| C5×#235 | 2 |
| C2×C3×C4×D5 | 2 |
| D5×#67 | 2 |
| #6782 | 2 |
| D5×D12 | 2 |
| C4×D3×D5 | 2 |
| #6773 | 2 |
| #6772 | 2 |
| #6771 | 2 |
| D5×Dic6 | 2 |
| D5×#41 | 3 |
| C2×#235 | 5 |