Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
332 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 119 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 | C23×D15 |
| commutator, socle, cosocle | C2×C3×C5 | C24 |
| Fitting | C2×C3×C5×D4 | C2 |
| hypercenter | C2×D4 | D15 |
| hypocenter | C3×C5 | H(5,𝔽2) |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C2 ◁ C2×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×C5×D4 | C2 | semidirect |
| 2. C2×#1220 | C2 | semidirect |
| 3. #6819 | C2 | semidirect |
| 4. D4×D15 | C2 | semidirect |
| 5. #6817 | C2 | semidirect |
| 7. C23×C3×C5 | C22 | semidirect |
| 8. C22×D15 | C22 | semidirect |
| 9. C3×C5×D4 | C22 | semidirect |
| 10. C2×C3×C4×C5 | C22 | semidirect |
| 11. #1220 | C22 | semidirect |
| 12. #1220 | C22 | semidirect |
| 13. C2×Dic15 | C22 | semidirect |
| 14. D60 | C22 | semidirect |
| 15. C4×D15 | C22 | semidirect |
| 16. Dic30 | C22 | semidirect |
| 18. C2×C5×D4 | D3 | semidirect |
| 30. C2×C3×D4 | D5 | semidirect |
| 35. C23×C5 | C2×D3 | semidirect |
| 37. C5×D4 | C2×D3 | semidirect |
| 38. C2×C4×C5 | C2×D3 | semidirect |
| 50. C23×C3 | C2×D5 | semidirect |
| 52. C3×D4 | C2×D5 | semidirect |
| 53. C2×C3×C4 | C2×D5 | semidirect |
| 71. C2×D4 | D15 | semidirect |
| 72. C3×C5 | H(5,𝔽2) | semidirect |
| 85. C23 | C2×D15 | semidirect |
| 90. D4 | C2×D15 | semidirect |
| 93. C2×C4 | C2×D15 | semidirect |
| 98. C5 | #1004 | semidirect |
| 106. C3 | #4144 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×D4 | 2 |
| C2×#1220 | 2 |
| #6819 | 2 |
| D4×D15 | 2 |
| #6817 | 2 |
| #4144 | 3 |
| #1004 | 5 |