Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
328 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×D15 |
| commutator, socle, cosocle | C2×C3×C5 | C24 |
| Frattini | C2 | C23×D15 |
| Fitting | C3×C5×#41 | C2 |
| hypercenter | #41 | D15 |
| hypocenter | C3×C5 | C2×#41 |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C4 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C5×#41 | C2 | semidirect |
| 2. #6821 | C2 | semidirect |
| 3. Q8×D15 | C2 | semidirect |
| 4. #6819 | C2 | semidirect |
| 5. D4×D15 | C2 | semidirect |
| 6. #6817 | C2 | semidirect |
| 7. C2×C4×D15 | C2 | semidirect |
| 10. C3×C5×Q8 | C22 | semidirect |
| 11. C3×C5×D4 | C22 | semidirect |
| 12. C2×C3×C4×C5 | C22 | semidirect |
| 13. #1220 | C22 | semidirect |
| 14. C2×Dic15 | C22 | semidirect |
| 15. D60 | C22 | semidirect |
| 18. C4×D15 | C22 | semidirect |
| 19. C4×D15 | C22 | semidirect |
| 20. Dic30 | C22 | semidirect |
| 22. C5×#41 | D3 | semidirect |
| 37. C3×#41 | D5 | semidirect |
| 45. C5×Q8 | C2×D3 | semidirect |
| 46. C5×D4 | C2×D3 | semidirect |
| 47. C2×C4×C5 | C2×D3 | semidirect |
| 60. D15 | #41 | direct (N × H) |
| 62. C3×Q8 | C2×D5 | semidirect |
| 63. C3×D4 | C2×D5 | semidirect |
| 64. C2×C3×C4 | C2×D5 | semidirect |
| 84. #41 | D15 | direct (N × H) |
| 88. C3×C5 | C2×#41 | semidirect |
| 103. Q8 | C2×D15 | semidirect |
| 106. D4 | C2×D15 | semidirect |
| 112. C2×C4 | C2×D15 | semidirect |
| 117. C5 | D3×#41 | semidirect |
| 126. C3 | D5×#41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#41 | 2 |
| #6821 | 2 |
| Q8×D15 | 2 |
| #6819 | 2 |
| D4×D15 | 2 |
| #6817 | 2 |
| C2×C4×D15 | 2 |
| D5×#41 | 3 |
| D3×#41 | 5 |