Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
328 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 174 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C3×C4 | C22×D5 |
| commutator, cosocle | C2×C5 | C24×C3 |
| Frattini | C2 | C23×C3×D5 |
| Fitting | C3×C5×#41 | C2 |
| socle | C2×C3×C5 | C24 |
| hypercenter | C3×#41 | D5 |
| hypocenter | C5 | C2×C3×#41 |
| LCS | G ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C3×C4 ◁ C3×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C5×#41 | C2 | semidirect |
| 2. C3×#713 | C2 | semidirect |
| 3. C3×Q8×D5 | C2 | semidirect |
| 4. C3×#711 | C2 | semidirect |
| 5. C3×D4×D5 | C2 | semidirect |
| 6. C3×#709 | C2 | semidirect |
| 7. C2×C3×C4×D5 | C2 | semidirect |
| 8. D5×#41 | C3 | direct (N × H) |
| 10. C3×C5×Q8 | C22 | semidirect |
| 11. C3×C5×D4 | C22 | semidirect |
| 12. C2×C3×C4×C5 | C22 | semidirect |
| 13. C3×C22⋊D5 | C22 | semidirect |
| 14. C2×C3×Dic5 | C22 | semidirect |
| 15. C3×D20 | C22 | semidirect |
| 18. C3×C4×D5 | C22 | semidirect |
| 19. C3×C4×D5 | C22 | semidirect |
| 20. C3×Dic10 | C22 | semidirect |
| 22. C5×#41 | C2×C3 | semidirect |
| 23. #713 | C2×C3 | semidirect |
| 24. Q8×D5 | C2×C3 | semidirect |
| 25. #711 | C2×C3 | semidirect |
| 26. D4×D5 | C2×C3 | semidirect |
| 27. #709 | C2×C3 | semidirect |
| 28. C2×C4×D5 | C2×C3 | semidirect |
| 40. C3×#41 | D5 | direct (N × H) |
| 45. C5×Q8 | C22×C3 | semidirect |
| 46. C5×D4 | C22×C3 | semidirect |
| 47. C2×C4×C5 | C22×C3 | semidirect |
| 48. C22⋊D5 | C22×C3 | semidirect |
| 49. C2×Dic5 | C22×C3 | semidirect |
| 50. D20 | C22×C3 | semidirect |
| 53. C4×D5 | C22×C3 | semidirect |
| 54. C4×D5 | C22×C3 | semidirect |
| 55. Dic10 | C22×C3 | semidirect |
| 60. C3×D5 | #41 | direct (N × H) |
| 63. C3×Q8 | C2×D5 | semidirect |
| 66. C3×D4 | C2×D5 | semidirect |
| 72. C2×C3×C4 | C2×D5 | semidirect |
| 84. #41 | C3×D5 | direct (N × H) |
| 88. C3×C5 | C2×#41 | semidirect |
| 100. D5 | C3×#41 | direct (N × H) |
| 103. Q8 | C2×C3×D5 | semidirect |
| 106. D4 | C2×C3×D5 | semidirect |
| 112. C2×C4 | C2×C3×D5 | semidirect |
| 117. C5 | C2×C3×#41 | semidirect |
| 126. C3 | D5×#41 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#41 | 2 |
| C3×#713 | 2 |
| C3×Q8×D5 | 2 |
| C3×#711 | 2 |
| C3×D4×D5 | 2 |
| C3×#709 | 2 |
| C2×C3×C4×D5 | 2 |
| D5×#41 | 3 |
| C2×C3×#41 | 5 |