Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
472 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 132 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D3×D5 |
| commutator, cosocle | C2×C3×C5 | C24 |
| Frattini | C2 | C22×D3×D5 |
| Fitting | C23×C3×C5 | C22 |
| socle | C22×C3×C5 | C23 |
| hypercenter | C23 | D3×D5 |
| hypocenter | C3×C5 | C22×D4 |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C23 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C3×D5 | C2 | semidirect |
| 2. C22×D3×D5 | C2 | semidirect |
| 3. C2×#1220 | C2 | semidirect |
| 4. C2×C5×#67 | C2 | semidirect |
| 5. D5×#67 | C2 | direct (N × H) |
| 6. C2×#1202 | C2 | semidirect |
| 7. C2×#1201 | C2 | semidirect |
| 8. C2×D5×Dic3 | C2 | semidirect |
| 10. C23×C3×C5 | C22 | semidirect |
| 11. C22×D15 | C22 | semidirect |
| 12. C22×C5×D3 | C22 | semidirect |
| 15. C22×C3×D5 | C22 | semidirect |
| 16. C22×C3×D5 | C22 | semidirect |
| 18. C2×D3×D5 | C22 | semidirect |
| 19. #1220 | C22 | semidirect |
| 20. C2×Dic15 | C22 | semidirect |
| 21. C5×#67 | C22 | semidirect |
| 22. C2×C5×Dic3 | C22 | semidirect |
| 23. #1202 | C22 | semidirect |
| 24. #1201 | C22 | semidirect |
| 25. D5×Dic3 | C22 | semidirect |
| 28. C23×D5 | D3 | semidirect |
| 37. C22×C3×C5 | C23 | semidirect |
| 39. C2×D15 | C23 | semidirect |
| 41. C2×C5×D3 | C23 | semidirect |
| 44. C2×C3×D5 | D4 | semidirect |
| 46. C2×C3×D5 | C23 | semidirect |
| 48. Dic15 | C23 | semidirect |
| 49. C5×Dic3 | C23 | semidirect |
| 56. C2×#67 | D5 | direct (N × H) |
| 59. C23×C5 | C2×D3 | semidirect |
| 65. C22×D5 | C2×D3 | semidirect |
| 66. C22×D5 | C2×D3 | semidirect |
| 76. C2×C3×C5 | C2×D4 | semidirect |
| 80. C3×D5 | C2×D4 | semidirect |
| 86. C23×C3 | C2×D5 | semidirect |
| 90. C22×D3 | C2×D5 | semidirect |
| 94. #67 | C2×D5 | direct (N × H) |
| 97. C2×Dic3 | C2×D5 | semidirect |
| 102. C22×C5 | C22×D3 | semidirect |
| 108. C2×D5 | #67 | direct (N × H) |
| 110. C2×D5 | C22×D3 | semidirect |
| 121. C3×C5 | C22×D4 | semidirect |
| 129. C22×C3 | C22×D5 | semidirect |
| 134. C2×D3 | C22×D5 | semidirect |
| 136. Dic3 | C22×D5 | semidirect |
| 139. C2×C5 | C2×#67 | semidirect |
| 143. D5 | C2×#67 | direct (N × H) |
| 152. C23 | D3×D5 | semidirect |
| 163. C2×C3 | D4×D5 | semidirect |
| 167. C5 | C22×#67 | semidirect |
| 180. C22 | C2×D3×D5 | semidirect |
| 183. C3 | C2×D4×D5 | semidirect |
| 189. C2 | D5×#67 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×D5 | 2 |
| C22×D3×D5 | 2 |
| C2×#1220 | 2 |
| C2×C5×#67 | 2 |
| D5×#67 | 2 |
| C2×#1202 | 2 |
| C2×#1201 | 2 |
| C2×D5×Dic3 | 2 |
| C2×D4×D5 | 3 |
| C22×#67 | 5 |