Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
328 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 178 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C5 | C22×D3 |
| commutator, cosocle | C2×C3 | C24×C5 |
| Frattini | C2 | C23×C5×D3 |
| Fitting | C2×C3×C5×D4 | C2 |
| socle | C22×C3×C5 | C23 |
| hypercenter | C2×C5×D4 | D3 |
| hypocenter | C3 | C2×C5×#41 |
| LCS | G ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C22×C5 ◁ C2×C5×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×C5×#67 | C2 | semidirect |
| 3. C22×C5×Dic3 | C2 | semidirect |
| 4. C5×#237 | C2 | direct (N × H) |
| 5. C2×C4×C5×D3 | C2 | semidirect |
| 6. C2×C5×Dic6 | C2 | semidirect |
| 10. C3×C5×D4 | C22 | semidirect |
| 12. C5×#67 | C22 | semidirect |
| 15. C2×C5×Dic3 | C22 | semidirect |
| 16. C4×C5×D3 | C22 | semidirect |
| 17. C5×Dic6 | C22 | semidirect |
| 18. C2×#237 | C5 | direct (N × H) |
| 22. C2×C5×D4 | D3 | semidirect |
| 33. C2×C3×D4 | C2×C5 | semidirect |
| 34. C2×#67 | C2×C5 | semidirect |
| 35. C22×Dic3 | C2×C5 | semidirect |
| 36. #237 | C2×C5 | direct (N × H) |
| 37. C2×C4×D3 | C2×C5 | semidirect |
| 38. C2×Dic6 | C2×C5 | semidirect |
| 43. C5×D4 | C2×D3 | semidirect |
| 51. C2×C3×C5 | #41 | semidirect |
| 56. C3×D4 | C22×C5 | semidirect |
| 58. #67 | C22×C5 | semidirect |
| 61. C2×Dic3 | C22×C5 | semidirect |
| 62. C4×D3 | C22×C5 | semidirect |
| 63. Dic6 | C22×C5 | semidirect |
| 75. C2×D4 | C5×D3 | semidirect |
| 78. C3×C5 | C2×#41 | semidirect |
| 89. C2×C5 | #237 | direct (N × H) |
| 95. D4 | C2×C5×D3 | semidirect |
| 102. C2×C3 | C5×#41 | semidirect |
| 105. C5 | C2×#237 | direct (N × H) |
| 114. C3 | C2×C5×#41 | semidirect |
| 117. C2 | C5×#237 | direct (N × H) |
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×C5×#67 | 2 |
| C22×C5×Dic3 | 2 |
| C5×#237 | 2 |
| C2×C4×C5×D3 | 2 |
| C2×C5×Dic6 | 2 |
| C2×C5×#41 | 3 |
| C2×#237 | 5 |