Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
328 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 116 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 | C2×#41 |
| 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. C22×Dic15 | C2 | semidirect |
| 2. C2×C5×#67 | C2 | semidirect |
| 3. C2×C3×C22⋊D5 | C2 | semidirect |
| 4. C2×#1204 | C2 | semidirect |
| 5. C2×#1201 | C2 | semidirect |
| 6. C2×D3×Dic5 | C2 | semidirect |
| 7. #6780 | C2 | direct (N × H) |
| 8. C2×D5×Dic3 | C2 | semidirect |
| 15. C2×Dic15 | C22 | semidirect |
| 16. C5×#67 | C22 | semidirect |
| 18. C3×C22⋊D5 | C22 | semidirect |
| 20. #1204 | C22 | semidirect |
| 21. #1201 | C22 | semidirect |
| 22. D3×Dic5 | C22 | semidirect |
| 23. D5×Dic3 | C22 | semidirect |
| 27. C2×C22⋊D5 | D3 | semidirect |
| 46. C2×#67 | D5 | semidirect |
| 58. C22⋊D5 | C2×D3 | semidirect |
| 68. C2×C3×C5 | #41 | semidirect |
| 78. #67 | C2×D5 | semidirect |
| 105. C3×C5 | C2×#41 | semidirect |
| 119. C2×C5 | #237 | semidirect |
| 138. C2×C3 | #711 | semidirect |
| 141. C5 | C2×#237 | semidirect |
| 153. C3 | C2×#711 | semidirect |
| 157. C2 | #6780 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic15 | 2 |
| C2×C5×#67 | 2 |
| C2×C3×C22⋊D5 | 2 |
| C2×#1204 | 2 |
| C2×#1201 | 2 |
| C2×D3×Dic5 | 2 |
| #6780 | 2 |
| C2×D5×Dic3 | 2 |
| C2×#711 | 3 |
| C2×#237 | 5 |