Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
1780 conjugacy classes of subgroups; only the 568 normal subgroups are shown.
This group has 1780 conjugacy classes of subgroups — too many to draw. Only its 568 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D3×D5 |
| commutator, cosocle | C2×C3×C5 | C25 |
| Frattini | C2 | C23×D3×D5 |
| Fitting | C24×C3×C5 | C22 |
| socle | C23×C3×C5 | C23 |
| hypercenter | C24 | D3×D5 |
| hypocenter | C3×C5 | C22×#41 |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C23 ◁ C24 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×Dic15 | C2 | semidirect |
| 2. C22×C5×#67 | C2 | semidirect |
| 3. C22×C3×C22⋊D5 | C2 | semidirect |
| 4. C22×#1204 | C2 | semidirect |
| 5. C22×#1201 | C2 | semidirect |
| 6. C22×D3×Dic5 | C2 | semidirect |
| 7. C2×#6780 | C2 | direct (N × H) |
| 8. C22×D5×Dic3 | C2 | semidirect |
| 15. C22×Dic15 | C22 | semidirect |
| 16. C2×C5×#67 | C22 | semidirect |
| 18. C2×C3×C22⋊D5 | C22 | semidirect |
| 20. C2×#1204 | C22 | semidirect |
| 21. C2×#1201 | C22 | semidirect |
| 22. C2×D3×Dic5 | C22 | semidirect |
| 23. #6780 | C22 | direct (N × H) |
| 24. C2×D5×Dic3 | C22 | semidirect |
| 28. C22×C22⋊D5 | D3 | semidirect |
| 43. C2×Dic15 | C23 | semidirect |
| 44. C5×#67 | C23 | semidirect |
| 46. C3×C22⋊D5 | C23 | semidirect |
| 48. #1204 | C23 | semidirect |
| 49. #1201 | C23 | semidirect |
| 50. D3×Dic5 | C23 | semidirect |
| 51. D5×Dic3 | C23 | semidirect |
| 54. C22×#67 | D5 | semidirect |
| 66. C2×C22⋊D5 | C2×D3 | semidirect |
| 77. C22×C3×C5 | #41 | semidirect |
| 94. C2×#67 | C2×D5 | semidirect |
| 113. C22⋊D5 | C22×D3 | semidirect |
| 130. C2×C3×C5 | C2×#41 | semidirect |
| 144. #67 | C22×D5 | semidirect |
| 155. C22×C5 | #237 | semidirect |
| 179. C3×C5 | C22×#41 | semidirect |
| 183. C22×C3 | #711 | semidirect |
| 194. C2×C5 | C2×#237 | semidirect |
| 217. C2×C3 | C2×#711 | semidirect |
| 220. C5 | C22×#237 | semidirect |
| 226. C22 | #6780 | direct (N × H) |
| 233. C3 | C22×#711 | semidirect |
| 237. C2 | C2×#6780 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic15 | 2 |
| C22×C5×#67 | 2 |
| C22×C3×C22⋊D5 | 2 |
| C22×#1204 | 2 |
| C22×#1201 | 2 |
| C22×D3×Dic5 | 2 |
| C2×#6780 | 2 |
| C22×D5×Dic3 | 2 |
| C22×#711 | 3 |
| C22×#237 | 5 |