Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
180 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×C5×D8 | C2 | semidirect |
| 2. C5×#904 | C2 | semidirect |
| 3. C5×#827 | C2 | semidirect |
| 4. C5×#826 | C2 | semidirect |
| 5. C5×#812 | C2 | semidirect |
| 12. C5×Dic12 | C22 | semidirect |
| 13. C5×D24 | C22 | semidirect |
| 15. C5×C3⋊C16 | C22 | semidirect |
| 16. #5147 | C5 | direct (N × H) |
| 18. C2×C5×D8 | D3 | semidirect |
| 32. C2×C3×D8 | C2×C5 | semidirect |
| 33. #904 | C2×C5 | semidirect |
| 34. #827 | C2×C5 | semidirect |
| 35. #826 | C2×C5 | semidirect |
| 36. #812 | C2×C5 | semidirect |
| 59. Dic12 | C22×C5 | semidirect |
| 60. D24 | C22×C5 | semidirect |
| 62. C3⋊C16 | C22×C5 | semidirect |
| 74. C2×D8 | C5×D3 | semidirect |
| 108. C3×C5 | #509 | semidirect |
| 134. C5 | #5147 | direct (N × H) |
| 142. C3 | C5×#509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×D8 | 2 |
| C5×#904 | 2 |
| C5×#827 | 2 |
| C5×#826 | 2 |
| C5×#812 | 2 |
| C5×#509 | 3 |
| #5147 | 5 |