Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
248 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 86 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. C3×C4×C5×D4 | C2 | semidirect |
| 2. C2×C5×#214 | C2 | semidirect |
| 4. C5×#875 | C2 | semidirect |
| 5. C5×#810 | C2 | semidirect |
| 6. C5×#809 | C2 | semidirect |
| 7. C5×C4⋊(C3⋊C8) | C2 | semidirect |
| 22. #5016 | C5 | direct (N × H) |
| 26. C4×C5×D4 | D3 | semidirect |
| 46. C3×C4×D4 | C2×C5 | semidirect |
| 47. C2×#214 | C2×C5 | semidirect |
| 49. #875 | C2×C5 | semidirect |
| 50. #810 | C2×C5 | semidirect |
| 51. #809 | C2×C5 | semidirect |
| 52. C4⋊(C3⋊C8) | C2×C5 | semidirect |
| 112. C4×D4 | C5×D3 | semidirect |
| 163. C3×C5 | #463 | semidirect |
| 203. C5 | #5016 | direct (N × H) |
| 217. C3 | C5×#463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C5×D4 | 2 |
| C2×C5×#214 | 2 |
| C2×C5×#213 | 2 |
| C5×#875 | 2 |
| C5×#810 | 2 |
| C5×#809 | 2 |
| C5×C4⋊(C3⋊C8) | 2 |
| C5×#463 | 3 |
| #5016 | 5 |