Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
444 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 214 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×C5×#125 | C2 | semidirect |
| 4. C5×#888 | C2 | semidirect |
| 5. C5×#887 | C2 | semidirect |
| 7. C5×#870 | C2 | semidirect |
| 22. #5688 | C5 | direct (N × H) |
| 25. C5×#125 | D3 | semidirect |
| 38. C4×C5×D3 | Q8 | semidirect |
| 40. C3×#125 | C2×C5 | semidirect |
| 43. #888 | C2×C5 | semidirect |
| 44. #887 | C2×C5 | semidirect |
| 46. #870 | C2×C5 | semidirect |
| 95. #125 | C5×D3 | semidirect |
| 111. C4×D3 | C5×Q8 | semidirect |
| 135. C3×C5 | #533 | semidirect |
| 161. C5 | #5688 | direct (N × H) |
| 171. C3 | C5×#533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#125 | 2 |
| C5×#896 | 2 |
| C5×#892 | 2 |
| C5×#888 | 2 |
| C5×#887 | 2 |
| C42×C5×D3 | 2 |
| C5×#870 | 2 |
| C5×#533 | 3 |
| #5688 | 5 |