Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
308 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 120 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 |
|---|---|---|
| 4. #65689 | C3 | direct (N × H) |
| 9. C3×C42×C5 | C4 | semidirect |
| 10. C3×C4×Dic5 | C4 | semidirect |
| 11. C3×C4×Dic5 | C4 | semidirect |
| 33. C42×C5 | C3×C4 | semidirect |
| 34. C4×Dic5 | C3×C4 | semidirect |
| 35. C4×Dic5 | C3×C4 | semidirect |
| 52. C3×C42 | AGL(1,𝔽5) | semidirect |
| 95. C42 | C3×AGL(1,𝔽5) | semidirect |
| 96. C3×C5 | #382 | semidirect |
| 124. C5 | C3×#382 | semidirect |
| 134. C3 | #65689 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4⋊AGL(1,𝔽5) | 2 |
| C3×C42×D5 | 2 |
| C3×(C2×AGL(1,𝔽5))⋊C4 | 2 |
| #65689 | 3 |
| C3×#382 | 5 |