Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
496 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 496 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. C5×#1010 | C2 | semidirect |
| 2. C3×C5×#131 | C2 | semidirect |
| 3. C5×#909 | C2 | semidirect |
| 4. C2×C5×Dic12 | C2 | semidirect |
| 5. C5×#904 | C2 | semidirect |
| 18. #5753 | C5 | direct (N × H) |
| 23. C5×#131 | D3 | semidirect |
| 35. #1010 | C2×C5 | semidirect |
| 36. C3×#131 | C2×C5 | semidirect |
| 37. #909 | C2×C5 | semidirect |
| 38. C2×Dic12 | C2×C5 | semidirect |
| 39. #904 | C2×C5 | semidirect |
| 83. #131 | C5×D3 | semidirect |
| 114. C3×C5 | #578 | semidirect |
| 137. C5 | #5753 | direct (N × H) |
| 143. C3 | C5×#578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1010 | 2 |
| C3×C5×#131 | 2 |
| C5×#909 | 2 |
| C2×C5×Dic12 | 2 |
| C5×#904 | 2 |
| C5×#578 | 3 |
| #5753 | 5 |