Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
304 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 2. C3×C5×#124 | C2 | semidirect |
| 3. C5×#942 | C2 | semidirect |
| 4. C5×#833 | C2 | semidirect |
| 5. C5×#805 | C2 | semidirect |
| 7. C2×C3×C5×Q8 | C22 | semidirect |
| 14. C3×C42×C5 | C22 | semidirect |
| 17. C5×#208 | C22 | semidirect |
| 18. #5061 | C5 | direct (N × H) |
| 21. C5×#124 | D3 | semidirect |
| 39. C3×#124 | C2×C5 | semidirect |
| 40. #942 | C2×C5 | semidirect |
| 41. #833 | C2×C5 | semidirect |
| 42. #805 | C2×C5 | semidirect |
| 45. C2×C5×Q8 | C2×D3 | semidirect |
| 53. C42×C5 | C2×D3 | semidirect |
| 64. C2×C3×Q8 | C22×C5 | semidirect |
| 71. C3×C42 | C22×C5 | semidirect |
| 74. #208 | C22×C5 | semidirect |
| 91. #124 | C5×D3 | semidirect |
| 123. C2×Q8 | C2×C5×D3 | semidirect |
| 131. C42 | C2×C5×D3 | semidirect |
| 132. C3×C5 | #455 | semidirect |
| 164. C5 | #5061 | direct (N × H) |
| 174. C3 | C5×#455 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1004 | 2 |
| C3×C5×#124 | 2 |
| C5×#942 | 2 |
| C5×#833 | 2 |
| C5×#805 | 2 |
| C5×#455 | 3 |
| #5061 | 5 |