Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
180 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 62 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×#919 | C2 | semidirect |
| 2. C5×D3×D8 | C2 | semidirect |
| 3. C3×C5×SD32 | C2 | semidirect |
| 4. C5×#828 | C2 | semidirect |
| 5. C5×#826 | C2 | semidirect |
| 6. C5×D48 | C2 | semidirect |
| 7. C5×#798 | C2 | semidirect |
| 11. C3×C5×Q16 | C22 | semidirect |
| 16. C5×D24 | C22 | semidirect |
| 18. C3×C5×C16 | C22 | semidirect |
| 19. C5×C3⋊C16 | C22 | semidirect |
| 20. #4914 | C5 | direct (N × H) |
| 24. C5×SD32 | D3 | semidirect |
| 39. #919 | C2×C5 | semidirect |
| 40. D3×D8 | C2×C5 | semidirect |
| 41. C3×SD32 | C2×C5 | semidirect |
| 42. #828 | C2×C5 | semidirect |
| 43. #826 | C2×C5 | semidirect |
| 44. D48 | C2×C5 | semidirect |
| 45. #798 | C2×C5 | semidirect |
| 48. C5×Q16 | C2×D3 | semidirect |
| 56. C5×C16 | C2×D3 | semidirect |
| 68. C3×Q16 | C22×C5 | semidirect |
| 73. D24 | C22×C5 | semidirect |
| 75. C3×C16 | C22×C5 | semidirect |
| 76. C3⋊C16 | C22×C5 | semidirect |
| 91. SD32 | C5×D3 | semidirect |
| 121. Q16 | C2×C5×D3 | semidirect |
| 129. C16 | C2×C5×D3 | semidirect |
| 130. C3×C5 | #509 | semidirect |
| 160. C5 | #4914 | direct (N × H) |
| 169. C3 | C5×#509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#919 | 2 |
| C5×D3×D8 | 2 |
| C3×C5×SD32 | 2 |
| C5×#828 | 2 |
| C5×#826 | 2 |
| C5×D48 | 2 |
| C5×#798 | 2 |
| C5×#509 | 3 |
| #4914 | 5 |