Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
228 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 228 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. C5×D3×C4⋊C4 | C2 | semidirect |
| 3. C3×C5×#102 | C2 | semidirect |
| 4. C5×#832 | C2 | semidirect |
| 5. C5×(C2×D3)⋊C8 | C2 | semidirect |
| 6. C5×#817 | C2 | semidirect |
| 7. C5×#808 | C2 | semidirect |
| 20. #4777 | C5 | direct (N × H) |
| 26. C5×#102 | D3 | semidirect |
| 44. D3×C4⋊C4 | C2×C5 | semidirect |
| 45. C3×#102 | C2×C5 | semidirect |
| 46. #832 | C2×C5 | semidirect |
| 47. (C2×D3)⋊C8 | C2×C5 | semidirect |
| 48. #817 | C2×C5 | semidirect |
| 49. #808 | C2×C5 | semidirect |
| 106. #102 | C5×D3 | semidirect |
| 152. C3×C5 | #481 | semidirect |
| 191. C5 | #4777 | direct (N × H) |
| 205. C3 | C5×#481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#938 | 2 |
| C5×D3×C4⋊C4 | 2 |
| C3×C5×#102 | 2 |
| C5×#832 | 2 |
| C5×(C2×D3)⋊C8 | 2 |
| C5×#817 | 2 |
| C5×#808 | 2 |
| C5×#481 | 3 |
| #4777 | 5 |