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. C3×C5×2−1+4 | C2 | semidirect |
| 2. C5×#1010 | C2 | semidirect |
| 3. C5×#951 | C2 | semidirect |
| 4. C5×#950 | C2 | semidirect |
| 5. C5×#948 | C2 | semidirect |
| 6. C2×C5×#216 | C2 | semidirect |
| 7. C5×#942 | C2 | semidirect |
| 25. #5838 | C5 | direct (N × H) |
| 27. C5×2−1+4 | D3 | semidirect |
| 50. C3×2−1+4 | C2×C5 | semidirect |
| 51. #1010 | C2×C5 | semidirect |
| 52. #951 | C2×C5 | semidirect |
| 53. #950 | C2×C5 | semidirect |
| 54. #948 | C2×C5 | semidirect |
| 55. C2×#216 | C2×C5 | semidirect |
| 56. #942 | C2×C5 | semidirect |
| 115. 2−1+4 | C5×D3 | semidirect |
| 165. C3×C5 | #578 | semidirect |
| 198. C5 | #5838 | direct (N × H) |
| 206. C3 | C5×#578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×2−1+4 | 2 |
| C5×#1010 | 2 |
| C5×#951 | 2 |
| C5×#950 | 2 |
| C5×#948 | 2 |
| C2×C5×#216 | 2 |
| C5×#942 | 2 |
| C5×#578 | 3 |
| #5838 | 5 |