Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
432 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 90 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×#563 | C2 | semidirect |
| 2. C5×#5095 | C2 | semidirect |
| 4. C5×#4548 | C2 | semidirect |
| 5. C5×#4542 | C2 | semidirect |
| 20. #71959 | C5 | direct (N × H) |
| 21. C5×#563 | D3 | semidirect |
| 50. C3×#563 | C2×C5 | semidirect |
| 51. #5095 | C2×C5 | semidirect |
| 53. #4548 | C2×C5 | semidirect |
| 54. #4542 | C2×C5 | semidirect |
| 125. #563 | C5×D3 | semidirect |
| 253. C3×C5 | #2203 | semidirect |
| 291. C5 | #71959 | direct (N × H) |
| 302. C3 | C5×#2203 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#563 | 2 |
| C5×#5095 | 2 |
| C5×#5062 | 2 |
| C5×#4548 | 2 |
| C5×#4542 | 2 |
| C5×#2203 | 3 |
| #71959 | 5 |