Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
412 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 98 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×#5067 | C2 | semidirect |
| 4. C5×#4543 | C2 | semidirect |
| 5. C5×#4540 | C2 | semidirect |
| 20. #71955 | C5 | direct (N × H) |
| 21. C5×#563 | D3 | semidirect |
| 46. C3×#563 | C2×C5 | semidirect |
| 47. #5067 | C2×C5 | semidirect |
| 49. #4543 | C2×C5 | semidirect |
| 50. #4540 | C2×C5 | semidirect |
| 114. #563 | C5×D3 | semidirect |
| 228. C3×C5 | #1657 | semidirect |
| 263. C5 | #71955 | direct (N × H) |
| 274. C3 | C5×#1657 | 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×#5067 | 2 |
| C5×#5058 | 2 |
| C5×#4543 | 2 |
| C5×#4540 | 2 |
| C5×#1657 | 3 |
| #71955 | 5 |