Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
372 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 110 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×#493 | C2 | semidirect |
| 2. C2×C5×#826 | C2 | semidirect |
| 3. C4×C5×D24 | C2 | semidirect |
| 4. C5×#4562 | C2 | semidirect |
| 5. C5×C4⋊(C3⋊C16) | C2 | semidirect |
| 17. #71293 | C5 | direct (N × H) |
| 19. C5×#493 | D3 | semidirect |
| 37. C5×D24 | D4 | semidirect |
| 39. C3×#493 | C2×C5 | semidirect |
| 40. C2×#826 | C2×C5 | semidirect |
| 41. C4×D24 | C2×C5 | semidirect |
| 42. #4562 | C2×C5 | semidirect |
| 43. C4⋊(C3⋊C16) | C2×C5 | semidirect |
| 98. #493 | C5×D3 | semidirect |
| 110. C3×C4×C5 | D16 | semidirect |
| 128. D24 | C5×D4 | semidirect |
| 186. C4×C5 | #826 | semidirect |
| 205. C3×C5 | #2206 | semidirect |
| 214. C3×C4 | C5×D16 | semidirect |
| 244. C5 | #71293 | direct (N × H) |
| 254. C4 | C5×#826 | semidirect |
| 257. C3 | C5×#2206 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#493 | 2 |
| C2×C5×#826 | 2 |
| C4×C5×D24 | 2 |
| C5×#4562 | 2 |
| C5×C4⋊(C3⋊C16) | 2 |
| C5×#2206 | 3 |
| #71293 | 5 |