Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
444 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 64 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. C5×#519⋊C3 | C2 | semidirect |
| 2. C5×#5421 | C2 | semidirect |
| 3. C5×#5421 | C2 | semidirect |
| 4. C5×#5394 | C2 | semidirect |
| 5. C5×C4⋊GL(2,𝔽3) | C2 | semidirect |
| 6. C4×C5×GL(2,𝔽3) | C2 | semidirect |
| 7. C5×#5389 | C2 | semidirect |
| 17. #85358 | C5 | direct (N × H) |
| 19. C5×#519 | D3 | semidirect |
| 44. #519⋊C3 | C2×C5 | semidirect |
| 45. #5421 | C2×C5 | semidirect |
| 46. #5421 | C2×C5 | semidirect |
| 47. #5394 | C2×C5 | semidirect |
| 48. C4⋊GL(2,𝔽3) | C2×C5 | semidirect |
| 49. C4×GL(2,𝔽3) | C2×C5 | semidirect |
| 50. #5389 | C2×C5 | semidirect |
| 152. #519 | C5×D3 | semidirect |
| 396. C5 | #85358 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#519⋊C3 | 2 |
| C5×#5421 | 2 |
| C5×#5394 | 2 |
| C5×C4⋊GL(2,𝔽3) | 2 |
| C4×C5×GL(2,𝔽3) | 2 |
| C5×#5389 | 2 |
| C5×#3126 | 3 |
| C5×#884 | 4 |
| #85358 | 5 |