Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
392 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 68 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×#557⋊C3 | C2 | semidirect |
| 5. C5×#5389 | C2 | semidirect |
| 6. C5×#5389 | C2 | semidirect |
| 7. C5×#5386 | C2 | semidirect |
| 17. #85423 | C5 | direct (N × H) |
| 18. C5×#557 | D3 | semidirect |
| 36. C5×GL(2,𝔽3) | Q8 | semidirect |
| 42. #557⋊C3 | C2×C5 | semidirect |
| 46. #5389 | C2×C5 | semidirect |
| 47. #5389 | C2×C5 | semidirect |
| 48. #5386 | C2×C5 | semidirect |
| 141. #557 | C5×D3 | semidirect |
| 169. GL(2,𝔽3) | C5×Q8 | semidirect |
| 344. C5 | #85423 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#557⋊C3 | 2 |
| C5×#5394 | 2 |
| C4×C5×GL(2,𝔽3) | 2 |
| C5×#5389 | 2 |
| C5×#5386 | 2 |
| C5×#3388 | 3 |
| C5×#896 | 4 |
| #85423 | 5 |