Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
462 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 462 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 |
| 2. C5×#5394 | C2 | semidirect |
| 3. C5×C4⋊GL(2,𝔽3) | C2 | semidirect |
| 4. C5×C4⋊GL(2,𝔽3) | C2 | semidirect |
| 5. C4×C5×GL(2,𝔽3) | C2 | semidirect |
| 13. #85422 | C5 | direct (N × H) |
| 14. C5×#557 | D3 | semidirect |
| 33. #557⋊C3 | C2×C5 | semidirect |
| 34. #5394 | C2×C5 | semidirect |
| 35. C4⋊GL(2,𝔽3) | C2×C5 | semidirect |
| 36. C4⋊GL(2,𝔽3) | C2×C5 | semidirect |
| 37. C4×GL(2,𝔽3) | C2×C5 | semidirect |
| 73. C5×SL(2,𝔽3) | #41 | semidirect |
| 108. #557 | C5×D3 | semidirect |
| 200. SL(2,𝔽3) | C5×#41 | semidirect |
| 288. C5 | #85422 | 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 |
| C5×C4⋊GL(2,𝔽3) | 2 |
| C4×C5×GL(2,𝔽3) | 2 |
| C5×#3368 | 3 |
| C5×#895 | 4 |
| #85422 | 5 |