Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
450 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 450 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×D4×SL(2,𝔽3) | C2 | semidirect |
| 2. C5×#5421 | C2 | semidirect |
| 3. C5×#5420 | C2 | semidirect |
| 4. C4×C5×GL(2,𝔽3) | C2 | semidirect |
| 5. C5×#5391 | C2 | semidirect |
| 13. #85400 | C5 | direct (N × H) |
| 15. C5×D4×Q8 | D3 | semidirect |
| 33. D4×SL(2,𝔽3) | C2×C5 | semidirect |
| 34. #5421 | C2×C5 | semidirect |
| 35. #5420 | C2×C5 | semidirect |
| 36. C4×GL(2,𝔽3) | C2×C5 | semidirect |
| 37. #5391 | C2×C5 | semidirect |
| 110. D4×Q8 | C5×D3 | semidirect |
| 288. C5 | #85400 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D4×SL(2,𝔽3) | 2 |
| C5×#5421 | 2 |
| C5×#5420 | 2 |
| C4×C5×GL(2,𝔽3) | 2 |
| C5×#5391 | 2 |
| C5×#3329 | 3 |
| C5×#938 | 4 |
| #85400 | 5 |