Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
550 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 72 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. C2×C5×#985 | C2 | semidirect |
| 2. C5×C4⋊(#41⋊C3) | C2 | semidirect |
| 3. C5×#5425 | C2 | semidirect |
| 4. C4×C5×GL(2,𝔽3) | C2 | semidirect |
| 5. C5×C4⋊#226 | C2 | semidirect |
| 14. #85407 | C5 | direct (N × H) |
| 16. C5×#550 | D3 | semidirect |
| 30. C5×GL(2,𝔽3) | D4 | semidirect |
| 35. C2×#985 | C2×C5 | semidirect |
| 36. C4⋊(#41⋊C3) | C2×C5 | semidirect |
| 37. #5425 | C2×C5 | semidirect |
| 38. C4×GL(2,𝔽3) | C2×C5 | semidirect |
| 39. C4⋊#226 | C2×C5 | semidirect |
| 120. #550 | C5×D3 | semidirect |
| 142. GL(2,𝔽3) | C5×D4 | semidirect |
| 226. C4×C5 | #985 | semidirect |
| 306. C5 | #85407 | direct (N × H) |
| 320. C4 | C5×#985 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#985 | 2 |
| C5×C4⋊(#41⋊C3) | 2 |
| C5×#5425 | 2 |
| C4×C5×GL(2,𝔽3) | 2 |
| C5×C4⋊#226 | 2 |
| C5×#3284 | 3 |
| C5×D3×C4⋊C4 | 4 |
| #85407 | 5 |