Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
480 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 480 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. C4×C5×#41⋊C3 | C2 | semidirect |
| 2. C5×#5427 | C2 | semidirect |
| 3. C5×C4⋊GL(2,𝔽3) | C2 | semidirect |
| 4. C4×C5×GL(2,𝔽3) | C2 | semidirect |
| 5. C5×#5391 | C2 | semidirect |
| 13. #85345 | C5 | direct (N × H) |
| 15. C4×C5×#41 | D3 | semidirect |
| 33. C4×#41⋊C3 | C2×C5 | semidirect |
| 34. #5427 | C2×C5 | semidirect |
| 35. C4⋊GL(2,𝔽3) | C2×C5 | semidirect |
| 36. C4×GL(2,𝔽3) | C2×C5 | semidirect |
| 37. #5391 | C2×C5 | semidirect |
| 73. C5×SL(2,𝔽3) | #41 | semidirect |
| 111. C4×#41 | C5×D3 | semidirect |
| 201. SL(2,𝔽3) | C5×#41 | semidirect |
| 291. C5 | #85345 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×#41⋊C3 | 2 |
| C5×#5427 | 2 |
| C5×C4⋊GL(2,𝔽3) | 2 |
| C4×C5×GL(2,𝔽3) | 2 |
| C5×#5391 | 2 |
| C5×#3106 | 3 |
| C4×C5×D12 | 4 |
| #85345 | 5 |