Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
556 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 69 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×#91955 | C2 | semidirect |
| 2. C4×C5×#41⋊C3 | C2 | semidirect |
| 3. #11752114 | C2 | semidirect |
| 4. C4⋊(C5⋊GL(2,𝔽3)) | C2 | semidirect |
| 5. C4⋊(C5⋊#226) | C2 | semidirect |
| 15. C4×C5×#41 | D3 | semidirect |
| 28. C5×#41⋊C3 | D4 | semidirect |
| 36. C4×#41⋊C3 | D5 | semidirect |
| 86. C5×#41 | D12 | semidirect |
| 122. C4×#41 | D15 | semidirect |
| 141. #41⋊C3 | D20 | semidirect |
| 229. C4×C5 | #985 | semidirect |
| 234. #41 | D60 | semidirect |
| 311. C5 | #85344 | semidirect |
| 326. C4 | #91955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#91955 | 2 |
| C4×C5×#41⋊C3 | 2 |
| #11752114 | 2 |
| C4⋊(C5⋊GL(2,𝔽3)) | 2 |
| C4⋊(C5⋊#226) | 2 |
| #10614256 | 3 |
| C4×D60 | 4 |
| #85344 | 5 |