Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
482 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 482 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×C4×C5×SL(2,𝔽3) | C2 | semidirect |
| 2. C5×#5421 | C2 | semidirect |
| 3. C5×#5394 | C2 | semidirect |
| 4. C5×C4⋊GL(2,𝔽3) | C2 | semidirect |
| 5. C5×#5391 | C2 | semidirect |
| 13. #85332 | C5 | direct (N × H) |
| 15. C2×C4×C5×Q8 | D3 | semidirect |
| 33. C2×C4×SL(2,𝔽3) | C2×C5 | semidirect |
| 34. #5421 | C2×C5 | semidirect |
| 35. #5394 | C2×C5 | semidirect |
| 36. C4⋊GL(2,𝔽3) | C2×C5 | semidirect |
| 37. #5391 | C2×C5 | semidirect |
| 74. C5×SL(2,𝔽3) | #41 | semidirect |
| 112. C2×C4×Q8 | C5×D3 | semidirect |
| 206. SL(2,𝔽3) | C5×#41 | semidirect |
| 299. C5 | #85332 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×SL(2,𝔽3) | 2 |
| C5×#5421 | 2 |
| C5×#5394 | 2 |
| C5×C4⋊GL(2,𝔽3) | 2 |
| C5×#5391 | 2 |
| C5×#3112 | 3 |
| C5×#930 | 4 |
| #85332 | 5 |