Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
610 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 75 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. C22×C5⋊#226 | C2 | semidirect |
| 3. C2×Dic5×SL(2,𝔽3) | C2 | semidirect |
| 4. #11751601 | C2 | direct (N × H) |
| 8. C2×C5⋊#226 | C22 | semidirect |
| 12. Dic5×SL(2,𝔽3) | C22 | semidirect |
| 15. C2×Q8×Dic5 | D3 | semidirect |
| 46. Q8×Dic5 | C2×D3 | semidirect |
| 262. C2×C5 | #5395 | semidirect |
| 298. C5 | C2×#5395 | semidirect |
| 315. C2 | #11751601 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5⋊#226 | 2 |
| C22×C5×GL(2,𝔽3) | 2 |
| C2×Dic5×SL(2,𝔽3) | 2 |
| #11751601 | 2 |
| C2×#65455 | 3 |
| C2×(C2×D3)⋊Dic5 | 4 |
| C2×#5395 | 5 |