Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
452 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 2. C5×#5419 | C2 | semidirect |
| 3. C2×C5×#859 | C2 | semidirect |
| 4. C5×#5391 | C2 | semidirect |
| 5. C4×C5×#226 | C2 | semidirect |
| 13. #85393 | C5 | direct (N × H) |
| 34. #5419 | C2×C5 | semidirect |
| 35. C2×#859 | C2×C5 | semidirect |
| 36. #5391 | C2×C5 | semidirect |
| 37. C4×#226 | C2×C5 | semidirect |
| 143. C5×D4 | #226 | semidirect |
| 257. D4 | C5×#226 | semidirect |
| 275. C5 | #85393 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D4×SL(2,𝔽3) | 2 |
| C5×#5419 | 2 |
| C2×C5×#859 | 2 |
| C5×#5391 | 2 |
| C4×C5×#226 | 2 |
| C5×#3299 | 3 |
| C5×D4×Dic3 | 4 |
| #85393 | 5 |