Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
514 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 514 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×C5×#984 | C2 | semidirect |
| 3. C5×#5425 | C2 | semidirect |
| 4. C5×C4⋊#226 | C2 | semidirect |
| 5. C4×C5×#226 | C2 | semidirect |
| 14. #85404 | C5 | direct (N × H) |
| 30. C5×#226 | D4 | semidirect |
| 35. C2×#984 | C2×C5 | semidirect |
| 37. #5425 | C2×C5 | semidirect |
| 38. C4⋊#226 | C2×C5 | semidirect |
| 39. C4×#226 | C2×C5 | semidirect |
| 139. #226 | C5×D4 | semidirect |
| 218. C4×C5 | #984 | semidirect |
| 293. C5 | #85404 | direct (N × H) |
| 305. C4 | C5×#984 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#984 | 2 |
| C5×C4⋊(#41⋊C3) | 2 |
| C5×#5425 | 2 |
| C5×C4⋊#226 | 2 |
| C4×C5×#226 | 2 |
| C5×#3278 | 3 |
| C5×#888 | 4 |
| #85404 | 5 |