Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
386 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 4. C5×C4⋊#226 | C2 | semidirect |
| 5. C5×#5389 | C2 | semidirect |
| 6. C5×#5388 | C2 | semidirect |
| 7. C4×C5×#226 | C2 | semidirect |
| 17. #85352 | C5 | direct (N × H) |
| 47. C4⋊#226 | C2×C5 | semidirect |
| 48. #5389 | C2×C5 | semidirect |
| 49. #5388 | C2×C5 | semidirect |
| 50. C4×#226 | C2×C5 | semidirect |
| 358. C5 | #85352 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#519⋊C3 | 2 |
| C5×#5419 | 2 |
| C5×C4⋊#226 | 2 |
| C5×#5389 | 2 |
| C5×#5388 | 2 |
| C4×C5×#226 | 2 |
| C5×#3127 | 3 |
| C5×#879 | 4 |
| #85352 | 5 |