Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
436 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 3. C5×#5091 | C2 | semidirect |
| 5. C5×#4456 | C2 | semidirect |
| 18. #71270 | C5 | direct (N × H) |
| 41. #5091 | C2×C5 | semidirect |
| 43. #4456 | C2×C5 | semidirect |
| 194. C3×C5 | #1630 | semidirect |
| 225. C5 | #71270 | direct (N × H) |
| 235. C3 | C5×#1630 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5713 | 2 |
| C3×C5×#492 | 2 |
| C5×#5091 | 2 |
| C5×#4544 | 2 |
| C5×#4456 | 2 |
| C5×#1630 | 3 |
| #71270 | 5 |