Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
564 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 134 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. C5×#5500 | C2 | semidirect |
| 4. C3×C5×#343 | C2 | semidirect |
| 5. C5×#4555 | C2 | semidirect |
| 18. #68995 | C5 | direct (N × H) |
| 22. C5×#343 | D3 | semidirect |
| 31. C2×C5×D12 | Q8 | semidirect |
| 45. #5500 | C2×C5 | semidirect |
| 48. C3×#343 | C2×C5 | semidirect |
| 49. #4555 | C2×C5 | semidirect |
| 118. #343 | C5×D3 | semidirect |
| 143. C2×D12 | C5×Q8 | semidirect |
| 253. C3×C5 | #2027 | semidirect |
| 303. C5 | #68995 | direct (N × H) |
| 320. C3 | C5×#2027 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5500 | 2 |
| C5×#5131 | 2 |
| C5×#4988 | 2 |
| C3×C5×#343 | 2 |
| C5×#4555 | 2 |
| C5×#2027 | 3 |
| #68995 | 5 |