Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
412 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 90 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×#5672 | C2 | semidirect |
| 3. C5×#4713 | C2 | semidirect |
| 4. C3×C5×#329 | C2 | semidirect |
| 5. C5×#4465 | C2 | semidirect |
| 20. #68354 | C5 | direct (N × H) |
| 25. C5×#329 | D3 | semidirect |
| 46. #5672 | C2×C5 | semidirect |
| 48. #4713 | C2×C5 | semidirect |
| 49. C3×#329 | C2×C5 | semidirect |
| 50. #4465 | C2×C5 | semidirect |
| 118. #329 | C5×D3 | semidirect |
| 228. C3×C5 | #1657 | semidirect |
| 263. C5 | #68354 | direct (N × H) |
| 274. C3 | C5×#1657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5672 | 2 |
| C5×#5058 | 2 |
| C5×#4713 | 2 |
| C3×C5×#329 | 2 |
| C5×#4465 | 2 |
| C5×#1657 | 3 |
| #68354 | 5 |