Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
532 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 532 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 |
|---|---|---|
| 1. C5×#5500 | C2 | semidirect |
| 4. C3×C5×#324 | C2 | semidirect |
| 5. C5×#4467 | C2 | semidirect |
| 20. #68138 | C5 | direct (N × H) |
| 25. C5×#324 | D3 | semidirect |
| 48. #5500 | C2×C5 | semidirect |
| 51. C3×#324 | C2×C5 | semidirect |
| 52. #4467 | C2×C5 | semidirect |
| 80. C2×C3×C4×C5 | SD16 | semidirect |
| 131. #324 | C5×D3 | semidirect |
| 194. C2×C4×C5 | #204 | semidirect |
| 229. C2×C3×C4 | C5×SD16 | semidirect |
| 281. C3×C5 | #1599 | semidirect |
| 328. C2×C4 | C5×#204 | semidirect |
| 337. C5 | #68138 | direct (N × H) |
| 356. C3 | C5×#1599 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5500 | 2 |
| C5×#4991 | 2 |
| C5×#4731 | 2 |
| C3×C5×#324 | 2 |
| C5×#4467 | 2 |
| C5×#1599 | 3 |
| #68138 | 5 |