Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
544 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 98 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×#5515 | C2 | semidirect |
| 2. C5×#4991 | C2 | semidirect |
| 4. C5×#4731 | C2 | semidirect |
| 5. C3×C5×#324 | C2 | semidirect |
| 6. C5×#4470 | C2 | semidirect |
| 7. C5×#4467 | C2 | semidirect |
| 28. #68130 | C5 | direct (N × H) |
| 35. C5×#324 | D3 | semidirect |
| 68. #5515 | C2×C5 | semidirect |
| 69. #4991 | C2×C5 | semidirect |
| 71. #4731 | C2×C5 | semidirect |
| 72. C3×#324 | C2×C5 | semidirect |
| 73. #4470 | C2×C5 | semidirect |
| 74. #4467 | C2×C5 | semidirect |
| 186. #324 | C5×D3 | semidirect |
| 391. C3×C5 | #1597 | semidirect |
| 463. C5 | #68130 | direct (N × H) |
| 487. C3 | C5×#1597 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5515 | 2 |
| C5×#4991 | 2 |
| C5×#4732 | 2 |
| C5×#4731 | 2 |
| C3×C5×#324 | 2 |
| C5×#4470 | 2 |
| C5×#4467 | 2 |
| C5×#1597 | 3 |
| #68130 | 5 |