Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
432 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 432 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 |
|---|---|---|
| 3. C5×#4983 | C2 | semidirect |
| 4. C5×#4971 | C2 | semidirect |
| 6. C5×#4469 | C2 | semidirect |
| 7. C5×#4467 | C2 | semidirect |
| 28. #71166 | C5 | direct (N × H) |
| 66. #4983 | C2×C5 | semidirect |
| 67. #4971 | C2×C5 | semidirect |
| 69. #4469 | C2×C5 | semidirect |
| 70. #4467 | C2×C5 | semidirect |
| 338. C3×C5 | #1609 | semidirect |
| 394. C5 | #71166 | direct (N × H) |
| 412. C3 | C5×#1609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5602 | 2 |
| C3×C5×#480 | 2 |
| C5×#4983 | 2 |
| C5×#4971 | 2 |
| C5×#4537 | 2 |
| C5×#4469 | 2 |
| C5×#4467 | 2 |
| C5×#1609 | 3 |
| #71166 | 5 |