Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
520 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 72 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. C2×C5×#984 | C2 | semidirect |
| 2. C22×C5×#226 | C2 | semidirect |
| 4. C5×#5425 | C2 | semidirect |
| 5. C5×#5419 | C2 | semidirect |
| 6. C5×C4⋊#226 | C2 | semidirect |
| 7. C5×#5388 | C2 | semidirect |
| 19. #85376 | C5 | direct (N × H) |
| 42. C5×#226 | D4 | semidirect |
| 48. C2×#984 | C2×C5 | semidirect |
| 49. C22×#226 | C2×C5 | semidirect |
| 51. #5425 | C2×C5 | semidirect |
| 52. #5419 | C2×C5 | semidirect |
| 53. C4⋊#226 | C2×C5 | semidirect |
| 54. #5388 | C2×C5 | semidirect |
| 205. #226 | C5×D4 | semidirect |
| 309. C22×C5 | #984 | semidirect |
| 431. C5 | #85376 | direct (N × H) |
| 437. C22 | C5×#984 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#984 | 2 |
| C22×C5×#226 | 2 |
| C5×#548⋊C3 | 2 |
| C5×#5425 | 2 |
| C5×#5419 | 2 |
| C5×C4⋊#226 | 2 |
| C5×#5388 | 2 |
| C5×#3270 | 3 |
| C5×#878 | 4 |
| #85376 | 5 |