Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
508 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 64 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×#5926 | C2 | semidirect |
| 2. C5×#5924 | C2 | semidirect |
| 3. C5×#577⋊C3 | C2 | semidirect |
| 4. C5×#5430 | C2 | semidirect |
| 5. C5×#5429 | C2 | semidirect |
| 6. C5×#5406 | C2 | semidirect |
| 7. C5×#5404 | C2 | semidirect |
| 10. C5×#994 | C22 | semidirect |
| 15. C5×#984 | C22 | semidirect |
| 19. C5×#131⋊C3 | C22 | semidirect |
| 20. C5×GU(2,𝔽3) | C22 | semidirect |
| 21. #85469 | C5 | direct (N × H) |
| 25. C5×#577 | D3 | semidirect |
| 43. C5×GL(2,𝔽3) | D4 | semidirect |
| 45. C5×#226 | D4 | semidirect |
| 51. #5926 | C2×C5 | semidirect |
| 52. #5924 | C2×C5 | semidirect |
| 53. #577⋊C3 | C2×C5 | semidirect |
| 54. #5430 | C2×C5 | semidirect |
| 55. #5429 | C2×C5 | semidirect |
| 56. #5406 | C2×C5 | semidirect |
| 57. #5404 | C2×C5 | semidirect |
| 61. C5×H(5,𝔽2) | C2×D3 | semidirect |
| 91. C5×#131 | C2×D3 | semidirect |
| 119. #994 | C22×C5 | semidirect |
| 124. #984 | C22×C5 | semidirect |
| 128. #131⋊C3 | C22×C5 | semidirect |
| 129. GU(2,𝔽3) | C22×C5 | semidirect |
| 197. #577 | C5×D3 | semidirect |
| 223. GL(2,𝔽3) | C5×D4 | semidirect |
| 225. #226 | C5×D4 | semidirect |
| 276. H(5,𝔽2) | C2×C5×D3 | semidirect |
| 306. #131 | C2×C5×D3 | semidirect |
| 476. C5 | #85469 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5926 | 2 |
| C5×#5924 | 2 |
| C5×#577⋊C3 | 2 |
| C5×#5430 | 2 |
| C5×#5429 | 2 |
| C5×#5406 | 2 |
| C5×#5404 | 2 |
| C5×#3291 | 3 |
| C5×D3×SD16 | 4 |
| #85469 | 5 |