Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
452 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 68 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×D4×SL(2,𝔽3) | C2 | semidirect |
| 2. C5×#5421 | C2 | semidirect |
| 3. C5×#5421 | C2 | semidirect |
| 4. C5×#5420 | C2 | semidirect |
| 5. C2×C5×#859 | C2 | semidirect |
| 6. C5×#5394 | C2 | semidirect |
| 7. C5×#5389 | C2 | semidirect |
| 17. #85401 | C5 | direct (N × H) |
| 19. C5×D4×Q8 | D3 | semidirect |
| 44. D4×SL(2,𝔽3) | C2×C5 | semidirect |
| 45. #5421 | C2×C5 | semidirect |
| 46. #5421 | C2×C5 | semidirect |
| 47. #5420 | C2×C5 | semidirect |
| 48. C2×#859 | C2×C5 | semidirect |
| 49. #5394 | C2×C5 | semidirect |
| 50. #5389 | C2×C5 | semidirect |
| 154. D4×Q8 | C5×D3 | semidirect |
| 402. C5 | #85401 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D4×SL(2,𝔽3) | 2 |
| C5×#5421 | 2 |
| C5×#5420 | 2 |
| C2×C5×#859 | 2 |
| C5×#5394 | 2 |
| C5×#5389 | 2 |
| C5×#3320 | 3 |
| C5×#939 | 4 |
| #85401 | 5 |