Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
448 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 448 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×C4×C5×SL(2,𝔽3) | C2 | semidirect |
| 3. C5×#5419 | C2 | semidirect |
| 4. C5×#5395 | C2 | semidirect |
| 5. C4×C5×GL(2,𝔽3) | C2 | semidirect |
| 6. C5×#5389 | C2 | semidirect |
| 7. C4×C5×#226 | C2 | semidirect |
| 17. #85329 | C5 | direct (N × H) |
| 19. C2×C4×C5×Q8 | D3 | semidirect |
| 44. C2×C4×SL(2,𝔽3) | C2×C5 | semidirect |
| 46. #5419 | C2×C5 | semidirect |
| 47. #5395 | C2×C5 | semidirect |
| 48. C4×GL(2,𝔽3) | C2×C5 | semidirect |
| 49. #5389 | C2×C5 | semidirect |
| 50. C4×#226 | C2×C5 | semidirect |
| 151. C2×C4×Q8 | C5×D3 | semidirect |
| 381. C5 | #85329 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×SL(2,𝔽3) | 2 |
| C5×#5421 | 2 |
| C5×#5419 | 2 |
| C5×#5395 | 2 |
| C4×C5×GL(2,𝔽3) | 2 |
| C5×#5389 | 2 |
| C4×C5×#226 | 2 |
| C5×#3108 | 3 |
| C4×C5×#67 | 4 |
| #85329 | 5 |