Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
550 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 550 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×#983 | C2 | semidirect |
| 2. C5×D4×SL(2,𝔽3) | C2 | semidirect |
| 3. C5×#5419 | C2 | semidirect |
| 4. C4×C5×GL(2,𝔽3) | C2 | semidirect |
| 5. C5×C4⋊#226 | C2 | semidirect |
| 14. #85399 | C5 | direct (N × H) |
| 16. C5×D4×Q8 | D3 | semidirect |
| 31. C5×GL(2,𝔽3) | D4 | semidirect |
| 35. C2×#983 | C2×C5 | semidirect |
| 36. D4×SL(2,𝔽3) | C2×C5 | semidirect |
| 37. #5419 | C2×C5 | semidirect |
| 38. C4×GL(2,𝔽3) | C2×C5 | semidirect |
| 39. C4⋊#226 | C2×C5 | semidirect |
| 121. D4×Q8 | C5×D3 | semidirect |
| 146. GL(2,𝔽3) | C5×D4 | semidirect |
| 230. C4×C5 | #983 | semidirect |
| 312. C5 | #85399 | direct (N × H) |
| 326. C4 | C5×#983 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#983 | 2 |
| C5×D4×SL(2,𝔽3) | 2 |
| C5×#5419 | 2 |
| C4×C5×GL(2,𝔽3) | 2 |
| C5×C4⋊#226 | 2 |
| C5×#3276 | 3 |
| C5×#938 | 4 |
| #85399 | 5 |