Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
398 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 398 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. C5×Q8×SL(2,𝔽3) | C2 | semidirect |
| 4. C5×#5391 | C2 | semidirect |
| 5. C5×#5389 | C2 | semidirect |
| 13. #85431 | C5 | direct (N × H) |
| 14. C5×Q82 | D3 | semidirect |
| 28. C5×GL(2,𝔽3) | Q8 | semidirect |
| 32. Q8×SL(2,𝔽3) | C2×C5 | semidirect |
| 35. #5391 | C2×C5 | semidirect |
| 36. #5389 | C2×C5 | semidirect |
| 103. Q82 | C5×D3 | semidirect |
| 125. GL(2,𝔽3) | C5×Q8 | semidirect |
| 261. C5 | #85431 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q8×SL(2,𝔽3) | 2 |
| C5×#5394 | 2 |
| C4×C5×GL(2,𝔽3) | 2 |
| C5×#5391 | 2 |
| C5×#5389 | 2 |
| C5×#3385 | 3 |
| C5×#946 | 4 |
| #85431 | 5 |