Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
418 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 418 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×#557⋊C3 | C2 | semidirect |
| 4. C5×#5391 | C2 | semidirect |
| 5. C5×#5386 | C2 | semidirect |
| 13. #85424 | C5 | direct (N × H) |
| 14. C5×#557 | D3 | semidirect |
| 28. C5×GL(2,𝔽3) | Q8 | semidirect |
| 32. #557⋊C3 | C2×C5 | semidirect |
| 35. #5391 | C2×C5 | semidirect |
| 36. #5386 | C2×C5 | semidirect |
| 71. C5×SL(2,𝔽3) | C2×Q8 | semidirect |
| 104. #557 | C5×D3 | semidirect |
| 126. GL(2,𝔽3) | C5×Q8 | semidirect |
| 187. SL(2,𝔽3) | C2×C5×Q8 | semidirect |
| 263. C5 | #85424 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#557⋊C3 | 2 |
| C5×#5394 | 2 |
| C4×C5×GL(2,𝔽3) | 2 |
| C5×#5391 | 2 |
| C5×#5386 | 2 |
| C5×#3386 | 3 |
| C5×#897 | 4 |
| #85424 | 5 |