Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
412 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 3. C5×#5391 | C2 | semidirect |
| 4. C5×#5389 | C2 | semidirect |
| 5. C5×#5386 | C2 | semidirect |
| 13. #85318 | C5 | direct (N × H) |
| 27. C2×C5×SL(2,𝔽3) | Q8 | semidirect |
| 34. #5391 | C2×C5 | semidirect |
| 35. #5389 | C2×C5 | semidirect |
| 36. #5386 | C2×C5 | semidirect |
| 83. C2×C5×Q8 | Dic6 | semidirect |
| 127. C2×SL(2,𝔽3) | C5×Q8 | semidirect |
| 209. C2×Q8 | C5×Dic6 | semidirect |
| 270. C5 | #85318 | 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×#5420 | 2 |
| C5×#5391 | 2 |
| C5×#5389 | 2 |
| C5×#5386 | 2 |
| C5×#3078 | 3 |
| C5×#924 | 4 |
| #85318 | 5 |