Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
438 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 4. C5×#5389 | C2 | direct (N × H) |
| 11. C2×#5389 | C5 | direct (N × H) |
| 30. #5389 | C2×C5 | direct (N × H) |
| 203. C2×C5 | #5389 | direct (N × H) |
| 230. C5 | C2×#5389 | direct (N × H) |
| 243. C2 | C5×#5389 | 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 |
| C2×C5×#859 | 2 |
| C5×#5389 | 2 |
| C2×C5×#479 | 3 |
| C2×C5×Dic3⋊C4 | 4 |
| C2×#5389 | 5 |