Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
534 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 108 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×#5386 | C2 | direct (N × H) |
| 9. C2×#5386 | C5 | direct (N × H) |
| 21. C2×C5×SL(2,𝔽3) | Q8 | semidirect |
| 25. #5386 | C2×C5 | direct (N × H) |
| 48. C5×SL(2,𝔽3) | C2×Q8 | semidirect |
| 57. C2×C5×Q8 | Dic6 | semidirect |
| 89. C2×SL(2,𝔽3) | C5×Q8 | semidirect |
| 96. C5×Q8 | C2×Dic6 | semidirect |
| 133. SL(2,𝔽3) | C2×C5×Q8 | semidirect |
| 148. C2×Q8 | C5×Dic6 | semidirect |
| 170. C2×C5 | #5386 | direct (N × H) |
| 179. Q8 | C2×C5×Dic6 | semidirect |
| 195. C5 | C2×#5386 | direct (N × H) |
| 207. C2 | C5×#5386 | 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×#5386 | 2 |
| C2×C5×#475 | 3 |
| C22×C5×Dic6 | 4 |
| C2×#5386 | 5 |