Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
500 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 2. #11749372 | C2 | semidirect |
| 3. #11746369 | C2 | semidirect |
| 4. C3×#64768 | C2 | semidirect |
| 5. #11746013 | C2 | semidirect |
| 24. #64768 | D3 | semidirect |
| 284. C3×C5 | #2132 | semidirect |
| 334. C5 | #69172 | semidirect |
| 349. C3 | #10602613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5725 | 2 |
| #11749372 | 2 |
| #11746369 | 2 |
| C3×#64768 | 2 |
| #11746013 | 2 |
| #10602613 | 3 |
| #69172 | 5 |