Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
280 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 227. C3×C5 | #1696 | semidirect |
| 260. C5 | #71153 | semidirect |
| 271. C3 | #10602173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5078 | 2 |
| C3×#65380 | 2 |
| #11746954 | 2 |
| #11746861 | 2 |
| #11746367 | 2 |
| #11745866 | 2 |
| #11745862 | 2 |
| #10602173 | 3 |
| #71153 | 5 |