Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
328 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 52 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 |
|---|---|---|
| 12. #73115 | C5 | direct (N × H) |
| 107. C5×A4 | #101 | semidirect |
| 182. C22×C5 | #824 | semidirect |
| 225. A4 | C5×#101 | semidirect |
| 263. C5 | #73115 | direct (N × H) |
| 271. C22 | C5×#824 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×A4⋊Q8 | 2 |
| C5×A4×M16 | 2 |
| C5×#5409 | 2 |
| C5×#1901 | 3 |
| C5×#824 | 4 |
| #73115 | 5 |