Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
364 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 1. C5×C3⋊#564 | C2 | semidirect |
| 4. C3×C5×#330 | C2 | semidirect |
| 5. C5×#4465 | C2 | semidirect |
| 18. #68375 | C5 | direct (N × H) |
| 23. C5×#330 | D3 | semidirect |
| 39. C3⋊#564 | C2×C5 | semidirect |
| 42. C3×#330 | C2×C5 | semidirect |
| 43. #4465 | C2×C5 | semidirect |
| 96. #330 | C5×D3 | semidirect |
| 177. C3×C5 | #1658 | semidirect |
| 202. C5 | #68375 | direct (N × H) |
| 211. C3 | C5×#1658 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C3⋊#564 | 2 |
| C5×#5067 | 2 |
| C5×#4713 | 2 |
| C3×C5×#330 | 2 |
| C5×#4465 | 2 |
| C5×#1658 | 3 |
| #68375 | 5 |