Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
368 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 368 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 |
|---|---|---|
| 2. C5×#5069 | C2 | semidirect |
| 4. C5×#4702 | C2 | semidirect |
| 5. C3×C5×#330 | C2 | semidirect |
| 6. C5×#4465 | C2 | semidirect |
| 28. #68379 | C5 | direct (N × H) |
| 34. C5×#330 | D3 | semidirect |
| 64. #5069 | C2×C5 | semidirect |
| 66. #4702 | C2×C5 | semidirect |
| 67. C3×#330 | C2×C5 | semidirect |
| 68. #4465 | C2×C5 | semidirect |
| 159. #330 | C5×D3 | semidirect |
| 300. C3×C5 | #1664 | semidirect |
| 340. C5 | #68379 | direct (N × H) |
| 354. C3 | C5×#1664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5699 | 2 |
| C5×#5069 | 2 |
| C5×#4714 | 2 |
| C5×#4702 | 2 |
| C3×C5×#330 | 2 |
| C5×#4465 | 2 |
| C5×#4464 | 2 |
| C5×#1664 | 3 |
| #68379 | 5 |