Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
500 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 110 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×#4751 | C2 | semidirect |
| 3. C3×C5×#356 | C2 | semidirect |
| 4. C5×#4548 | C2 | semidirect |
| 5. C5×#4477 | C2 | semidirect |
| 20. #69172 | C5 | direct (N × H) |
| 24. C5×#356 | D3 | semidirect |
| 52. #4751 | C2×C5 | semidirect |
| 53. C3×#356 | C2×C5 | semidirect |
| 54. #4548 | C2×C5 | semidirect |
| 55. #4477 | C2×C5 | semidirect |
| 136. #356 | C5×D3 | semidirect |
| 284. C3×C5 | #2132 | semidirect |
| 334. C5 | #69172 | direct (N × H) |
| 349. C3 | C5×#2132 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5725 | 2 |
| C5×#4751 | 2 |
| C3×C5×#356 | 2 |
| C5×#4548 | 2 |
| C5×#4477 | 2 |
| C5×#2132 | 3 |
| #69172 | 5 |