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 |
|---|---|---|
| 3. C5×#5082 | C2 | semidirect |
| 4. C5×#5081 | C2 | semidirect |
| 6. C5×#4465 | C2 | semidirect |
| 7. C5×#4465 | C2 | semidirect |
| 28. #71247 | C5 | direct (N × H) |
| 65. #5082 | C2×C5 | semidirect |
| 66. #5081 | C2×C5 | semidirect |
| 68. #4465 | C2×C5 | semidirect |
| 69. #4465 | C2×C5 | semidirect |
| 300. C3×C5 | #1664 | semidirect |
| 340. C5 | #71247 | 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×#5672 | 2 |
| C3×C5×#489 | 2 |
| C5×#5082 | 2 |
| C5×#5081 | 2 |
| C5×#4540 | 2 |
| C5×#4465 | 2 |
| C5×#1664 | 3 |
| #71247 | 5 |