Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
496 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 82 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×#5683 | C2 | semidirect |
| 2. C5×#5062 | C2 | semidirect |
| 3. C5×#4753 | C2 | semidirect |
| 4. C3×C5×#355 | C2 | semidirect |
| 5. C5×#4477 | C2 | semidirect |
| 7. C5×#1007 | C22 | semidirect |
| 16. C3×C5×#101 | C22 | semidirect |
| 17. C5×#836 | C22 | semidirect |
| 20. #69160 | C5 | direct (N × H) |
| 25. C5×#355 | D3 | semidirect |
| 50. #5683 | C2×C5 | semidirect |
| 51. #5062 | C2×C5 | semidirect |
| 52. #4753 | C2×C5 | semidirect |
| 53. C3×#355 | C2×C5 | semidirect |
| 54. #4477 | C2×C5 | semidirect |
| 67. C5×#101 | C2×D3 | semidirect |
| 92. #1007 | C22×C5 | semidirect |
| 101. C3×#101 | C22×C5 | semidirect |
| 102. #836 | C22×C5 | semidirect |
| 133. #355 | C5×D3 | semidirect |
| 206. #101 | C2×C5×D3 | semidirect |
| 272. C3×C5 | #2202 | semidirect |
| 319. C5 | #69160 | direct (N × H) |
| 333. C3 | C5×#2202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5683 | 2 |
| C5×#5062 | 2 |
| C5×#4753 | 2 |
| C3×C5×#355 | 2 |
| C5×#4477 | 2 |
| C5×#2202 | 3 |
| #69160 | 5 |