Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
496 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 496 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. C3×C5×H(3,𝔽4) | C2 | semidirect |
| 2. C5×#5062 | C2 | semidirect |
| 3. C5×#4542 | C2 | semidirect |
| 5. C5×#1007 | C22 | semidirect |
| 10. C5×#836 | C22 | semidirect |
| 12. #71951 | C5 | direct (N × H) |
| 13. C5×H(3,𝔽4) | D3 | semidirect |
| 30. C3×H(3,𝔽4) | C2×C5 | semidirect |
| 31. #5062 | C2×C5 | semidirect |
| 32. #4542 | C2×C5 | semidirect |
| 55. #1007 | C22×C5 | semidirect |
| 60. #836 | C22×C5 | semidirect |
| 76. H(3,𝔽4) | C5×D3 | semidirect |
| 162. C3×C5 | #2202 | semidirect |
| 193. C5 | #71951 | direct (N × H) |
| 202. C3 | C5×#2202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×H(3,𝔽4) | 2 |
| C5×#5062 | 2 |
| C5×#4542 | 2 |
| C5×#2202 | 3 |
| #71951 | 5 |