Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
540 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 540 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×#5061 | C2 | semidirect |
| 3. C5×#5032 | C2 | semidirect |
| 4. C5×#4541 | C2 | semidirect |
| 5. C5×#4536 | C2 | semidirect |
| 20. #71950 | C5 | direct (N × H) |
| 21. C5×H(3,𝔽4) | D3 | semidirect |
| 26. C24×C3×C5 | D4 | semidirect |
| 28. C2×C3×C5×Q8 | D4 | semidirect |
| 42. C3×C5×C22⋊C4 | D4 | semidirect |
| 44. C3×C42×C5 | D4 | semidirect |
| 50. C3×H(3,𝔽4) | C2×C5 | semidirect |
| 51. #5061 | C2×C5 | semidirect |
| 52. #5032 | C2×C5 | semidirect |
| 53. #4541 | C2×C5 | semidirect |
| 54. #4536 | C2×C5 | semidirect |
| 106. C24×C5 | #67 | semidirect |
| 110. C2×C5×Q8 | #67 | semidirect |
| 127. C5×C22⋊C4 | #67 | semidirect |
| 129. C42×C5 | #67 | semidirect |
| 130. H(3,𝔽4) | C5×D3 | semidirect |
| 151. C24×C3 | C5×D4 | semidirect |
| 153. C2×C3×Q8 | C5×D4 | semidirect |
| 167. C3×C22⋊C4 | C5×D4 | semidirect |
| 169. C3×C42 | C5×D4 | semidirect |
| 257. C24 | C5×#67 | semidirect |
| 261. C2×Q8 | C5×#67 | semidirect |
| 278. C22⋊C4 | C5×#67 | semidirect |
| 280. C42 | C5×#67 | semidirect |
| 281. C3×C5 | #2199 | semidirect |
| 332. C5 | #71950 | direct (N × H) |
| 349. C3 | C5×#2199 | 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×#5061 | 2 |
| C5×#5032 | 2 |
| C5×#4541 | 2 |
| C5×#4536 | 2 |
| C5×#2199 | 3 |
| #71950 | 5 |