Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
628 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 130 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×#5076 | C2 | semidirect |
| 3. C5×#5008 | C2 | semidirect |
| 4. C5×#4544 | C2 | semidirect |
| 5. C5×D4⋊(C3⋊C8) | C2 | semidirect |
| 13. C5×#869 | C22 | semidirect |
| 16. C5×C4⋊(C3⋊C8) | C22 | semidirect |
| 17. C4×C5×C3⋊C8 | C22 | semidirect |
| 18. #71907 | C5 | direct (N × H) |
| 42. #5076 | C2×C5 | semidirect |
| 43. #5008 | C2×C5 | semidirect |
| 44. #4544 | C2×C5 | semidirect |
| 45. D4⋊(C3⋊C8) | C2×C5 | semidirect |
| 67. C3×C5×D4 | SD16 | semidirect |
| 83. #869 | C22×C5 | semidirect |
| 86. C4⋊(C3⋊C8) | C22×C5 | semidirect |
| 87. C4×C3⋊C8 | C22×C5 | semidirect |
| 149. C5×D4 | #214 | semidirect |
| 182. C3×D4 | C5×SD16 | semidirect |
| 221. C3×C5 | #1629 | semidirect |
| 248. D4 | C5×#214 | semidirect |
| 261. C5 | #71907 | direct (N × H) |
| 274. C3 | C5×#1629 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×D42 | 2 |
| C5×#5076 | 2 |
| C5×#5008 | 2 |
| C5×#4544 | 2 |
| C5×D4⋊(C3⋊C8) | 2 |
| C5×#1629 | 3 |
| #71907 | 5 |