Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
632 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 106 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×#5483 | C2 | semidirect |
| 3. C5×#4731 | C2 | semidirect |
| 4. C3×C5×#323 | C2 | semidirect |
| 5. C5×#4467 | C2 | semidirect |
| 20. #68114 | C5 | direct (N × H) |
| 25. C5×#323 | D3 | semidirect |
| 39. C2×C5×Dic6 | D4 | semidirect |
| 46. C5×C4⋊Dic3 | D4 | semidirect |
| 50. #5483 | C2×C5 | semidirect |
| 52. #4731 | C2×C5 | semidirect |
| 53. C3×#323 | C2×C5 | semidirect |
| 54. #4467 | C2×C5 | semidirect |
| 73. C23×C3×C5 | SD16 | semidirect |
| 140. #323 | C5×D3 | semidirect |
| 176. C2×Dic6 | C5×D4 | semidirect |
| 183. C4⋊Dic3 | C5×D4 | semidirect |
| 198. C23×C5 | #204 | semidirect |
| 241. C23×C3 | C5×SD16 | semidirect |
| 313. C3×C5 | #1596 | semidirect |
| 354. C23 | C5×#204 | semidirect |
| 380. C5 | #68114 | direct (N × H) |
| 403. C3 | C5×#1596 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5483 | 2 |
| C5×#4960 | 2 |
| C5×#4731 | 2 |
| C3×C5×#323 | 2 |
| C5×#4467 | 2 |
| C5×#1596 | 3 |
| #68114 | 5 |