Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
632 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 114 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×#543 | C2 | semidirect |
| 2. C5×#5046 | C2 | semidirect |
| 4. C5×#4538 | C2 | semidirect |
| 5. C5×#4525 | C2 | semidirect |
| 20. #71892 | C5 | direct (N × H) |
| 21. C5×#543 | D3 | semidirect |
| 29. C2×C3×C5×Q8 | D4 | semidirect |
| 43. C3×C5×C4⋊C4 | D4 | semidirect |
| 50. C3×#543 | C2×C5 | semidirect |
| 51. #5046 | C2×C5 | semidirect |
| 53. #4538 | C2×C5 | semidirect |
| 54. #4525 | C2×C5 | semidirect |
| 73. C23×C3×C5 | SD16 | semidirect |
| 115. C2×C5×Q8 | #67 | semidirect |
| 131. C5×C4⋊C4 | #67 | semidirect |
| 136. #543 | C5×D3 | semidirect |
| 166. C2×C3×Q8 | C5×D4 | semidirect |
| 180. C3×C4⋊C4 | C5×D4 | semidirect |
| 198. C23×C5 | #215 | semidirect |
| 241. C23×C3 | C5×SD16 | semidirect |
| 292. C2×Q8 | C5×#67 | semidirect |
| 308. C4⋊C4 | C5×#67 | semidirect |
| 313. C3×C5 | #1596 | semidirect |
| 354. C23 | C5×#215 | semidirect |
| 380. C5 | #71892 | 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 |
|---|---|
| C3×C5×#543 | 2 |
| C5×#5046 | 2 |
| C5×#4960 | 2 |
| C5×#4538 | 2 |
| C5×#4525 | 2 |
| C5×#1596 | 3 |
| #71892 | 5 |