Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1296 conjugacy classes of subgroups; only the 528 normal subgroups are shown.
This group has 1296 conjugacy classes of subgroups — too many to draw. Only its 528 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C3×C5 | C24 |
| commutator | C22 | C23×C3×C4×C5 |
| Frattini, cosocle | C23 | C24×C3×C5 |
| prime radical | C2×C3×C5×#127 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C3×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×C5×#386 | C2 | semidirect |
| 3. C3×C5×#383 | C2 | semidirect |
| 4. C5×#2380 | C3 | direct (N × H) |
| 7. C3×C5×#127 | C4 | semidirect |
| 11. C3×#2380 | C5 | direct (N × H) |
| 13. C5×#386 | C2×C3 | semidirect |
| 14. C5×#383 | C2×C3 | semidirect |
| 18. C2×C3×C5×D4 | C2×C4 | semidirect |
| 23. C3×C42×C5 | C2×C4 | semidirect |
| 25. C3×#386 | C2×C5 | semidirect |
| 26. C3×#383 | C2×C5 | semidirect |
| 29. C5×#127 | C3×C4 | semidirect |
| 33. #2380 | C3×C5 | direct (N × H) |
| 45. C3×#127 | C4×C5 | semidirect |
| 52. C2×C5×D4 | C2×C3×C4 | semidirect |
| 57. C42×C5 | C2×C3×C4 | semidirect |
| 59. #386 | C2×C3×C5 | semidirect |
| 60. #383 | C2×C3×C5 | semidirect |
| 71. C2×C3×D4 | C2×C4×C5 | semidirect |
| 76. C3×C42 | C2×C4×C5 | semidirect |
| 88. #127 | C3×C4×C5 | semidirect |
| 114. C2×D4 | C2×C3×C4×C5 | semidirect |
| 119. C42 | C2×C3×C4×C5 | semidirect |
| 120. C3×C5 | #2380 | direct (N × H) |
| 143. C5 | C3×#2380 | direct (N × H) |
| 151. C3 | C5×#2380 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×#127 | 2 |
| C3×C5×#386 | 2 |
| C3×C5×#383 | 2 |
| C5×#2380 | 3 |
| C3×#2380 | 5 |