Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
686 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | D4×A4 |
| commutator, cosocle | #41 | C23×C3×C5 |
| Frattini | C4 | C23×C5×A4 |
| Fitting | C2×C5×#578 | C3 |
| hypercenter | C2×C5×D8 | A4 |
| hypocenter | Q8 | C2×C3×C5×D4 |
| LCS | G ▷ #41 ▷ Q8 | |
| UCS | C1 ◁ C22×C5 ◁ C2×C4×C5 ◁ C2×C5×D8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×2−1+4⋊C3 | C2 | semidirect |
| 2. C5×#578⋊C3 | C2 | direct (N × H) |
| 3. C2×C5×#131⋊C3 | C2 | semidirect |
| 4. C2×C5×#578 | C3 | semidirect |
| 6. C5×2−1+4⋊C3 | C22 | semidirect |
| 10. C5×#131⋊C3 | C22 | semidirect |
| 11. C2×#578⋊C3 | C5 | direct (N × H) |
| 12. C2×C5×2−1+4 | C2×C3 | semidirect |
| 14. C5×#578 | C2×C3 | semidirect |
| 18. C2×C5×#131 | C2×C3 | semidirect |
| 26. C2×2−1+4⋊C3 | C2×C5 | semidirect |
| 27. #578⋊C3 | C2×C5 | direct (N × H) |
| 28. C2×#131⋊C3 | C2×C5 | semidirect |
| 32. C5×2−1+4 | C22×C3 | semidirect |
| 49. C5×#131 | C22×C3 | semidirect |
| 52. C2×#578 | C3×C5 | semidirect |
| 60. 2−1+4⋊C3 | C22×C5 | semidirect |
| 64. #131⋊C3 | C22×C5 | semidirect |
| 101. C2×2−1+4 | C2×C3×C5 | semidirect |
| 103. #578 | C2×C3×C5 | semidirect |
| 107. C2×#131 | C2×C3×C5 | semidirect |
| 151. 2−1+4 | C22×C3×C5 | semidirect |
| 168. #131 | C22×C3×C5 | semidirect |
| 236. C2×C5 | #578⋊C3 | direct (N × H) |
| 269. C5 | C2×#578⋊C3 | direct (N × H) |
| 285. C2 | C5×#578⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×2−1+4⋊C3 | 2 |
| C5×#578⋊C3 | 2 |
| C2×C5×#131⋊C3 | 2 |
| C2×C5×#578 | 3 |
| C2×C3×C5×D8 | 4 |
| C2×#578⋊C3 | 5 |