Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
514 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C5 | D4×S4 |
| commutator, cosocle | #41⋊C3 | C23×C5 |
| Frattini | C4 | C22×C5×S4 |
| Fitting | C5×#576 | D3 |
| hypercenter | C5×Q16 | S4 |
| hypocenter | SL(2,𝔽3) | C2×C5×D4 |
| LCS | G ▷ #41⋊C3 ▷ SL(2,𝔽3) | |
| UCS | C1 ◁ C2×C5 ◁ C4×C5 ◁ C5×Q16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#5925 | C2 | semidirect |
| 2. C5×#576⋊C3 | C2 | semidirect |
| 3. C5×#5429 | C2 | semidirect |
| 4. C5×#5407 | C2 | semidirect |
| 5. C5×#5404 | C2 | semidirect |
| 7. C5×#994 | C22 | semidirect |
| 9. C5×#986 | C22 | semidirect |
| 13. C5×#131⋊C3 | C22 | semidirect |
| 14. C5×GU(2,𝔽3) | C22 | semidirect |
| 15. #85468 | C5 | direct (N × H) |
| 18. C5×#576 | D3 | semidirect |
| 31. C5×GL(2,𝔽3) | D4 | semidirect |
| 32. C5×#226 | D4 | semidirect |
| 37. #5925 | C2×C5 | semidirect |
| 38. #576⋊C3 | C2×C5 | semidirect |
| 39. #5429 | C2×C5 | semidirect |
| 40. #5407 | C2×C5 | semidirect |
| 41. #5404 | C2×C5 | semidirect |
| 81. #994 | C22×C5 | semidirect |
| 83. #986 | C22×C5 | semidirect |
| 87. #131⋊C3 | C22×C5 | semidirect |
| 88. GU(2,𝔽3) | C22×C5 | semidirect |
| 132. #576 | C5×D3 | semidirect |
| 150. GL(2,𝔽3) | C5×D4 | semidirect |
| 151. #226 | C5×D4 | semidirect |
| 320. C5 | #85468 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5925 | 2 |
| C5×#576⋊C3 | 2 |
| C5×#5429 | 2 |
| C5×#5407 | 2 |
| C5×#5404 | 2 |
| C5×#3292 | 3 |
| C5×#919 | 4 |
| #85468 | 5 |