Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1468 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 1468 conjugacy classes of subgroups — too many to draw. Only its 200 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 | C23×S4 |
| commutator, cosocle, hypocenter | SL(2,𝔽3) | C24×C5 |
| Frattini | C2 | C23×C5×S4 |
| Fitting | C2×C5×H(5,𝔽2) | D3 |
| hypercenter | C2×C5×Q8 | S4 |
| LCS | G ▷ SL(2,𝔽3) | |
| UCS | C1 ◁ C2×C5 ◁ C2×C5×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×#994 | C2 | semidirect |
| 2. C5×#5925 | C2 | semidirect |
| 3. C5×#5924 | C2 | semidirect |
| 4. C5×#5923 | C2 | semidirect |
| 7. C5×#994 | C22 | semidirect |
| 8. C2×C5×#41⋊C3 | C22 | semidirect |
| 9. C5×#986 | C22 | semidirect |
| 10. C5×#985 | C22 | semidirect |
| 11. C5×#984 | C22 | semidirect |
| 12. C5×#983 | C22 | semidirect |
| 13. #87493 | C5 | direct (N × H) |
| 15. C2×C5×H(5,𝔽2) | D3 | semidirect |
| 29. C5×GL(2,𝔽3) | C23 | semidirect |
| 30. C5×#226 | C23 | semidirect |
| 31. C2×#994 | C2×C5 | semidirect |
| 32. #5925 | C2×C5 | semidirect |
| 33. #5924 | C2×C5 | semidirect |
| 34. #5923 | C2×C5 | semidirect |
| 70. #994 | C22×C5 | semidirect |
| 71. C2×#41⋊C3 | C22×C5 | semidirect |
| 72. #986 | C22×C5 | semidirect |
| 73. #985 | C22×C5 | semidirect |
| 74. #984 | C22×C5 | semidirect |
| 75. #983 | C22×C5 | semidirect |
| 113. C2×H(5,𝔽2) | C5×D3 | semidirect |
| 131. GL(2,𝔽3) | C23×C5 | semidirect |
| 132. #226 | C23×C5 | semidirect |
| 277. C5 | #87493 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#994 | 2 |
| C5×#5925 | 2 |
| C5×#5924 | 2 |
| C5×#5923 | 2 |
| C5×#3585 | 3 |
| C5×#1007 | 4 |
| #87493 | 5 |