Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1518 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 1518 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 | C5×#585 | D3 |
| hypercenter | C5×#41 | S4 |
| LCS | G ▷ SL(2,𝔽3) | |
| UCS | C1 ◁ C2×C5 ◁ C5×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#5945 | C2 | semidirect |
| 2. C5×#5926 | C2 | semidirect |
| 3. C5×#5925 | C2 | semidirect |
| 4. C5×#5923 | C2 | semidirect |
| 5. C2×C5×#986 | C2 | semidirect |
| 8. C5×2−1+4⋊C3 | C22 | semidirect |
| 9. C5×#994 | C22 | semidirect |
| 10. C2×C5×#41⋊C3 | C22 | semidirect |
| 11. C5×#986 | C22 | semidirect |
| 12. C5×#986 | C22 | semidirect |
| 13. C5×#985 | C22 | semidirect |
| 14. C5×#984 | C22 | semidirect |
| 15. C5×#983 | C22 | semidirect |
| 16. C2×C5×GL(2,𝔽3) | C22 | semidirect |
| 17. #87498 | C5 | direct (N × H) |
| 18. C5×#585 | D3 | semidirect |
| 35. C5×#41⋊C3 | C23 | semidirect |
| 36. C2×C5×SL(2,𝔽3) | C23 | semidirect |
| 37. C5×GL(2,𝔽3) | C23 | semidirect |
| 38. C5×#226 | C23 | semidirect |
| 39. #5945 | C2×C5 | semidirect |
| 40. #5926 | C2×C5 | semidirect |
| 41. #5925 | C2×C5 | semidirect |
| 42. #5923 | C2×C5 | semidirect |
| 43. C2×#986 | C2×C5 | semidirect |
| 45. C5×2−1+4 | C2×D3 | semidirect |
| 51. C5×H(5,𝔽2) | C2×D3 | semidirect |
| 56. C2×C5×#41 | C2×D3 | semidirect |
| 94. 2−1+4⋊C3 | C22×C5 | semidirect |
| 95. #994 | C22×C5 | semidirect |
| 96. C2×#41⋊C3 | C22×C5 | semidirect |
| 97. #986 | C22×C5 | semidirect |
| 98. #986 | C22×C5 | semidirect |
| 99. #985 | C22×C5 | semidirect |
| 100. #984 | C22×C5 | semidirect |
| 101. #983 | C22×C5 | semidirect |
| 102. C2×GL(2,𝔽3) | C22×C5 | semidirect |
| 157. #585 | C5×D3 | semidirect |
| 180. #41⋊C3 | C23×C5 | semidirect |
| 181. C2×SL(2,𝔽3) | C23×C5 | semidirect |
| 182. GL(2,𝔽3) | C23×C5 | semidirect |
| 183. #226 | C23×C5 | semidirect |
| 221. 2−1+4 | C2×C5×D3 | semidirect |
| 227. H(5,𝔽2) | C2×C5×D3 | semidirect |
| 232. C2×#41 | C2×C5×D3 | semidirect |
| 390. C5 | #87498 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5945 | 2 |
| C5×#5926 | 2 |
| C5×#5925 | 2 |
| C5×#5923 | 2 |
| C2×C5×#986 | 2 |
| C5×#3585 | 3 |
| C5×#1009 | 4 |
| #87498 | 5 |