Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1514 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 1514 conjugacy classes of subgroups — too many to draw. Only its 204 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C5 | C2×S4 |
| commutator, cosocle, hypocenter | SL(2,𝔽3) | C24×C5 |
| Frattini | C2 | C23×C5×S4 |
| Fitting | C22×C5×#41 | D3 |
| socle | C22×C5 | C22×S4 |
| hypercenter | C22×C4×C5 | S4 |
| LCS | G ▷ SL(2,𝔽3) | |
| UCS | C1 ◁ C2×C4×C5 ◁ C22×C4×C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C5×#41⋊C3 | C2 | semidirect |
| 2. C5×#5923 | C2 | direct (N × H) |
| 3. C2×C5×#986 | C2 | semidirect |
| 4. C2×C5×#985 | C2 | semidirect |
| 5. C2×C5×#984 | C2 | semidirect |
| 6. C2×C5×#983 | C2 | semidirect |
| 10. C2×C5×#41⋊C3 | C22 | semidirect |
| 11. C2×C5×#41⋊C3 | C22 | semidirect |
| 12. C22×C5×SL(2,𝔽3) | C22 | semidirect |
| 13. C5×#986 | C22 | semidirect |
| 14. C5×#985 | C22 | semidirect |
| 15. C5×#984 | C22 | semidirect |
| 16. C5×#983 | C22 | semidirect |
| 17. C2×C5×GL(2,𝔽3) | C22 | semidirect |
| 18. C2×C5×#226 | C22 | semidirect |
| 19. C2×#5923 | C5 | direct (N × H) |
| 21. C22×C5×#41 | D3 | semidirect |
| 40. C5×#41⋊C3 | C23 | semidirect |
| 42. C2×C5×SL(2,𝔽3) | C23 | semidirect |
| 43. C5×GL(2,𝔽3) | C23 | semidirect |
| 44. C5×#226 | C23 | semidirect |
| 45. C22×#41⋊C3 | C2×C5 | semidirect |
| 46. #5923 | C2×C5 | direct (N × H) |
| 47. C2×#986 | C2×C5 | semidirect |
| 48. C2×#985 | C2×C5 | semidirect |
| 49. C2×#984 | C2×C5 | semidirect |
| 50. C2×#983 | C2×C5 | semidirect |
| 62. C2×C5×#41 | C2×D3 | semidirect |
| 109. C2×#41⋊C3 | C22×C5 | semidirect |
| 110. C2×#41⋊C3 | C22×C5 | semidirect |
| 111. C22×SL(2,𝔽3) | C22×C5 | semidirect |
| 112. #986 | C22×C5 | semidirect |
| 113. #985 | C22×C5 | semidirect |
| 114. #984 | C22×C5 | semidirect |
| 115. #983 | C22×C5 | semidirect |
| 116. C2×GL(2,𝔽3) | C22×C5 | semidirect |
| 117. C2×#226 | C22×C5 | semidirect |
| 183. C22×#41 | C5×D3 | semidirect |
| 210. #41⋊C3 | C23×C5 | semidirect |
| 212. C2×SL(2,𝔽3) | C23×C5 | semidirect |
| 213. GL(2,𝔽3) | C23×C5 | semidirect |
| 214. #226 | C23×C5 | semidirect |
| 270. C2×#41 | C2×C5×D3 | semidirect |
| 412. C2×C5 | #5923 | direct (N × H) |
| 462. C5 | C2×#5923 | direct (N × H) |
| 485. C2 | C5×#5923 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×#41⋊C3 | 2 |
| C5×#5923 | 2 |
| C2×C5×#986 | 2 |
| C2×C5×#985 | 2 |
| C2×C5×#984 | 2 |
| C2×C5×#983 | 2 |
| C2×C5×#575 | 3 |
| C2×C5×#235 | 4 |
| C2×#5923 | 5 |