Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1476 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 1476 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×C5×2−1+4 | D3 |
| hypercenter | C2×C5×D4 | S4 |
| LCS | G ▷ SL(2,𝔽3) | |
| UCS | C1 ◁ C2×C5 ◁ C2×C5×D4 | |
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×#5927 | C2 | semidirect |
| 3. C5×#5926 | C2 | semidirect |
| 4. C5×#5923 | C2 | semidirect |
| 5. C2×C5×#983 | C2 | semidirect |
| 8. C5×2−1+4⋊C3 | C22 | semidirect |
| 9. C2×C5×#41⋊C3 | C22 | semidirect |
| 10. C22×C5×SL(2,𝔽3) | C22 | semidirect |
| 11. C5×#986 | C22 | semidirect |
| 12. C5×#985 | C22 | semidirect |
| 13. C5×#984 | C22 | semidirect |
| 14. C5×#983 | C22 | semidirect |
| 15. C5×#983 | C22 | semidirect |
| 16. C2×C5×GL(2,𝔽3) | C22 | semidirect |
| 17. C2×C5×#226 | C22 | semidirect |
| 18. #87496 | C5 | direct (N × H) |
| 20. C2×C5×2−1+4 | D3 | semidirect |
| 40. C2×2−1+4⋊C3 | C2×C5 | semidirect |
| 41. #5927 | C2×C5 | semidirect |
| 42. #5926 | C2×C5 | semidirect |
| 43. #5923 | C2×C5 | semidirect |
| 44. C2×#983 | C2×C5 | semidirect |
| 48. C5×2−1+4 | C2×D3 | semidirect |
| 57. C2×C5×#41 | C2×D3 | semidirect |
| 59. C22×C5×Q8 | C2×D3 | semidirect |
| 100. 2−1+4⋊C3 | C22×C5 | semidirect |
| 101. C2×#41⋊C3 | C22×C5 | semidirect |
| 102. C22×SL(2,𝔽3) | C22×C5 | semidirect |
| 103. #986 | C22×C5 | semidirect |
| 104. #985 | C22×C5 | semidirect |
| 105. #984 | C22×C5 | semidirect |
| 106. #983 | C22×C5 | semidirect |
| 107. #983 | C22×C5 | semidirect |
| 108. C2×GL(2,𝔽3) | C22×C5 | semidirect |
| 109. C2×#226 | C22×C5 | semidirect |
| 170. C2×2−1+4 | C5×D3 | semidirect |
| 237. 2−1+4 | C2×C5×D3 | semidirect |
| 246. C2×#41 | C2×C5×D3 | semidirect |
| 248. C22×Q8 | C2×C5×D3 | semidirect |
| 417. C5 | #87496 | 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×#5927 | 2 |
| C5×#5926 | 2 |
| C5×#5923 | 2 |
| C2×C5×#983 | 2 |
| C5×#3586 | 3 |
| C5×#1004 | 4 |
| #87496 | 5 |