Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
552 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×#986 | C2 | semidirect |
| 2. C2×C5×#985 | C2 | semidirect |
| 3. C5×C4⋊(#41⋊C3) | C2 | semidirect |
| 4. C5×#5427 | C2 | semidirect |
| 5. C5×#5425 | C2 | semidirect |
| 6. C5×#5395 | C2 | semidirect |
| 7. C5×#5394 | C2 | semidirect |
| 10. C2×C5×#41⋊C3 | C22 | semidirect |
| 15. C2×C5×#226 | C22 | semidirect |
| 17. C4×C5×SL(2,𝔽3) | C22 | semidirect |
| 18. C5×#859 | C22 | semidirect |
| 19. #85409 | C5 | direct (N × H) |
| 22. C5×#550 | D3 | semidirect |
| 41. C5×GL(2,𝔽3) | D4 | semidirect |
| 48. C2×#986 | C2×C5 | semidirect |
| 49. C2×#985 | C2×C5 | semidirect |
| 50. C4⋊(#41⋊C3) | C2×C5 | semidirect |
| 51. #5427 | C2×C5 | semidirect |
| 52. #5425 | C2×C5 | semidirect |
| 53. #5395 | C2×C5 | semidirect |
| 54. #5394 | C2×C5 | semidirect |
| 110. C2×#41⋊C3 | C22×C5 | semidirect |
| 115. C2×#226 | C22×C5 | semidirect |
| 117. C4×SL(2,𝔽3) | C22×C5 | semidirect |
| 118. #859 | C22×C5 | semidirect |
| 175. #550 | C5×D3 | semidirect |
| 206. GL(2,𝔽3) | C5×D4 | semidirect |
| 454. C5 | #85409 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#986 | 2 |
| C2×C5×#985 | 2 |
| C5×C4⋊(#41⋊C3) | 2 |
| C5×#5427 | 2 |
| C5×#5425 | 2 |
| C5×#5395 | 2 |
| C5×#5394 | 2 |
| C5×#3268 | 3 |
| C5×#894 | 4 |
| #85409 | 5 |