Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1384 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 1384 conjugacy classes of subgroups — too many to draw. Only its 235 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×C5⋊D5 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C52×#123 | C2 |
| hypercenter | #123 | C5⋊D5 |
| hypocenter | C52 | #534 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D4×C5⋊D5 | C2 | semidirect |
| 2. C22×C4⋊(C5⋊D5) | C2 | semidirect |
| 3. C52×#123 | C2 | semidirect |
| 4. #11717257 | C2 | semidirect |
| 5. #11717249 | C2 | semidirect |
| 6. #11717215 | C2 | semidirect |
| 7. #11717214 | C2 | semidirect |
| 8. #11717204 | C2 | semidirect |
| 9. #11717202 | C2 | semidirect |
| 10. #11717202 | C2 | semidirect |
| 11. C22⋊C4×C5⋊D5 | C2 | semidirect |
| 13. C23×C5⋊D5 | C22 | semidirect |
| 14. C23×C5⋊D5 | C22 | semidirect |
| 16. C22×C4×C52 | C22 | semidirect |
| 18. C2×C22⋊(C5⋊D5) | C22 | semidirect |
| 19. C2×C22⋊(C5⋊D5) | C22 | semidirect |
| 23. C2×C4⋊(C5⋊D5) | C22 | semidirect |
| 24. C2×C4⋊(C5⋊D5) | C22 | semidirect |
| 25. C2×C4⋊(C5⋊D5) | C22 | semidirect |
| 26. C2×C4×C5⋊D5 | C22 | semidirect |
| 27. C2×C4×C5⋊D5 | C22 | semidirect |
| 28. C52×C4⋊C4 | C22 | semidirect |
| 29. C52×C22⋊C4 | C22 | semidirect |
| 30. C52×C22⋊C4 | C22 | semidirect |
| 31. C22⋊#1039 | C22 | semidirect |
| 32. #87808 | C22 | semidirect |
| 33. #87808 | C22 | semidirect |
| 34. #87808 | C22 | semidirect |
| 35. #87808 | C22 | semidirect |
| 36. #87806 | C22 | semidirect |
| 45. C22×C5⋊D5 | D4 | semidirect |
| 68. C5×#123 | D5 | semidirect |
| 103. C22×C4×C5 | C2×D5 | semidirect |
| 115. C5×C4⋊C4 | C2×D5 | semidirect |
| 116. C5×C22⋊C4 | C2×D5 | semidirect |
| 117. C5×C22⋊C4 | C2×D5 | semidirect |
| 165. #123 | C5⋊D5 | semidirect |
| 172. C52 | #534 | semidirect |
| 210. C22×C4 | C2×C5⋊D5 | semidirect |
| 212. C4⋊C4 | C2×C5⋊D5 | semidirect |
| 218. C22⋊C4 | C2×C5⋊D5 | semidirect |
| 219. C22⋊C4 | C2×C5⋊D5 | semidirect |
| 256. C5 | #65987 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×C5⋊D5 | 2 |
| C22×C4⋊(C5⋊D5) | 2 |
| C52×#123 | 2 |
| #11717257 | 2 |
| #11717249 | 2 |
| #11717215 | 2 |
| #11717214 | 2 |
| #11717204 | 2 |
| #11717202 | 2 |
| C22⋊C4×C5⋊D5 | 2 |
| #65987 | 5 |