Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1335 conjugacy classes of subgroups; only the 525 normal subgroups are shown.
This group has 1335 conjugacy classes of subgroups — too many to draw. Only its 525 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 | C22×D25 |
| commutator, cosocle | C2×C25 | C25 |
| Frattini | C2×C5 | C24×D5 |
| Fitting | C2×#41×C25 | C2 |
| socle | C22×C5 | C23×D5 |
| hypercenter | C2×#41 | D25 |
| hypocenter | C25 | C22×#41 |
| LCS | G ▷ C2×C25 ▷ C25 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#41×C25 | C2 | semidirect |
| 2. #41×D25 | C2 | direct (N × H) |
| 3. C2×#87748 | C2 | semidirect |
| 4. C2×Q8×D25 | C2 | semidirect |
| 5. C2×#87746 | C2 | semidirect |
| 6. C2×D4×D25 | C2 | semidirect |
| 7. C2×#87744 | C2 | semidirect |
| 8. C22×C4×D25 | C2 | semidirect |
| 10. #41×C25 | C22 | semidirect |
| 11. C2×Q8×C25 | C22 | semidirect |
| 12. C2×D4×C25 | C22 | semidirect |
| 13. C22×C4×C25 | C22 | semidirect |
| 14. C2×C22⋊D25 | C22 | semidirect |
| 15. C22×Dic25 | C22 | semidirect |
| 16. #87748 | C22 | semidirect |
| 17. Q8×D25 | C22 | semidirect |
| 18. #87746 | C22 | semidirect |
| 19. D4×D25 | C22 | semidirect |
| 20. #87744 | C22 | semidirect |
| 21. C2×D100 | C22 | semidirect |
| 24. C2×C4×D25 | C22 | semidirect |
| 25. C2×C4×D25 | C22 | semidirect |
| 26. C2×C4×D25 | C22 | semidirect |
| 27. C2×Dic50 | C22 | semidirect |
| 34. Q8×C25 | C23 | semidirect |
| 35. D4×C25 | C23 | semidirect |
| 38. C2×C4×C25 | C23 | semidirect |
| 39. C22⋊D25 | C23 | semidirect |
| 42. C2×Dic25 | C23 | semidirect |
| 43. D100 | C23 | semidirect |
| 46. C4×D25 | C23 | semidirect |
| 47. C4×D25 | C23 | semidirect |
| 48. Dic50 | C23 | semidirect |
| 62. C2×D25 | #41 | direct (N × H) |
| 90. C2×C25 | C2×#41 | semidirect |
| 93. D25 | C2×#41 | direct (N × H) |
| 118. C2×#41 | D25 | direct (N × H) |
| 122. C25 | C22×#41 | semidirect |
| 139. #41 | C2×D25 | direct (N × H) |
| 142. C2×Q8 | C2×D25 | semidirect |
| 146. C2×D4 | C2×D25 | semidirect |
| 153. C22×C4 | C2×D25 | semidirect |
| 165. Q8 | C22×D25 | semidirect |
| 168. D4 | C22×D25 | semidirect |
| 178. C2×C4 | C22×D25 | semidirect |
| 195. C2 | #41×D25 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41×C25 | 2 |
| #41×D25 | 2 |
| C2×#87748 | 2 |
| C2×Q8×D25 | 2 |
| C2×#87746 | 2 |
| C2×D4×D25 | 2 |
| C2×#87744 | 2 |
| C22×C4×D25 | 2 |
| C2×D5×#41 | 5 |