Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1347 conjugacy classes of subgroups; only the 517 normal subgroups are shown.
This group has 1347 conjugacy classes of subgroups — too many to draw. Only its 517 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C23×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 | C2×H(5,𝔽2) |
| LCS | G ▷ C2×C25 ▷ C25 | |
| UCS | C1 ◁ C22 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#41×C25 | C2 | semidirect |
| 2. #11716568 | C2 | direct (N × H) |
| 3. C2×#87748 | C2 | semidirect |
| 4. C2×D4×D25 | C2 | semidirect |
| 5. C2×#87744 | C2 | semidirect |
| 6. C22×D100 | C2 | semidirect |
| 7. C23×D25 | C22 | semidirect |
| 8. #41×C25 | C22 | semidirect |
| 9. C2×Q8×C25 | C22 | semidirect |
| 10. C2×D4×C25 | C22 | semidirect |
| 11. C22×C4×C25 | C22 | semidirect |
| 12. C2×C22⋊D25 | C22 | semidirect |
| 13. #87748 | C22 | semidirect |
| 14. D4×D25 | C22 | semidirect |
| 15. #87744 | C22 | semidirect |
| 16. C2×D100 | C22 | semidirect |
| 17. C2×D100 | C22 | semidirect |
| 18. C2×D100 | C22 | semidirect |
| 19. C2×C4×D25 | C22 | semidirect |
| 20. C2×Dic50 | C22 | semidirect |
| 25. C22×D25 | C23 | semidirect |
| 26. Q8×C25 | C23 | semidirect |
| 27. D4×C25 | C23 | semidirect |
| 30. C2×C4×C25 | C23 | semidirect |
| 31. C22⋊D25 | C23 | semidirect |
| 33. D100 | C23 | semidirect |
| 34. D100 | C23 | semidirect |
| 35. C4×D25 | C23 | semidirect |
| 36. Dic50 | C23 | semidirect |
| 68. C2×C25 | H(5,𝔽2) | semidirect |
| 89. C2×#41 | D25 | semidirect |
| 92. C25 | C2×H(5,𝔽2) | semidirect |
| 105. #41 | C2×D25 | semidirect |
| 107. C2×Q8 | C2×D25 | semidirect |
| 113. C2×D4 | C2×D25 | semidirect |
| 115. C22×C4 | C2×D25 | semidirect |
| 125. Q8 | C22×D25 | semidirect |
| 129. D4 | C22×D25 | semidirect |
| 134. C2×C4 | C22×D25 | semidirect |
| 147. C2 | #11716568 | 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 |
| #11716568 | 2 |
| C2×#87748 | 2 |
| C2×D4×D25 | 2 |
| C2×#87744 | 2 |
| C22×D100 | 2 |
| C2×#4149 | 5 |