Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
5956 conjugacy classes of subgroups; only the 3205 normal subgroups are shown.
This group has 5956 conjugacy classes of subgroups — too many to draw. Only its 3205 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C24×D79 |
| commutator, cosocle | C2×C79 | C26 |
| Frattini | C2 | C25×D79 |
| Fitting | C2×H(5,𝔽2)×C79 | C2 |
| socle | C22×C79 | C25 |
| hypercenter | C2×H(5,𝔽2) | D79 |
| hypocenter | C79 | C2×#585 |
| LCS | G ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C22 ◁ C2×H(5,𝔽2) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19099398 | C2 | direct (N × H) |
| 2. C2×#14579208 | C2 | semidirect |
| 3. C2×#14579206 | C2 | semidirect |
| 4. C22×#11929623 | C2 | semidirect |
| 5. C2×#41×D79 | C2 | semidirect |
| 6. C2×H(5,𝔽2)×C79 | C2 | semidirect |
| 7. #14579208 | C22 | semidirect |
| 8. #14579206 | C22 | semidirect |
| 9. C2×#11929625 | C22 | semidirect |
| 10. C2×#11929624 | C22 | semidirect |
| 11. C2×#11929623 | C22 | semidirect |
| 12. C2×#11929623 | C22 | semidirect |
| 13. C2×#11929623 | C22 | semidirect |
| 14. #41×D79 | C22 | semidirect |
| 15. C22×Dic158 | C22 | semidirect |
| 16. C2×Q8×D79 | C22 | semidirect |
| 17. C22×C22⋊D79 | C22 | semidirect |
| 18. C2×D4×D79 | C22 | semidirect |
| 19. C23×Dic79 | C22 | semidirect |
| 20. C22×C4×D79 | C22 | semidirect |
| 21. H(5,𝔽2)×C79 | C22 | semidirect |
| 22. C2×#41×C79 | C22 | semidirect |
| 23. C22×D4×C79 | C22 | semidirect |
| 25. #11929625 | C23 | semidirect |
| 26. #11929624 | C23 | semidirect |
| 27. #11929623 | C23 | semidirect |
| 28. #11929623 | C23 | semidirect |
| 30. C2×Dic158 | C23 | semidirect |
| 31. Q8×D79 | C23 | semidirect |
| 34. C2×C22⋊D79 | C23 | semidirect |
| 35. D4×D79 | C23 | semidirect |
| 38. C22×Dic79 | C23 | semidirect |
| 41. C2×C4×D79 | C23 | semidirect |
| 43. #41×C79 | C23 | semidirect |
| 46. C2×D4×C79 | C23 | semidirect |
| 78. C2×C79 | #585 | semidirect |
| 82. C79 | C2×#585 | semidirect |
| 86. C2×H(5,𝔽2) | D79 | semidirect |
| 91. H(5,𝔽2) | C2×D79 | semidirect |
| 98. C2×#41 | C2×D79 | semidirect |
| 103. C22×D4 | C2×D79 | semidirect |
| 112. #41 | C22×D79 | semidirect |
| 122. C2×D4 | C22×D79 | semidirect |
| 161. C2 | #19099398 | direct (N × H) |