Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
2032 conjugacy classes of subgroups; only the 536 normal subgroups are shown.
This group has 2032 conjugacy classes of subgroups — too many to draw. Only its 536 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D52 |
| commutator, cosocle | C2×C52 | C25 |
| Frattini | C2 | C23×D52 |
| Fitting | C22×C4×C52 | C22 |
| socle | C22×C52 | C24 |
| hypercenter | C22×C4 | D52 |
| hypocenter | C52 | C2×H(5,𝔽2) |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C4⋊(C5⋊D5) | C2 | semidirect |
| 2. C2×C5×#709 | C2 | semidirect |
| 3. C2×#87886 | C2 | semidirect |
| 4. #11717473 | C2 | direct (N × H) |
| 5. C2×D5×D20 | C2 | semidirect |
| 6. C2×#87874 | C2 | semidirect |
| 7. C23×C5⋊D5 | C22 | semidirect |
| 8. C22×D52 | C22 | semidirect |
| 9. C22×C4×C52 | C22 | semidirect |
| 10. C2×C4⋊(C5⋊D5) | C22 | semidirect |
| 11. C2×C4⋊(C5⋊D5) | C22 | semidirect |
| 12. C2×C5×C22⋊D5 | C22 | semidirect |
| 13. C5×#709 | C22 | semidirect |
| 14. C2×C5×D20 | C22 | semidirect |
| 15. C2×C4×C5×D5 | C22 | semidirect |
| 16. C2×C5×Dic10 | C22 | semidirect |
| 17. #87886 | C22 | semidirect |
| 18. C2×#6038 | C22 | semidirect |
| 19. C2×#6036 | C22 | semidirect |
| 20. D5×D20 | C22 | semidirect |
| 21. #87874 | C22 | semidirect |
| 26. C22×C5⋊D5 | C23 | semidirect |
| 29. C2×D52 | C23 | semidirect |
| 31. C2×C4×C52 | C23 | semidirect |
| 32. C4⋊(C5⋊D5) | C23 | semidirect |
| 33. C5×C22⋊D5 | C23 | semidirect |
| 35. C5×D20 | C23 | semidirect |
| 36. C4×C5×D5 | C23 | semidirect |
| 37. C5×Dic10 | C23 | semidirect |
| 38. #6038 | C23 | semidirect |
| 39. #6036 | C23 | semidirect |
| 46. C2×#709 | D5 | semidirect |
| 70. C22×C4×C5 | C2×D5 | semidirect |
| 72. C2×C22⋊D5 | C2×D5 | semidirect |
| 77. #709 | C2×D5 | semidirect |
| 85. C2×D20 | C2×D5 | semidirect |
| 87. C2×C4×D5 | C2×D5 | semidirect |
| 88. C2×Dic10 | C2×D5 | semidirect |
| 91. C2×C52 | H(5,𝔽2) | semidirect |
| 116. C2×C4×C5 | C22×D5 | semidirect |
| 118. C22⋊D5 | C22×D5 | semidirect |
| 124. D20 | C22×D5 | semidirect |
| 126. C4×D5 | C22×D5 | semidirect |
| 127. Dic10 | C22×D5 | semidirect |
| 134. C52 | C2×H(5,𝔽2) | semidirect |
| 171. C22×C4 | D52 | semidirect |
| 177. C2×C5 | #4149 | semidirect |
| 198. C2×C4 | C2×D52 | semidirect |
| 200. C5 | C2×#4149 | semidirect |
| 215. C2 | #11717473 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊(C5⋊D5) | 2 |
| C2×C5×#709 | 2 |
| C2×#87886 | 2 |
| #11717473 | 2 |
| C2×D5×D20 | 2 |
| C2×#87874 | 2 |
| C2×#4149 | 5 |