Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
3592 conjugacy classes of subgroups; only the 867 normal subgroups are shown.
This group has 3592 conjugacy classes of subgroups — too many to draw. Only its 867 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×C5⋊D5 |
| commutator, cosocle | C2×C52 | C25 |
| Frattini | C2 | C24×C5⋊D5 |
| Fitting | C22×C52×D4 | C2 |
| socle | C22×C52 | C24 |
| hypercenter | C22×D4 | C5⋊D5 |
| hypocenter | C52 | C2×H(5,𝔽2) |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C52×D4 | C2 | semidirect |
| 2. C22×C22⋊(C5⋊D5) | C2 | semidirect |
| 3. #11717517 | C2 | direct (N × H) |
| 4. C2×#87902 | C2 | semidirect |
| 5. C2×D4×C5⋊D5 | C2 | semidirect |
| 6. C2×#87900 | C2 | semidirect |
| 7. C24×C52 | C22 | semidirect |
| 8. C23×C5⋊D5 | C22 | semidirect |
| 9. C2×C52×D4 | C22 | semidirect |
| 10. C2×C52×D4 | C22 | semidirect |
| 11. C22×C4×C52 | C22 | semidirect |
| 12. C2×C22⋊(C5⋊D5) | C22 | semidirect |
| 13. C2×C22⋊(C5⋊D5) | C22 | semidirect |
| 14. C2×C22⋊(C5⋊D5) | C22 | semidirect |
| 15. C22×#1039 | C22 | semidirect |
| 16. #87902 | C22 | semidirect |
| 17. D4×C5⋊D5 | C22 | semidirect |
| 18. #87900 | C22 | semidirect |
| 19. C2×C4⋊(C5⋊D5) | C22 | semidirect |
| 20. C2×C4×C5⋊D5 | C22 | semidirect |
| 21. C2×#6045 | C22 | semidirect |
| 26. C23×C52 | C23 | semidirect |
| 29. C22×C5⋊D5 | C23 | semidirect |
| 30. C52×D4 | C23 | semidirect |
| 32. C2×C4×C52 | C23 | semidirect |
| 33. C22⋊(C5⋊D5) | C23 | semidirect |
| 34. C22⋊(C5⋊D5) | C23 | semidirect |
| 36. C2×#1039 | C23 | semidirect |
| 37. C4⋊(C5⋊D5) | C23 | semidirect |
| 38. C4×C5⋊D5 | C23 | semidirect |
| 39. #6045 | C23 | semidirect |
| 40. C22×C5×D4 | D5 | semidirect |
| 57. C24×C5 | C2×D5 | semidirect |
| 59. C2×C5×D4 | C2×D5 | semidirect |
| 60. C2×C5×D4 | C2×D5 | semidirect |
| 61. C22×C4×C5 | C2×D5 | semidirect |
| 75. C2×C52 | H(5,𝔽2) | semidirect |
| 81. C23×C5 | C22×D5 | semidirect |
| 85. C5×D4 | C22×D5 | semidirect |
| 87. C2×C4×C5 | C22×D5 | semidirect |
| 100. C22×D4 | C5⋊D5 | semidirect |
| 101. C52 | C2×H(5,𝔽2) | semidirect |
| 114. C24 | C2×C5⋊D5 | semidirect |
| 123. C2×D4 | C2×C5⋊D5 | semidirect |
| 124. C2×D4 | C2×C5⋊D5 | semidirect |
| 127. C22×C4 | C2×C5⋊D5 | semidirect |
| 130. C2×C5 | #4144 | semidirect |
| 139. C23 | C22×C5⋊D5 | semidirect |
| 144. D4 | C22×C5⋊D5 | semidirect |
| 149. C2×C4 | C22×C5⋊D5 | semidirect |
| 150. C5 | C2×#4144 | semidirect |
| 165. C2 | #11717517 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×D4 | 2 |
| C22×C22⋊(C5⋊D5) | 2 |
| #11717517 | 2 |
| C2×#87902 | 2 |
| C2×D4×C5⋊D5 | 2 |
| C2×#87900 | 2 |
| C2×#4144 | 5 |