Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1960 conjugacy classes of subgroups; only the 536 normal subgroups are shown.
This group has 1960 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 | C2×C52×Q8 | C22 |
| socle | C22×C52 | C24 |
| hypercenter | C2×Q8 | D52 |
| hypocenter | C52 | C2×H(5,𝔽2) |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#87904 | C2 | semidirect |
| 2. C2×C5×#713 | C2 | semidirect |
| 3. #11717485 | C2 | direct (N × H) |
| 4. C2×#87877 | C2 | semidirect |
| 5. C2×D5×D20 | C2 | semidirect |
| 6. C2×#87873 | C2 | semidirect |
| 7. C22×D52 | C22 | semidirect |
| 8. C2×C52×Q8 | C22 | semidirect |
| 9. #87904 | C22 | semidirect |
| 10. C2×C4⋊(C5⋊D5) | C22 | semidirect |
| 11. C2×C4×C5⋊D5 | C22 | semidirect |
| 12. C5×#713 | C22 | semidirect |
| 13. C2×C5×D20 | C22 | semidirect |
| 14. C2×C4×C5×D5 | C22 | semidirect |
| 15. C2×#6039 | C22 | semidirect |
| 16. C2×#6038 | C22 | semidirect |
| 17. C2×#6037 | C22 | semidirect |
| 18. #87877 | C22 | semidirect |
| 19. D5×D20 | C22 | semidirect |
| 20. #87873 | C22 | semidirect |
| 25. C2×D52 | C23 | semidirect |
| 26. C52×Q8 | C23 | semidirect |
| 29. C4⋊(C5⋊D5) | C23 | semidirect |
| 30. C4×C5⋊D5 | C23 | semidirect |
| 32. C5×D20 | C23 | semidirect |
| 33. C4×C5×D5 | C23 | semidirect |
| 34. #6039 | C23 | semidirect |
| 35. #6038 | C23 | semidirect |
| 36. #6037 | C23 | semidirect |
| 41. C2×#713 | D5 | semidirect |
| 58. C2×C5×Q8 | C2×D5 | semidirect |
| 65. #713 | C2×D5 | semidirect |
| 73. C2×D20 | C2×D5 | semidirect |
| 76. C2×C4×D5 | C2×D5 | semidirect |
| 79. C2×C52 | H(5,𝔽2) | semidirect |
| 90. C5×Q8 | C22×D5 | semidirect |
| 104. D20 | C22×D5 | semidirect |
| 107. C4×D5 | C22×D5 | semidirect |
| 115. C52 | C2×H(5,𝔽2) | semidirect |
| 138. C2×Q8 | D52 | semidirect |
| 150. C2×C5 | #4149 | semidirect |
| 160. Q8 | C2×D52 | semidirect |
| 171. C5 | C2×#4149 | semidirect |
| 183. C2 | #11717485 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87904 | 2 |
| C2×C5×#713 | 2 |
| #11717485 | 2 |
| C2×#87877 | 2 |
| C2×D5×D20 | 2 |
| C2×#87873 | 2 |
| C2×#4149 | 5 |