Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
586 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 586 conjugacy classes of subgroups — too many to draw. Only its 136 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | D5×D20 |
| commutator, cosocle | C4×C52 | C24 |
| Frattini | C4 | C22×D52 |
| Fitting | C2×C52×C8 | C22 |
| socle | C2×C52 | C22×D4 |
| hypercenter | C2×C8 | D52 |
| hypocenter | C52 | #575 |
| LCS | G ▷ C4×C52 ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ C2×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D5×#709 | C2 | semidirect |
| 2. #11717224 | C2 | semidirect |
| 3. C5×#4050 | C2 | semidirect |
| 4. C2×C5×#676 | C2 | semidirect |
| 5. #11716947 | C2 | semidirect |
| 6. #11716919 | C2 | semidirect |
| 7. #11716918 | C2 | semidirect |
| 8. #11716913 | C2 | semidirect |
| 9. #11716912 | C2 | semidirect |
| 10. #87900 | C22 | semidirect |
| 11. C5×#709 | C22 | semidirect |
| 15. D5×D20 | C22 | semidirect |
| 20. D5×Dic10 | C22 | semidirect |
| 21. C2×C52×C8 | C22 | semidirect |
| 22. #87802 | C22 | semidirect |
| 23. #87801 | C22 | semidirect |
| 24. #87800 | C22 | semidirect |
| 25. C2×C5×#168 | C22 | semidirect |
| 26. C5×Dic20 | C22 | semidirect |
| 27. C5×D40 | C22 | semidirect |
| 28. C5×#677 | C22 | semidirect |
| 29. C5×#676 | C22 | semidirect |
| 30. C5×#676 | C22 | semidirect |
| 31. #87776 | C22 | semidirect |
| 32. #87774 | C22 | semidirect |
| 33. #87773 | C22 | semidirect |
| 34. #87771 | C22 | semidirect |
| 78. #4050 | D5 | semidirect |
| 79. C2×#676 | D5 | semidirect |
| 108. #709 | C2×D5 | semidirect |
| 121. C2×C5×C8 | C2×D5 | semidirect |
| 122. C2×C5×C8 | C2×D5 | semidirect |
| 127. C2×#168 | C2×D5 | semidirect |
| 132. Dic20 | C2×D5 | semidirect |
| 137. D40 | C2×D5 | semidirect |
| 143. #677 | C2×D5 | semidirect |
| 144. #676 | C2×D5 | semidirect |
| 145. #676 | C2×D5 | semidirect |
| 216. C52 | #575 | semidirect |
| 268. C2×C8 | D52 | semidirect |
| 307. C5 | #66082 | semidirect |
| 308. C5 | #66102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#709 | 2 |
| #11717224 | 2 |
| C5×#4050 | 2 |
| C2×C5×#676 | 2 |
| #11716947 | 2 |
| #11716919 | 2 |
| #11716918 | 2 |
| #11716913 | 2 |
| #11716912 | 2 |
| #66102 | 5 |
| #66082 | 5 |