Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
578 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 152 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×#6037 |
| commutator, cosocle | C4×C52 | C24 |
| Frattini | C4 | C22×D52 |
| Fitting | C52×#41 | C22 |
| socle | C2×C52 | C22×D4 |
| hypercenter | #41 | D52 |
| hypocenter | C52 | #577 |
| LCS | G ▷ C4×C52 ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#4150 | C2 | semidirect |
| 2. C5×#4149 | C2 | semidirect |
| 3. #11717268 | C2 | semidirect |
| 4. #11716945 | C2 | semidirect |
| 5. C2×#87772 | C2 | semidirect |
| 6. #11716941 | C2 | semidirect |
| 7. #11716940 | C2 | semidirect |
| 14. C5×#709 | C22 | semidirect |
| 16. C2×C5×Dic10 | C22 | semidirect |
| 17. #87804 | C22 | semidirect |
| 18. C2×#6029 | C22 | semidirect |
| 19. #87775 | C22 | semidirect |
| 20. #87772 | C22 | semidirect |
| 21. #87772 | C22 | semidirect |
| 22. #87772 | C22 | semidirect |
| 23. #87770 | C22 | semidirect |
| 45. #4150 | D5 | semidirect |
| 46. #4149 | D5 | semidirect |
| 82. #709 | C2×D5 | semidirect |
| 84. C2×Dic10 | C2×D5 | semidirect |
| 152. C52 | #577 | semidirect |
| 216. C5 | #66170 | semidirect |
| 217. C5 | #66171 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4150 | 2 |
| C5×#4149 | 2 |
| #11717268 | 2 |
| #11716945 | 2 |
| C2×#87772 | 2 |
| #11716941 | 2 |
| #11716940 | 2 |
| #66171 | 5 |
| #66170 | 5 |