Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
584 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 184 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D52 |
| commutator, socle | C2×C52 | C23×C4 |
| Fitting | C2×C52×C8 | C22 |
| prime radical | #11717471 | C2 |
| cosocle | C4×C52 | C24 |
| hypercenter | C2×C8 | D52 |
| hypocenter | C52 | #568 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C4 ◁ C2×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#87799 | C2 | semidirect |
| 3. C5×#4047 | C2 | semidirect |
| 4. #11716936 | C2 | semidirect |
| 5. #11716933 | C2 | semidirect |
| 6. #11716922 | C2 | semidirect |
| 7. D5×#676 | C2 | semidirect |
| 17. C2×C52×C8 | C22 | semidirect |
| 18. C2×#6029 | C22 | semidirect |
| 20. #87799 | C22 | semidirect |
| 21. C5×#681 | C22 | semidirect |
| 22. C5×#676 | C22 | semidirect |
| 23. C5×C8×D5 | C22 | semidirect |
| 25. #87768 | C22 | semidirect |
| 26. #87767 | C22 | semidirect |
| 27. D5×#168 | C22 | semidirect |
| 57. #4047 | D5 | semidirect |
| 88. C2×C5×C8 | C2×D5 | semidirect |
| 90. #681 | C2×D5 | semidirect |
| 102. #676 | C2×D5 | semidirect |
| 105. C8×D5 | C2×D5 | semidirect |
| 157. C52 | #568 | semidirect |
| 198. C2×C8 | D52 | semidirect |
| 230. C5 | #66084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717471 | 2 |
| C2×#87799 | 2 |
| C5×#4047 | 2 |
| #11716936 | 2 |
| #11716933 | 2 |
| #11716922 | 2 |
| D5×#676 | 2 |
| #66084 | 5 |