Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
680 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 192 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 | C52×#41 | C22 |
| prime radical | #41×C5⋊D5 | C2 |
| cosocle | C4×C52 | C24 |
| hypercenter | #41 | D52 |
| hypocenter | C52 | #568 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C4 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#4094 | C2 | semidirect |
| 3. C2×#87769 | C2 | semidirect |
| 4. #11716936 | C2 | semidirect |
| 5. #11716935 | C2 | semidirect |
| 13. C5×#681 | C22 | semidirect |
| 14. C2×C5×#168 | C22 | semidirect |
| 17. #87769 | C22 | semidirect |
| 18. #87767 | C22 | semidirect |
| 37. #4094 | D5 | semidirect |
| 66. #681 | C2×D5 | semidirect |
| 67. C2×#168 | C2×D5 | semidirect |
| 111. C52 | #568 | semidirect |
| 164. C5 | #66084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×C5⋊D5 | 2 |
| C5×#4094 | 2 |
| C2×#87769 | 2 |
| #11716936 | 2 |
| #11716935 | 2 |
| #66084 | 5 |