Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
232 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | D52⋊C2 |
| commutator | C5⋊D5 | C22×C8 |
| Frattini | C4 | C2×D52⋊C2 |
| Fitting | C52×C8 | D4 |
| socle | C2×C52 | C4×D4 |
| prime radical | C2×D52⋊C2 | C4 |
| cosocle | C4×C5⋊D5 | C23 |
| hypocenter | C52 | C8×D4 |
| LCS | G ▷ C5⋊D5 ▷ C52 | |
| UCS | C1 ◁ C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C8×D52 | C2 | semidirect |
| 3. C8×#1044 | C2 | semidirect |
| 4. #11716790 | C2 | semidirect |
| 5. #11716784 | C2 | semidirect |
| 19. D52⋊C2 | C8 | direct (N × H) |
| 25. C52×C8 | D4 | semidirect |
| 26. #6029 | D4 | semidirect |
| 33. D52 | C2×C8 | semidirect |
| 35. #1044 | C2×C8 | semidirect |
| 76. C52 | C8×D4 | semidirect |
| 120. C8 | D52⋊C2 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D52⋊C2 | 2 |
| C8×D52 | 2 |
| C8×#1044 | 2 |
| #11716790 | 2 |
| #11716784 | 2 |
| C8×D4 | 25 |