Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
788 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D52⋊C2 |
| commutator, cosocle | C2×C5⋊D5 | C24 |
| Frattini | C2 | C22×D52⋊C2 |
| Fitting | C2×C4×C52 | D4 |
| socle | C22×C52 | C2×D4 |
| hypercenter | C2×C4 | D52⋊C2 |
| hypocenter | C52 | C2×#127 |
| LCS | G ▷ C2×C5⋊D5 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×D52⋊C2 | C2 | semidirect |
| 2. C2×#87877 | C2 | semidirect |
| 3. C2×C4×#1044 | C2 | semidirect |
| 4. #11717389 | C2 | direct (N × H) |
| 8. C2×D52⋊C2 | C22 | semidirect |
| 13. #87877 | C22 | semidirect |
| 14. C4×#1044 | C22 | semidirect |
| 20. C2×#1044 | D4 | semidirect |
| 23. C2×C4×C52 | D4 | semidirect |
| 24. C2×#1039 | D4 | semidirect |
| 25. C4×C5⋊D5 | D4 | semidirect |
| 39. #1044 | C2×D4 | semidirect |
| 40. C4×C52 | C2×D4 | semidirect |
| 41. #1039 | C2×D4 | semidirect |
| 53. C2×C52 | #127 | semidirect |
| 55. C5⋊D5 | #127 | semidirect |
| 82. C52 | C2×#127 | semidirect |
| 135. C2×C4 | D52⋊C2 | semidirect |
| 148. C4 | C2×D52⋊C2 | semidirect |
| 152. C2 | #11717389 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D52⋊C2 | 2 |
| C2×#87877 | 2 |
| C2×C4×#1044 | 2 |
| #11717389 | 2 |
| C2×#127 | 25 |