Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1335 conjugacy classes of subgroups; only the 541 normal subgroups are shown.
This group has 1335 conjugacy classes of subgroups — too many to draw. Only its 541 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D25 |
| commutator, cosocle | C2×C25 | C25 |
| Frattini | C2×C5 | C24×D5 |
| Fitting | C22×D4×C25 | C2 |
| socle | C23×C5 | C22×D5 |
| hypercenter | C22×D4 | D25 |
| hypocenter | C25 | C22×#41 |
| LCS | G ▷ C2×C25 ▷ C25 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×D4×C25 | C2 | semidirect |
| 2. C22×C22⋊D25 | C2 | semidirect |
| 3. C23×Dic25 | C2 | semidirect |
| 4. C2×#87746 | C2 | direct (N × H) |
| 5. C22×C4×D25 | C2 | semidirect |
| 6. C22×Dic50 | C2 | semidirect |
| 9. C2×D4×C25 | C22 | semidirect |
| 11. C2×C22⋊D25 | C22 | semidirect |
| 14. C22×Dic25 | C22 | semidirect |
| 15. #87746 | C22 | direct (N × H) |
| 16. C2×C4×D25 | C22 | semidirect |
| 17. C2×Dic50 | C22 | semidirect |
| 24. D4×C25 | C23 | semidirect |
| 26. C22⋊D25 | C23 | semidirect |
| 29. C2×Dic25 | C23 | semidirect |
| 30. C4×D25 | C23 | semidirect |
| 31. Dic50 | C23 | semidirect |
| 39. C22×C25 | #41 | semidirect |
| 60. C2×C25 | C2×#41 | semidirect |
| 79. C22×D4 | D25 | semidirect |
| 82. C25 | C22×#41 | semidirect |
| 97. C2×D4 | C2×D25 | semidirect |
| 114. D4 | C22×D25 | semidirect |
| 124. C22 | #87746 | direct (N × H) |
| 132. C2 | C2×#87746 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×C25 | 2 |
| C22×C22⋊D25 | 2 |
| C23×Dic25 | 2 |
| C2×#87746 | 2 |
| C22×C4×D25 | 2 |
| C22×Dic50 | 2 |
| C22×#711 | 5 |