Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
468 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C23×D25 |
| commutator, cosocle | C22×C25 | C24 |
| Frattini, socle | C22×C5 | C23×D5 |
| Fitting | C4×D4×C25 | C2 |
| hypercenter | C4×D4 | D25 |
| hypocenter | C25 | #550 |
| LCS | G ▷ C22×C25 ▷ C25 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#87744 | C2 | semidirect |
| 2. C4×D4×C25 | C2 | semidirect |
| 3. #11716502 | C2 | semidirect |
| 4. #11716492 | C2 | semidirect |
| 5. #11716455 | C2 | semidirect |
| 6. #11716446 | C2 | semidirect |
| 7. #11716436 | C2 | semidirect |
| 8. C4×Dic50 | C2 | semidirect |
| 43. Dic50 | D4 | semidirect |
| 62. C4×C25 | #41 | semidirect |
| 112. C4×D4 | D25 | semidirect |
| 113. C25 | #550 | semidirect |
| 178. C4 | #87744 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87744 | 2 |
| C4×D4×C25 | 2 |
| #11716502 | 2 |
| #11716492 | 2 |
| #11716455 | 2 |
| #11716446 | 2 |
| #11716436 | 2 |
| C4×Dic50 | 2 |
| #65887 | 5 |