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 | C25×#127 | C2 |
| hypercenter | #127 | D25 |
| hypocenter | C25 | #550 |
| LCS | G ▷ C22×C25 ▷ C25 | |
| UCS | C1 ◁ C22 ◁ #127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#87746 | C2 | semidirect |
| 2. C25×#127 | C2 | semidirect |
| 3. #11716502 | C2 | semidirect |
| 4. #11716501 | C2 | semidirect |
| 5. #11716500 | C2 | semidirect |
| 6. D4×Dic25 | C2 | semidirect |
| 7. C4×D100 | C2 | semidirect |
| 8. C4×Dic50 | C2 | semidirect |
| 43. Dic50 | D4 | semidirect |
| 61. C4×C25 | #41 | semidirect |
| 107. #127 | D25 | semidirect |
| 113. C25 | #550 | semidirect |
| 179. C4 | #87746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87746 | 2 |
| C25×#127 | 2 |
| #11716502 | 2 |
| #11716501 | 2 |
| #11716500 | 2 |
| D4×Dic25 | 2 |
| C4×D100 | 2 |
| C4×Dic50 | 2 |
| #66052 | 5 |