Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
354 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 115 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×#124 | C2 |
| hypercenter | #124 | D25 |
| hypocenter | C25 | #555 |
| LCS | G ▷ C22×C25 ▷ C25 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C25×#124 | C2 | semidirect |
| 2. #11716509 | C2 | semidirect |
| 3. #11716506 | C2 | semidirect |
| 4. #11716501 | C2 | semidirect |
| 5. #11716447 | C2 | semidirect |
| 6. #11716446 | C2 | semidirect |
| 7. #11716443 | C2 | semidirect |
| 8. #11716439 | C2 | semidirect |
| 9. #11716434 | C2 | semidirect |
| 118. #124 | D25 | semidirect |
| 124. C25 | #555 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×#124 | 2 |
| #11716509 | 2 |
| #11716506 | 2 |
| #11716501 | 2 |
| #11716447 | 2 |
| #11716446 | 2 |
| #11716443 | 2 |
| #11716439 | 2 |
| #11716434 | 2 |
| #66004 | 5 |