Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
483 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 483 conjugacy classes of subgroups — too many to draw. Only its 91 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 | C23×C25 | C23 |
| Frattini, socle | C23×C5 | C22×D5 |
| Fitting | C2×C22⋊C4×C25 | C2 |
| hypercenter | C2×C22⋊C4 | D25 |
| hypocenter | C25 | #392 |
| LCS | G ▷ C23×C25 ▷ C25 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C22⋊D25 | C2 | semidirect |
| 2. C22×D100 | C2 | semidirect |
| 3. C2×C22⋊C4×C25 | C2 | semidirect |
| 4. C2×#87720 | C2 | semidirect |
| 5. #11716379 | C2 | semidirect |
| 23. C23×C25 | D4 | semidirect |
| 31. C22×D25 | D4 | semidirect |
| 35. C2×C4×C25 | D4 | semidirect |
| 39. C2×Dic25 | D4 | semidirect |
| 111. C2×C22⋊C4 | D25 | semidirect |
| 113. C25 | #392 | semidirect |
| 164. C23 | D100 | semidirect |
| 174. C2×C4 | C22⋊D25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊D25 | 2 |
| C22×D100 | 2 |
| C2×C22⋊C4×C25 | 2 |
| C2×#87720 | 2 |
| #11716379 | 2 |
| #65249 | 5 |