Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
225 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 225 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C25 | C2×D4 |
| commutator | C4 | C22×C4×C25 |
| Frattini, cosocle | C2×C4×C5 | C23×C5 |
| socle | C22×C5 | C2×C5×D4 |
| prime radical | C23×C5 | C5×D4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C25 ◁ C22×C4×C25 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C25×#103 | C2 | semidirect |
| 7. C2×Q8×C25 | C4 | semidirect |
| 52. #419 | C25 | direct (N × H) |
| 71. #103 | C2×C25 | semidirect |
| 72. C25 | #419 | direct (N × H) |
| 83. C2×Q8 | C4×C25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×C25 | 2 |
| C2×M16×C25 | 2 |
| C25×#117 | 2 |
| C25×#103 | 2 |
| C5×#419 | 5 |