Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
207 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 207 conjugacy classes of subgroups — too many to draw. Only its 171 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C25 | C22 |
| commutator | C2 | C22×C8×C25 |
| Frattini, cosocle | C2×C4×C5 | C23×C5 |
| socle, prime radical | C23×C5 | C2×C4×C5 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C25 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C25×C4⋊C8 | C2 | direct (N × H) |
| 14. C2×C4×C25 | C8 | semidirect |
| 31. C4×C25 | C2×C8 | semidirect |
| 41. C2×C4⋊C8 | C25 | direct (N × H) |
| 42. C2×C25 | C4⋊C8 | direct (N × H) |
| 58. C4⋊C8 | C2×C25 | direct (N × H) |
| 59. C25 | C2×C4⋊C8 | direct (N × H) |
| 82. C2×C4 | C8×C25 | semidirect |
| 97. C4 | C2×C8×C25 | semidirect |
| 100. C2 | C25×C4⋊C8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×C25 | 2 |
| C2×C42×C25 | 2 |
| C25×C4⋊C8 | 2 |
| C2×C5×C4⋊C8 | 5 |