Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
201 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 201 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C25 | C22 |
| commutator | C2 | C22×C8×C25 |
| Frattini, cosocle | C2×C4×C5 | C23×C5 |
| socle | C22×C5 | C22×C4×C5 |
| prime radical | C2×C5×D4 | C4×C5 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C25 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C8×C25 | C2 | semidirect |
| 3. C25×C4⋊C8 | C2 | semidirect |
| 4. C25×C22⋊C8 | C2 | semidirect |
| 5. C4×C8×C25 | C2 | semidirect |
| 17. D4×C25 | C8 | direct (N × H) |
| 26. C8×C25 | D4 | direct (N × H) |
| 34. C22×C25 | C2×C8 | semidirect |
| 38. C4×C25 | C2×C8 | semidirect |
| 50. C8×D4 | C25 | direct (N × H) |
| 66. C22×C8 | C2×C25 | semidirect |
| 68. C4⋊C8 | C2×C25 | semidirect |
| 69. C22⋊C8 | C2×C25 | semidirect |
| 70. C4×C8 | C2×C25 | semidirect |
| 71. C25 | C8×D4 | direct (N × H) |
| 95. D4 | C8×C25 | direct (N × H) |
| 104. C8 | D4×C25 | direct (N × H) |
| 108. C22 | C2×C8×C25 | semidirect |
| 112. C4 | C2×C8×C25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×C25 | 2 |
| C4×D4×C25 | 2 |
| C25×C4⋊C8 | 2 |
| C25×C22⋊C8 | 2 |
| C4×C8×C25 | 2 |
| C5×C8×D4 | 5 |