Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
303 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 303 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23×C25 | D4 |
| commutator | C4 | C22×C4×C25 |
| Frattini, cosocle | C2×C4×C5 | C23×C5 |
| socle | C23×C5 | C5×D4 |
| prime radical | C22×C5×D4 | C2×C5 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C25 ◁ C22×C4×C25 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C8×C25 | C2 | semidirect |
| 3. C2×C4⋊C4×C25 | C2 | semidirect |
| 4. C25×#102 | C2 | direct (N × H) |
| 8. C2×D4×C25 | C4 | semidirect |
| 13. C2×C8×C25 | C22 | semidirect |
| 15. C4⋊C4×C25 | C22 | semidirect |
| 24. D4×C25 | C2×C4 | semidirect |
| 59. C2×#102 | C25 | direct (N × H) |
| 61. C2×C25 | #102 | direct (N × H) |
| 81. C22×C8 | C2×C25 | semidirect |
| 82. C2×C4⋊C4 | C2×C25 | semidirect |
| 83. #102 | C2×C25 | direct (N × H) |
| 84. C25 | C2×#102 | direct (N × H) |
| 100. C2×D4 | C4×C25 | semidirect |
| 105. C2×C8 | C22×C25 | semidirect |
| 107. C4⋊C4 | C22×C25 | semidirect |
| 120. D4 | C2×C4×C25 | semidirect |
| 142. C2 | C25×#102 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×C25 | 2 |
| C22×C8×C25 | 2 |
| C2×C4⋊C4×C25 | 2 |
| C25×#102 | 2 |
| C2×C5×#102 | 5 |