Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
156 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C25 | #121 |
| commutator | C2×C4 | C23×C25 |
| Frattini, cosocle | C2×C4×C5 | C23×C5 |
| socle | C2×C5 | C5×#121 |
| prime radical | C5×AGL(1,ℤ/8) | C2×C5 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C25 ◁ C2×C4×C25 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C25×#137 | C2 | semidirect |
| 3. C2×SD16×C25 | C2 | semidirect |
| 4. C25×#131 | C2 | semidirect |
| 5. C25×#108 | C2 | semidirect |
| 6. C25×#101 | C2 | semidirect |
| 7. C25×#100 | C2 | semidirect |
| 70. #471 | C25 | direct (N × H) |
| 91. #137 | C2×C25 | semidirect |
| 93. C2×SD16 | C2×C25 | semidirect |
| 94. #131 | C2×C25 | semidirect |
| 95. #108 | C2×C25 | semidirect |
| 96. #101 | C2×C25 | semidirect |
| 97. #100 | C2×C25 | semidirect |
| 98. C25 | #471 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×#137 | 2 |
| C25×AGL(1,ℤ/8) | 2 |
| C2×SD16×C25 | 2 |
| C25×#131 | 2 |
| C25×#108 | 2 |
| C25×#101 | 2 |
| C25×#100 | 2 |
| C5×#471 | 5 |