Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
141 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 141 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C25 | C23 |
| commutator | C22 | C22×C4×C25 |
| Frattini, cosocle | C2×C4×C5 | C23×C5 |
| socle, prime radical | C22×C5 | C22×C4×C5 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C25 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 23. C8×C25 | Q8 | semidirect |
| 44. #446 | C25 | direct (N × H) |
| 62. C25 | #446 | direct (N × H) |
| 89. C8 | Q8×C25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×C25 | 2 |
| C25×C4⋊C8 | 2 |
| C25×#97 | 2 |
| C4×C8×C25 | 2 |
| C5×#446 | 5 |