Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1191 conjugacy classes of subgroups; only the 517 normal subgroups are shown.
This group has 1191 conjugacy classes of subgroups — too many to draw. Only its 517 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C23×D25 |
| commutator, cosocle | C2×C25 | C25 |
| Frattini | C2×C5 | C24×D5 |
| Fitting | C22×Q8×C25 | C2 |
| socle | C22×C5 | C23×D5 |
| hypercenter | C22×Q8 | D25 |
| hypocenter | C25 | C2×2−1+4 |
| LCS | G ▷ C2×C25 ▷ C25 | |
| UCS | C1 ◁ C22 ◁ C22×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Q8×C25 | C2 | semidirect |
| 2. #11716566 | C2 | direct (N × H) |
| 3. C2×#87748 | C2 | semidirect |
| 4. C2×Q8×D25 | C2 | semidirect |
| 5. C2×#87744 | C2 | semidirect |
| 7. C2×Q8×C25 | C22 | semidirect |
| 10. #87748 | C22 | semidirect |
| 11. Q8×D25 | C22 | semidirect |
| 12. #87744 | C22 | semidirect |
| 51. C2×C25 | 2−1+4 | semidirect |
| 68. C22×Q8 | D25 | semidirect |
| 69. C25 | C2×2−1+4 | semidirect |
| 82. C2×Q8 | C2×D25 | semidirect |
| 111. C2 | #11716566 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×C25 | 2 |
| #11716566 | 2 |
| C2×#87748 | 2 |
| C2×Q8×D25 | 2 |
| C2×#87744 | 2 |
| C2×#4147 | 5 |