Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
680 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 170 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×#1044 |
| commutator, socle | C2×C52 | C23×C4 |
| Fitting | C2×C52×D4 | C4 |
| prime radical | C2×#87902 | C2 |
| cosocle | #1039 | C24 |
| hypercenter | C2×D4 | #1044 |
| hypocenter | C52 | #568 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 ◁ C2×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#87867 | C2 | semidirect |
| 3. #11717452 | C2 | semidirect |
| 4. #11717448 | C2 | semidirect |
| 13. #87867 | C22 | semidirect |
| 14. C2×#6034 | C22 | semidirect |
| 15. #87863 | C22 | semidirect |
| 16. #87862 | C22 | semidirect |
| 98. C52 | #568 | semidirect |
| 151. C5 | #66256 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87902 | 2 |
| C2×#87867 | 2 |
| #11717452 | 2 |
| #11717448 | 2 |
| #66256 | 5 |