Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
292 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D52⋊C2 |
| commutator, cosocle | C2×#1039 | C23 |
| Fitting | C2×C4×C52 | D4 |
| socle | C22×C52 | C2×D4 |
| hypercenter | C2×C4 | D52⋊C2 |
| hypocenter | C52 | #493 |
| LCS | G ▷ C2×#1039 ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#87837 | C2 | semidirect |
| 2. #11717032 | C2 | semidirect |
| 3. C4×#6034 | C2 | semidirect |
| 17. #6034 | D4 | semidirect |
| 24. C4×C52 | D8 | semidirect |
| 25. #1039 | D8 | semidirect |
| 55. C52 | #493 | semidirect |
| 100. C4 | #87837 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87837 | 2 |
| #11717032 | 2 |
| C4×#6034 | 2 |
| #493 | 25 |