Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
196 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C2×D52 |
| commutator, socle | C2×C52 | C22×C8 |
| Fitting | C2×C52×C8 | C22 |
| prime radical | C5×#709 | C4 |
| cosocle | C52×C8 | C23 |
| hypercenter | C2×C8 | D52 |
| hypocenter | C52 | #504 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C8 ◁ C2×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#87756 | C2 | semidirect |
| 3. C5×#3944 | C2 | semidirect |
| 4. #11716584 | C2 | semidirect |
| 5. D5×#672 | C2 | semidirect |
| 28. #3944 | D5 | semidirect |
| 87. C52 | #504 | semidirect |
| 126. C5 | #65196 | semidirect |
| 127. C5 | #65429 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4047 | 2 |
| C2×#87756 | 2 |
| C5×#3944 | 2 |
| #11716584 | 2 |
| D5×#672 | 2 |
| #65429 | 5 |
| #65196 | 5 |