Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
396 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×#6038 |
| commutator, cosocle | C2×C4×C52 | C23 |
| Frattini | C2×C4 | C2×D52 |
| Fitting | C42×C52 | C22 |
| socle | C22×C52 | C2×D4 |
| hypercenter | C42 | D52 |
| hypocenter | C52 | #496 |
| LCS | G ▷ C2×C4×C52 ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11717194 | C2 | semidirect |
| 2. C5×#4021 | C2 | semidirect |
| 3. C2×#87774 | C2 | semidirect |
| 4. C2×#87771 | C2 | semidirect |
| 5. C5×#3935 | C2 | semidirect |
| 27. C5×#168 | D4 | semidirect |
| 33. #4021 | D5 | semidirect |
| 38. #3935 | D5 | semidirect |
| 100. #168 | D20 | semidirect |
| 106. C52 | #496 | semidirect |
| 160. C5 | #65001 | semidirect |
| 161. C5 | #65347 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717194 | 2 |
| C5×#4021 | 2 |
| C2×#87774 | 2 |
| C2×#87771 | 2 |
| C5×#3935 | 2 |
| #65347 | 5 |
| #65001 | 5 |