Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1168 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 237 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 | C23×C5⋊D5 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C52×C22⋊Q8 | C2 |
| hypercenter | C22⋊Q8 | C5⋊D5 |
| hypocenter | C52 | #547 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#87904 | C2 | semidirect |
| 2. C2×#87900 | C2 | semidirect |
| 3. C52×C22⋊Q8 | C2 | semidirect |
| 4. #11717264 | C2 | semidirect |
| 5. C4×C22⋊(C5⋊D5) | C2 | semidirect |
| 6. #11717217 | C2 | semidirect |
| 7. #11717214 | C2 | semidirect |
| 8. #11717213 | C2 | semidirect |
| 9. C4⋊C4×C5⋊D5 | C2 | semidirect |
| 10. #11717204 | C2 | semidirect |
| 11. #11717203 | C2 | semidirect |
| 54. C4⋊(C5⋊D5) | D4 | semidirect |
| 62. C5×C22⋊Q8 | D5 | semidirect |
| 88. #1039 | #41 | semidirect |
| 149. C22⋊Q8 | C5⋊D5 | semidirect |
| 154. C52 | #547 | semidirect |
| 226. C5 | #65965 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87904 | 2 |
| C2×#87900 | 2 |
| C52×C22⋊Q8 | 2 |
| #11717264 | 2 |
| C4×C22⋊(C5⋊D5) | 2 |
| #11717217 | 2 |
| #11717214 | 2 |
| #11717213 | 2 |
| C4⋊C4×C5⋊D5 | 2 |
| #11717204 | 2 |
| #11717203 | 2 |
| #65965 | 5 |