Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
378 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C23×D25 |
| commutator, cosocle | C22×C25 | C24 |
| Frattini, socle | C22×C5 | C23×D5 |
| Fitting | C25×#123 | C2 |
| hypercenter | #123 | D25 |
| hypocenter | C25 | #560 |
| LCS | G ▷ C22×C25 ▷ C25 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C25×#123 | C2 | semidirect |
| 2. #11716502 | C2 | semidirect |
| 3. #11716499 | C2 | semidirect |
| 4. #11716492 | C2 | semidirect |
| 5. #11716460 | C2 | semidirect |
| 6. #11716457 | C2 | semidirect |
| 7. #11716446 | C2 | semidirect |
| 8. #11716445 | C2 | semidirect |
| 9. #11716444 | C2 | semidirect |
| 12. C22×C4×C25 | C22 | semidirect |
| 15. C2×C22⋊D25 | C22 | semidirect |
| 18. C2×D100 | C22 | semidirect |
| 19. C2×C4×D25 | C22 | semidirect |
| 20. C4⋊C4×C25 | C22 | semidirect |
| 22. C22⋊C4×C25 | C22 | semidirect |
| 27. #87720 | C22 | semidirect |
| 28. C4⋊Dic25 | C22 | semidirect |
| 29. #87718 | C22 | semidirect |
| 30. C4×Dic25 | C22 | semidirect |
| 129. #123 | D25 | semidirect |
| 135. C25 | #560 | semidirect |
| 162. C22×C4 | C2×D25 | semidirect |
| 165. C4⋊C4 | C2×D25 | semidirect |
| 172. C22⋊C4 | C2×D25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×#123 | 2 |
| #11716502 | 2 |
| #11716499 | 2 |
| #11716492 | 2 |
| #11716460 | 2 |
| #11716457 | 2 |
| #11716446 | 2 |
| #11716445 | 2 |
| #11716444 | 2 |
| #66000 | 5 |