Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
375 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 375 conjugacy classes of subgroups — too many to draw. Only its 117 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×C22⋊Q8 | C2 |
| hypercenter | C22⋊Q8 | D25 |
| hypocenter | C25 | #538 |
| LCS | G ▷ C22×C25 ▷ C25 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C25×C22⋊Q8 | C2 | semidirect |
| 2. #11716509 | C2 | semidirect |
| 3. #11716492 | C2 | semidirect |
| 4. C2×#87720 | C2 | semidirect |
| 5. #11716460 | C2 | semidirect |
| 6. #11716457 | C2 | semidirect |
| 7. #11716456 | C2 | semidirect |
| 8. #11716444 | C2 | semidirect |
| 9. #11716443 | C2 | semidirect |
| 11. C2×Q8×C25 | C22 | semidirect |
| 17. C2×D100 | C22 | semidirect |
| 18. C2×C4×D25 | C22 | semidirect |
| 19. C4⋊C4×C25 | C22 | semidirect |
| 20. C4⋊C4×C25 | C22 | semidirect |
| 26. #87720 | C22 | semidirect |
| 27. #87720 | C22 | semidirect |
| 28. C4⋊Dic25 | C22 | semidirect |
| 29. #87718 | C22 | semidirect |
| 30. C4×Dic25 | C22 | semidirect |
| 129. C22⋊Q8 | D25 | semidirect |
| 135. C25 | #538 | semidirect |
| 154. C2×Q8 | C2×D25 | semidirect |
| 164. C4⋊C4 | C2×D25 | semidirect |
| 165. C4⋊C4 | C2×D25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×C22⋊Q8 | 2 |
| #11716509 | 2 |
| #11716492 | 2 |
| C2×#87720 | 2 |
| #11716460 | 2 |
| #11716457 | 2 |
| #11716456 | 2 |
| #11716444 | 2 |
| #11716443 | 2 |
| #65978 | 5 |