Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
519 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 519 conjugacy classes of subgroups — too many to draw. Only its 141 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 | C2×C22⋊C4×C25 | C2 |
| hypercenter | C2×C22⋊C4 | D25 |
| hypocenter | C25 | #534 |
| LCS | G ▷ C22×C25 ▷ C25 | |
| UCS | C1 ◁ C22 ◁ C2×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C22⋊D25 | C2 | semidirect |
| 2. C2×C22⋊C4×C25 | C2 | semidirect |
| 3. #11716492 | C2 | semidirect |
| 4. #11716448 | C2 | semidirect |
| 5. #11716444 | C2 | semidirect |
| 7. C23×D25 | C22 | semidirect |
| 8. C22×C4×C25 | C22 | semidirect |
| 11. C2×C22⋊D25 | C22 | semidirect |
| 12. C22×Dic25 | C22 | semidirect |
| 13. C2×D100 | C22 | semidirect |
| 14. C22⋊C4×C25 | C22 | semidirect |
| 15. #87720 | C22 | semidirect |
| 16. C4⋊Dic25 | C22 | semidirect |
| 19. C23×C25 | D4 | semidirect |
| 83. C2×C22⋊C4 | D25 | semidirect |
| 84. C25 | #534 | semidirect |
| 103. C22×C4 | C2×D25 | semidirect |
| 106. C22⋊C4 | C2×D25 | semidirect |
| 116. C23 | D100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊D25 | 2 |
| C2×C22⋊C4×C25 | 2 |
| #11716492 | 2 |
| #11716448 | 2 |
| #11716444 | 2 |
| #65827 | 5 |