Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
390 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 390 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×#120 | C2 |
| hypercenter | #120 | D25 |
| hypocenter | C25 | H(3,𝔽4) |
| LCS | G ▷ C22×C25 ▷ C25 | |
| UCS | C1 ◁ C22 ◁ #120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C25×#120 | C2 | semidirect |
| 2. #11716515 | C2 | semidirect |
| 3. #11716499 | C2 | semidirect |
| 4. #11716498 | C2 | semidirect |
| 5. #11716447 | C2 | semidirect |
| 6. C24×C25 | C22 | semidirect |
| 7. C23×D25 | C22 | semidirect |
| 10. C2×Dic50 | C22 | semidirect |
| 11. C22⋊C4×C25 | C22 | semidirect |
| 12. C22⋊Dic25 | C22 | semidirect |
| 13. C22⋊Dic25 | C22 | semidirect |
| 14. #87720 | C22 | semidirect |
| 15. C4×Dic25 | C22 | semidirect |
| 70. #120 | D25 | semidirect |
| 71. C25 | H(3,𝔽4) | semidirect |
| 82. C24 | C2×D25 | semidirect |
| 89. 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×#120 | 2 |
| #11716515 | 2 |
| #11716499 | 2 |
| #11716498 | 2 |
| #11716447 | 2 |
| #65928 | 5 |