Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
465 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 465 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D25 |
| commutator, cosocle | C22×C25 | C24 |
| Frattini, socle | C22×C5 | C23×D5 |
| Fitting | C4×D4×C25 | C2 |
| hypercenter | C4×D4 | D25 |
| hypocenter | C25 | #532 |
| LCS | G ▷ C22×C25 ▷ C25 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#87744 | C2 | semidirect |
| 2. C4×D4×C25 | C2 | semidirect |
| 3. #11716502 | C2 | semidirect |
| 4. #11716500 | C2 | semidirect |
| 5. C4×C22⋊D25 | C2 | semidirect |
| 6. #11716457 | C2 | semidirect |
| 7. #11716450 | C2 | semidirect |
| 8. #11716447 | C2 | semidirect |
| 9. #11716446 | C2 | semidirect |
| 10. C4×D100 | C2 | semidirect |
| 11. C42×D25 | C2 | semidirect |
| 58. C4×D25 | D4 | semidirect |
| 84. C4×C25 | #41 | semidirect |
| 88. Dic25 | #41 | semidirect |
| 152. C4×D4 | D25 | semidirect |
| 154. C25 | #532 | semidirect |
| 243. C4 | #87744 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87744 | 2 |
| C4×D4×C25 | 2 |
| #11716502 | 2 |
| #11716500 | 2 |
| C4×C22⋊D25 | 2 |
| #11716457 | 2 |
| #11716450 | 2 |
| #11716447 | 2 |
| #11716446 | 2 |
| C4×D100 | 2 |
| C42×D25 | 2 |
| #65882 | 5 |