Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
639 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 639 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D25 |
| commutator, cosocle | C22×C25 | C24 |
| Frattini | C22×C5 | C23×D5 |
| Fitting | C2×C4⋊C4×C25 | C2 |
| socle | C23×C5 | C22×D5 |
| hypercenter | C2×C4⋊C4 | D25 |
| hypocenter | C25 | C2×#121 |
| LCS | G ▷ C22×C25 ▷ C25 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×D100 | C2 | semidirect |
| 2. C22×D100 | C2 | semidirect |
| 3. C22×C4×D25 | C2 | semidirect |
| 4. C2×C4⋊C4×C25 | C2 | semidirect |
| 5. C2×#87720 | C2 | semidirect |
| 6. #11716457 | C2 | direct (N × H) |
| 14. C2×D100 | C22 | semidirect |
| 15. C2×D100 | C22 | semidirect |
| 17. C2×C4×D25 | C22 | semidirect |
| 18. C4⋊C4×C25 | C22 | semidirect |
| 19. #87720 | C22 | semidirect |
| 27. C22×D25 | D4 | semidirect |
| 31. C2×C4×C25 | D4 | semidirect |
| 56. C2×D25 | C2×D4 | semidirect |
| 58. C4×C25 | C2×D4 | semidirect |
| 74. C2×C25 | #121 | semidirect |
| 102. C2×C4⋊C4 | D25 | semidirect |
| 104. C25 | C2×#121 | semidirect |
| 131. C4⋊C4 | C2×D25 | semidirect |
| 154. C2×C4 | D100 | semidirect |
| 172. C4 | C2×D100 | semidirect |
| 175. C2 | #11716457 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D100 | 2 |
| C22×C4×D25 | 2 |
| C2×C4⋊C4×C25 | 2 |
| C2×#87720 | 2 |
| #11716457 | 2 |
| C2×#4041 | 5 |