Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1336 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1336 conjugacy classes of subgroups — too many to draw. Only its 291 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×C5⋊D5 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C22×C52×D4 | C2 |
| hypercenter | C22×D4 | C5⋊D5 |
| hypocenter | C52 | #535 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C52×D4 | C2 | semidirect |
| 2. C2×#87900 | C2 | semidirect |
| 3. #11717273 | C2 | semidirect |
| 4. #11717260 | C2 | semidirect |
| 5. #11717258 | C2 | semidirect |
| 6. #11717256 | C2 | semidirect |
| 7. #11717246 | C2 | semidirect |
| 14. C2×C22⋊(C5⋊D5) | C22 | semidirect |
| 16. C2×C4⋊(C5⋊D5) | C22 | semidirect |
| 17. C2×C4×C5⋊D5 | C22 | semidirect |
| 18. C2×#6045 | C22 | semidirect |
| 20. C22⋊#1039 | C22 | semidirect |
| 21. C4⋊#1039 | C22 | semidirect |
| 22. C4×#1039 | C22 | semidirect |
| 31. C2×C4×C52 | D4 | semidirect |
| 41. C22×C5×D4 | D5 | semidirect |
| 88. C2×C4×C5 | C22⋊D5 | semidirect |
| 99. C22×D4 | C5⋊D5 | semidirect |
| 105. C52 | #535 | semidirect |
| 152. C2×C4 | C22⋊(C5⋊D5) | semidirect |
| 155. C5 | #66139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×D4 | 2 |
| C2×#87900 | 2 |
| #11717273 | 2 |
| #11717260 | 2 |
| #11717258 | 2 |
| #11717256 | 2 |
| #11717246 | 2 |
| #66139 | 5 |