Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
728 conjugacy classes of subgroups; only the 208 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 208 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | D52 |
| commutator | C2×C52 | C23×C4 |
| Frattini | C22 | C22×D52 |
| Fitting | C42×C52 | C22 |
| socle, cosocle | C22×C52 | C24 |
| prime radical | C2×#87873 | C2 |
| hypocenter | C52 | C4×#41 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C42×C5⋊D5 | C2 | semidirect |
| 3. C42×C5×D5 | C2 | semidirect |
| 4. C4×#6039 | C2 | semidirect |
| 5. C4×#6038 | C2 | semidirect |
| 6. C4×#6037 | C2 | semidirect |
| 7. #11716992 | C2 | semidirect |
| 8. #11716973 | C2 | semidirect |
| 16. #87873 | C4 | direct (N × H) |
| 34. C4×C5⋊D5 | C2×C4 | semidirect |
| 38. C4×C5×D5 | C2×C4 | semidirect |
| 39. #6039 | C2×C4 | semidirect |
| 40. #6038 | C2×C4 | semidirect |
| 41. #6037 | C2×C4 | semidirect |
| 52. C42×D5 | D5 | semidirect |
| 60. C4×C52 | #41 | semidirect |
| 125. C4×D5 | C4×D5 | semidirect |
| 135. C52 | C4×#41 | semidirect |
| 151. C4×C5 | #709 | semidirect |
| 199. C5 | C4×#709 | semidirect |
| 209. C4 | #87873 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87873 | 2 |
| C42×C5⋊D5 | 2 |
| C42×C5×D5 | 2 |
| C4×#6039 | 2 |
| C4×#6038 | 2 |
| C4×#6037 | 2 |
| #11716992 | 2 |
| #11716973 | 2 |
| C4×#709 | 5 |