Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
538 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 134 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 | C22×D52 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C2×C52×Q8 | C22 |
| prime radical | #11717026 | C2 |
| hypercenter | C2×Q8 | D52 |
| hypocenter | C52 | #529 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q8×#1039 | C2 | semidirect |
| 2. C5×#4093 | C2 | semidirect |
| 3. C5×#4092 | C2 | semidirect |
| 5. #11717020 | C2 | semidirect |
| 6. #11717017 | C2 | semidirect |
| 7. #11717003 | C2 | semidirect |
| 8. #11716996 | C2 | semidirect |
| 9. C4×D5×Dic5 | C2 | semidirect |
| 10. #11716988 | C2 | semidirect |
| 11. #11716977 | C2 | semidirect |
| 57. #4093 | D5 | semidirect |
| 58. #4092 | D5 | semidirect |
| 204. C52 | #529 | semidirect |
| 298. C5 | #65958 | semidirect |
| 299. C5 | #66014 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#1039 | 2 |
| C5×#4093 | 2 |
| C5×#4092 | 2 |
| #11717026 | 2 |
| #11717020 | 2 |
| #11717017 | 2 |
| #11717003 | 2 |
| #11716996 | 2 |
| C4×D5×Dic5 | 2 |
| #11716988 | 2 |
| #11716977 | 2 |
| #66014 | 5 |
| #65958 | 5 |