Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
502 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 128 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 | #542 |
| 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 |
| 4. #11717036 | C2 | semidirect |
| 5. #11717033 | C2 | semidirect |
| 7. #11717017 | C2 | semidirect |
| 8. #11717007 | C2 | semidirect |
| 9. #11717003 | C2 | semidirect |
| 10. #11716980 | C2 | semidirect |
| 11. #11716973 | C2 | semidirect |
| 56. #4093 | D5 | semidirect |
| 57. #4092 | D5 | semidirect |
| 201. C52 | #542 | semidirect |
| 294. C5 | #65977 | semidirect |
| 295. C5 | #66016 | 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 |
| #11717036 | 2 |
| #11717033 | 2 |
| #11717026 | 2 |
| #11717017 | 2 |
| #11717007 | 2 |
| #11717003 | 2 |
| #11716980 | 2 |
| #11716973 | 2 |
| #66016 | 5 |
| #65977 | 5 |