Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
506 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 506 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 | #11717034 | 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. #11717266 | C2 | semidirect |
| 2. C5×#4093 | C2 | semidirect |
| 3. C5×Q8×Dic5 | C2 | semidirect |
| 4. #11717036 | C2 | semidirect |
| 6. #11717014 | C2 | semidirect |
| 7. Dic5×D20 | C2 | semidirect |
| 8. #11717011 | C2 | semidirect |
| 9. #11716992 | C2 | semidirect |
| 10. #11716978 | C2 | semidirect |
| 11. #11716970 | C2 | semidirect |
| 56. #4093 | D5 | semidirect |
| 60. Q8×Dic5 | D5 | semidirect |
| 202. C52 | #542 | semidirect |
| 298. C5 | #65916 | semidirect |
| 299. C5 | #66016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717266 | 2 |
| C5×#4093 | 2 |
| C5×Q8×Dic5 | 2 |
| #11717036 | 2 |
| #11717034 | 2 |
| #11717014 | 2 |
| Dic5×D20 | 2 |
| #11717011 | 2 |
| #11716992 | 2 |
| #11716978 | 2 |
| #11716970 | 2 |
| #66016 | 5 |
| #65916 | 5 |