Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
498 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 132 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 | C2×#6037 | C22 |
| hypercenter | C2×Q8 | D52 |
| hypocenter | C52 | #552 |
| 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×#4092 | C2 | semidirect |
| 3. C5×#4092 | C2 | semidirect |
| 5. D5×C4⋊Dic5 | C2 | semidirect |
| 7. #11716996 | C2 | semidirect |
| 8. #11716991 | C2 | semidirect |
| 9. #11716980 | C2 | semidirect |
| 10. #11716963 | C2 | semidirect |
| 11. #11716959 | C2 | semidirect |
| 55. #4092 | D5 | semidirect |
| 56. #4092 | D5 | semidirect |
| 198. C52 | #552 | semidirect |
| 290. C5 | #65973 | semidirect |
| 291. C5 | #65976 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#1039 | 2 |
| C5×#4092 | 2 |
| C4×#6037 | 2 |
| D5×C4⋊Dic5 | 2 |
| #11717003 | 2 |
| #11716996 | 2 |
| #11716991 | 2 |
| #11716980 | 2 |
| #11716963 | 2 |
| #11716959 | 2 |
| #65976 | 5 |
| #65973 | 5 |