Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
558 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 558 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 | C2 | C2×#87877 |
| commutator, cosocle | C4×C52 | C24 |
| Frattini | C4 | C22×D52 |
| Fitting | C2×C52×C8 | C22 |
| socle | C2×C52 | C22×D4 |
| hypercenter | C2×C8 | D52 |
| hypocenter | C52 | #578 |
| LCS | G ▷ C4×C52 ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C2×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11717462 | C2 | semidirect |
| 2. #11717221 | C2 | semidirect |
| 3. C2×C5×Dic20 | C2 | semidirect |
| 4. C5×#4050 | C2 | semidirect |
| 5. #11716945 | C2 | semidirect |
| 6. #11716929 | C2 | semidirect |
| 7. #11716928 | C2 | semidirect |
| 8. #11716920 | C2 | semidirect |
| 61. C2×Dic20 | D5 | semidirect |
| 62. #4050 | D5 | semidirect |
| 176. C52 | #578 | semidirect |
| 248. C5 | #66100 | semidirect |
| 249. C5 | #66105 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717462 | 2 |
| #11717221 | 2 |
| C2×C5×Dic20 | 2 |
| C5×#4050 | 2 |
| #11716945 | 2 |
| #11716929 | 2 |
| #11716928 | 2 |
| #11716920 | 2 |
| #66105 | 5 |
| #66100 | 5 |