Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
196 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | D5×D40 |
| commutator, cosocle | C52×C8 | C23 |
| Frattini | C8 | C2×D52 |
| Fitting | C52×C16 | C22 |
| socle | C2×C52 | C2×D8 |
| hypercenter | C16 | D52 |
| hypocenter | C52 | #508 |
| LCS | G ▷ C52×C8 ▷ C4×C52 ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11716926 | C2 | semidirect |
| 2. #11716666 | C2 | semidirect |
| 3. C5×Dic40 | C2 | semidirect |
| 4. C5×D5×C16 | C2 | semidirect |
| 5. #11716590 | C2 | semidirect |
| 27. Dic40 | D5 | semidirect |
| 32. D5×C16 | D5 | semidirect |
| 79. C52 | #508 | semidirect |
| 115. C5 | #65193 | semidirect |
| 116. C5 | #65208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11716926 | 2 |
| #11716666 | 2 |
| C5×Dic40 | 2 |
| C5×D5×C16 | 2 |
| #11716590 | 2 |
| #65208 | 5 |
| #65193 | 5 |