Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
336 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #11717094 |
| commutator, cosocle | C2×C4×C52 | C23 |
| Frattini | C2×C4 | C2×D52 |
| Fitting | C52×#41 | C22 |
| socle | C2×C52 | #120 |
| hypercenter | #41 | D52 |
| hypocenter | C52 | #454 |
| LCS | G ▷ C2×C4×C52 ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#4150 | C2 | semidirect |
| 2. C5×#4095 | C2 | semidirect |
| 3. #11716981 | C2 | semidirect |
| 4. #11716941 | C2 | semidirect |
| 5. #11716704 | C2 | semidirect |
| 6. #11716609 | C2 | semidirect |
| 7. #11716601 | C2 | semidirect |
| 50. #4150 | D5 | semidirect |
| 53. #4095 | D5 | semidirect |
| 176. C52 | #454 | semidirect |
| 258. C5 | #65490 | semidirect |
| 259. C5 | #65534 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4150 | 2 |
| C5×#4095 | 2 |
| #11716981 | 2 |
| #11716941 | 2 |
| #11716704 | 2 |
| #11716609 | 2 |
| #11716601 | 2 |
| #65534 | 5 |
| #65490 | 5 |