Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
262 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #11717024 |
| commutator, cosocle | C2×C4×C52 | C23 |
| Frattini | C2×C4 | C2×D52 |
| Fitting | C52×M16 | C22 |
| socle | C2×C52 | #121 |
| hypercenter | M16 | D52 |
| hypocenter | C52 | #472 |
| LCS | G ▷ C2×C4×C52 ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ M16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#4053 | C2 | semidirect |
| 2. #11716943 | C2 | semidirect |
| 3. C2×#87771 | C2 | semidirect |
| 4. #11716941 | C2 | semidirect |
| 5. #11716690 | C2 | semidirect |
| 6. C5×#3955 | C2 | semidirect |
| 7. #11716618 | C2 | semidirect |
| 47. #4053 | D5 | semidirect |
| 53. #3955 | D5 | semidirect |
| 149. C52 | #472 | semidirect |
| 218. C5 | #65038 | semidirect |
| 219. C5 | #65431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4053 | 2 |
| #11716943 | 2 |
| C2×#87771 | 2 |
| #11716941 | 2 |
| #11716690 | 2 |
| C5×#3955 | 2 |
| #11716618 | 2 |
| #65431 | 5 |
| #65038 | 5 |