Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
272 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #1044 |
| commutator, hypocenter | C52 | C22×C16 |
| Frattini | C4 | C22×#1044 |
| Fitting | C2×C52×C8 | C4 |
| socle | C22×C52 | C2×C8 |
| prime radical | C22×C5⋊D5 | C8 |
| cosocle | #6029 | C23 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#87765 | C2 | semidirect |
| 3. #11716882 | C2 | direct (N × H) |
| 9. #87765 | C22 | semidirect |
| 24. C2×C5⋊D5 | C16 | semidirect |
| 41. C2×C52 | C2×C16 | semidirect |
| 43. C5⋊D5 | C2×C16 | semidirect |
| 63. C52 | C22×C16 | semidirect |
| 84. C2×C5 | D5⋊C16 | semidirect |
| 97. C5 | C2×D5⋊C16 | semidirect |
| 105. C2 | #11716882 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×C5⋊D5 | 2 |
| C2×#87765 | 2 |
| #11716882 | 2 |
| C2×D5⋊C16 | 5 |