Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
216 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C5 | C2×D4 |
| commutator | C2×C4 | C22×C4×C5 |
| Frattini, cosocle | C42 | C23×C5 |
| socle | C22×C5 | C2×C22⋊C4 |
| prime radical | C5×#121 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C5 ◁ C2×C42×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#431 | C2 | semidirect |
| 3. C5×#423 | C2 | semidirect |
| 4. C5×Q8⋊C8 | C2 | semidirect |
| 5. C5×D4⋊C8 | C2 | semidirect |
| 23. #1495 | C5 | direct (N × H) |
| 51. #431 | C2×C5 | semidirect |
| 52. #423 | C2×C5 | semidirect |
| 53. Q8⋊C8 | C2×C5 | semidirect |
| 54. D4⋊C8 | C2×C5 | semidirect |
| 164. C5 | #1495 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#529 | 2 |
| C5×#431 | 2 |
| C5×#423 | 2 |
| C5×Q8⋊C8 | 2 |
| C5×D4⋊C8 | 2 |
| #1495 | 5 |