Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
162 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 84 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 | C4×D4 |
| prime radical | C2×C5×D4 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C5 ◁ C4×C5×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#446 | C2 | semidirect |
| 4. C5×#335 | C2 | semidirect |
| 5. C5×Q8⋊C8 | C2 | semidirect |
| 7. C5×#322 | C2 | semidirect |
| 23. #1592 | C5 | direct (N × H) |
| 42. #446 | C2×C5 | semidirect |
| 45. #335 | C2×C5 | semidirect |
| 46. Q8⋊C8 | C2×C5 | semidirect |
| 48. #322 | C2×C5 | semidirect |
| 68. C5×C8 | M16 | semidirect |
| 137. C8 | C5×M16 | semidirect |
| 138. C5 | #1592 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#446 | 2 |
| C4×C5×SD16 | 2 |
| C5×#436 | 2 |
| C5×#335 | 2 |
| C5×Q8⋊C8 | 2 |
| C5×D4⋊C8 | 2 |
| C5×#322 | 2 |
| #1592 | 5 |