Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
184 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C5 | #121 |
| commutator | C2×C4 | C22×C4×C5 |
| Frattini, cosocle | C22×C4 | C23×C5 |
| socle | C2×C5 | #389 |
| prime radical | C23×C5 | C2×Q8 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C5 ◁ C22×C4×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 14. C5×#108 | C4 | semidirect |
| 17. #1953 | C5 | direct (N × H) |
| 61. #108 | C4×C5 | semidirect |
| 107. C5 | #1953 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#430 | 2 |
| C2×C5×#108 | 2 |
| C5×#405 | 2 |
| C5×#344 | 2 |
| #1953 | 5 |