Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
224 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 152 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 | C4 | C2×C42×C5 |
| Frattini, cosocle | C22×C4 | C23×C5 |
| socle | C22×C5 | C4×D4 |
| prime radical | C23×C5 | #41 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C5 ◁ C22×C5×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 11. C5×#108 | C4 | semidirect |
| 12. C5×#107 | C4 | semidirect |
| 13. C5×#106 | C4 | semidirect |
| 15. C5×#97 | C4 | semidirect |
| 17. #1773 | C5 | direct (N × H) |
| 59. #108 | C4×C5 | semidirect |
| 60. #107 | C4×C5 | semidirect |
| 61. #106 | C4×C5 | semidirect |
| 63. #97 | C4×C5 | semidirect |
| 110. C5 | #1773 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#108 | 2 |
| C5×#427 | 2 |
| C5×#405 | 2 |
| C2×C5×#97 | 2 |
| C5×#339 | 2 |
| #1773 | 5 |