Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
772 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 212 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C5 | C2×#120 |
| commutator, Frattini, cosocle | C23 | C24×C5 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C5 ◁ C22×C4×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#585 | C2 | semidirect |
| 2. C5×#535 | C2 | semidirect |
| 3. C5×B(4,𝔽2) | C2 | semidirect |
| 4. C5×#410 | C2 | semidirect |
| 10. C22×C5×D4 | C22 | semidirect |
| 14. C5×#120 | C22 | semidirect |
| 15. C5×#117 | C22 | semidirect |
| 16. C5×#99 | C22 | semidirect |
| 17. #3027 | C5 | direct (N × H) |
| 25. C2×C5×Q8 | D4 | semidirect |
| 31. C2×C5×D4 | D4 | semidirect |
| 34. C22×C4×C5 | D4 | semidirect |
| 40. #585 | C2×C5 | semidirect |
| 41. #535 | C2×C5 | semidirect |
| 42. B(4,𝔽2) | C2×C5 | semidirect |
| 43. #410 | C2×C5 | semidirect |
| 69. C22×D4 | C22×C5 | semidirect |
| 73. #120 | C22×C5 | semidirect |
| 74. #117 | C22×C5 | semidirect |
| 75. #99 | C22×C5 | semidirect |
| 94. C2×Q8 | C5×D4 | semidirect |
| 100. C2×D4 | C5×D4 | semidirect |
| 103. C22×C4 | C5×D4 | semidirect |
| 133. C5 | #3027 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#585 | 2 |
| C5×#535 | 2 |
| C5×B(4,𝔽2) | 2 |
| C5×#410 | 2 |
| #3027 | 5 |