Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
380 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #65249 |
| commutator, cosocle | C22×C4×C5 | C23 |
| Frattini | C22×C4 | C22×D5 |
| Fitting | C5×#418 | C2 |
| socle | C2×C5 | #392 |
| hypercenter | #418 | D5 |
| hypocenter | C5 | #2008 |
| LCS | G ▷ C22×C4×C5 ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #418 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #66139 | C2 | semidirect |
| 2. C2×#4078 | C2 | semidirect |
| 3. #66082 | C2 | semidirect |
| 4. C5×#418 | C2 | semidirect |
| 5. #65295 | C2 | semidirect |
| 6. #65294 | C2 | semidirect |
| 7. #64776 | C2 | semidirect |
| 52. C2×D20 | D4 | semidirect |
| 56. C2×Dic10 | D4 | semidirect |
| 59. C2×C5×C8 | D4 | semidirect |
| 70. #681 | D4 | semidirect |
| 80. #418 | D5 | semidirect |
| 202. C2×C8 | C22⋊D5 | semidirect |
| 257. C5 | #2008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66139 | 2 |
| C2×#4078 | 2 |
| #66082 | 2 |
| C5×#418 | 2 |
| #65295 | 2 |
| #65294 | 2 |
| #64776 | 2 |
| #2008 | 5 |