Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
584 conjugacy classes of subgroups; only the 208 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 208 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C5 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×AGL(1,ℤ/8) | C2 | semidirect |
| 2. C2×C5×#127 | C2 | semidirect |
| 3. C4×C5×#41 | C2 | semidirect |
| 4. C5×#460 | C2 | semidirect |
| 5. C5×#459 | C2 | semidirect |
| 6. C5×#423 | C2 | semidirect |
| 7. C5×#418 | C2 | semidirect |
| 12. C2×C5×SD16 | C22 | semidirect |
| 13. C2×C5×D8 | C22 | semidirect |
| 18. C4×C5×Q8 | C22 | semidirect |
| 20. C4×C5×D4 | C22 | semidirect |
| 25. C5×C4⋊C8 | C22 | semidirect |
| 26. C5×#102 | C22 | semidirect |
| 27. #3038 | C5 | direct (N × H) |
| 30. C5×#41 | D4 | semidirect |
| 58. C2×AGL(1,ℤ/8) | C2×C5 | semidirect |
| 59. C2×#127 | C2×C5 | semidirect |
| 60. C4×#41 | C2×C5 | semidirect |
| 61. #460 | C2×C5 | semidirect |
| 62. #459 | C2×C5 | semidirect |
| 63. #423 | C2×C5 | semidirect |
| 64. #418 | C2×C5 | semidirect |
| 71. C5×Q8 | C2×D4 | semidirect |
| 79. C5×D4 | C2×D4 | semidirect |
| 96. C2×SD16 | C22×C5 | semidirect |
| 97. C2×D8 | C22×C5 | semidirect |
| 102. C4×Q8 | C22×C5 | semidirect |
| 104. C4×D4 | C22×C5 | semidirect |
| 109. C4⋊C8 | C22×C5 | semidirect |
| 110. #102 | C22×C5 | semidirect |
| 123. C4×C5 | AGL(1,ℤ/8) | semidirect |
| 128. #41 | C5×D4 | semidirect |
| 167. Q8 | C2×C5×D4 | semidirect |
| 175. D4 | C2×C5×D4 | semidirect |
| 188. C5 | #3038 | direct (N × H) |
| 201. C4 | C5×AGL(1,ℤ/8) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×AGL(1,ℤ/8) | 2 |
| C2×C5×#127 | 2 |
| C4×C5×#41 | 2 |
| C5×#460 | 2 |
| C5×#459 | 2 |
| C5×#423 | 2 |
| C5×#418 | 2 |
| #3038 | 5 |