Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1936 conjugacy classes of subgroups; only the 926 normal subgroups are shown.
This group has 1936 conjugacy classes of subgroups — too many to draw. Only its 926 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23×C5 | C22×D5 |
| commutator, cosocle | C2×C5 | C25×C5 |
| Frattini | C2 | C24×C5×D5 |
| Fitting | C22×C52×Q8 | C2 |
| socle | C23×C52 | C23 |
| hypercenter | C22×C5×Q8 | D5 |
| hypocenter | C5 | C22×C5×#41 |
| LCS | G ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C23×C5 ◁ C22×C5×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C52×Q8 | C2 | semidirect |
| 2. C2×C5×#713 | C2 | direct (N × H) |
| 3. C22×C5×D20 | C2 | semidirect |
| 4. C22×C4×C5×D5 | C2 | semidirect |
| 6. C2×C52×Q8 | C22 | semidirect |
| 9. C5×#713 | C22 | direct (N × H) |
| 10. C2×C5×D20 | C22 | semidirect |
| 11. C2×C4×C5×D5 | C22 | semidirect |
| 13. C22×#713 | C5 | direct (N × H) |
| 17. C52×Q8 | C23 | semidirect |
| 20. C5×D20 | C23 | semidirect |
| 21. C4×C5×D5 | C23 | semidirect |
| 24. C22×C5×Q8 | D5 | semidirect |
| 25. C22×C5×Q8 | C2×C5 | semidirect |
| 28. C2×#713 | C2×C5 | direct (N × H) |
| 29. C22×D20 | C2×C5 | semidirect |
| 30. C22×C4×D5 | C2×C5 | semidirect |
| 31. C22×C52 | #41 | semidirect |
| 41. C2×C5×Q8 | C2×D5 | semidirect |
| 42. C2×C5×Q8 | C22×C5 | semidirect |
| 50. #713 | C22×C5 | direct (N × H) |
| 51. C2×D20 | C22×C5 | semidirect |
| 52. C2×C4×D5 | C22×C5 | semidirect |
| 54. C2×C52 | C2×#41 | semidirect |
| 65. C5×Q8 | C22×D5 | semidirect |
| 66. C5×Q8 | C23×C5 | semidirect |
| 74. D20 | C23×C5 | semidirect |
| 75. C4×D5 | C23×C5 | semidirect |
| 77. C22×Q8 | C5×D5 | semidirect |
| 80. C52 | C22×#41 | semidirect |
| 85. C22×C5 | #713 | direct (N × H) |
| 86. C22×C5 | C5×#41 | semidirect |
| 98. C2×Q8 | C2×C5×D5 | semidirect |
| 106. C2×C5 | C2×#713 | direct (N × H) |
| 107. C2×C5 | C2×C5×#41 | semidirect |
| 114. Q8 | C22×C5×D5 | semidirect |
| 120. C5 | C22×#713 | direct (N × H) |
| 121. C5 | C22×C5×#41 | semidirect |
| 124. C22 | C5×#713 | direct (N × H) |
| 129. C2 | C2×C5×#713 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×Q8 | 2 |
| C2×C5×#713 | 2 |
| C22×C5×D20 | 2 |
| C22×C4×C5×D5 | 2 |
| C22×C5×#41 | 5 |
| C22×#713 | 5 |