Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
496 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 232 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×C52 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C52 |
| prime radical | C52×#121 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C52 ◁ C22×C4×C52 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C52×SD16 | C2 | semidirect |
| 2. C22×C52×C8 | C2 | semidirect |
| 3. C52×C22⋊Q8 | C2 | semidirect |
| 5. C52×#106 | C2 | semidirect |
| 6. C52×#103 | C2 | semidirect |
| 7. C52×#102 | C2 | semidirect |
| 21. C5×#465 | C5 | direct (N × H) |
| 37. C52×C8 | D4 | semidirect |
| 38. C2×C5×SD16 | C2×C5 | semidirect |
| 39. C22×C5×C8 | C2×C5 | semidirect |
| 40. C5×C22⋊Q8 | C2×C5 | semidirect |
| 42. C5×#106 | C2×C5 | semidirect |
| 43. C5×#103 | C2×C5 | semidirect |
| 44. C5×#102 | C2×C5 | semidirect |
| 50. C22×C52 | SD16 | semidirect |
| 71. #465 | C52 | direct (N × H) |
| 92. C5×C8 | C5×D4 | semidirect |
| 93. C2×SD16 | C2×C52 | semidirect |
| 94. C22×C8 | C2×C52 | semidirect |
| 95. C22⋊Q8 | C2×C52 | semidirect |
| 97. #106 | C2×C52 | semidirect |
| 98. #103 | C2×C52 | semidirect |
| 99. #102 | C2×C52 | semidirect |
| 100. C52 | #465 | direct (N × H) |
| 106. C22×C5 | C5×SD16 | semidirect |
| 147. C8 | C52×D4 | semidirect |
| 148. C5 | C5×#465 | direct (N × H) |
| 154. C22 | C52×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×SD16 | 2 |
| C22×C52×C8 | 2 |
| C52×C22⋊Q8 | 2 |
| C52×#121 | 2 |
| C52×#106 | 2 |
| C52×#103 | 2 |
| C52×#102 | 2 |
| C5×#465 | 5 |