Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
512 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 512 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×#127 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C52 ◁ C42×C52 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C52×SD16 | C2 | semidirect |
| 3. C4×C52×Q8 | C2 | semidirect |
| 4. C52×C4⋊C8 | C2 | semidirect |
| 5. C52×#102 | C2 | semidirect |
| 16. C5×#460 | C5 | direct (N × H) |
| 19. C52×Q8 | D4 | semidirect |
| 30. C2×C5×SD16 | C2×C5 | semidirect |
| 32. C4×C5×Q8 | C2×C5 | semidirect |
| 33. C5×C4⋊C8 | C2×C5 | semidirect |
| 34. C5×#102 | C2×C5 | semidirect |
| 42. C4×C52 | SD16 | semidirect |
| 55. #460 | C52 | direct (N × H) |
| 62. C5×Q8 | C5×D4 | semidirect |
| 73. C2×SD16 | C2×C52 | semidirect |
| 75. C4×Q8 | C2×C52 | semidirect |
| 76. C4⋊C8 | C2×C52 | semidirect |
| 77. #102 | C2×C52 | semidirect |
| 78. C52 | #460 | direct (N × H) |
| 86. C4×C5 | C5×SD16 | semidirect |
| 105. Q8 | C52×D4 | semidirect |
| 116. C5 | C5×#460 | direct (N × H) |
| 124. C4 | 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 |
| C52×#127 | 2 |
| C4×C52×Q8 | 2 |
| C52×C4⋊C8 | 2 |
| C52×#102 | 2 |
| C5×#460 | 5 |