Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
560 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 560 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 |
| 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×D8 | C2 | semidirect |
| 2. C52×#127 | C2 | semidirect |
| 3. C4×C52×D4 | C2 | semidirect |
| 4. C52×C4⋊C8 | C2 | semidirect |
| 5. C52×#102 | C2 | semidirect |
| 16. C5×#459 | C5 | direct (N × H) |
| 24. C52×D4 | D4 | semidirect |
| 31. C2×C5×D8 | C2×C5 | semidirect |
| 32. C5×#127 | C2×C5 | semidirect |
| 33. C4×C5×D4 | C2×C5 | semidirect |
| 34. C5×C4⋊C8 | C2×C5 | semidirect |
| 35. C5×#102 | C2×C5 | semidirect |
| 45. C4×C52 | D8 | semidirect |
| 58. #459 | C52 | direct (N × H) |
| 71. C5×D4 | C5×D4 | semidirect |
| 78. C2×D8 | C2×C52 | semidirect |
| 79. #127 | C2×C52 | semidirect |
| 80. C4×D4 | C2×C52 | semidirect |
| 81. C4⋊C8 | C2×C52 | semidirect |
| 82. #102 | C2×C52 | semidirect |
| 83. C52 | #459 | direct (N × H) |
| 93. C4×C5 | C5×D8 | semidirect |
| 118. D4 | C52×D4 | semidirect |
| 125. C5 | C5×#459 | direct (N × H) |
| 135. C4 | C52×D8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×D8 | 2 |
| C52×#127 | 2 |
| C4×C52×D4 | 2 |
| C52×C4⋊C8 | 2 |
| C52×#102 | 2 |
| C5×#459 | 5 |