Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
156 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C25 | C2×D4 |
| commutator | C4 | C22×C4×C25 |
| Frattini, cosocle | C2×C4×C5 | C23×C5 |
| socle | C2×C5 | C4×C5×D4 |
| prime radical | C5×#135 | C2×C5 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C25 ◁ C2×C8×C25 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C25×#131 | C2 | semidirect |
| 3. C25×#108 | C2 | semidirect |
| 4. C25×#104 | C2 | semidirect |
| 5. C25×#97 | C2 | semidirect |
| 7. Q16×C25 | C4 | semidirect |
| 8. SD16×C25 | C4 | semidirect |
| 9. D8×C25 | C4 | semidirect |
| 48. #444 | C25 | direct (N × H) |
| 63. #131 | C2×C25 | semidirect |
| 64. #108 | C2×C25 | semidirect |
| 65. #104 | C2×C25 | semidirect |
| 66. #97 | C2×C25 | semidirect |
| 67. C25 | #444 | direct (N × H) |
| 75. Q16 | C4×C25 | semidirect |
| 76. SD16 | C4×C25 | semidirect |
| 77. D8 | C4×C25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×#135 | 2 |
| C25×#131 | 2 |
| C25×#108 | 2 |
| C25×#104 | 2 |
| C25×#97 | 2 |
| C5×#444 | 5 |