Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
696 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 152 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D52 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C42×C52 | C22 |
| hypercenter | C42 | D52 |
| hypocenter | C52 | #532 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#87874 | C2 | semidirect |
| 2. C2×#87870 | C2 | semidirect |
| 3. #11717195 | C2 | semidirect |
| 4. C5×#4021 | C2 | semidirect |
| 5. C42×C5×D5 | C2 | semidirect |
| 6. #11717029 | C2 | semidirect |
| 7. #11717024 | C2 | semidirect |
| 8. #11716998 | C2 | semidirect |
| 9. #11716983 | C2 | semidirect |
| 44. C4×C5×D5 | D4 | semidirect |
| 65. #4021 | D5 | semidirect |
| 68. C42×D5 | D5 | semidirect |
| 82. C5×Dic5 | #41 | semidirect |
| 172. C4×D5 | D20 | semidirect |
| 186. C52 | #532 | semidirect |
| 218. Dic5 | #709 | semidirect |
| 272. C5 | #65811 | semidirect |
| 273. C5 | #66002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87874 | 2 |
| C2×#87870 | 2 |
| #11717195 | 2 |
| C5×#4021 | 2 |
| C42×C5×D5 | 2 |
| #11717029 | 2 |
| #11717024 | 2 |
| #11716998 | 2 |
| #11716983 | 2 |
| #66002 | 5 |
| #65811 | 5 |