Finite Group Databasebeta

← C25×C4×C132 #72199167

Subgroups — C25×C4×C132 #72199167

Order 21632.

84416 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C26×C132C211yesmaximal, characteristic
2C24×C4×C132C2162yesmaximal, direct product factor
3C25×C132C4132yesdirect product factor
4C25×C132C22131yes—
5C23×C4×C132C221620yesdirect product factor
6C24×C132C2×C41496yesdirect product factor
7C24×C132C231155yes—
8C22×C4×C132C2311240yesdirect product factor
9C25×C4×C13C13114yesmaximal, direct product factor
10C23×C132C22×C411240yesdirect product factor
11C23×C132C241155yes—
12C2×C4×C132C241496yesdirect product factor
13C26×C13C2×C13114yes—
14C24×C4×C13C2×C131868yesdirect product factor
15C22×C132C23×C41620yesdirect product factor
16C22×C132C25131yes—
17C4×C132C25132yesdirect product factor
18C25×C13C4×C131448yesdirect product factor
19C25×C13C22×C131434yes—
20C23×C4×C13C22×C1318680yesdirect product factor
21C2×C132C24×C4162yesdirect product factor
22C2×C132C2611yescharacteristic
23C24×C13C2×C4×C1316944yesdirect product factor
24C24×C13C23×C1312170yes—
25C22×C4×C13C23×C13117360yesdirect product factor
26C132C25×C411yescharacteristic, direct product factor, Sylow
27C25×C4C13211yescharacteristic, direct product factor, Sylow
28C23×C13C22×C4×C13117360yesdirect product factor
29C23×C13C24×C1312170yes—
30C2×C4×C13C24×C1316944yesdirect product factor
31C26C2×C13211yescharacteristic
32C24×C4C2×C132162yesdirect product factor
33C22×C13C23×C4×C1318680yesdirect product factor
34C22×C13C25×C131434yes—
35C4×C13C25×C131448yesdirect product factor
36C25C4×C132132yesdirect product factor
37C25C22×C132131yes—
38C23×C4C22×C1321620yesdirect product factor
39C2×C13C24×C4×C131868yesdirect product factor
40C2×C13C26×C13114yes—
41C24C2×C4×C1321496yesdirect product factor
42C24C23×C1321155yes—
43C22×C4C23×C13211240yesdirect product factor
44C13C25×C4×C13114yesdirect product factor
45C23C22×C4×C13211240yesdirect product factor
46C23C24×C1321155yes—
47C2×C4C24×C1321496yesdirect product factor
48C22C23×C4×C1321620yesdirect product factor
49C22C25×C132131yes—
50C4C25×C132132yesdirect product factor
51C2C24×C4×C132162yesdirect product factor
52C2C26×C13211yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C26×C132
socle, prime radicalC26×C132C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C24×C4×C132C2direct (N × H)
3. C25×C132C4direct (N × H)
5. C23×C4×C132C22direct (N × H)
6. C24×C132C2×C4direct (N × H)
8. C22×C4×C132C23direct (N × H)
9. C25×C4×C13C13direct (N × H)
10. C23×C132C22×C4direct (N × H)
12. C2×C4×C132C24direct (N × H)
14. C24×C4×C13C2×C13direct (N × H)
15. C22×C132C23×C4direct (N × H)
17. C4×C132C25direct (N × H)
18. C25×C13C4×C13direct (N × H)
20. C23×C4×C13C22×C13direct (N × H)
21. C2×C132C24×C4direct (N × H)
23. C24×C13C2×C4×C13direct (N × H)
25. C22×C4×C13C23×C13direct (N × H)
26. C132C25×C4direct (N × H)
27. C25×C4C132direct (N × H)
28. C23×C13C22×C4×C13direct (N × H)
30. C2×C4×C13C24×C13direct (N × H)
32. C24×C4C2×C132direct (N × H)
33. C22×C13C23×C4×C13direct (N × H)
35. C4×C13C25×C13direct (N × H)
36. C25C4×C132direct (N × H)
38. C23×C4C22×C132direct (N × H)
39. C2×C13C24×C4×C13direct (N × H)
41. C24C2×C4×C132direct (N × H)
43. C22×C4C23×C132direct (N × H)
44. C13C25×C4×C13direct (N × H)
45. C23C22×C4×C132direct (N × H)
47. C2×C4C24×C132direct (N × H)
48. C22C23×C4×C132direct (N × H)
50. C4C25×C132direct (N × H)
51. C2C24×C4×C132direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C26×C1322
C24×C4×C1322
C25×C4×C1313