Finite Group Databasebeta

← C26×C32×C25 #72192580

Subgroups — C26×C32×C25 #72192580

Order 14400.

50850 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C25×C32×C25C2163yesmaximal, direct product factor
2C26×C3×C25C314yesmaximal, direct product factor
3C24×C32×C25C221651yesdirect product factor
4C26×C32×C5C511yesmaximal, characteristic
5C25×C3×C25C2×C31252yesdirect product factor
6C23×C32×C25C2311395yesdirect product factor
7C26×C25C3211yescharacteristic, direct product factor, Hall
8C25×C32×C5C2×C5163yes—
9C24×C3×C25C22×C312604yesdirect product factor
10C26×C3×C5C3×C514yes—
11C22×C32×C25C241651yesdirect product factor
12C25×C25C2×C32163yesdirect product factor
13C24×C32×C5C22×C51651yes—
14C23×C3×C25C23×C315580yesdirect product factor
15C26×C32C2511yescharacteristic, direct product factor, Hall
16C25×C3×C5C2×C3×C51252yes—
17C2×C32×C25C25163yesdirect product factor
18C24×C25C22×C321651yesdirect product factor
19C23×C32×C5C23×C511395yes—
20C26×C5C32×C511yescharacteristic
21C22×C3×C25C24×C312604yesdirect product factor
22C25×C32C2×C25163yesdirect product factor
23C24×C3×C5C22×C3×C512604yes—
24C32×C25C2611yescharacteristic, direct product factor, Hall
25C23×C25C23×C3211395yesdirect product factor
26C26×C3C3×C2514yesdirect product factor
27C22×C32×C5C24×C51651yes—
28C25×C5C2×C32×C5163yes—
29C2×C3×C25C25×C31252yesdirect product factor
30C24×C32C22×C251651yesdirect product factor
31C23×C3×C5C23×C3×C515580yes—
32C22×C25C24×C321651yesdirect product factor
33C25×C3C2×C3×C251252yesdirect product factor
34C2×C32×C5C25×C5163yes—
35C24×C5C22×C32×C51651yes—
36C3×C25C26×C314yesdirect product factor
37C23×C32C23×C2511395yesdirect product factor
38C26C32×C2511yescharacteristic, direct product factor, Sylow
39C22×C3×C5C24×C3×C512604yes—
40C2×C25C25×C32163yesdirect product factor
41C24×C3C22×C3×C2512604yesdirect product factor
42C32×C5C26×C511yescharacteristic
43C23×C5C23×C32×C511395yes—
44C22×C32C24×C251651yesdirect product factor
45C25C2×C32×C25163yesdirect product factor
46C2×C3×C5C25×C3×C51252yes—
47C25C26×C3211yescharacteristic, direct product factor, Sylow
48C23×C3C23×C3×C2515580yesdirect product factor
49C22×C5C24×C32×C51651yes—
50C2×C32C25×C25163yesdirect product factor
51C24C22×C32×C251651yesdirect product factor
52C3×C5C26×C3×C514yes—
53C22×C3C24×C3×C2512604yesdirect product factor
54C2×C5C25×C32×C5163yes—
55C32C26×C2511yescharacteristic, direct product factor, Sylow
56C23C23×C32×C2511395yesdirect product factor
57C2×C3C25×C3×C251252yesdirect product factor
58C5C26×C32×C511yescharacteristic
59C22C24×C32×C251651yesdirect product factor
60C3C26×C3×C2514yesdirect product factor
61C2C25×C32×C25163yesdirect product factor
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC5C26×C32×C5
socle, prime radicalC26×C32×C5C5
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C25×C32×C25C2direct (N × H)
2. C26×C3×C25C3direct (N × H)
3. C24×C32×C25C22direct (N × H)
5. C25×C3×C25C2×C3direct (N × H)
6. C23×C32×C25C23direct (N × H)
7. C26×C25C32direct (N × H)
9. C24×C3×C25C22×C3direct (N × H)
11. C22×C32×C25C24direct (N × H)
12. C25×C25C2×C32direct (N × H)
14. C23×C3×C25C23×C3direct (N × H)
15. C26×C32C25direct (N × H)
17. C2×C32×C25C25direct (N × H)
18. C24×C25C22×C32direct (N × H)
21. C22×C3×C25C24×C3direct (N × H)
22. C25×C32C2×C25direct (N × H)
24. C32×C25C26direct (N × H)
25. C23×C25C23×C32direct (N × H)
26. C26×C3C3×C25direct (N × H)
29. C2×C3×C25C25×C3direct (N × H)
30. C24×C32C22×C25direct (N × H)
32. C22×C25C24×C32direct (N × H)
33. C25×C3C2×C3×C25direct (N × H)
36. C3×C25C26×C3direct (N × H)
37. C23×C32C23×C25direct (N × H)
38. C26C32×C25direct (N × H)
40. C2×C25C25×C32direct (N × H)
41. C24×C3C22×C3×C25direct (N × H)
44. C22×C32C24×C25direct (N × H)
45. C25C2×C32×C25direct (N × H)
47. C25C26×C32direct (N × H)
48. C23×C3C23×C3×C25direct (N × H)
50. C2×C32C25×C25direct (N × H)
51. C24C22×C32×C25direct (N × H)
53. C22×C3C24×C3×C25direct (N × H)
55. C32C26×C25direct (N × H)
56. C23C23×C32×C25direct (N × H)
57. C2×C3C25×C3×C25direct (N × H)
59. C22C24×C32×C25direct (N × H)
60. C3C26×C3×C25direct (N × H)
61. C2C25×C32×C25direct (N × H)

Maximal subgroups

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

subgroupindex
C25×C32×C252
C26×C3×C253
C26×C32×C55