Finite Group Databasebeta

← C26×C4×C53 #27270606

Subgroups — C26×C4×C53 #27270606

Order 13568.

111198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C27×C53C211yesmaximal, characteristic
2C25×C4×C53C21126yesmaximal, direct product factor
3C26×C53C4164yesdirect product factor
4C26×C53C22163yes—
5C24×C4×C53C2212604yesdirect product factor
6C25×C53C2×C412016yesdirect product factor
7C25×C53C231651yes—
8C23×C4×C53C23111160yesdirect product factor
9C24×C53C22×C4110416yesdirect product factor
10C24×C53C2411395yes—
11C22×C4×C53C24110416yesdirect product factor
12C23×C53C23×C4111160yesdirect product factor
13C23×C53C251651yes—
14C2×C4×C53C2512016yesdirect product factor
15C26×C4C5311yesmaximal, characteristic, direct product factor, Sylow
16C22×C53C24×C412604yesdirect product factor
17C22×C53C26163yes—
18C4×C53C26164yesdirect product factor
19C27C2×C5311yescharacteristic
20C25×C4C2×C531126yesdirect product factor
21C2×C53C25×C41126yesdirect product factor
22C2×C53C2711yescharacteristic
23C26C4×C53164yesdirect product factor
24C26C22×C53163yes—
25C24×C4C22×C5312604yesdirect product factor
26C53C26×C411yescharacteristic, direct product factor, Sylow
27C25C2×C4×C5312016yesdirect product factor
28C25C23×C531651yes—
29C23×C4C23×C53111160yesdirect product factor
30C24C22×C4×C53110416yesdirect product factor
31C24C24×C5311395yes—
32C22×C4C24×C53110416yesdirect product factor
33C23C23×C4×C53111160yesdirect product factor
34C23C25×C531651yes—
35C2×C4C25×C5312016yesdirect product factor
36C22C24×C4×C5312604yesdirect product factor
37C22C26×C53163yes—
38C4C26×C53164yesdirect product factor
39C2C25×C4×C531126yesdirect product factor
40C2C27×C5311yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C27×C53
socle, prime radicalC27×C53C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C25×C4×C53C2direct (N × H)
3. C26×C53C4direct (N × H)
5. C24×C4×C53C22direct (N × H)
6. C25×C53C2×C4direct (N × H)
8. C23×C4×C53C23direct (N × H)
9. C24×C53C22×C4direct (N × H)
11. C22×C4×C53C24direct (N × H)
12. C23×C53C23×C4direct (N × H)
14. C2×C4×C53C25direct (N × H)
15. C26×C4C53direct (N × H)
16. C22×C53C24×C4direct (N × H)
18. C4×C53C26direct (N × H)
20. C25×C4C2×C53direct (N × H)
21. C2×C53C25×C4direct (N × H)
23. C26C4×C53direct (N × H)
25. C24×C4C22×C53direct (N × H)
26. C53C26×C4direct (N × H)
27. C25C2×C4×C53direct (N × H)
29. C23×C4C23×C53direct (N × H)
30. C24C22×C4×C53direct (N × H)
32. C22×C4C24×C53direct (N × H)
33. C23C23×C4×C53direct (N × H)
35. C2×C4C25×C53direct (N × H)
36. C22C24×C4×C53direct (N × H)
38. C4C26×C53direct (N × H)
39. C2C25×C4×C53direct (N × H)

Maximal subgroups

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

subgroupindex
C27×C532
C25×C4×C532
C26×C453