Finite Group Databasebeta

← C26×C4×C13 #15749433

Subgroups — C26×C4×C13 #15749433

Order 3328.

111198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C27×C13C211yesmaximal, characteristic
2C25×C4×C13C21126yesmaximal, direct product factor
3C26×C13C4164yesdirect product factor
4C26×C13C22163yes—
5C24×C4×C13C2212604yesdirect product factor
6C25×C13C2×C412016yesdirect product factor
7C25×C13C231651yes—
8C23×C4×C13C23111160yesdirect product factor
9C26×C4C1311yesmaximal, characteristic, direct product factor, Sylow
10C24×C13C22×C4110416yesdirect product factor
11C24×C13C2411395yes—
12C22×C4×C13C24110416yesdirect product factor
13C27C2×C1311yescharacteristic
14C25×C4C2×C131126yesdirect product factor
15C23×C13C23×C4111160yesdirect product factor
16C23×C13C251651yes—
17C2×C4×C13C2512016yesdirect product factor
18C26C4×C13164yesdirect product factor
19C26C22×C13163yes—
20C24×C4C22×C1312604yesdirect product factor
21C22×C13C24×C412604yesdirect product factor
22C22×C13C26163yes—
23C4×C13C26164yesdirect product factor
24C25C2×C4×C1312016yesdirect product factor
25C25C23×C131651yes—
26C23×C4C23×C13111160yesdirect product factor
27C2×C13C25×C41126yesdirect product factor
28C2×C13C2711yescharacteristic
29C24C22×C4×C13110416yesdirect product factor
30C24C24×C1311395yes—
31C22×C4C24×C13110416yesdirect product factor
32C13C26×C411yescharacteristic, direct product factor, Sylow
33C23C23×C4×C13111160yesdirect product factor
34C23C25×C131651yes—
35C2×C4C25×C1312016yesdirect product factor
36C22C24×C4×C1312604yesdirect product factor
37C22C26×C13163yes—
38C4C26×C13164yesdirect product factor
39C2C25×C4×C131126yesdirect product factor
40C2C27×C1311yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C27×C13
socle, prime radicalC27×C13C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C25×C4×C13C2direct (N × H)
3. C26×C13C4direct (N × H)
5. C24×C4×C13C22direct (N × H)
6. C25×C13C2×C4direct (N × H)
8. C23×C4×C13C23direct (N × H)
9. C26×C4C13direct (N × H)
10. C24×C13C22×C4direct (N × H)
12. C22×C4×C13C24direct (N × H)
14. C25×C4C2×C13direct (N × H)
15. C23×C13C23×C4direct (N × H)
17. C2×C4×C13C25direct (N × H)
18. C26C4×C13direct (N × H)
20. C24×C4C22×C13direct (N × H)
21. C22×C13C24×C4direct (N × H)
23. C4×C13C26direct (N × H)
24. C25C2×C4×C13direct (N × H)
26. C23×C4C23×C13direct (N × H)
27. C2×C13C25×C4direct (N × H)
29. C24C22×C4×C13direct (N × H)
31. C22×C4C24×C13direct (N × H)
32. C13C26×C4direct (N × H)
33. C23C23×C4×C13direct (N × H)
35. C2×C4C25×C13direct (N × H)
36. C22C24×C4×C13direct (N × H)
38. C4C26×C13direct (N × H)
39. C2C25×C4×C13direct (N × H)

Maximal subgroups

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

subgroupindex
C27×C132
C25×C4×C132
C26×C413