Finite Group Databasebeta

← C26×C4×C59 #28475203

Subgroups — C26×C4×C59 #28475203

Order 15104.

111198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C27×C59C211yesmaximal, characteristic
2C25×C4×C59C21126yesmaximal, direct product factor
3C26×C59C4164yesdirect product factor
4C26×C59C22163yes—
5C24×C4×C59C2212604yesdirect product factor
6C25×C59C2×C412016yesdirect product factor
7C25×C59C231651yes—
8C23×C4×C59C23111160yesdirect product factor
9C24×C59C22×C4110416yesdirect product factor
10C24×C59C2411395yes—
11C22×C4×C59C24110416yesdirect product factor
12C23×C59C23×C4111160yesdirect product factor
13C23×C59C251651yes—
14C2×C4×C59C2512016yesdirect product factor
15C26×C4C5911yesmaximal, characteristic, direct product factor, Sylow
16C22×C59C24×C412604yesdirect product factor
17C22×C59C26163yes—
18C4×C59C26164yesdirect product factor
19C27C2×C5911yescharacteristic
20C25×C4C2×C591126yesdirect product factor
21C2×C59C25×C41126yesdirect product factor
22C2×C59C2711yescharacteristic
23C26C4×C59164yesdirect product factor
24C26C22×C59163yes—
25C24×C4C22×C5912604yesdirect product factor
26C59C26×C411yescharacteristic, direct product factor, Sylow
27C25C2×C4×C5912016yesdirect product factor
28C25C23×C591651yes—
29C23×C4C23×C59111160yesdirect product factor
30C24C22×C4×C59110416yesdirect product factor
31C24C24×C5911395yes—
32C22×C4C24×C59110416yesdirect product factor
33C23C23×C4×C59111160yesdirect product factor
34C23C25×C591651yes—
35C2×C4C25×C5912016yesdirect product factor
36C22C24×C4×C5912604yesdirect product factor
37C22C26×C59163yes—
38C4C26×C59164yesdirect product factor
39C2C25×C4×C591126yesdirect product factor
40C2C27×C5911yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C27×C59
socle, prime radicalC27×C59C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C25×C4×C59C2direct (N × H)
3. C26×C59C4direct (N × H)
5. C24×C4×C59C22direct (N × H)
6. C25×C59C2×C4direct (N × H)
8. C23×C4×C59C23direct (N × H)
9. C24×C59C22×C4direct (N × H)
11. C22×C4×C59C24direct (N × H)
12. C23×C59C23×C4direct (N × H)
14. C2×C4×C59C25direct (N × H)
15. C26×C4C59direct (N × H)
16. C22×C59C24×C4direct (N × H)
18. C4×C59C26direct (N × H)
20. C25×C4C2×C59direct (N × H)
21. C2×C59C25×C4direct (N × H)
23. C26C4×C59direct (N × H)
25. C24×C4C22×C59direct (N × H)
26. C59C26×C4direct (N × H)
27. C25C2×C4×C59direct (N × H)
29. C23×C4C23×C59direct (N × H)
30. C24C22×C4×C59direct (N × H)
32. C22×C4C24×C59direct (N × H)
33. C23C23×C4×C59direct (N × H)
35. C2×C4C25×C59direct (N × H)
36. C22C24×C4×C59direct (N × H)
38. C4C26×C59direct (N × H)
39. C2C25×C4×C59direct (N × H)

Maximal subgroups

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

subgroupindex
C27×C592
C25×C4×C592
C26×C459