Finite Group Databasebeta

← C26×C4×C79 #34174783

Subgroups — C26×C4×C79 #34174783

Order 20224.

111198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C27×C79C211yesmaximal, characteristic
2C25×C4×C79C21126yesmaximal, direct product factor
3C26×C79C4164yesdirect product factor
4C26×C79C22163yes—
5C24×C4×C79C2212604yesdirect product factor
6C25×C79C2×C412016yesdirect product factor
7C25×C79C231651yes—
8C23×C4×C79C23111160yesdirect product factor
9C24×C79C22×C4110416yesdirect product factor
10C24×C79C2411395yes—
11C22×C4×C79C24110416yesdirect product factor
12C23×C79C23×C4111160yesdirect product factor
13C23×C79C251651yes—
14C2×C4×C79C2512016yesdirect product factor
15C22×C79C24×C412604yesdirect product factor
16C22×C79C26163yes—
17C4×C79C26164yesdirect product factor
18C26×C4C7911yesmaximal, characteristic, direct product factor, Sylow
19C2×C79C25×C41126yesdirect product factor
20C2×C79C2711yescharacteristic
21C27C2×C7911yescharacteristic
22C25×C4C2×C791126yesdirect product factor
23C79C26×C411yescharacteristic, direct product factor, Sylow
24C26C4×C79164yesdirect product factor
25C26C22×C79163yes—
26C24×C4C22×C7912604yesdirect product factor
27C25C2×C4×C7912016yesdirect product factor
28C25C23×C791651yes—
29C23×C4C23×C79111160yesdirect product factor
30C24C22×C4×C79110416yesdirect product factor
31C24C24×C7911395yes—
32C22×C4C24×C79110416yesdirect product factor
33C23C23×C4×C79111160yesdirect product factor
34C23C25×C791651yes—
35C2×C4C25×C7912016yesdirect product factor
36C22C24×C4×C7912604yesdirect product factor
37C22C26×C79163yes—
38C4C26×C79164yesdirect product factor
39C2C25×C4×C791126yesdirect product factor
40C2C27×C7911yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C27×C79
socle, prime radicalC27×C79C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C25×C4×C79C2direct (N × H)
3. C26×C79C4direct (N × H)
5. C24×C4×C79C22direct (N × H)
6. C25×C79C2×C4direct (N × H)
8. C23×C4×C79C23direct (N × H)
9. C24×C79C22×C4direct (N × H)
11. C22×C4×C79C24direct (N × H)
12. C23×C79C23×C4direct (N × H)
14. C2×C4×C79C25direct (N × H)
15. C22×C79C24×C4direct (N × H)
17. C4×C79C26direct (N × H)
18. C26×C4C79direct (N × H)
19. C2×C79C25×C4direct (N × H)
22. C25×C4C2×C79direct (N × H)
23. C79C26×C4direct (N × H)
24. C26C4×C79direct (N × H)
26. C24×C4C22×C79direct (N × H)
27. C25C2×C4×C79direct (N × H)
29. C23×C4C23×C79direct (N × H)
30. C24C22×C4×C79direct (N × H)
32. C22×C4C24×C79direct (N × H)
33. C23C23×C4×C79direct (N × H)
35. C2×C4C25×C79direct (N × H)
36. C22C24×C4×C79direct (N × H)
38. C4C26×C79direct (N × H)
39. C2C25×C4×C79direct (N × H)

Maximal subgroups

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

subgroupindex
C27×C792
C25×C4×C792
C26×C479