Finite Group Databasebeta

← C2×C32×C5×Q8 #10624292

Subgroups — C2×C32×C5×Q8 #10624292

Order 720.

228 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C5×Q8C214yesmaximal, direct product factor
2C2×C32×C4×C5C213yesmaximal
3C2×C3×C5×Q8C314yesmaximal, direct product factor
4C22×C32×C5C2211yescharacteristic
5C32×C4×C5C2216yes—
6C2×C32×Q8C511yesmaximal, characteristic, direct product factor, Hall
7C3×C5×Q8C2×C3116yesdirect product factor
8C2×C3×C4×C5C2×C3112yes—
9C2×C32×C5Q812yesdirect product factor
10C2×C32×C5C2311yescharacteristic
11C2×C5×Q8C3211yescharacteristic, direct product factor, Hall
12C32×Q8C2×C514yesdirect product factor
13C2×C32×C4C2×C513yes—
14C22×C3×C5C22×C314yes—
15C3×C4×C5C22×C3124yes—
16C2×C3×Q8C3×C514yesdirect product factor
17C32×C5C2×Q811yescharacteristic, direct product factor, Hall
18C5×Q8C2×C3214yesdirect product factor
19C2×C4×C5C2×C3213yes—
20C22×C32C22×C511yescharacteristic
21C32×C4C22×C516yes—
22C2×C3×C5C3×Q818yesdirect product factor
23C2×C3×C5C23×C314yes—
24C3×Q8C2×C3×C5116yesdirect product factor
25C2×C3×C4C2×C3×C5112yes—
26C22×C5C22×C3211yescharacteristic
27C4×C5C22×C3216yes—
28C2×C32C5×Q812yesdirect product factor
29C2×C32C23×C511yescharacteristic
30C2×Q8C32×C511yescharacteristic, direct product factor, Sylow
31C3×C5C2×C3×Q814yesdirect product factor
32C22×C3C22×C3×C514yes—
33C3×C4C22×C3×C5124yes—
34C2×C5C32×Q812yesdirect product factor
35C2×C5C23×C3211yescharacteristic
36C32C2×C5×Q811yescharacteristic, direct product factor, Sylow
37Q8C2×C32×C514yesdirect product factor
38C2×C4C2×C32×C513yes—
39C2×C3C3×C5×Q818yesdirect product factor
40C2×C3C23×C3×C514yes—
41C5C2×C32×Q811yescharacteristic, direct product factor, Sylow
42C22C22×C32×C511yescharacteristic
43C4C22×C32×C516yes—
44C3C2×C3×C5×Q814yesdirect product factor
45C2C32×C5×Q812yesdirect product factor
46C2C23×C32×C511yescharacteristic
subgroupG/H
center, socle, prime radicalC22×C32×C5C22
commutator, Frattini, cosocleC2C23×C32×C5
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C22×C32×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C32×C5×Q8C2direct (N × H)
3. C2×C3×C5×Q8C3direct (N × H)
6. C2×C32×Q8C5direct (N × H)
7. C3×C5×Q8C2×C3direct (N × H)
9. C2×C32×C5Q8direct (N × H)
11. C2×C5×Q8C32direct (N × H)
12. C32×Q8C2×C5direct (N × H)
16. C2×C3×Q8C3×C5direct (N × H)
17. C32×C5C2×Q8direct (N × H)
18. C5×Q8C2×C32direct (N × H)
22. C2×C3×C5C3×Q8direct (N × H)
24. C3×Q8C2×C3×C5direct (N × H)
28. C2×C32C5×Q8direct (N × H)
30. C2×Q8C32×C5direct (N × H)
31. C3×C5C2×C3×Q8direct (N × H)
34. C2×C5C32×Q8direct (N × H)
36. C32C2×C5×Q8direct (N × H)
37. Q8C2×C32×C5direct (N × H)
39. C2×C3C3×C5×Q8direct (N × H)
41. C5C2×C32×Q8direct (N × H)
44. C3C2×C3×C5×Q8direct (N × H)
45. C2C32×C5×Q8direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5×Q82
C2×C32×C4×C52
C2×C3×C5×Q83
C2×C32×Q85