Finite Group Databasebeta

← C22×C3×C5×Q8 #92106

Subgroups — C22×C3×C5×Q8 #92106

Order 480.

312 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×Q8C2112yesmaximal, direct product factor
2C22×C3×C4×C5C213yesmaximal
3C22×C5×Q8C311yesmaximal, characteristic, direct product factor, Hall
4C23×C3×C5C2211yescharacteristic
5C3×C5×Q8C22116yesdirect product factor
6C2×C3×C4×C5C22118yes—
7C22×C3×Q8C511yesmaximal, characteristic, direct product factor, Hall
8C2×C5×Q8C2×C3112yesdirect product factor
9C22×C4×C5C2×C313yes—
10C22×C3×C5Q814yesdirect product factor
11C22×C3×C5C2313yes—
12C3×C4×C5C23112yes—
13C2×C3×Q8C2×C5112yesdirect product factor
14C22×C3×C4C2×C513yes—
15C23×C5C22×C311yescharacteristic
16C5×Q8C22×C3116yesdirect product factor
17C2×C4×C5C22×C3118yes—
18C22×Q8C3×C511yescharacteristic, direct product factor, Sylow
19C2×C3×C5C2×Q816yesdirect product factor
20C2×C3×C5C2411yescharacteristic
21C23×C3C22×C511yescharacteristic
22C3×Q8C22×C5116yesdirect product factor
23C2×C3×C4C22×C5118yes—
24C22×C5C3×Q814yesdirect product factor
25C22×C5C23×C313yes—
26C4×C5C23×C3112yes—
27C2×Q8C2×C3×C5112yesdirect product factor
28C22×C4C2×C3×C513yes—
29C3×C5C22×Q811yescharacteristic, direct product factor, Hall
30C22×C3C5×Q814yesdirect product factor
31C22×C3C23×C513yes—
32C3×C4C23×C5112yes—
33C2×C5C2×C3×Q816yesdirect product factor
34C2×C5C24×C311yescharacteristic
35C23C22×C3×C511yescharacteristic
36Q8C22×C3×C5116yesdirect product factor
37C2×C4C22×C3×C5118yes—
38C2×C3C2×C5×Q816yesdirect product factor
39C2×C3C24×C511yescharacteristic
40C5C22×C3×Q811yescharacteristic, direct product factor, Sylow
41C22C3×C5×Q814yesdirect product factor
42C22C23×C3×C513yes—
43C4C23×C3×C5112yes—
44C3C22×C5×Q811yescharacteristic, direct product factor, Sylow
45C2C2×C3×C5×Q816yesdirect product factor
46C2C24×C3×C511yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C3×C5C22
commutator, Frattini, cosocleC2C24×C3×C5
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C23×C3×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×Q8C2direct (N × H)
3. C22×C5×Q8C3direct (N × H)
5. C3×C5×Q8C22direct (N × H)
7. C22×C3×Q8C5direct (N × H)
8. C2×C5×Q8C2×C3direct (N × H)
10. C22×C3×C5Q8direct (N × H)
13. C2×C3×Q8C2×C5direct (N × H)
16. C5×Q8C22×C3direct (N × H)
18. C22×Q8C3×C5direct (N × H)
19. C2×C3×C5C2×Q8direct (N × H)
22. C3×Q8C22×C5direct (N × H)
24. C22×C5C3×Q8direct (N × H)
27. C2×Q8C2×C3×C5direct (N × H)
29. C3×C5C22×Q8direct (N × H)
30. C22×C3C5×Q8direct (N × H)
33. C2×C5C2×C3×Q8direct (N × H)
36. Q8C22×C3×C5direct (N × H)
38. C2×C3C2×C5×Q8direct (N × H)
40. C5C22×C3×Q8direct (N × H)
41. C22C3×C5×Q8direct (N × H)
44. C3C22×C5×Q8direct (N × H)
45. C2C2×C3×C5×Q8direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×Q82
C22×C3×C4×C52
C22×C5×Q83
C22×C3×Q85