Finite Group Databasebeta

← C3⋊(((C31⋊C3)⋊C5)⋊D7) #34086199

Subgroups — C3⋊(((C31⋊C3)⋊C5)⋊D7) #34086199

Order 19530.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C7×(C31⋊C3)⋊C5C211yesmaximal, characteristic, complemented, Hall
2((C31⋊C3)⋊C5)⋊D7—31nomaximal
3C3⋊(C7⋊(D31⋊C5))C311yesmaximal, characteristic, complemented
4C3⋊((C31⋊C3)⋊D7)C511yesmaximal, characteristic, complemented, Hall
5C7×(C31⋊C3)⋊C5—21no—
6C7×(C31⋊C3)⋊C5D311yescharacteristic, complemented
7C3×C7×ΓL(1,𝔽32)C2×C311yescharacteristic, complemented
8C3⋊AGL(1,𝔽31)—71nomaximal, Hall
9C7⋊(D31⋊C5)—31noHall
10C3×C7×C31⋊C3C2×C511yescharacteristic, complemented, Hall
11C3×(C31⋊C3)⋊C5D711yescharacteristic, complemented, Hall
12D651C3×C511yescharacteristic, complemented
13(C31⋊C3)⋊D7—31no—
14C7×ΓL(1,𝔽32)C3×D311yescharacteristic, complemented, Hall
15C3⋊(D31⋊C5)—71no—
16AGL(1,𝔽31)—211no—
17C3×C7×C31C2×C3×C511yescharacteristic, complemented
18C7×C31⋊C3—21no—
19C7×C31⋊C3C5×D311yescharacteristic, complemented
20C3×C5×D21—311nomaximal, Hall
21C3⋊(D31⋊C3)—71noHall
22C3×ΓL(1,𝔽32)C3×D711yescharacteristic, complemented
23(C31⋊C3)⋊C5—21no—
24(C31⋊C3)⋊C5D2111yescharacteristic, complemented
25D217—31noHall
26C32×C5×C7—311noHall
27D31⋊C5—211noHall
28C3×C31⋊C3C5×D711yescharacteristic, complemented, Hall
29C7×C31C3×C5×D311yescharacteristic, complemented, Hall
30C5×D21—311no—
31C3×C5×D7—931no—
32D93—71no—
33D31⋊C3—211no—
34ΓL(1,𝔽32)C3×D2111yescharacteristic, complemented, Hall
35C3×D21—1551noHall
36C3×C5×C7—311no—
37C3×C5×C7—311no—
38C3×C5×C7—621no—
39C3×C31C3×C5×D711yescharacteristic, complemented
40C31⋊C3—21no—
41C31⋊C3C5×D2111yescharacteristic, complemented
42C3×C5×D3—2171noHall
43C5×D7—931noHall
44C32×C7—1551noHall
45D31—211noHall
46C32×C5—311noHall
47D21—1551no—
48C3×D7—931no—
49C5×C7—311noHall
50C31C3×C5×D2111yescharacteristic, complemented, Sylow
51C2×C3×C5—6511no—
52C5×D3—2171no—
53C3×C7—3101no—
54C3×C7—1551no—
55C3×C7AGL(1,𝔽31)11yescharacteristic, complemented
56C3×D3—10851noHall
57C3×C5—311no—
58C3×C5—311no—
59C3×C5—621no—
60D7—4651noHall
61C2×C5—6511noHall
62C32—1551noSylow
63C7C3⋊AGL(1,𝔽31)11yescharacteristic, complemented, Sylow
64C2×C3—32551no—
65D3—10851no—
66C5—311noSylow
67C3—3101no—
68C3—1551no—
69C3((C31⋊C3)⋊C5)⋊D711yescharacteristic, complemented
70C2—32551noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C7×C31C2×C3×C5
LCSG ▷ C3×C7×C31
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C7×(C31⋊C3)⋊C5C2semidirect
3. C3⋊(C7⋊(D31⋊C5))C3semidirect
4. C3⋊((C31⋊C3)⋊D7)C5semidirect
6. C7×(C31⋊C3)⋊C5D3semidirect
7. C3×C7×ΓL(1,𝔽32)C2×C3semidirect
10. C3×C7×C31⋊C3C2×C5semidirect
11. C3×(C31⋊C3)⋊C5D7semidirect
12. D651C3×C5semidirect
14. C7×ΓL(1,𝔽32)C3×D3semidirect
17. C3×C7×C31C2×C3×C5semidirect
19. C7×C31⋊C3C5×D3semidirect
22. C3×ΓL(1,𝔽32)C3×D7semidirect
24. (C31⋊C3)⋊C5D21semidirect
28. C3×C31⋊C3C5×D7semidirect
29. C7×C31C3×C5×D3semidirect
34. ΓL(1,𝔽32)C3×D21semidirect
39. C3×C31C3×C5×D7semidirect
41. C31⋊C3C5×D21semidirect
50. C31C3×C5×D21semidirect
55. C3×C7AGL(1,𝔽31)semidirect
63. C7C3⋊AGL(1,𝔽31)semidirect
69. C3((C31⋊C3)⋊C5)⋊D7semidirect

Maximal subgroups

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

subgroupindex
C3×C7×(C31⋊C3)⋊C52
((C31⋊C3)⋊C5)⋊D73
C3⋊(C7⋊(D31⋊C5))3
C3⋊((C31⋊C3)⋊D7)5
C3⋊AGL(1,𝔽31)7
C3×C5×D2131