Finite Group Databasebeta

← C3⋊#20301291 #36348014

Subgroups — C3⋊#20301291 #36348014

Order 22050.

260 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C52⋊#3861C211yesmaximal, characteristic, complemented, Hall
2C3⋊(C5⋊(C5⋊(C7⋊D7)))C311yesmaximal, characteristic, complemented
3#20301291—31nomaximal
4C52⋊#3861—21no—
5C52⋊#3861D311yescharacteristic, complemented
6C3×C52×C72C2×C311yescharacteristic, complemented
7C3⋊#11760386—78nomaximal
8C5⋊(C5⋊(C7⋊D7))—31noHall
9C3×C7⋊(C52⋊C3)—78no—
10C3⋊(C5⋊(C7⋊D7))—152no—
11C52×C72C3×D311yescharacteristic, complemented, Hall
12C3⋊(C5⋊D35)—78no—
13#11760386—218no—
14C3⋊#64424—251nomaximal, Hall
15C3×C5×C72—32no—
16C3×C52×C7AGL(1,𝔽7)18yescomplemented
17C7⋊(C52⋊C3)—78no—
18C7⋊(C52⋊C3)—148no—
19C5⋊(C7⋊D7)—452no—
20C3⋊((C5⋊D5)⋊C3)—491noHall
21C3×#3861—251noHall
22C5⋊D35—218no—
23C3⋊(C7⋊D7)—251no—
24#64424—751no—
25C5×C72—32no—
26C3×C52⋊C3—491noHall
27D105—10516no—
28C52×C7C3⋊AGL(1,𝔽7)18yescomplemented
29C3⋊(C5⋊D5)—491no—
30(C5⋊D5)⋊C3—1471no—
31C3×C72(C5⋊D5)⋊C311yescharacteristic, complemented
32#3861—251no—
33#3861—501no—
34C3⋊AGL(1,𝔽7)—1758no—
35C3×C5×C7—316no—
36C7⋊D7—751noHall
37C3×C52#6442411yescharacteristic, complemented
38C52⋊C3—491no—
39C52⋊C3—981no—
40D35—31516no—
41C3×ΓL(1,𝔽8)—1758no—
42C5⋊D5—1471noHall
43C72C3⋊((C5⋊D5)⋊C3)11yescharacteristic, complemented, Sylow
44D21—1758no—
45AGL(1,𝔽7)—5258no—
46C5×C7—316no—
47D15—7352no—
48C52C3⋊#6442411yescharacteristic, complemented, Sylow
49C3×C7#1176038618yescomplemented
50ΓL(1,𝔽8)—3508no—
51ΓL(1,𝔽8)—1758no—
52C3×D3—12251noHall
53C3×C5—32no—
54D7—5258no—
55D5—22052no—
56C32—12251noSylow
57C7C3⋊#1176038618yescomplemented
58C2×C3—36751no—
59D3—12251no—
60C5—32no—
61C3—24501no—
62C3—12251no—
63C3#2030129111yescharacteristic, complemented
64C2—36751noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C72C2×C3
LCSG ▷ C3×C52×C72
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C52⋊#3861C2semidirect
2. C3⋊(C5⋊(C5⋊(C7⋊D7)))C3semidirect
5. C52⋊#3861D3semidirect
6. C3×C52×C72C2×C3semidirect
11. C52×C72C3×D3semidirect
16. C3×C52×C7AGL(1,𝔽7)semidirect
28. C52×C7C3⋊AGL(1,𝔽7)semidirect
31. C3×C72(C5⋊D5)⋊C3semidirect
37. C3×C52#64424semidirect
43. C72C3⋊((C5⋊D5)⋊C3)semidirect
48. C52C3⋊#64424semidirect
49. C3×C7#11760386semidirect
57. C7C3⋊#11760386semidirect
63. C3#20301291semidirect

Maximal subgroups

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

subgroupindex
C3×C52⋊#38612
C3⋊(C5⋊(C5⋊(C7⋊D7)))3
#203012913
C3⋊#117603867
C3⋊#6442425