Finite Group Databasebeta

← C3×(C5⋊D5)⋊#3861 #36347953

Subgroups — C3×(C5⋊D5)⋊#3861 #36347953

Order 22050.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C52⋊#3861C211yesmaximal, characteristic, complemented, Hall
2C3×C72×C5⋊D5C311yesmaximal, characteristic, complemented
3(C5⋊D5)⋊#3861C313yesmaximal, direct product factor
4C52⋊#3861C2×C313yescomplemented
5C3×C52×C72C2×C311yescharacteristic, complemented
6C3×(C5⋊D5)⋊ΓL(1,𝔽8)—71nomaximal
7C3×(C5⋊D5)⋊ΓL(1,𝔽8)—77nomaximal
8C72×C5⋊D5C3211yescharacteristic, complemented, Hall
9C3×C7⋊(C52⋊C3)—71no—
10C3×C7⋊(C52⋊C3)—77no—
11C3×C72×D5—152no—
12C52×C72C2×C3211yescharacteristic, complemented, Hall
13C3×C7×C5⋊D5ΓL(1,𝔽8)11yescharacteristic, complemented
14C3×C7×C5⋊D5ΓL(1,𝔽8)17yescomplemented
15(C5⋊D5)⋊ΓL(1,𝔽8)—73no—
16(C5⋊D5)⋊ΓL(1,𝔽8)—721no—
17C2×C3×#3861—251nomaximal, Hall
18C3×C5×C72—32no—
19C3×C52×C7C2×ΓL(1,𝔽8)11yescharacteristic, complemented
20C3×C52×C7C2×ΓL(1,𝔽8)17yescomplemented
21C7⋊(C52⋊C3)—73no—
22C7⋊(C52⋊C3)—721no—
23C72×D5—152no—
24C3×(C5⋊D5)⋊C3—491noHall
25C3×#3861—251noHall
26C7×C5⋊D5C3×ΓL(1,𝔽8)11yescharacteristic, complemented
27C7×C5⋊D5C3×ΓL(1,𝔽8)17yescomplemented
28C2×C3×C72—751no—
29C2×#3861—253no—
30C5×C72—32no—
31C3×C52⋊C3—491noHall
32C3×C7×D5—152no—
33C3×C7×D5—1514no—
34C52×C7C2×C3×ΓL(1,𝔽8)11yescharacteristic, complemented
35C52×C7C2×C3×ΓL(1,𝔽8)17yescomplemented
36C3×C5⋊D5#386111yescharacteristic, complemented
37(C5⋊D5)⋊C3—493no—
38C3×C72(C5⋊D5)⋊C311yescharacteristic, complemented
39#3861—253no—
40C2×C3×ΓL(1,𝔽8)—1751no—
41C2×C3×ΓL(1,𝔽8)—1757no—
42C3×C5×C7—32no—
43C3×C5×C7—314no—
44C2×C72—751noHall
45C3×C52C2×#386111yescharacteristic, complemented
46C52⋊C3—493no—
47C7×D5—152no—
48C7×D5—1514no—
49C3×ΓL(1,𝔽8)—1751no—
50C3×ΓL(1,𝔽8)—1757no—
51C5⋊D5C3×#386111yescharacteristic, complemented, Hall
52C72C3×(C5⋊D5)⋊C311yescharacteristic, complemented, Sylow
53C2×C3×C7—251no—
54C2×C3×C7—757no—
55C2×ΓL(1,𝔽8)—1753no—
56C2×ΓL(1,𝔽8)—17521no—
57C5×C7—32no—
58C5×C7—314no—
59C3×D5—152no—
60C52C2×C3×#386111yescharacteristic, complemented, Sylow
61C3×C7(C5⋊D5)⋊ΓL(1,𝔽8)11yescharacteristic, complemented
62C3×C7(C5⋊D5)⋊ΓL(1,𝔽8)17yescomplemented
63ΓL(1,𝔽8)—1753no—
64ΓL(1,𝔽8)—17521no—
65C2×C32—12251noHall
66C3×C5—32no—
67C2×C7—251no—
68C2×C7—757no—
69D5—152no—
70C32—12251noSylow
71C7C3×(C5⋊D5)⋊ΓL(1,𝔽8)11yescharacteristic, complemented
72C7C3×(C5⋊D5)⋊ΓL(1,𝔽8)17yescomplemented
73C2×C3—751no—
74C2×C3—12253no—
75C5—32no—
76C3—12253no—
77C3(C5⋊D5)⋊#386111yescharacteristic, direct product factor
78C2—751noSylow
subgroupG/H
center, hypercenterC3(C5⋊D5)⋊#3861
commutator, cosocle, hypocenterC52×C72C2×C32
FrattiniC1G
Fitting, socleC3×C52×C72C2×C3
LCSG ▷ C52×C72
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C52⋊#3861C2semidirect
2. C3×C72×C5⋊D5C3semidirect
3. (C5⋊D5)⋊#3861C3direct (N × H)
4. C52⋊#3861C2×C3semidirect
5. C3×C52×C72C2×C3semidirect
8. C72×C5⋊D5C32semidirect
12. C52×C72C2×C32semidirect
13. C3×C7×C5⋊D5ΓL(1,𝔽8)semidirect
14. C3×C7×C5⋊D5ΓL(1,𝔽8)semidirect
19. C3×C52×C7C2×ΓL(1,𝔽8)semidirect
20. C3×C52×C7C2×ΓL(1,𝔽8)semidirect
26. C7×C5⋊D5C3×ΓL(1,𝔽8)semidirect
27. C7×C5⋊D5C3×ΓL(1,𝔽8)semidirect
34. C52×C7C2×C3×ΓL(1,𝔽8)semidirect
35. C52×C7C2×C3×ΓL(1,𝔽8)semidirect
36. C3×C5⋊D5#3861semidirect
38. C3×C72(C5⋊D5)⋊C3semidirect
45. C3×C52C2×#3861semidirect
51. C5⋊D5C3×#3861semidirect
52. C72C3×(C5⋊D5)⋊C3semidirect
60. C52C2×C3×#3861semidirect
61. C3×C7(C5⋊D5)⋊ΓL(1,𝔽8)semidirect
62. C3×C7(C5⋊D5)⋊ΓL(1,𝔽8)semidirect
71. C7C3×(C5⋊D5)⋊ΓL(1,𝔽8)semidirect
72. C7C3×(C5⋊D5)⋊ΓL(1,𝔽8)semidirect
77. C3(C5⋊D5)⋊#3861direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C52⋊#38612
C3×C72×C5⋊D53
(C5⋊D5)⋊#38613
C3×(C5⋊D5)⋊ΓL(1,𝔽8)7
C2×C3×#386125