Finite Group Databasebeta

← C3⋊(C7⋊#13049931) #41032071

Subgroups — C3⋊(C7⋊#13049931) #41032071

Order 27300.

128 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C7×C5⋊D65C211yesmaximal, characteristic
2C7⋊#13049931—31nomaximal, Hall
3C3×C52×C7×C13C411yescharacteristic, complemented, Hall
4C3⋊(C7⋊#63121)—51nomaximal
5C3⋊(C7⋊#63122)—51nomaximal
6C7×C5⋊D65D311yescharacteristic
7C3⋊#13049931—71nomaximal, Hall
8C3×C7×D65—51no—
9C3×C7×D65—51no—
10C3×C7×D65—102no—
11C52×C7×C13Dic311yescharacteristic, complemented, Hall
12C3⋊(C7⋊#1044)—131nomaximal, Hall
13C3×C5⋊D65D711yescharacteristic
14C7⋊#63122—151no—
15C7⋊#63121—151no—
16C3×C5×C7×C13—22no—
17C3×C5×C7×C13AGL(1,𝔽5)11yescharacteristic, complemented
18C3×C5×C7×C13AGL(1,𝔽5)11yescharacteristic, complemented
19#13049931—211noHall
20C3⋊(C7⋊#261)—251noHall
21C3×C7×C5⋊D5—131no—
22C3×C52×C13Dic711yescharacteristic, complemented, Hall
23C7×D65—51no—
24C7×D65—51no—
25C7×D65—102no—
26C3⋊#63122—351no—
27C3⋊#63121—351no—
28C7⋊#1044—391noHall
29C5⋊D65D2111yescharacteristic
30C3×C7×D13—251no—
31C3×C52×C7#26111yescharacteristic, complemented, Hall
32C5×C7×C13—22no—
33C5×C7×C13ΓL(1,𝔽16)11yescharacteristic, complemented
34C5×C7×C13ΓL(1,𝔽16)11yescharacteristic, complemented
35C3⋊(C7⋊AGL(1,𝔽5))—651no—
36C3⋊(C7⋊AGL(1,𝔽5))—651no—
37C3×D65—51no—
38C3×D65—51no—
39C3×D65—102no—
40C7⋊#261—751noHall
41C7×C5⋊D5—131no—
42C52×C13Dic2111yescharacteristic, complemented, Hall
43C3⋊#1044—911noHall
44C3×C7×C13#104411yescharacteristic, complemented, Hall
45#63122—1051no—
46#63121—1051no—
47C3×C7×D5—651no—
48C3×C7×D5—651no—
49C3×C7×D5—1302no—
50C3×C5×C13—22no—
51C3×C5×C13C7⋊AGL(1,𝔽5)11yescharacteristic, complemented
52C3×C5×C13C7⋊AGL(1,𝔽5)11yescharacteristic, complemented
53C7×D13—251no—
54C52×C7C3⋊#26111yescharacteristic, complemented, Hall
55C3⋊#261—1751noHall
56C3×C5⋊D5—131no—
57C7⋊AGL(1,𝔽5)—1951no—
58C7⋊AGL(1,𝔽5)—1951no—
59D65—51no—
60D65—51no—
61D65—102no—
62C3×C5×C7—22no—
63C3×C5×C7#6312111yescharacteristic, complemented
64C3×C5×C7#6312211yescharacteristic, complemented
65#1044—2731noHall
66C7×C13C3⋊#104411yescharacteristic, complemented, Hall
67Dic21—3251noHall
68C3×D13—251no—
69C3×C52C7⋊#26111yescharacteristic, complemented, Hall
70C7×D5—651no—
71C7×D5—651no—
72C7×D5—1302no—
73C5×C13—22no—
74C5×C13C3⋊(C7⋊AGL(1,𝔽5))11yescharacteristic, complemented
75C5×C13C3⋊(C7⋊AGL(1,𝔽5))11yescharacteristic, complemented
76ΓL(1,𝔽16)—4551no—
77ΓL(1,𝔽16)—4551no—
78#261—5251noHall
79C5⋊D5—131no—
80C2×C3×C7—3251no—
81C3×C13C7⋊#104411yescharacteristic, complemented, Hall
82C5×C7—22no—
83C5×C7C3⋊#6312111yescharacteristic, complemented
84C5×C7C3⋊#6312211yescharacteristic, complemented
85C3×D5—651no—
86C3×D5—651no—
87C3×D5—1302no—
88Dic7—9751noHall
89D13—251no—
90C52C3⋊(C7⋊#261)11yescharacteristic, complemented, Sylow
91C3×C7#1304993111yescharacteristic, complemented, Hall
92AGL(1,𝔽5)—13651no—
93AGL(1,𝔽5)—13651no—
94C3×C5—22no—
95C3×C5C7⋊#6312111yescharacteristic, complemented
96C3×C5C7⋊#6312211yescharacteristic, complemented
97C2×C7—3251no—
98C13C3⋊(C7⋊#1044)11yescharacteristic, complemented, Sylow
99Dic3—22751noHall
100D5—651no—
101D5—651no—
102D5—1302no—
103C7C3⋊#1304993111yescharacteristic, complemented, Sylow
104C2×C3—3251no—
105C5—22no—
106C5C3⋊(C7⋊#63122)11yescharacteristic, complemented
107C5C3⋊(C7⋊#63121)11yescharacteristic, complemented
108C4—68251noSylow
109C3C7⋊#1304993111yescharacteristic, complemented, Sylow
110C2—3251no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C52×C7×C13C4
prime radical, cosocleC3×C7×C5⋊D65C2
LCSG ▷ C3×C52×C7×C13
UCSC1

Complements

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

NH ≅ G/Ntype
3. C3×C52×C7×C13C4semidirect
11. C52×C7×C13Dic3semidirect
17. C3×C5×C7×C13AGL(1,𝔽5)semidirect
18. C3×C5×C7×C13AGL(1,𝔽5)semidirect
22. C3×C52×C13Dic7semidirect
31. C3×C52×C7#261semidirect
33. C5×C7×C13ΓL(1,𝔽16)semidirect
34. C5×C7×C13ΓL(1,𝔽16)semidirect
42. C52×C13Dic21semidirect
44. C3×C7×C13#1044semidirect
51. C3×C5×C13C7⋊AGL(1,𝔽5)semidirect
52. C3×C5×C13C7⋊AGL(1,𝔽5)semidirect
54. C52×C7C3⋊#261semidirect
63. C3×C5×C7#63121semidirect
64. C3×C5×C7#63122semidirect
66. C7×C13C3⋊#1044semidirect
69. C3×C52C7⋊#261semidirect
74. C5×C13C3⋊(C7⋊AGL(1,𝔽5))semidirect
75. C5×C13C3⋊(C7⋊AGL(1,𝔽5))semidirect
81. C3×C13C7⋊#1044semidirect
83. C5×C7C3⋊#63121semidirect
84. C5×C7C3⋊#63122semidirect
90. C52C3⋊(C7⋊#261)semidirect
91. C3×C7#13049931semidirect
95. C3×C5C7⋊#63121semidirect
96. C3×C5C7⋊#63122semidirect
98. C13C3⋊(C7⋊#1044)semidirect
103. C7C3⋊#13049931semidirect
106. C5C3⋊(C7⋊#63122)semidirect
107. C5C3⋊(C7⋊#63121)semidirect
109. C3C7⋊#13049931semidirect

Maximal subgroups

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

subgroupindex
C3×C7×C5⋊D652
C7⋊#130499313
C3⋊(C7⋊#63121)5
C3⋊(C7⋊#63122)5
C3⋊#130499317
C3⋊(C7⋊#1044)13