Finite Group Databasebeta

← C3⋊(C7⋊#13049934) #41032007

Subgroups — C3⋊(C7⋊#13049934) #41032007

Order 27300.

104 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 41 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×C5×C7×D65C211yesmaximal, characteristic
2C7⋊#13049934—31nomaximal, Hall
3C3×C52×C7×C13C411yescharacteristic, complemented, Hall
4C3⋊(C7⋊#63118)—51nomaximal
5C3⋊(C7⋊#63121)—51nomaximal
6C5×C7×D65D311yescharacteristic
7C3⋊#13049934—71nomaximal, Hall
8C3×C7×D65D511yescharacteristic
9C3×C5×C7×D13—51no—
10C52×C7×C13Dic311yescharacteristic, complemented, Hall
11C3⋊(C7⋊#1042)—131nomaximal, Hall
12C3×C5×D65D711yescharacteristic
13C7⋊#63118—151no—
14C7⋊#63121—151no—
15C3×C5×C7×C13—41no—
16C3×C5×C7×C13Dic511yescharacteristic, complemented
17C3×C5×C7×C13AGL(1,𝔽5)11yescharacteristic, complemented
18#13049934—211noHall
19C3⋊(C7⋊#261)—251noHall
20C3×C5×C7×D5—131no—
21C3×C52×C13Dic711yescharacteristic, complemented, Hall
22C7×D65D1511yescharacteristic
23C5×C7×D13—51no—
24C3⋊#63118—351no—
25C3⋊#63121—351no—
26C7⋊#1042—391noHall
27C5×D65D2111yescharacteristic
28C3×C7×D13—51no—
29C3×C52×C7#26111yescharacteristic, complemented, Hall
30C5×C7×C13—41no—
31C5×C7×C13Dic1511yescharacteristic, complemented
32C5×C7×C13ΓL(1,𝔽16)11yescharacteristic, complemented
33C3⋊(C7⋊AGL(1,𝔽5))—651no—
34Dic105—651no—
35C3×D65D3511yescharacteristic
36C3×C5×D13—51no—
37C7⋊#261—751noHall
38C5×C7×D5—131no—
39C52×C13Dic2111yescharacteristic, complemented, Hall
40C3⋊#1042—911noHall
41C3×C7×C13#104211yescharacteristic, complemented, Hall
42#63121—1051no—
43#63118—1051no—
44C2×C3×C5×C7—651no—
45C3×C7×D5—131no—
46C3×C5×C13—41no—
47C3×C5×C13Dic3511yescharacteristic, complemented
48C3×C5×C13C7⋊AGL(1,𝔽5)11yescharacteristic, complemented
49C7×D13—51no—
50C52×C7C3⋊#26111yescharacteristic, complemented, Hall
51C3⋊#261—1751noHall
52C3×C5×D5—131no—
53C7⋊AGL(1,𝔽5)—1951no—
54Dic35—1951no—
55D65D10511yescharacteristic
56C5×D13—51no—
57C3×C5×C7—41no—
58C3×C5×C7#6311811yescharacteristic, complemented
59C3×C5×C7#6312111yescharacteristic, complemented
60#1042—2731noHall
61C7×C13C3⋊#104211yescharacteristic, complemented, Hall
62Dic21—3251noHall
63C3×D13—51no—
64C3×C52C7⋊#26111yescharacteristic, complemented, Hall
65C2×C5×C7—651no—
66C7×D5—131no—
67C5×C13—41no—
68C5×C13Dic10511yescharacteristic, complemented
69C5×C13C3⋊(C7⋊AGL(1,𝔽5))11yescharacteristic, complemented
70ΓL(1,𝔽16)—4551no—
71Dic15—4551no—
72#261—5251noHall
73C5×D5—131no—
74C2×C3×C7—651no—
75C3×C13C7⋊#104211yescharacteristic, complemented, Hall
76C5×C7—41no—
77C5×C7C3⋊#6312111yescharacteristic, complemented
78C5×C7C3⋊#6311811yescharacteristic, complemented
79C2×C3×C5—651no—
80C3×D5—131no—
81Dic7—9751noHall
82D13—51no—
83C52C3⋊(C7⋊#261)11yescharacteristic, complemented, Sylow
84C3×C7#1304993411yescharacteristic, complemented, Hall
85AGL(1,𝔽5)—13651no—
86Dic5—13651no—
87C3×C5—41no—
88C3×C5C7⋊#6312111yescharacteristic, complemented
89C3×C5C7⋊#6311811yescharacteristic, complemented
90C2×C7—651no—
91C13C3⋊(C7⋊#1042)11yescharacteristic, complemented, Sylow
92Dic3—22751noHall
93C2×C5—651no—
94D5—131no—
95C7C3⋊#1304993411yescharacteristic, complemented, Sylow
96C2×C3—651no—
97C5—41no—
98C5C3⋊(C7⋊#63121)11yescharacteristic, complemented
99C5C3⋊(C7⋊#63118)11yescharacteristic, complemented
100C4—68251noSylow
101C3C7⋊#1304993411yescharacteristic, complemented, Sylow
102C2—651no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C52×C7×C13C4
prime radical, cosocleC3×C5×C7×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
10. C52×C7×C13Dic3semidirect
16. C3×C5×C7×C13Dic5semidirect
17. C3×C5×C7×C13AGL(1,𝔽5)semidirect
21. C3×C52×C13Dic7semidirect
29. C3×C52×C7#261semidirect
31. C5×C7×C13Dic15semidirect
32. C5×C7×C13ΓL(1,𝔽16)semidirect
39. C52×C13Dic21semidirect
41. C3×C7×C13#1042semidirect
47. C3×C5×C13Dic35semidirect
48. C3×C5×C13C7⋊AGL(1,𝔽5)semidirect
50. C52×C7C3⋊#261semidirect
58. C3×C5×C7#63118semidirect
59. C3×C5×C7#63121semidirect
61. C7×C13C3⋊#1042semidirect
64. C3×C52C7⋊#261semidirect
68. C5×C13Dic105semidirect
69. C5×C13C3⋊(C7⋊AGL(1,𝔽5))semidirect
75. C3×C13C7⋊#1042semidirect
77. C5×C7C3⋊#63121semidirect
78. C5×C7C3⋊#63118semidirect
83. C52C3⋊(C7⋊#261)semidirect
84. C3×C7#13049934semidirect
88. C3×C5C7⋊#63121semidirect
89. C3×C5C7⋊#63118semidirect
91. C13C3⋊(C7⋊#1042)semidirect
95. C7C3⋊#13049934semidirect
98. C5C3⋊(C7⋊#63121)semidirect
99. C5C3⋊(C7⋊#63118)semidirect
101. C3C7⋊#13049934semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C7×D652
C7⋊#130499343
C3⋊(C7⋊#63118)5
C3⋊(C7⋊#63121)5
C3⋊#130499347
C3⋊(C7⋊#1042)13