Finite Group Databasebeta

← C3⋊((C19⋊C3)⋊(C7⋊AGL(1,𝔽5))) #37561332

Subgroups — C3⋊((C19⋊C3)⋊(C7⋊AGL(1,𝔽5))) #37561332

Order 23940.

112 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 38 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×D5×C19⋊C3C211yesmaximal, characteristic
2C3⋊(C7⋊(C19⋊AGL(1,𝔽5)))C311yesmaximal, characteristic, complemented
3(C19⋊C3)⋊(C7⋊AGL(1,𝔽5))—31nomaximal
4C3×C5×C7×C19⋊C3C411yescharacteristic, complemented, Hall
5C3⋊((C19⋊C3)⋊Dic7)—51nomaximal, Hall
6C7×D5×C19⋊C3—21no—
7C7×D5×C19⋊C3D311yescharacteristic
8C3×C7×D5×C19C2×C311yescharacteristic
9C3⋊((C19⋊C3)⋊AGL(1,𝔽5))—71nomaximal, Hall
10C7⋊(C19⋊AGL(1,𝔽5))—31noHall
11C2×C3×C7×C19⋊C3—51no—
12C3×C5×C7×C19C3×C411yescharacteristic, complemented
13C5×C7×C19⋊C3—21no—
14C5×C7×C19⋊C3Dic311yescharacteristic, complemented
15C3×D5×C19⋊C3D711yescharacteristic
16Dic399—51no—
17(C19⋊C3)⋊Dic7—151no—
18C7×D5×C19C3×D311yescharacteristic
19C3×C3⋊(C7⋊AGL(1,𝔽5))—191nomaximal, Hall
20C3×C7×C19⋊C3AGL(1,𝔽5)11yescharacteristic, complemented, Hall
21C3⋊(C19⋊AGL(1,𝔽5))—71no—
22(C19⋊C3)⋊AGL(1,𝔽5)—211no—
23C3×C5×C19⋊C3Dic711yescharacteristic, complemented, Hall
24C2×C3×C7×C19—51no—
25C2×C7×C19⋊C3—51no—
26C2×C7×C19⋊C3—101no—
27C3⋊((C19⋊C3)⋊C4)—351noHall
28C5×C7×C19C3×Dic311yescharacteristic, complemented, Hall
29C32×C7×D5—381no—
30C3×D5×C19C3×D711yescharacteristic
31D5×C19⋊C3—21no—
32D5×C19⋊C3D2111yescharacteristic
33Dic133—151noHall
34C3⋊(C7⋊AGL(1,𝔽5))—191no—
35C3×C7⋊AGL(1,𝔽5)—571no—
36C3×C7×C19C3×AGL(1,𝔽5)11yescharacteristic, complemented
37C7×C19⋊C3—21no—
38C7×C19⋊C3ΓL(1,𝔽16)11yescharacteristic, complemented
39C19⋊AGL(1,𝔽5)—211noHall
40C2×C3×C19⋊C3—51no—
41C32×C5×C7—381noHall
42C3×C5×C19C3×Dic711yescharacteristic, complemented
43C5×C19⋊C3—21no—
44C5×C19⋊C3Dic2111yescharacteristic, complemented
45C2×C7×C19—51no—
46C3×Dic21—951noHall
47Dic57—351no—
48(C19⋊C3)⋊C4—1051no—
49C3×C7×D5—381no—
50C3×C7×D5—381no—
51C3×C7×D5D19⋊C311yescharacteristic
52D5×C19C3×D2111yescharacteristic
53C3×ΓL(1,𝔽16)—1331noHall
54C3×C19⋊C3C7⋊AGL(1,𝔽5)11yescharacteristic, complemented, Hall
55C7⋊AGL(1,𝔽5)—571noHall
56C7×C19C3×ΓL(1,𝔽16)11yescharacteristic, complemented, Hall
57C2×C32×C7—1901no—
58C2×C3×C19—51no—
59C2×C19⋊C3—51no—
60C2×C19⋊C3—101no—
61C3×C5×C7—381no—
62C3×C5×C7—381no—
63C3×C5×C7(C19⋊C3)⋊C411yescharacteristic, complemented
64C5×C19C3×Dic2111yescharacteristic, complemented, Hall
65C32×D5—381no—
66Dic21—951no—
67C3×Dic7—2851no—
68Dic19—1051noHall
69C7×D5C3⋊(D19⋊C3)11yescharacteristic
70C32×C7—381noHall
71ΓL(1,𝔽16)—1331no—
72C3×AGL(1,𝔽5)—3991no—
73C3×C19C3×C7⋊AGL(1,𝔽5)11yescharacteristic, complemented
74C19⋊C3—21no—
75C19⋊C3C3⋊(C7⋊AGL(1,𝔽5))11yescharacteristic, complemented
76C32×C5—381noHall
77C2×C3×C7—51no—
78C2×C3×C7—1901no—
79C2×C3×C7—1901no—
80C2×C19—51no—
81C3×Dic3—6651noHall
82C5×C7C3⋊((C19⋊C3)⋊C4)11yescharacteristic, complemented, Hall
83C3×D5—381no—
84C3×D5—381no—
85C3×D5(C19⋊C3)⋊D711yescharacteristic
86Dic7—2851noHall
87C3×C7—381no—
88C3×C7—381no—
89C3×C7(C19⋊C3)⋊AGL(1,𝔽5)11yescharacteristic, complemented
90AGL(1,𝔽5)—3991noHall
91C19C3×C3⋊(C7⋊AGL(1,𝔽5))11yescharacteristic, complemented, Sylow
92C2×C32—1901no—
93C3×C5—381no—
94C3×C5—381no—
95C3×C5(C19⋊C3)⋊Dic711yescharacteristic, complemented
96C2×C7—51no—
97C3×C4—19951no—
98Dic3—6651no—
99D5C3⋊((C19⋊C3)⋊D7)11yescharacteristic
100C32—381noSylow
101C7C3⋊((C19⋊C3)⋊AGL(1,𝔽5))11yescharacteristic, complemented, Sylow
102C2×C3—51no—
103C2×C3—1901no—
104C2×C3—1901no—
105C5C3⋊((C19⋊C3)⋊Dic7)11yescharacteristic, complemented, Sylow
106C4—19951noSylow
107C3—381no—
108C3—381no—
109C3(C19⋊C3)⋊(C7⋊AGL(1,𝔽5))11yescharacteristic, complemented
110C2—51no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C5×C7×C19C3×C4
prime radicalC3×C7×D5×C19⋊C3C2
cosocleC3×C7×D5×C19C2×C3
LCSG ▷ C3×C5×C7×C19
UCSC1

Complements

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

NH ≅ G/Ntype
2. C3⋊(C7⋊(C19⋊AGL(1,𝔽5)))C3semidirect
4. C3×C5×C7×C19⋊C3C4semidirect
12. C3×C5×C7×C19C3×C4semidirect
14. C5×C7×C19⋊C3Dic3semidirect
20. C3×C7×C19⋊C3AGL(1,𝔽5)semidirect
23. C3×C5×C19⋊C3Dic7semidirect
28. C5×C7×C19C3×Dic3semidirect
36. C3×C7×C19C3×AGL(1,𝔽5)semidirect
38. C7×C19⋊C3ΓL(1,𝔽16)semidirect
42. C3×C5×C19C3×Dic7semidirect
44. C5×C19⋊C3Dic21semidirect
54. C3×C19⋊C3C7⋊AGL(1,𝔽5)semidirect
56. C7×C19C3×ΓL(1,𝔽16)semidirect
63. C3×C5×C7(C19⋊C3)⋊C4semidirect
64. C5×C19C3×Dic21semidirect
73. C3×C19C3×C7⋊AGL(1,𝔽5)semidirect
75. C19⋊C3C3⋊(C7⋊AGL(1,𝔽5))semidirect
82. C5×C7C3⋊((C19⋊C3)⋊C4)semidirect
89. C3×C7(C19⋊C3)⋊AGL(1,𝔽5)semidirect
91. C19C3×C3⋊(C7⋊AGL(1,𝔽5))semidirect
95. C3×C5(C19⋊C3)⋊Dic7semidirect
101. C7C3⋊((C19⋊C3)⋊AGL(1,𝔽5))semidirect
105. C5C3⋊((C19⋊C3)⋊Dic7)semidirect
109. C3(C19⋊C3)⋊(C7⋊AGL(1,𝔽5))semidirect

Maximal subgroups

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

subgroupindex
C3×C7×D5×C19⋊C32
C3⋊(C7⋊(C19⋊AGL(1,𝔽5)))3
(C19⋊C3)⋊(C7⋊AGL(1,𝔽5))3
C3⋊((C19⋊C3)⋊Dic7)5
C3⋊((C19⋊C3)⋊AGL(1,𝔽5))7
C3×C3⋊(C7⋊AGL(1,𝔽5))19