Finite Group Databasebeta

← C3×C3⋊(C11⋊#63120) #38788197

Subgroups — C3×C3⋊(C11⋊#63120) #38788197

Order 25740.

112 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 50 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
1C32×D5×C11×C13C211yesmaximal, characteristic
2C3⋊(C11⋊#63120)C311yesmaximal, characteristic, direct product factor
3C3×C11⋊#63120—31nomaximal
4C32×C5×C11×C13C411yescharacteristic, complemented, Hall
5C3×Dic429—51nomaximal, Hall
6C3×D5×C11×C13—21no—
7C3×D5×C11×C13D311yescharacteristic
8C3×D5×C11×C13C2×C311yescharacteristic
9C11⋊#63120—31noHall
10C2×C32×C11×C13—51no—
11C3×C3⋊#63120—111nomaximal, Hall
12C3×C5×C11×C13—21no—
13C3×C5×C11×C13Dic311yescharacteristic, complemented
14C3×C5×C11×C13C3×C411yescharacteristic, complemented
15C3×C3⋊(C11⋊AGL(1,𝔽5))—131nomaximal, Hall
16Dic429—51no—
17C3×Dic143—151no—
18D5×C11×C13C3×D311yescharacteristic
19C32×C11×C13AGL(1,𝔽5)11yescharacteristic, complemented, Hall
20C32×D5×C13D1111yescharacteristic
21C32×D5×C11D1311yescharacteristic
22C2×C3×C11×C13—51no—
23C2×C3×C11×C13—51no—
24C2×C3×C11×C13—101no—
25C3⋊#63120—111no—
26C3×#63120—331no—
27C5×C11×C13C3×Dic311yescharacteristic, complemented, Hall
28C3⋊(C11⋊AGL(1,𝔽5))—131no—
29C3×C11⋊AGL(1,𝔽5)—391no—
30C32×C5×C13Dic1111yescharacteristic, complemented, Hall
31Dic143—151noHall
32C32×C5×C11Dic1311yescharacteristic, complemented, Hall
33C3×Dic39—551noHall
34C3×C11×C13—21no—
35C3×C11×C13C3×AGL(1,𝔽5)11yescharacteristic, complemented
36C3×C11×C13ΓL(1,𝔽16)11yescharacteristic, complemented
37C3×Dic33—651noHall
38C3×D5×C13—21no—
39C3×D5×C13C3×D1111yescharacteristic
40C3×D5×C13D3311yescharacteristic
41C3×D5×C11—21no—
42C3×D5×C11C3×D1311yescharacteristic
43C3×D5×C11D3911yescharacteristic
44C2×C11×C13—51no—
45#63120—331noHall
46C2×C32×C13—51no—
47C11⋊AGL(1,𝔽5)—391noHall
48C2×C32×C11—51no—
49C3×C5×C13—21no—
50C3×C5×C13C3×Dic1111yescharacteristic, complemented
51C3×C5×C13Dic3311yescharacteristic, complemented
52C3×ΓL(1,𝔽16)—1431noHall
53C3×C5×C11—21no—
54C3×C5×C11C3×Dic1311yescharacteristic, complemented
55C3×C5×C11Dic3911yescharacteristic, complemented
56Dic39—551no—
57C3×Dic13—1651no—
58C11×C13C3×ΓL(1,𝔽16)11yescharacteristic, complemented, Hall
59Dic33—651no—
60C3×Dic11—1951no—
61D5×C13C3×D3311yescharacteristic
62C32×C13C11⋊AGL(1,𝔽5)11yescharacteristic, complemented, Hall
63D5×C11C3×D3911yescharacteristic
64C32×C11#6312011yescharacteristic, complemented, Hall
65C32×D5D14311yescharacteristic
66C2×C3×C13—51no—
67C2×C3×C13—51no—
68C2×C3×C13—101no—
69C2×C3×C11—51no—
70C2×C3×C11—51no—
71C2×C3×C11—101no—
72C5×C13C3×Dic3311yescharacteristic, complemented, Hall
73ΓL(1,𝔽16)—1431no—
74C3×AGL(1,𝔽5)—4291no—
75C5×C11C3×Dic3911yescharacteristic, complemented, Hall
76Dic13—1651noHall
77C32×C5Dic14311yescharacteristic, complemented, Hall
78Dic11—1951noHall
79C3×C13—21no—
80C3×C13C3×C11⋊AGL(1,𝔽5)11yescharacteristic, complemented
81C3×C13C3⋊(C11⋊AGL(1,𝔽5))11yescharacteristic, complemented
82C3×Dic3—7151noHall
83C3×C11—21no—
84C3×C11C3×#6312011yescharacteristic, complemented
85C3×C11C3⋊#6312011yescharacteristic, complemented
86C3×D5—21no—
87C3×D5C3×D14311yescharacteristic
88C3×D5D42911yescharacteristic
89C2×C13—51no—
90C2×C11—51no—
91AGL(1,𝔽5)—4291noHall
92C2×C32—51no—
93C3×C5—21no—
94C3×C5C3×Dic14311yescharacteristic, complemented
95C3×C5Dic42911yescharacteristic, complemented
96C13C3×C3⋊(C11⋊AGL(1,𝔽5))11yescharacteristic, complemented, Sylow
97C3×C4—21451no—
98Dic3—7151no—
99C11C3×C3⋊#6312011yescharacteristic, complemented, Sylow
100D5C3×D42911yescharacteristic
101C32C11⋊#6312011yescharacteristic, complemented, Sylow
102C2×C3—51no—
103C2×C3—51no—
104C2×C3—101no—
105C5C3×Dic42911yescharacteristic, complemented, Sylow
106C4—21451noSylow
107C3—21no—
108C3C3×C11⋊#6312011yescharacteristic, complemented
109C3C3⋊(C11⋊#63120)11yescharacteristic, direct product factor
110C2—51no—
subgroupG/H
center, hypercenterC3C3⋊(C11⋊#63120)
commutator, hypocenterC3×C5×C11×C13C3×C4
FrattiniC1G
Fitting, socleC32×C5×C11×C13C4
prime radicalC32×D5×C11×C13C2
cosocleC3×D5×C11×C13C2×C3
LCSG ▷ C3×C5×C11×C13
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
2. C3⋊(C11⋊#63120)C3direct (N × H)
4. C32×C5×C11×C13C4semidirect
13. C3×C5×C11×C13Dic3semidirect
14. C3×C5×C11×C13C3×C4semidirect
19. C32×C11×C13AGL(1,𝔽5)semidirect
27. C5×C11×C13C3×Dic3semidirect
30. C32×C5×C13Dic11semidirect
32. C32×C5×C11Dic13semidirect
35. C3×C11×C13C3×AGL(1,𝔽5)semidirect
36. C3×C11×C13ΓL(1,𝔽16)semidirect
50. C3×C5×C13C3×Dic11semidirect
51. C3×C5×C13Dic33semidirect
54. C3×C5×C11C3×Dic13semidirect
55. C3×C5×C11Dic39semidirect
58. C11×C13C3×ΓL(1,𝔽16)semidirect
62. C32×C13C11⋊AGL(1,𝔽5)semidirect
64. C32×C11#63120semidirect
72. C5×C13C3×Dic33semidirect
75. C5×C11C3×Dic39semidirect
77. C32×C5Dic143semidirect
80. C3×C13C3×C11⋊AGL(1,𝔽5)semidirect
81. C3×C13C3⋊(C11⋊AGL(1,𝔽5))semidirect
84. C3×C11C3×#63120semidirect
85. C3×C11C3⋊#63120semidirect
94. C3×C5C3×Dic143semidirect
95. C3×C5Dic429semidirect
96. C13C3×C3⋊(C11⋊AGL(1,𝔽5))semidirect
99. C11C3×C3⋊#63120semidirect
101. C32C11⋊#63120semidirect
105. C5C3×Dic429semidirect
108. C3C3×C11⋊#63120semidirect
109. C3C3⋊(C11⋊#63120)direct (N × H)

Maximal subgroups

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

subgroupindex
C32×D5×C11×C132
C3⋊(C11⋊#63120)3
C3×C11⋊#631203
C3×Dic4295
C3×C3⋊#6312011
C3×C3⋊(C11⋊AGL(1,𝔽5))13