Finite Group Databasebeta

← C3×D5×D11×C13⋊C3 #38788074

Subgroups — C3×D5×D11×C13⋊C3 #38788074

Order 25740.

240 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 80 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×C13⋊C3×D55C211yesmaximal, characteristic, complemented
2C3×D5×C11×C13⋊C3C211yesmaximal, characteristic, complemented
3C3×C5×D11×C13⋊C3C211yesmaximal, characteristic, complemented
4C3×D5×C13×D11C311yesmaximal, characteristic, complemented
5D5×D11×C13⋊C3C313yesmaximal, direct product factor
6C3×C5×C11×C13⋊C3C2211yescharacteristic, complemented, Hall
7C2×C3×D11×C13⋊C3—51nomaximal, Hall
8C13⋊C3×D55C2×C313yescomplemented
9D5×C11×C13⋊C3C2×C313yescomplemented
10C5×D11×C13⋊C3C2×C313yescomplemented
11C3×C13×D55C2×C311yescharacteristic, complemented
12C3×D5×C11×C13C2×C311yescharacteristic, complemented
13C3×C5×C13×D11C2×C311yescharacteristic, complemented
14D5×C13×D11C3211yescharacteristic, complemented, Hall
15C2×C3×C11×C13⋊C3—51no—
16C3×D11×C13⋊C3—51no—
17C3×D11×C13⋊C3D511yescharacteristic, direct product factor
18C2×C3×D5×C13⋊C3—111nomaximal, Hall
19C5×C11×C13⋊C3C22×C313yescomplemented
20C3×C5×C11×C13C22×C311yescharacteristic, complemented
21C32×D5×D11—131nomaximal, Hall
22C2×C3×C13×D11—51no—
23C2×D11×C13⋊C3—53no—
24C13×D55C2×C3211yescharacteristic, complemented
25D5×C11×C13C2×C3211yescharacteristic, complemented
26C5×C13×D11C2×C3211yescharacteristic, complemented
27C3×C11×C13⋊C3C2×D511yescharacteristic, complemented, Hall
28C2×C3×C5×C13⋊C3—111no—
29C3×D5×C13⋊C3—111no—
30C3×D5×C13⋊C3D1111yescharacteristic, direct product factor
31C32×D55—131no—
32C32×D5×C11—131no—
33C32×C5×D11—131no—
34C2×C3×C11×C13—51no—
35C3×C13×D11—51no—
36C3×C13×D11C3×D511yescharacteristic, complemented
37C2×C11×C13⋊C3—53no—
38D11×C13⋊C3—53no—
39D11×C13⋊C3C3×D513yesdirect product factor
40C2×C3×D5×C13—111no—
41C2×D5×C13⋊C3—113no—
42C5×C11×C13C22×C3211yescharacteristic, complemented, Hall
43C3×D5×D11—133no—
44C3×D5×D11C13⋊C311yescharacteristic, direct product factor
45C3×C5×C13⋊C3C2×D1111yescharacteristic, complemented, Hall
46C2×C13×D11—51noHall
47C32×C5×C11—131noHall
48C22×C3×C13⋊C3—551noHall
49C3×C11×C13C2×C3×D511yescharacteristic, complemented
50C11×C13⋊C3C2×C3×D513yescomplemented
51C2×C32×D11—651noHall
52C2×C3×C5×C13—111no—
53C3×D5×C13—111no—
54C3×D5×C13C3×D1111yescharacteristic, complemented
55C2×C5×C13⋊C3—113no—
56D5×C13⋊C3—113no—
57D5×C13⋊C3C3×D1113yesdirect product factor
58C3×D55—133no—
59C3×D55C2×C13⋊C311yescharacteristic, complemented
60C3×D5×C11—133no—
61C3×D5×C11C2×C13⋊C311yescharacteristic, complemented
62C3×C5×D11—133no—
63C3×C5×D11C2×C13⋊C311yescharacteristic, complemented
64C2×C11×C13—51no—
65C13×D11—51no—
66C13×D11C32×D511yescharacteristic, complemented
67C2×D5×C13—111noHall
68C2×C3×C13⋊C3—51no—
69C2×C3×C13⋊C3—111no—
70C2×C3×C13⋊C3—551no—
71D5×D11C3×C13⋊C311yescharacteristic, direct product factor, Hall
72C2×C32×C11—651no—
73C32×D11—131no—
74C32×D11—651no—
75C3×C5×C13C2×C3×D1111yescharacteristic, complemented
76C5×C13⋊C3C2×C3×D1113yescomplemented
77C2×C32×D5—1431noHall
78C3×C5×C11—133no—
79C3×C5×C11C22×C13⋊C311yescharacteristic, complemented
80C22×C3×C13—551no—
81C22×C13⋊C3—553no—
82C11×C13C2×C32×D511yescharacteristic, complemented, Hall
83C2×C3×D11—51no—
84C2×C3×D11—653no—
85C2×C5×C13—111no—
86D5×C13—111no—
87D5×C13C32×D1111yescharacteristic, complemented
88C3×C13⋊C3D5×D1111yescharacteristic, direct product factor, Hall
89D55C2×C3×C13⋊C311yescharacteristic, complemented
90C5×D11C2×C3×C13⋊C311yescharacteristic, complemented
91D5×C11C2×C3×C13⋊C311yescharacteristic, complemented
92C32×C11—131noHall
93C2×C32×C5—1431no—
94C32×D5—131no—
95C32×D5—1431no—
96C2×C3×C13—51no—
97C2×C3×C13—111no—
98C2×C3×C13—551no—
99C2×C13⋊C3—53no—
100C2×C13⋊C3—113no—
101C2×C13⋊C3—553no—
102C2×C3×C11—51no—
103C2×C3×C11—653no—
104C3×D11—51no—
105C3×D11—133no—
106C3×D11—653no—
107C3×D11D5×C13⋊C311yescharacteristic, direct product factor
108C5×C13C2×C32×D1111yescharacteristic, complemented, Hall
109C2×C3×D5—111no—
110C2×C3×D5—1433no—
111C5×C11C22×C3×C13⋊C311yescharacteristic, complemented, Hall
112C22×C13—551noHall
113C32×C5—131noHall
114C2×D11—51noHall
115C3×C13C3×D5×D1111yescharacteristic, complemented
116C13⋊C3C3×D5×D1113yesdirect product factor
117C22×C32—7151noHall
118C3×C11—133no—
119C3×C11C2×D5×C13⋊C311yescharacteristic, complemented
120C2×C3×C5—111no—
121C2×C3×C5—1433no—
122C3×D5—111no—
123C3×D5—133no—
124C3×D5—1433no—
125C3×D5D11×C13⋊C311yescharacteristic, direct product factor
126C2×C13—51no—
127C2×C13—111no—
128C2×C13—551no—
129C2×C11—51no—
130D11—51no—
131D11C3×D5×C13⋊C311yescharacteristic, direct product factor
132C2×D5—111noHall
133C2×C32—651no—
134C2×C32—1431no—
135C2×C32—7151no—
136C3×C5—133no—
137C3×C5C2×D11×C13⋊C311yescharacteristic, complemented
138C13C32×D5×D1111yescharacteristic, complemented, Sylow
139C22×C3—551no—
140C22×C3—7153no—
141C11C2×C3×D5×C13⋊C311yescharacteristic, complemented, Sylow
142C2×C5—111no—
143D5—111no—
144D5C3×D11×C13⋊C311yescharacteristic, direct product factor
145C32—131noSylow
146C2×C3—51no—
147C2×C3—111no—
148C2×C3—551no—
149C2×C3—653no—
150C2×C3—1433no—
151C2×C3—7153no—
152C5C2×C3×D11×C13⋊C311yescharacteristic, complemented, Sylow
153C22—551noSylow
154C3—133no—
155C3D5×D11×C13⋊C311yescharacteristic, direct product factor
156C2—51no—
157C2—111no—
158C2—551no—
subgroupG/H
center, hypercenterC3D5×D11×C13⋊C3
commutator, cosocle, hypocenterC5×C11×C13C22×C32
FrattiniC1G
Fitting, socleC3×C5×C11×C13C22×C3
LCSG ▷ C5×C11×C13
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C13⋊C3×D55C2semidirect
2. C3×D5×C11×C13⋊C3C2semidirect
3. C3×C5×D11×C13⋊C3C2semidirect
4. C3×D5×C13×D11C3semidirect
5. D5×D11×C13⋊C3C3direct (N × H)
6. C3×C5×C11×C13⋊C3C22semidirect
8. C13⋊C3×D55C2×C3semidirect
9. D5×C11×C13⋊C3C2×C3semidirect
10. C5×D11×C13⋊C3C2×C3semidirect
11. C3×C13×D55C2×C3semidirect
12. C3×D5×C11×C13C2×C3semidirect
13. C3×C5×C13×D11C2×C3semidirect
14. D5×C13×D11C32semidirect
17. C3×D11×C13⋊C3D5direct (N × H)
19. C5×C11×C13⋊C3C22×C3semidirect
20. C3×C5×C11×C13C22×C3semidirect
24. C13×D55C2×C32semidirect
25. D5×C11×C13C2×C32semidirect
26. C5×C13×D11C2×C32semidirect
27. C3×C11×C13⋊C3C2×D5semidirect
30. C3×D5×C13⋊C3D11direct (N × H)
36. C3×C13×D11C3×D5semidirect
39. D11×C13⋊C3C3×D5direct (N × H)
42. C5×C11×C13C22×C32semidirect
44. C3×D5×D11C13⋊C3direct (N × H)
45. C3×C5×C13⋊C3C2×D11semidirect
49. C3×C11×C13C2×C3×D5semidirect
50. C11×C13⋊C3C2×C3×D5semidirect
54. C3×D5×C13C3×D11semidirect
57. D5×C13⋊C3C3×D11direct (N × H)
59. C3×D55C2×C13⋊C3semidirect
61. C3×D5×C11C2×C13⋊C3semidirect
63. C3×C5×D11C2×C13⋊C3semidirect
66. C13×D11C32×D5semidirect
71. D5×D11C3×C13⋊C3direct (N × H)
75. C3×C5×C13C2×C3×D11semidirect
76. C5×C13⋊C3C2×C3×D11semidirect
79. C3×C5×C11C22×C13⋊C3semidirect
82. C11×C13C2×C32×D5semidirect
87. D5×C13C32×D11semidirect
88. C3×C13⋊C3D5×D11direct (N × H)
89. D55C2×C3×C13⋊C3semidirect
90. C5×D11C2×C3×C13⋊C3semidirect
91. D5×C11C2×C3×C13⋊C3semidirect
107. C3×D11D5×C13⋊C3direct (N × H)
108. C5×C13C2×C32×D11semidirect
111. C5×C11C22×C3×C13⋊C3semidirect
115. C3×C13C3×D5×D11semidirect
116. C13⋊C3C3×D5×D11direct (N × H)
119. C3×C11C2×D5×C13⋊C3semidirect
125. C3×D5D11×C13⋊C3direct (N × H)
131. D11C3×D5×C13⋊C3direct (N × H)
137. C3×C5C2×D11×C13⋊C3semidirect
138. C13C32×D5×D11semidirect
141. C11C2×C3×D5×C13⋊C3semidirect
144. D5C3×D11×C13⋊C3direct (N × H)
152. C5C2×C3×D11×C13⋊C3semidirect
155. C3D5×D11×C13⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C13⋊C3×D552
C3×D5×C11×C13⋊C32
C3×C5×D11×C13⋊C32
C3×D5×C13×D113
D5×D11×C13⋊C33
C2×C3×D11×C13⋊C35
C2×C3×D5×C13⋊C311
C32×D5×D1113