Finite Group Databasebeta

← C3×C7×D5×D13⋊C3 #30655355

Subgroups — C3×C7×D5×D13⋊C3 #30655355

Order 16380.

240 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 96 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×C13⋊C3C211yesmaximal, characteristic, complemented
2C3×C7×C5⋊(D13⋊C3)C211yesmaximal, characteristic, complemented
3C3×C5×C7×D13⋊C3C211yesmaximal, characteristic, complemented
4C3×C7×D5×D13C311yesmaximal, characteristic, complemented
5C7×D5×D13⋊C3C313yesmaximal, direct product factor
6C3×C5×C7×C13⋊C3C2211yescharacteristic, complemented, Hall
7C2×C3×C7×D13⋊C3—51nomaximal, Hall
8C7×C5⋊(D13⋊C3)C2×C313yescomplemented
9C7×D5×C13⋊C3C2×C313yescomplemented
10C5×C7×D13⋊C3C2×C313yescomplemented
11C3×C7×D65C2×C311yescharacteristic, complemented
12C3×C7×D5×C13C2×C311yescharacteristic, complemented
13C3×C5×C7×D13C2×C311yescharacteristic, complemented
14C3×D5×D13⋊C3C711yesmaximal, characteristic, direct product factor, Hall
15C7×D5×D13C3211yescharacteristic, complemented, Hall
16C2×C3×C7×C13⋊C3—51no—
17C3×C7×D13⋊C3—51no—
18C3×C7×D13⋊C3D511yescharacteristic, direct product factor
19C3×C5×C7×C13C22×C311yescharacteristic, complemented
20C5×C7×C13⋊C3C22×C313yescomplemented
21C2×C32×C7×D5—131nomaximal, Hall
22C3×C5⋊(D13⋊C3)C2×C711yescharacteristic, complemented
23C3×D5×C13⋊C3C2×C711yescharacteristic, complemented
24C3×C5×D13⋊C3C2×C711yescharacteristic, complemented
25C2×C3×C7×D13—51no—
26C2×C7×D13⋊C3—53no—
27C7×D65C2×C3211yescharacteristic, complemented
28C7×D5×C13C2×C3211yescharacteristic, complemented
29C5×C7×D13C2×C3211yescharacteristic, complemented
30C3×C7×C13⋊C3C2×D511yescharacteristic, complemented, Hall
31C3×D5×D13C3×C711yescharacteristic, complemented
32D5×D13⋊C3C3×C713yesdirect product factor
33C2×C32×C5×C7—131no—
34C32×C7×D5—131no—
35C32×C7×D5—131no—
36C3×C5×C13⋊C3C22×C711yescharacteristic, complemented, Hall
37C2×C3×C7×C13—51no—
38C3×C7×D13—51no—
39C3×C7×D13C3×D511yescharacteristic, complemented
40C2×C7×C13⋊C3—53no—
41C7×D13⋊C3—53no—
42C7×D13⋊C3C3×D513yesdirect product factor
43C2×C3×D13⋊C3—51noHall
44C5×C7×C13C22×C3211yescharacteristic, complemented, Hall
45C2×C3×C7×D5—133no—
46C2×C3×C7×D5—391no—
47C3×D65C2×C3×C711yescharacteristic, complemented
48C3×D5×C13C2×C3×C711yescharacteristic, complemented
49C3×C5×D13C2×C3×C711yescharacteristic, complemented
50C5⋊(D13⋊C3)C2×C3×C713yescomplemented
51D5×C13⋊C3C2×C3×C713yescomplemented
52C5×D13⋊C3C2×C3×C713yescomplemented
53C2×C7×D13—51noHall
54C32×C5×C7—131noHall
55C3×C7×C13C2×C3×D511yescharacteristic, complemented
56C7×C13⋊C3C2×C3×D513yescomplemented
57D5×D13C32×C711yescharacteristic, complemented, Hall
58C22×C32×C7—651noHall
59C2×C3×C13⋊C3—51no—
60C3×D13⋊C3—51no—
61C3×D13⋊C3C7×D511yescharacteristic, direct product factor
62C2×C3×C5×C7—133no—
63C2×C3×C5×C7—391no—
64C3×C7×D5—133no—
65C3×C7×D5—133no—
66C3×C7×D5—391no—
67C3×C7×D5D13⋊C311yescharacteristic, direct product factor
68C3×C5×C13C22×C3×C711yescharacteristic, complemented
69C5×C13⋊C3C22×C3×C713yescomplemented
70C2×C7×C13—51no—
71C7×D13—51no—
72C7×D13C32×D511yescharacteristic, complemented
73C2×C32×D5—131noHall
74C2×C3×D13—51no—
75C2×D13⋊C3—53no—
76C2×C7×D5—391noHall
77D65C2×C32×C711yescharacteristic, complemented
78C5×D13C2×C32×C711yescharacteristic, complemented
79D5×C13C2×C32×C711yescharacteristic, complemented
80C2×C32×C7—131no—
81C2×C32×C7—651no—
82C2×C32×C7—651no—
83C3×C13⋊C3C2×C7×D511yescharacteristic, complemented, Hall
84C3×C5×C7—133no—
85C3×C5×C7C2×D13⋊C311yescharacteristic, complemented
86C7×C13C2×C32×D511yescharacteristic, complemented, Hall
87C2×C32×C5—131no—
88C32×D5—131no—
89C32×D5—131no—
90C22×C3×C7—653no—
91C22×C3×C7—1951no—
92C2×C3×C13—51no—
93C3×D13—51no—
94C3×D13C3×C7×D511yescharacteristic, complemented
95C2×C13⋊C3—53no—
96D13⋊C3—53no—
97D13⋊C3C3×C7×D513yesdirect product factor
98C2×C5×C7—391no—
99C7×D5—391no—
100C7×D5C3×D13⋊C311yescharacteristic, direct product factor
101C5×C13C22×C32×C711yescharacteristic, complemented, Hall
102C32×C7—131noHall
103C2×C3×D5—133no—
104C2×C3×D5—131no—
105C2×D13—51noHall
106C32×C5—131noHall
107C2×C3×C7—51no—
108C2×C3×C7—133no—
109C2×C3×C7—391no—
110C2×C3×C7—653no—
111C2×C3×C7—653no—
112C2×C3×C7—1951no—
113C3×C13C2×C3×C7×D511yescharacteristic, complemented
114C13⋊C3C2×C3×C7×D513yescomplemented
115C22×C32—651noHall
116C5×C7C2×C3×D13⋊C311yescharacteristic, complemented, Hall
117C2×C3×C5—133no—
118C2×C3×C5—391no—
119C3×D5—133no—
120C3×D5—133no—
121C3×D5—391no—
122C3×D5C7×D13⋊C311yescharacteristic, direct product factor
123C22×C7—1951noHall
124C2×C13—51no—
125D13—51no—
126D13C32×C7×D511yescharacteristic, complemented
127C3×C7—133no—
128C3×C7D5×D13⋊C311yescharacteristic, direct product factor
129C2×D5—131noHall
130C2×C32—131no—
131C2×C32—651no—
132C2×C32—651no—
133C3×C5—133no—
134C3×C5C2×C7×D13⋊C311yescharacteristic, complemented
135C2×C7—51no—
136C2×C7—391no—
137C2×C7—1951no—
138C13C2×C32×C7×D511yescharacteristic, complemented, Sylow
139C22×C3—653no—
140C22×C3—1951no—
141C2×C5—391no—
142D5—391no—
143D5C3×C7×D13⋊C311yescharacteristic, direct product factor
144C32—131noSylow
145C7C3×D5×D13⋊C311yescharacteristic, direct product factor, Sylow
146C2×C3—51no—
147C2×C3—133no—
148C2×C3—391no—
149C2×C3—653no—
150C2×C3—653no—
151C2×C3—1951no—
152C5C2×C3×C7×D13⋊C311yescharacteristic, complemented, Sylow
153C22—1951noSylow
154C3—133no—
155C3C7×D5×D13⋊C311yescharacteristic, direct product factor
156C2—51no—
157C2—391no—
158C2—1951no—
subgroupG/H
center, hypercenterC3×C7D5×D13⋊C3
commutator, cosocle, hypocenterC5×C13C22×C32×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C13C22×C3
LCSG ▷ C5×C13
UCSC1 ◁ C3×C7

Complements

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

NH ≅ G/Ntype
1. C3×C7×D5×C13⋊C3C2semidirect
2. C3×C7×C5⋊(D13⋊C3)C2semidirect
3. C3×C5×C7×D13⋊C3C2semidirect
4. C3×C7×D5×D13C3semidirect
5. C7×D5×D13⋊C3C3direct (N × H)
6. C3×C5×C7×C13⋊C3C22semidirect
8. C7×C5⋊(D13⋊C3)C2×C3semidirect
9. C7×D5×C13⋊C3C2×C3semidirect
10. C5×C7×D13⋊C3C2×C3semidirect
11. C3×C7×D65C2×C3semidirect
12. C3×C7×D5×C13C2×C3semidirect
13. C3×C5×C7×D13C2×C3semidirect
14. C3×D5×D13⋊C3C7direct (N × H)
15. C7×D5×D13C32semidirect
18. C3×C7×D13⋊C3D5direct (N × H)
19. C3×C5×C7×C13C22×C3semidirect
20. C5×C7×C13⋊C3C22×C3semidirect
22. C3×C5⋊(D13⋊C3)C2×C7semidirect
23. C3×D5×C13⋊C3C2×C7semidirect
24. C3×C5×D13⋊C3C2×C7semidirect
27. C7×D65C2×C32semidirect
28. C7×D5×C13C2×C32semidirect
29. C5×C7×D13C2×C32semidirect
30. C3×C7×C13⋊C3C2×D5semidirect
31. C3×D5×D13C3×C7semidirect
32. D5×D13⋊C3C3×C7direct (N × H)
36. C3×C5×C13⋊C3C22×C7semidirect
39. C3×C7×D13C3×D5semidirect
42. C7×D13⋊C3C3×D5direct (N × H)
44. C5×C7×C13C22×C32semidirect
47. C3×D65C2×C3×C7semidirect
48. C3×D5×C13C2×C3×C7semidirect
49. C3×C5×D13C2×C3×C7semidirect
50. C5⋊(D13⋊C3)C2×C3×C7semidirect
51. D5×C13⋊C3C2×C3×C7semidirect
52. C5×D13⋊C3C2×C3×C7semidirect
55. C3×C7×C13C2×C3×D5semidirect
56. C7×C13⋊C3C2×C3×D5semidirect
57. D5×D13C32×C7semidirect
61. C3×D13⋊C3C7×D5direct (N × H)
67. C3×C7×D5D13⋊C3direct (N × H)
68. C3×C5×C13C22×C3×C7semidirect
69. C5×C13⋊C3C22×C3×C7semidirect
72. C7×D13C32×D5semidirect
77. D65C2×C32×C7semidirect
78. C5×D13C2×C32×C7semidirect
79. D5×C13C2×C32×C7semidirect
83. C3×C13⋊C3C2×C7×D5semidirect
85. C3×C5×C7C2×D13⋊C3semidirect
86. C7×C13C2×C32×D5semidirect
94. C3×D13C3×C7×D5semidirect
97. D13⋊C3C3×C7×D5direct (N × H)
100. C7×D5C3×D13⋊C3direct (N × H)
101. C5×C13C22×C32×C7semidirect
113. C3×C13C2×C3×C7×D5semidirect
114. C13⋊C3C2×C3×C7×D5semidirect
116. C5×C7C2×C3×D13⋊C3semidirect
122. C3×D5C7×D13⋊C3direct (N × H)
126. D13C32×C7×D5semidirect
128. C3×C7D5×D13⋊C3direct (N × H)
134. C3×C5C2×C7×D13⋊C3semidirect
138. C13C2×C32×C7×D5semidirect
143. D5C3×C7×D13⋊C3direct (N × H)
145. C7C3×D5×D13⋊C3direct (N × H)
152. C5C2×C3×C7×D13⋊C3semidirect
155. C3C7×D5×D13⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C7×D5×C13⋊C32
C3×C7×C5⋊(D13⋊C3)2
C3×C5×C7×D13⋊C32
C3×C7×D5×D133
C7×D5×D13⋊C33
C2×C3×C7×D13⋊C35
C3×D5×D13⋊C37
C2×C32×C7×D513