Finite Group Databasebeta

← C7×D15×D13⋊C3 #30655451

Subgroups — C7×D15×D13⋊C3 #30655451

Order 16380.

176 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 54 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
1C7×D15×C13⋊C3C211yesmaximal, characteristic, complemented
2C7×C3⋊(C5⋊(D13⋊C3))C211yesmaximal, characteristic, complemented
3C3×C5×C7×D13⋊C3C211yesmaximal, characteristic, complemented
4C7×D13×D15C311yesmaximal, characteristic, complemented
5C7×D5×D13⋊C3—31nomaximal
6C3×C5×C7×C13⋊C3C2211yescharacteristic, complemented, Hall
7D3×C7×D13⋊C3—51nomaximal, Hall
8C7×C5⋊(D13⋊C3)—31no—
9C7×D5×C13⋊C3—31no—
10C5×C7×D13⋊C3—21no—
11C5×C7×D13⋊C3D311yescharacteristic, complemented
12C7×D195C2×C311yescharacteristic, complemented
13C7×C13×D15C2×C311yescharacteristic, complemented
14C3×C5×C7×D13C2×C311yescharacteristic, complemented
15D15×D13⋊C3C711yesmaximal, characteristic, direct product factor, Hall
16C7×D5×D13—31noHall
17C7×C3⋊(D13⋊C3)—51no—
18D3×C7×C13⋊C3—51no—
19C3×C7×D13⋊C3D511yescharacteristic, complemented
20C3×C5×C7×C13C22×C311yescharacteristic, complemented
21C5×C7×C13⋊C3—21no—
22C5×C7×C13⋊C3C2×D311yescharacteristic, complemented
23C2×C3×C7×D15—131nomaximal, Hall
24C3⋊(C5⋊(D13⋊C3))C2×C711yescharacteristic, complemented
25D15×C13⋊C3C2×C711yescharacteristic, complemented
26C3×C5×D13⋊C3C2×C711yescharacteristic, complemented
27D3×C7×D13—51no—
28C2×C7×D13⋊C3—151no—
29C7×D65—31no—
30C7×D5×C13—31no—
31C5×C7×D13C3×D311yescharacteristic, complemented
32C3×C7×C13⋊C3C2×D511yescharacteristic, complemented, Hall
33D13×D15C3×C711yescharacteristic, complemented
34D5×D13⋊C3—31no—
35C2×C32×C5×C7—131no—
36C3×C7×D15—131no—
37C3×C7×D15—131no—
38C3×C5×C13⋊C3C22×C711yescharacteristic, complemented, Hall
39C7×D39—51no—
40D3×C7×C13—51no—
41C3×C7×D13C3×D511yescharacteristic, complemented
42C2×C7×C13⋊C3—151no—
43C7×D13⋊C3—21no—
44C7×D13⋊C3—151no—
45C7×D13⋊C3D1511yescharacteristic, direct product factor
46D3×D13⋊C3—51noHall
47C5×C7×C13C2×C3×D311yescharacteristic, complemented, Hall
48C2×C7×D15—131no—
49C2×C3×C7×D5—391no—
50D195C2×C3×C711yescharacteristic, complemented
51C13×D15C2×C3×C711yescharacteristic, complemented
52C3×C5×D13C2×C3×C711yescharacteristic, complemented
53C5⋊(D13⋊C3)—31no—
54D5×C13⋊C3—31no—
55C5×D13⋊C3—21no—
56C5×D13⋊C3D3×C711yescharacteristic, complemented
57C2×C7×D13—151noHall
58C32×C5×C7—131noHall
59C3×C7×C13C2×C3×D511yescharacteristic, complemented
60C7×C13⋊C3—21no—
61C7×C13⋊C3C2×D1511yescharacteristic, complemented
62D5×D13—31noHall
63C2×C3×D3×C7—651noHall
64C3⋊(D13⋊C3)—51no—
65D3×C13⋊C3—51no—
66C3×D13⋊C3C7×D511yescharacteristic, complemented
67C2×C3×C5×C7—131no—
68C2×C3×C5×C7—131no—
69C2×C3×C5×C7—261no—
70C7×D15—131no—
71C7×D15D13⋊C311yescharacteristic, direct product factor
72C3×C7×D5—391no—
73C3×C7×D5—391no—
74C3×C5×C13C22×C3×C711yescharacteristic, complemented
75C5×C13⋊C3—21no—
76C5×C13⋊C3C2×D3×C711yescharacteristic, complemented
77C2×C7×C13—151no—
78C7×D13—151no—
79C7×D13C3×D1511yescharacteristic, complemented
80C2×C3×D15—131noHall
81D3×D13—51no—
82C2×D13⋊C3—151no—
83C2×C7×D5—391noHall
84D65—31no—
85C5×D13C3×D3×C711yescharacteristic, complemented
86D5×C13—31no—
87C2×C32×C7—131no—
88C3×D3×C7—651no—
89C3×D3×C7—651no—
90C3×C13⋊C3C2×C7×D511yescharacteristic, complemented, Hall
91C3×C5×C7—131no—
92C3×C5×C7—261no—
93C3×C5×C7C2×D13⋊C311yescharacteristic, complemented
94C7×C13C2×C3×D1511yescharacteristic, complemented, Hall
95C2×C32×C5—131no—
96C3×D15—131no—
97C3×D15—131no—
98C22×C3×C7—1951no—
99C2×D3×C7—651no—
100D39—51no—
101C3×D13C3×C7×D511yescharacteristic, complemented
102D3×C13—51no—
103C2×C13⋊C3—151no—
104D13⋊C3—21no—
105D13⋊C3—151no—
106D13⋊C3C7×D1511yescharacteristic, direct product factor
107C2×C5×C7—131no—
108C7×D5—31no—
109C7×D5—391no—
110C5×C13C2×C3×D3×C711yescharacteristic, complemented, Hall
111C32×C7—131noHall
112C2×D15—131no—
113C2×C3×D5—391no—
114C2×D13—151noHall
115C32×C5—131noHall
116C2×C3×C7—131no—
117C2×C3×C7—131no—
118C2×C3×C7—261no—
119C2×C3×C7—1951no—
120C2×C3×C7—1951no—
121D3×C7—51no—
122D3×C7—651no—
123C3×C13C2×C3×C7×D511yescharacteristic, complemented
124C13⋊C3—21no—
125C13⋊C3C2×C7×D1511yescharacteristic, complemented
126C2×C3×D3—651noHall
127C5×C7D3×D13⋊C311yescharacteristic, complemented, Hall
128C2×C3×C5—131no—
129C2×C3×C5—131no—
130C2×C3×C5—261no—
131D15—131no—
132D15C7×D13⋊C311yescharacteristic, direct product factor
133C3×D5—391no—
134C3×D5—391no—
135C22×C7—1951noHall
136C2×C13—151no—
137D13—151no—
138D13C3×C7×D1511yescharacteristic, complemented
139C3×C7—131no—
140C3×C7—261no—
141C3×C7D5×D13⋊C311yescharacteristic, complemented
142C2×D5—391noHall
143C2×C32—131no—
144C3×D3—651no—
145C3×D3—651no—
146C3×C5—131no—
147C3×C5—261no—
148C3×C5C2×C7×D13⋊C311yescharacteristic, complemented
149C2×C7—131no—
150C2×C7—151no—
151C2×C7—1951no—
152C13C2×C3×C7×D1511yescharacteristic, complemented, Sylow
153C22×C3—1951no—
154C2×D3—651no—
155C2×C5—131no—
156D5—31no—
157D5—391no—
158C32—131noSylow
159C7D15×D13⋊C311yescharacteristic, direct product factor, Sylow
160C2×C3—131no—
161C2×C3—131no—
162C2×C3—261no—
163C2×C3—1951no—
164C2×C3—1951no—
165D3—51no—
166D3—651no—
167C5D3×C7×D13⋊C311yescharacteristic, complemented, Sylow
168C22—1951noSylow
169C3—131no—
170C3—261no—
171C3C7×D5×D13⋊C311yescharacteristic, complemented
172C2—131no—
173C2—151no—
174C2—1951no—
subgroupG/H
center, hypercenterC7D15×D13⋊C3
commutator, cosocle, hypocenterC3×C5×C13C22×C3×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C13C22×C3
LCSG ▷ C3×C5×C13
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C7×D15×C13⋊C3C2semidirect
2. C7×C3⋊(C5⋊(D13⋊C3))C2semidirect
3. C3×C5×C7×D13⋊C3C2semidirect
4. C7×D13×D15C3semidirect
6. C3×C5×C7×C13⋊C3C22semidirect
11. C5×C7×D13⋊C3D3semidirect
12. C7×D195C2×C3semidirect
13. C7×C13×D15C2×C3semidirect
14. C3×C5×C7×D13C2×C3semidirect
15. D15×D13⋊C3C7direct (N × H)
19. C3×C7×D13⋊C3D5semidirect
20. C3×C5×C7×C13C22×C3semidirect
22. C5×C7×C13⋊C3C2×D3semidirect
24. C3⋊(C5⋊(D13⋊C3))C2×C7semidirect
25. D15×C13⋊C3C2×C7semidirect
26. C3×C5×D13⋊C3C2×C7semidirect
31. C5×C7×D13C3×D3semidirect
32. C3×C7×C13⋊C3C2×D5semidirect
33. D13×D15C3×C7semidirect
38. C3×C5×C13⋊C3C22×C7semidirect
41. C3×C7×D13C3×D5semidirect
45. C7×D13⋊C3D15direct (N × H)
47. C5×C7×C13C2×C3×D3semidirect
50. D195C2×C3×C7semidirect
51. C13×D15C2×C3×C7semidirect
52. C3×C5×D13C2×C3×C7semidirect
56. C5×D13⋊C3D3×C7semidirect
59. C3×C7×C13C2×C3×D5semidirect
61. C7×C13⋊C3C2×D15semidirect
66. C3×D13⋊C3C7×D5semidirect
71. C7×D15D13⋊C3direct (N × H)
74. C3×C5×C13C22×C3×C7semidirect
76. C5×C13⋊C3C2×D3×C7semidirect
79. C7×D13C3×D15semidirect
85. C5×D13C3×D3×C7semidirect
90. C3×C13⋊C3C2×C7×D5semidirect
93. C3×C5×C7C2×D13⋊C3semidirect
94. C7×C13C2×C3×D15semidirect
101. C3×D13C3×C7×D5semidirect
106. D13⋊C3C7×D15direct (N × H)
110. C5×C13C2×C3×D3×C7semidirect
123. C3×C13C2×C3×C7×D5semidirect
125. C13⋊C3C2×C7×D15semidirect
127. C5×C7D3×D13⋊C3semidirect
132. D15C7×D13⋊C3direct (N × H)
138. D13C3×C7×D15semidirect
141. C3×C7D5×D13⋊C3semidirect
148. C3×C5C2×C7×D13⋊C3semidirect
152. C13C2×C3×C7×D15semidirect
159. C7D15×D13⋊C3direct (N × H)
167. C5D3×C7×D13⋊C3semidirect
171. C3C7×D5×D13⋊C3semidirect

Maximal subgroups

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

subgroupindex
C7×D15×C13⋊C32
C7×C3⋊(C5⋊(D13⋊C3))2
C3×C5×C7×D13⋊C32
C7×D13×D153
C7×D5×D13⋊C33
D3×C7×D13⋊C35
D15×D13⋊C37
C2×C3×C7×D1513