Finite Group Databasebeta

← C5×D21×D13⋊C3 #30655413

Subgroups — C5×D21×D13⋊C3 #30655413

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
1C5×C13⋊C3×D21C211yesmaximal, characteristic, complemented
2C5×C3⋊((C13⋊C3)⋊D7)C211yesmaximal, characteristic, complemented
3C3×C5×C7×D13⋊C3C211yesmaximal, characteristic, complemented
4C5×D13×D21C311yesmaximal, characteristic, complemented
5C5×D7×D13⋊C3—31nomaximal
6C3×C5×C7×C13⋊C3C2211yescharacteristic, complemented, Hall
7D21×D13⋊C3C511yesmaximal, characteristic, direct product factor, Hall
8C5×(C13⋊C3)⋊D7—31no—
9C5×D7×C13⋊C3—31no—
10C5×C7×D13⋊C3—21no—
11C5×C7×D13⋊C3D311yescharacteristic, complemented
12C5×D273C2×C311yescharacteristic, complemented
13C5×C13×D21C2×C311yescharacteristic, complemented
14C3×C5×C7×D13C2×C311yescharacteristic, complemented
15C5×D3×D13⋊C3—71nomaximal, Hall
16C5×D7×D13—31noHall
17C3⋊((C13⋊C3)⋊D7)C2×C511yescharacteristic, complemented
18C13⋊C3×D21C2×C511yescharacteristic, complemented
19C3×C7×D13⋊C3C2×C511yescharacteristic, complemented
20C3×C5×C7×C13C22×C311yescharacteristic, complemented
21C5×C7×C13⋊C3—21no—
22C5×C7×C13⋊C3C2×D311yescharacteristic, complemented
23C2×C3×C5×D21—131nomaximal, Hall
24C5×C3⋊(D13⋊C3)—71no—
25C5×D3×C13⋊C3—71no—
26C3×C5×D13⋊C3D711yescharacteristic, complemented
27D13×D21C3×C511yescharacteristic, complemented
28D7×D13⋊C3—31no—
29C5×D91—31no—
30C5×C13×D7—31no—
31C5×C7×D13C3×D311yescharacteristic, complemented
32C3×C7×C13⋊C3C22×C511yescharacteristic, complemented, Hall
33C5×D3×D13—71no—
34C2×C5×D13⋊C3—211no—
35C2×C32×C5×C7—131no—
36C3×C5×D21—131no—
37C3×C5×D21—131no—
38C3×C5×C13⋊C3C2×D711yescharacteristic, complemented, Hall
39D273C2×C3×C511yescharacteristic, complemented
40C13×D21C2×C3×C511yescharacteristic, complemented
41C3×C7×D13C2×C3×C511yescharacteristic, complemented
42(C13⋊C3)⋊D7—31no—
43D7×C13⋊C3—31no—
44C7×D13⋊C3—21no—
45C7×D13⋊C3C5×D311yescharacteristic, complemented
46D3×D13⋊C3—71noHall
47C5×C7×C13C2×C3×D311yescharacteristic, complemented, Hall
48C2×C5×D21—131no—
49C2×C3×C5×D7—391no—
50C5×D39—71no—
51C5×D3×C13—71no—
52C3×C5×D13C3×D711yescharacteristic, complemented
53C2×C5×C13⋊C3—211no—
54C5×D13⋊C3—21no—
55C5×D13⋊C3—211no—
56C5×D13⋊C3D2111yescharacteristic, direct product factor
57D7×D13—31noHall
58C32×C5×C7—131noHall
59C3×C7×C13C22×C3×C511yescharacteristic, complemented
60C7×C13⋊C3—21no—
61C7×C13⋊C3C2×C5×D311yescharacteristic, complemented
62C2×C5×D13—211noHall
63C2×C3×D21—131noHall
64C3⋊(D13⋊C3)—71no—
65D3×C13⋊C3—71no—
66C3×D13⋊C3C5×D711yescharacteristic, complemented
67C2×C3×C5×C7—131no—
68C2×C3×C5×C7—131no—
69C2×C3×C5×C7—261no—
70C5×D21—131no—
71C5×D21D13⋊C311yescharacteristic, direct product factor
72C3×C5×D7—391no—
73C3×C5×D7—391no—
74C3×C5×C13C2×C3×D711yescharacteristic, complemented
75C5×C13⋊C3—21no—
76C5×C13⋊C3C2×D2111yescharacteristic, complemented
77D91—31no—
78C7×D13C3×C5×D311yescharacteristic, complemented
79C13×D7—31no—
80C2×C3×C5×D3—911noHall
81D3×D13—71no—
82C2×D13⋊C3—211no—
83C2×C5×D7—391noHall
84C2×C5×C13—211no—
85C5×D13—211no—
86C5×D13C3×D2111yescharacteristic, complemented
87C2×C32×C7—131no—
88C3×D21—131no—
89C3×D21—131no—
90C3×C13⋊C3C2×C5×D711yescharacteristic, complemented, Hall
91C3×C5×C7—131no—
92C3×C5×C7—261no—
93C3×C5×C7C2×D13⋊C311yescharacteristic, complemented
94C7×C13C2×C3×C5×D311yescharacteristic, complemented, Hall
95C2×C32×C5—131no—
96C3×C5×D3—911no—
97C3×C5×D3—911no—
98C2×D21—131no—
99C2×C3×D7—391no—
100D39—71no—
101C3×D13C3×C5×D711yescharacteristic, complemented
102D3×C13—71no—
103C2×C13⋊C3—211no—
104D13⋊C3—21no—
105D13⋊C3—211no—
106D13⋊C3C5×D2111yescharacteristic, direct product factor
107C2×C5×C7—131no—
108C5×D7—31no—
109C5×D7—391no—
110C5×C13C2×C3×D2111yescharacteristic, complemented, Hall
111C32×C7—131noHall
112C22×C3×C5—2731no—
113C2×C5×D3—911no—
114C2×D13—211noHall
115C32×C5—131noHall
116C2×C3×C7—131no—
117C2×C3×C7—131no—
118C2×C3×C7—261no—
119D21—131no—
120D21C5×D13⋊C311yescharacteristic, direct product factor
121C3×D7—391no—
122C3×D7—391no—
123C3×C13C2×C3×C5×D711yescharacteristic, complemented
124C13⋊C3—21no—
125C13⋊C3C2×C5×D2111yescharacteristic, complemented
126C2×C3×D3—911noHall
127C5×C7D3×D13⋊C311yescharacteristic, complemented, Hall
128C2×C3×C5—131no—
129C2×C3×C5—131no—
130C2×C3×C5—2731no—
131C2×C3×C5—2731no—
132C2×C3×C5—261no—
133C5×D3—71no—
134C5×D3—911no—
135C2×D7—391noHall
136C2×C13—211no—
137D13—211no—
138D13C3×C5×D2111yescharacteristic, complemented
139C3×C7—131no—
140C3×C7—261no—
141C3×C7C2×C5×D13⋊C311yescharacteristic, complemented
142C22×C5—2731noHall
143C2×C32—131no—
144C3×D3—911no—
145C3×D3—911no—
146C3×C5—131no—
147C3×C5—261no—
148C3×C5D7×D13⋊C311yescharacteristic, complemented
149C2×C7—131no—
150D7—31no—
151D7—391no—
152C13C2×C3×C5×D2111yescharacteristic, complemented, Sylow
153C22×C3—2731no—
154C2×D3—911no—
155C2×C5—131no—
156C2×C5—2731no—
157C2×C5—211no—
158C32—131noSylow
159C7C5×D3×D13⋊C311yescharacteristic, complemented, Sylow
160C2×C3—131no—
161C2×C3—131no—
162C2×C3—2731no—
163C2×C3—2731no—
164C2×C3—261no—
165D3—71no—
166D3—911no—
167C5D21×D13⋊C311yescharacteristic, direct product factor, Sylow
168C22—2731noSylow
169C3—131no—
170C3—261no—
171C3C5×D7×D13⋊C311yescharacteristic, complemented
172C2—131no—
173C2—2731no—
174C2—211no—
subgroupG/H
center, hypercenterC5D21×D13⋊C3
commutator, cosocle, hypocenterC3×C7×C13C22×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C13C22×C3
LCSG ▷ C3×C7×C13
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C5×C13⋊C3×D21C2semidirect
2. C5×C3⋊((C13⋊C3)⋊D7)C2semidirect
3. C3×C5×C7×D13⋊C3C2semidirect
4. C5×D13×D21C3semidirect
6. C3×C5×C7×C13⋊C3C22semidirect
7. D21×D13⋊C3C5direct (N × H)
11. C5×C7×D13⋊C3D3semidirect
12. C5×D273C2×C3semidirect
13. C5×C13×D21C2×C3semidirect
14. C3×C5×C7×D13C2×C3semidirect
17. C3⋊((C13⋊C3)⋊D7)C2×C5semidirect
18. C13⋊C3×D21C2×C5semidirect
19. C3×C7×D13⋊C3C2×C5semidirect
20. C3×C5×C7×C13C22×C3semidirect
22. C5×C7×C13⋊C3C2×D3semidirect
26. C3×C5×D13⋊C3D7semidirect
27. D13×D21C3×C5semidirect
31. C5×C7×D13C3×D3semidirect
32. C3×C7×C13⋊C3C22×C5semidirect
38. C3×C5×C13⋊C3C2×D7semidirect
39. D273C2×C3×C5semidirect
40. C13×D21C2×C3×C5semidirect
41. C3×C7×D13C2×C3×C5semidirect
45. C7×D13⋊C3C5×D3semidirect
47. C5×C7×C13C2×C3×D3semidirect
52. C3×C5×D13C3×D7semidirect
56. C5×D13⋊C3D21direct (N × H)
59. C3×C7×C13C22×C3×C5semidirect
61. C7×C13⋊C3C2×C5×D3semidirect
66. C3×D13⋊C3C5×D7semidirect
71. C5×D21D13⋊C3direct (N × H)
74. C3×C5×C13C2×C3×D7semidirect
76. C5×C13⋊C3C2×D21semidirect
78. C7×D13C3×C5×D3semidirect
86. C5×D13C3×D21semidirect
90. C3×C13⋊C3C2×C5×D7semidirect
93. C3×C5×C7C2×D13⋊C3semidirect
94. C7×C13C2×C3×C5×D3semidirect
101. C3×D13C3×C5×D7semidirect
106. D13⋊C3C5×D21direct (N × H)
110. C5×C13C2×C3×D21semidirect
120. D21C5×D13⋊C3direct (N × H)
123. C3×C13C2×C3×C5×D7semidirect
125. C13⋊C3C2×C5×D21semidirect
127. C5×C7D3×D13⋊C3semidirect
138. D13C3×C5×D21semidirect
141. C3×C7C2×C5×D13⋊C3semidirect
148. C3×C5D7×D13⋊C3semidirect
152. C13C2×C3×C5×D21semidirect
159. C7C5×D3×D13⋊C3semidirect
167. C5D21×D13⋊C3direct (N × H)
171. C3C5×D7×D13⋊C3semidirect

Maximal subgroups

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

subgroupindex
C5×C13⋊C3×D212
C5×C3⋊((C13⋊C3)⋊D7)2
C3×C5×C7×D13⋊C32
C5×D13×D213
C5×D7×D13⋊C33
D21×D13⋊C35
C5×D3×D13⋊C37
C2×C3×C5×D2113