Finite Group Databasebeta

← C3×C5×D3×C3⋊D3 #13108544

Subgroups — C3×C5×D3×C3⋊D3 #13108544

Order 1620.

448 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 88 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×C5×C3⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C32×C5×C3⋊D3C211yesmaximal, characteristic, complemented
3C33×C5×D3C211yesmaximal, characteristic, complemented
4C2×C3×C5×C3⋊D3—31nomaximal
5C5×D3×C3⋊D3C311yesmaximal, characteristic, direct product factor
6C3×C5×D32—34nomaximal
7C34×C5C2211yescharacteristic, complemented, Hall
8C3×D3×C3⋊D3C511yesmaximal, characteristic, direct product factor, Hall
9C2×C33×C5—31no—
10C5×C3⋊(C3⋊D3)C2×C311yescharacteristic, complemented
11C3×C5×C3⋊D3—21no—
12C3×C5×C3⋊D3—31no—
13C3×C5×C3⋊D3—34no—
14C3×C5×C3⋊D3—64no—
15C3×C5×C3⋊D3D311yescharacteristic, direct product factor
16C3×C5×C3⋊D3C2×C311yescharacteristic, complemented
17C32×C5×D3—24no—
18C32×C5×D3—34no—
19C32×C5×D3D314yescomplemented
20C32×C5×D3C2×C311yescharacteristic, complemented
21C2×C5×C3⋊D3—31no—
22C2×C3×C5×D3—94no—
23C2×C3×C5×D3—91no—
24C5×D32—34no—
25C3×C3⋊(C3⋊D3)C2×C511yescharacteristic, complemented
26C32×C3⋊D3C2×C511yescharacteristic, complemented
27C33×D3C2×C511yescharacteristic, complemented
28C33×C5—24no—
29C33×C5—24no—
30C33×C5—21no—
31C33×C5—44no—
32C33×C5C2×D311yescharacteristic, complemented
33C33×C5C2×D314yescomplemented
34C33×C5C22×C311yescharacteristic, complemented
35C2×C3×C3⋊D3—31no—
36D3×C3⋊D3C3×C511yescharacteristic, direct product factor
37C3×D32—34no—
38C2×C32×C5—31no—
39C2×C32×C5—34no—
40C2×C32×C5—64no—
41C2×C32×C5—91no—
42C5×C3⋊D3—31no—
43C5×C3⋊D3—34no—
44C5×C3⋊D3—64no—
45C5×C3⋊D3C3×D311yescharacteristic, direct product factor
46C3×C5×D3—24no—
47C3×C5×D3—34no—
48C3×C5×D3—34no—
49C3×C5×D3—64no—
50C3×C5×D3—94no—
51C3×C5×D3—91no—
52C3×C5×D3—184no—
53C3×C5×D3C3×D314yescomplemented
54C3×C5×D3C3⋊D311yescharacteristic, direct product factor
55C34C22×C511yescharacteristic, complemented, Sylow
56C22×C3×C5—271no—
57C2×C5×D3—94no—
58C2×C5×D3—91no—
59C2×C33—31no—
60C3⋊(C3⋊D3)C2×C3×C511yescharacteristic, complemented
61C3×C3⋊D3—21no—
62C3×C3⋊D3—31no—
63C3×C3⋊D3—34no—
64C3×C3⋊D3—64no—
65C3×C3⋊D3C5×D311yescharacteristic, direct product factor
66C3×C3⋊D3C2×C3×C511yescharacteristic, complemented
67C32×D3—24no—
68C32×D3—34no—
69C32×D3C5×D314yescomplemented
70C32×D3C2×C3×C511yescharacteristic, complemented
71C32×C5—24no—
72C32×C5—24no—
73C32×C5—24no—
74C32×C5—24no—
75C32×C5—24no—
76C32×C5—44no—
77C32×C5—412no—
78C32×C5—44no—
79C32×C5D3214yescomplemented
80C32×C5C2×C3×D314yescomplemented
81C32×C5C2×C3×D311yescharacteristic, complemented
82C32×C5C2×C3⋊D311yescharacteristic, complemented
83C2×C3⋊D3—31no—
84C2×C3×D3—94no—
85C2×C3×D3—91no—
86D32—34no—
87C2×C3×C5—34no—
88C2×C3×C5—31no—
89C2×C3×C5—64no—
90C2×C3×C5—91no—
91C2×C3×C5—91no—
92C2×C3×C5—181no—
93C2×C3×C5—271no—
94C5×D3—34no—
95C5×D3—94no—
96C5×D3—91no—
97C5×D3—184no—
98C5×D3C3×C3⋊D311yescharacteristic, direct product factor
99C33—24no—
100C33—24no—
101C33—21no—
102C33—44no—
103C33C2×C5×D311yescharacteristic, complemented
104C33C2×C5×D314yescomplemented
105C33C22×C3×C511yescharacteristic, complemented
106C22×C5—271noHall
107C2×C32—31no—
108C2×C32—34no—
109C2×C32—64no—
110C2×C32—91no—
111C3⋊D3—31no—
112C3⋊D3—34no—
113C3⋊D3—64no—
114C3⋊D3C3×C5×D311yescharacteristic, direct product factor
115C3×D3—24no—
116C3×D3—34no—
117C3×D3—34no—
118C3×D3—64no—
119C3×D3—94no—
120C3×D3—91no—
121C3×D3—184no—
122C3×D3C3×C5×D314yescomplemented
123C3×D3C5×C3⋊D311yescharacteristic, direct product factor
124C3×C5—24no—
125C3×C5—24no—
126C3×C5—21no—
127C3×C5—44no—
128C3×C5C3×D3214yescomplemented
129C3×C5D3×C3⋊D311yescharacteristic, direct product factor
130C3×C5C2×C3×C3⋊D311yescharacteristic, complemented
131C22×C3—271no—
132C2×D3—94no—
133C2×D3—91no—
134C2×C5—31no—
135C2×C5—91no—
136C2×C5—271no—
137C32—24no—
138C32—24no—
139C32—24no—
140C32—24no—
141C32—24no—
142C32—44no—
143C32—412no—
144C32—44no—
145C32C5×D3214yescomplemented
146C32C2×C3×C5×D314yescomplemented
147C32C2×C3×C5×D311yescharacteristic, complemented
148C32C2×C5×C3⋊D311yescharacteristic, complemented
149C2×C3—34no—
150C2×C3—31no—
151C2×C3—64no—
152C2×C3—91no—
153C2×C3—91no—
154C2×C3—181no—
155C2×C3—271no—
156D3—34no—
157D3—94no—
158D3—91no—
159D3—184no—
160D3C3×C5×C3⋊D311yescharacteristic, direct product factor
161C5C3×D3×C3⋊D311yescharacteristic, direct product factor, Sylow
162C22—271noSylow
163C3—24no—
164C3—24no—
165C3—21no—
166C3—44no—
167C3C3×C5×D3214yescomplemented
168C3C5×D3×C3⋊D311yescharacteristic, direct product factor
169C3C2×C3×C5×C3⋊D311yescharacteristic, complemented
170C2—31no—
171C2—91no—
172C2—271no—
subgroupG/H
center, hypercenterC3×C5D3×C3⋊D3
commutator, cosocle, hypocenterC33C22×C3×C5
FrattiniC1G
Fitting, socleC34×C5C22
LCSG ▷ C33
UCSC1 ◁ C3×C5

Complements

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

NH ≅ G/Ntype
1. C3×C5×C3⋊(C3⋊D3)C2semidirect
2. C32×C5×C3⋊D3C2semidirect
3. C33×C5×D3C2semidirect
5. C5×D3×C3⋊D3C3direct (N × H)
7. C34×C5C22semidirect
8. C3×D3×C3⋊D3C5direct (N × H)
10. C5×C3⋊(C3⋊D3)C2×C3semidirect
15. C3×C5×C3⋊D3D3direct (N × H)
16. C3×C5×C3⋊D3C2×C3semidirect
19. C32×C5×D3D3semidirect
20. C32×C5×D3C2×C3semidirect
25. C3×C3⋊(C3⋊D3)C2×C5semidirect
26. C32×C3⋊D3C2×C5semidirect
27. C33×D3C2×C5semidirect
32. C33×C5C2×D3semidirect
33. C33×C5C2×D3semidirect
34. C33×C5C22×C3semidirect
36. D3×C3⋊D3C3×C5direct (N × H)
45. C5×C3⋊D3C3×D3direct (N × H)
53. C3×C5×D3C3×D3semidirect
54. C3×C5×D3C3⋊D3direct (N × H)
55. C34C22×C5semidirect
60. C3⋊(C3⋊D3)C2×C3×C5semidirect
65. C3×C3⋊D3C5×D3direct (N × H)
66. C3×C3⋊D3C2×C3×C5semidirect
69. C32×D3C5×D3semidirect
70. C32×D3C2×C3×C5semidirect
79. C32×C5D32semidirect
80. C32×C5C2×C3×D3semidirect
81. C32×C5C2×C3×D3semidirect
82. C32×C5C2×C3⋊D3semidirect
98. C5×D3C3×C3⋊D3direct (N × H)
103. C33C2×C5×D3semidirect
104. C33C2×C5×D3semidirect
105. C33C22×C3×C5semidirect
114. C3⋊D3C3×C5×D3direct (N × H)
122. C3×D3C3×C5×D3semidirect
123. C3×D3C5×C3⋊D3direct (N × H)
128. C3×C5C3×D32semidirect
129. C3×C5D3×C3⋊D3direct (N × H)
130. C3×C5C2×C3×C3⋊D3semidirect
145. C32C5×D32semidirect
146. C32C2×C3×C5×D3semidirect
147. C32C2×C3×C5×D3semidirect
148. C32C2×C5×C3⋊D3semidirect
160. D3C3×C5×C3⋊D3direct (N × H)
161. C5C3×D3×C3⋊D3direct (N × H)
167. C3C3×C5×D32semidirect
168. C3C5×D3×C3⋊D3direct (N × H)
169. C3C2×C3×C5×C3⋊D3semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C3⋊(C3⋊D3)2
C32×C5×C3⋊D32
C33×C5×D32
C2×C3×C5×C3⋊D33
C5×D3×C3⋊D33
C3×C5×D323
C3×D3×C3⋊D35