Finite Group Databasebeta

← C3×C3⋊D3×D15 #13108546

Subgroups — C3×C3⋊D3×D15 #13108546

Order 1620.

448 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 72 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×C3⋊(C3⋊D15)C211yesmaximal, characteristic, complemented
2C32×C5×C3⋊D3C211yesmaximal, characteristic, complemented
3C33×D15C211yesmaximal, characteristic, complemented
4C3⋊D3×D15C311yesmaximal, characteristic, direct product factor
5C3×D3×D15—34nomaximal
6C3×D5×C3⋊D3—31nomaximal
7C34×C5C2211yescharacteristic, complemented, Hall
8C3×D3×C3⋊D3—51nomaximal, Hall
9C3⋊(C3⋊D15)C2×C311yescharacteristic, complemented
10C3×C3⋊D15—31no—
11C3×C3⋊D15—34no—
12C3×C3⋊D15—64no—
13C3×C5×C3⋊D3—21no—
14C3×C5×C3⋊D3D311yescharacteristic, complemented
15C3×C5×C3⋊D3C2×C311yescharacteristic, complemented
16C32×D15—24no—
17C32×D15D314yescomplemented
18C32×D15C2×C311yescharacteristic, complemented
19C32×C5×D3—34no—
20C33×D5—31no—
21C2×C3×D15—91no—
22D3×D15—34no—
23D5×C3⋊D3—31no—
24C3×D3×D5—94no—
25C3×C3⋊(C3⋊D3)—51no—
26C32×C3⋊D3D511yescharacteristic, complemented
27C33×D3—51no—
28C33×C5—24no—
29C33×C5—24no—
30C33×C5—21no—
31C33×C5—44no—
32C33×C5C2×D314yescomplemented
33C33×C5C2×D311yescharacteristic, complemented
34C33×C5C22×C311yescharacteristic, complemented
35C2×C3×C3⋊D3—151no—
36D3×C3⋊D3—51no—
37C3×D32—154no—
38C2×C32×C5—91no—
39C3⋊D15—31no—
40C3⋊D15—34no—
41C3⋊D15—64no—
42C5×C3⋊D3C3×D311yescharacteristic, complemented
43C3×D15—24no—
44C3×D15—94no—
45C3×D15—91no—
46C3×D15—184no—
47C3×D15C3×D314yescomplemented
48C3×D15C3⋊D311yescharacteristic, direct product factor
49C3×C5×D3—34no—
50C3×C5×D3—34no—
51C3×C5×D3—64no—
52C32×D5—31no—
53C32×D5—34no—
54C32×D5—64no—
55C34C2×D511yescharacteristic, complemented, Sylow
56C2×D15—91no—
57C2×C3×D5—271no—
58D3×D5—94no—
59C2×C33—151no—
60C3⋊(C3⋊D3)—51no—
61C3×C3⋊D3—21no—
62C3×C3⋊D3—151no—
63C3×C3⋊D3—154no—
64C3×C3⋊D3—304no—
65C3×C3⋊D3C3×D511yescharacteristic, complemented
66C3×C3⋊D3D1511yescharacteristic, direct product factor
67C32×D3—34no—
68C32×D3—51no—
69C32×D3—54no—
70C32×D3—104no—
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—151no—
84C2×C3×D3—454no—
85C2×C3×D3—451no—
86D32—154no—
87C2×C3×C5—91no—
88C2×C3×C5—91no—
89C2×C3×C5—181no—
90D15—94no—
91D15—91no—
92D15—184no—
93D15C3×C3⋊D311yescharacteristic, direct product factor
94C3×D5—34no—
95C3×D5—31no—
96C3×D5—64no—
97C3×D5—271no—
98C5×D3—34no—
99C33—24no—
100C33—24no—
101C33—21no—
102C33—44no—
103C33D3×D514yescomplemented
104C33C2×C3×D511yescharacteristic, complemented
105C33C2×D1511yescharacteristic, complemented
106C2×D5—271noHall
107C2×C32—91no—
108C2×C32—151no—
109C2×C32—154no—
110C2×C32—304no—
111C3⋊D3—151no—
112C3⋊D3—154no—
113C3⋊D3—304no—
114C3⋊D3C3×D1511yescharacteristic, direct product factor
115C3×D3—34no—
116C3×D3—34no—
117C3×D3—54no—
118C3×D3—51no—
119C3×D3—64no—
120C3×D3—104no—
121C3×D3—451no—
122C3×D3—454no—
123C3×D3—904no—
124C3×C5—24no—
125C3×C5—24no—
126C3×C5—21no—
127C3×C5—44no—
128C3×C5C3×D3214yescomplemented
129C3×C5D3×C3⋊D311yescharacteristic, complemented
130C3×C5C2×C3×C3⋊D311yescharacteristic, complemented
131C22×C3—1351no—
132C2×D3—454no—
133C2×D3—451no—
134C2×C5—91no—
135D5—31no—
136D5—271no—
137C32—24no—
138C32—24no—
139C32—24no—
140C32—24no—
141C32—24no—
142C32—44no—
143C32—412no—
144C32—44no—
145C32C3×D3×D514yescomplemented
146C32D5×C3⋊D311yescharacteristic, complemented
147C32D3×D1514yescomplemented
148C32C2×C3×D1511yescharacteristic, complemented
149C2×C3—91no—
150C2×C3—91no—
151C2×C3—154no—
152C2×C3—151no—
153C2×C3—181no—
154C2×C3—304no—
155C2×C3—1351no—
156D3—34no—
157D3—51no—
158D3—451no—
159D3—454no—
160D3—904no—
161C5C3×D3×C3⋊D311yescharacteristic, complemented, Sylow
162C22—1351noSylow
163C3—24no—
164C3—21no—
165C3—24no—
166C3—44no—
167C3C3×D5×C3⋊D311yescharacteristic, complemented
168C3C3×D3×D1514yescomplemented
169C3C3⋊D3×D1511yescharacteristic, direct product factor
170C2—91no—
171C2—151no—
172C2—1351no—
subgroupG/H
center, hypercenterC3C3⋊D3×D15
commutator, cosocle, hypocenterC33×C5C22×C3
FrattiniC1G
Fitting, socleC34×C5C22
LCSG ▷ C33×C5
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C3⋊(C3⋊D15)C2semidirect
2. C32×C5×C3⋊D3C2semidirect
3. C33×D15C2semidirect
4. C3⋊D3×D15C3direct (N × H)
7. C34×C5C22semidirect
9. C3⋊(C3⋊D15)C2×C3semidirect
14. C3×C5×C3⋊D3D3semidirect
15. C3×C5×C3⋊D3C2×C3semidirect
17. C32×D15D3semidirect
18. C32×D15C2×C3semidirect
26. C32×C3⋊D3D5semidirect
32. C33×C5C2×D3semidirect
33. C33×C5C2×D3semidirect
34. C33×C5C22×C3semidirect
42. C5×C3⋊D3C3×D3semidirect
47. C3×D15C3×D3semidirect
48. C3×D15C3⋊D3direct (N × H)
55. C34C2×D5semidirect
65. C3×C3⋊D3C3×D5semidirect
66. C3×C3⋊D3D15direct (N × H)
79. C32×C5D32semidirect
80. C32×C5C2×C3×D3semidirect
81. C32×C5C2×C3×D3semidirect
82. C32×C5C2×C3⋊D3semidirect
93. D15C3×C3⋊D3direct (N × H)
103. C33D3×D5semidirect
104. C33C2×C3×D5semidirect
105. C33C2×D15semidirect
114. C3⋊D3C3×D15direct (N × H)
128. C3×C5C3×D32semidirect
129. C3×C5D3×C3⋊D3semidirect
130. C3×C5C2×C3×C3⋊D3semidirect
145. C32C3×D3×D5semidirect
146. C32D5×C3⋊D3semidirect
147. C32D3×D15semidirect
148. C32C2×C3×D15semidirect
161. C5C3×D3×C3⋊D3semidirect
167. C3C3×D5×C3⋊D3semidirect
168. C3C3×D3×D15semidirect
169. C3C3⋊D3×D15direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C3⋊(C3⋊D15)2
C32×C5×C3⋊D32
C33×D152
C3⋊D3×D153
C3×D3×D153
C3×D5×C3⋊D33
C3×D3×C3⋊D35