Finite Group Databasebeta

← C3×D15⋊(C3⋊D3) #13108547

Subgroups — C3×D15⋊(C3⋊D3) #13108547

Order 1620.

448 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 70 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×C3⋊D15C211yesmaximal, characteristic, complemented
3C33×D15C211yesmaximal, characteristic, complemented
4D15⋊(C3⋊D3)C311yesmaximal, characteristic, direct product factor
5C3×(C3⋊D3)⋊D5—34nomaximal
6C3×D5×C3⋊D3—31nomaximal
7C34×C5C2211yescharacteristic, complemented, Hall
8C3×D3×C3⋊D3—51nomaximal, Hall
9C5×C3⋊(C3⋊D3)C2×C311yescharacteristic, complemented
10C3×C3⋊D15—21no—
11C3×C3⋊D15D311yescharacteristic, complemented
12C3×C3⋊D15C2×C311yescharacteristic, complemented
13C3×C5×C3⋊D3—31no—
14C3×C5×C3⋊D3—34no—
15C3×C5×C3⋊D3—64no—
16C32×D15—24no—
17C32×D15—34no—
18C32×D15D314yescomplemented
19C32×D15C2×C311yescharacteristic, complemented
20C33×D5—31no—
21(C3⋊D3)⋊D5—34no—
22D5×C3⋊D3—31no—
23C3×D3×D5—94no—
24C3×D3×D5—91no—
25C3×C3⋊(C3⋊D3)D511yescharacteristic, complemented
26C32×C3⋊D3—51no—
27C33×D3—51no—
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—151no—
36D3×C3⋊D3—51no—
37C3×D32—154no—
38C3⋊D15C3×D311yescharacteristic, complemented
39C5×C3⋊D3—31no—
40C5×C3⋊D3—34no—
41C5×C3⋊D3—64no—
42C3×D15—24no—
43C3×D15—34no—
44C3×D15—34no—
45C3×D15—64no—
46C3×D15C3×D314yescomplemented
47C3×D15C3⋊D311yescharacteristic, complemented
48C3×C5×D3—94no—
49C3×C5×D3—91no—
50C3×C5×D3—184no—
51C32×D5—31no—
52C32×D5—34no—
53C32×D5—64no—
54C32×D5—91no—
55C34C2×D511yescharacteristic, complemented, Sylow
56C2×C3×D5—271no—
57D3×D5—94no—
58D3×D5—91no—
59C2×C33—151no—
60C3⋊(C3⋊D3)C3×D511yescharacteristic, complemented
61C3×C3⋊D3—31no—
62C3×C3⋊D3—34no—
63C3×C3⋊D3—51no—
64C3×C3⋊D3—51no—
65C3×C3⋊D3—64no—
66C3×C3⋊D3—101no—
67C32×D3—51no—
68C32×D3—54no—
69C32×D3—104no—
70C32×D3—154no—
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—451no—
85C2×C3×D3—454no—
86D32—154no—
87C2×C3×C5—271no—
88D15—34no—
89D15C3×C3⋊D311yescharacteristic, complemented
90C3×D5—34no—
91C3×D5—31no—
92C3×D5—64no—
93C3×D5—91no—
94C3×D5—91no—
95C3×D5—181no—
96C5×D3—94no—
97C5×D3—91no—
98C5×D3—184no—
99C33—24no—
100C33—21no—
101C33—24no—
102C33—44no—
103C33D3×D511yescharacteristic, complemented
104C33D3×D514yescomplemented
105C33C2×C3×D511yescharacteristic, complemented
106C2×D5—271noHall
107C2×C32—151no—
108C2×C32—154no—
109C2×C32—304no—
110C2×C32—451no—
111C3⋊D3—31no—
112C3⋊D3—34no—
113C3⋊D3—51no—
114C3⋊D3—64no—
115C3×D3—54no—
116C3×D3—51no—
117C3×D3—91no—
118C3×D3—94no—
119C3×D3—104no—
120C3×D3—154no—
121C3×D3—154no—
122C3×D3—184no—
123C3×D3—304no—
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—451no—
133C2×D3—454no—
134C2×C5—271no—
135D5—31no—
136D5—91no—
137C32—24no—
138C32—24no—
139C32—24no—
140C32—24no—
141C32—24no—
142C32—44no—
143C32—412no—
144C32—44no—
145C32C3×D3×D514yescomplemented
146C32C3×D3×D511yescharacteristic, complemented
147C32D5×C3⋊D311yescharacteristic, complemented
148C32(C3⋊D3)⋊D514yescomplemented
149C2×C3—154no—
150C2×C3—151no—
151C2×C3—271no—
152C2×C3—304no—
153C2×C3—451no—
154C2×C3—451no—
155C2×C3—901no—
156D3—51no—
157D3—91no—
158D3—94no—
159D3—154no—
160D3—184no—
161C5C3×D3×C3⋊D311yescharacteristic, complemented, Sylow
162C22—1351noSylow
163C3—24no—
164C3—24no—
165C3—21no—
166C3—44no—
167C3C3×D5×C3⋊D311yescharacteristic, complemented
168C3C3×(C3⋊D3)⋊D514yescomplemented
169C3D15⋊(C3⋊D3)11yescharacteristic, direct product factor
170C2—151no—
171C2—271no—
172C2—451no—
subgroupG/H
center, hypercenterC3D15⋊(C3⋊D3)
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×C5×C3⋊(C3⋊D3)C2semidirect
2. C32×C3⋊D15C2semidirect
3. C33×D15C2semidirect
4. D15⋊(C3⋊D3)C3direct (N × H)
7. C34×C5C22semidirect
9. C5×C3⋊(C3⋊D3)C2×C3semidirect
11. C3×C3⋊D15D3semidirect
12. C3×C3⋊D15C2×C3semidirect
18. C32×D15D3semidirect
19. C32×D15C2×C3semidirect
25. C3×C3⋊(C3⋊D3)D5semidirect
32. C33×C5C2×D3semidirect
33. C33×C5C2×D3semidirect
34. C33×C5C22×C3semidirect
38. C3⋊D15C3×D3semidirect
46. C3×D15C3×D3semidirect
47. C3×D15C3⋊D3semidirect
55. C34C2×D5semidirect
60. C3⋊(C3⋊D3)C3×D5semidirect
79. C32×C5D32semidirect
80. C32×C5C2×C3×D3semidirect
81. C32×C5C2×C3×D3semidirect
82. C32×C5C2×C3⋊D3semidirect
89. D15C3×C3⋊D3semidirect
103. C33D3×D5semidirect
104. C33D3×D5semidirect
105. C33C2×C3×D5semidirect
128. C3×C5C3×D32semidirect
129. C3×C5D3×C3⋊D3semidirect
130. C3×C5C2×C3×C3⋊D3semidirect
145. C32C3×D3×D5semidirect
146. C32C3×D3×D5semidirect
147. C32D5×C3⋊D3semidirect
148. C32(C3⋊D3)⋊D5semidirect
161. C5C3×D3×C3⋊D3semidirect
167. C3C3×D5×C3⋊D3semidirect
168. C3C3×(C3⋊D3)⋊D5semidirect
169. C3D15⋊(C3⋊D3)direct (N × H)

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×C3⋊D152
C33×D152
D15⋊(C3⋊D3)3
C3×(C3⋊D3)⋊D53
C3×D5×C3⋊D33
C3×D3×C3⋊D35