Finite Group Databasebeta

← C3⋊D3×D5⋊C8 #13088664

Subgroups — C3⋊D3×D5⋊C8 #13088664

Order 1440.

456 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 116 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
1C4×D5×C3⋊D3C211yesmaximal, characteristic
2D5⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic, complemented
3C32×D5⋊C8C211yesmaximal, characteristic, complemented
4#10623967C212yesmaximal, complemented
5C3⋊D3×#170C212yesmaximal, complemented
6D3×D5⋊C8—34nomaximal
7C2×D5×C3⋊D3C411yescharacteristic
8C4×C3⋊D15C411yescharacteristic
9C4×C5×C3⋊D3C411yescharacteristic
10C32×C4×D5C2211yescharacteristic
11#67137C2211yescharacteristic
12C3⋊D3×Dic5C2211yescharacteristic
13D5×C3⋊Dic3C411yescharacteristic
14C3⋊(C3⋊#170)C2212yescomplemented
15C32×#170C2212yescomplemented
16C2×C8×C3⋊D3—51nomaximal, Hall
17C4×D3×D5—34no—
18D5⋊(C3⋊C8)—34no—
19C3×D5⋊C8D314yescomplemented
20#6738—38no—
21D3×#170—38no—
22C2×C3⋊D15C2×C411yescharacteristic
23C2×C5×C3⋊D3C2×C411yescharacteristic
24C2×C32×D5C2×C411yescharacteristic
25D5×C3⋊D3C814yescomplemented
26C32×C4×C5C2×C411yescharacteristic
27C3⋊Dic15C2×C411yescharacteristic
28C5×C3⋊Dic3C2×C411yescharacteristic
29C32×Dic5C2311yescharacteristic
30C2×D5⋊C8—91noHall
31C2×C4×C3⋊D3—51no—
32C2×C32×C8—51no—
33C2×C3⋊(C3⋊C8)—51no—
34C8×C3⋊D3—52no—
35C8×C3⋊D3—52no—
36C2×D3×D5—34no—
37C4×D15—34no—
38C4×C5×D3—34no—
39C3×C4×D5C2×D314yes—
40#1200—34no—
41D3×Dic5—34no—
42D5×Dic3—34no—
43C3⋊#170—38no—
44C3×#170C2×D318yescomplemented
45C2×D3×C8—154no—
46C2×C32×C5C22×C411yescharacteristic
47C3⋊D15C2×C812yescomplemented
48C5×C3⋊D3C2×C812yescomplemented
49C32×D5C2×C812yescomplemented
50C2×C4×D5—91no—
51C2×#170—92no—
52D5⋊C8—91no—
53D5⋊C8—92no—
54D5⋊C8C3⋊D311yescharacteristic, direct product factor
55C22×C3⋊D3—51no—
56C2×C32×C4—51no—
57C2×C3⋊Dic3—51no—
58C4×C3⋊D3—51no—
59C4×C3⋊D3—51no—
60C4×C3⋊D3—51no—
61C4×C3⋊D3AGL(1,𝔽5)11yescharacteristic
62C32×C8—52no—
63C3⋊(C3⋊C8)—52no—
64C2×D15—34no—
65C2×C5×D3—34no—
66C2×C3×D5C4×D314yes—
67D3×D5—316no—
68C3×C4×C5C4×D314yes—
69Dic15—34no—
70C3×Dic5C22×D314yes—
71C5×Dic3—34no—
72C2×C4×D3—154no—
73C2×C3×C8—54no—
74C2×C3⋊C8—154no—
75D3×C8—158no—
76D3×C8—158no—
77C32×C5C22×C811yescharacteristic, complemented, Hall
78C22×D5—91no—
79C2×C4×C5—91no—
80C2×Dic5—91no—
81C4×D5—91no—
82C4×D5—91no—
83C4×D5—91no—
84C4×D5C2×C3⋊D311yescharacteristic
85#170—92no—
86#170C2×C3⋊D312yescomplemented
87C22×C32—51no—
88C2×C3⋊D3—51no—
89C2×C3⋊D3—54no—
90C2×C3⋊D3C2×AGL(1,𝔽5)11yescharacteristic
91C32×C4—51no—
92C32×C4C2×AGL(1,𝔽5)11yescharacteristic
93C3⋊Dic3—51no—
94C3⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
95C22×C8—451noSylow
96C2×C3×C5C2×C4×D314yes—
97D15—38no—
98C3×D5D3×C818yescomplemented
99C5×D3—38no—
100C22×D3—154no—
101C2×C3×C4—54no—
102C2×Dic3—154no—
103C4×D3—34no—
104C4×D3—154no—
105C4×D3—154no—
106C4×D3—154no—
107C3×C8—58no—
108C3⋊C8—158no—
109C22×C5—91no—
110C2×D5—91no—
111C2×D5—94no—
112C2×D5C4×C3⋊D311yescharacteristic
113C4×C5—91no—
114C4×C5C4×C3⋊D311yescharacteristic
115Dic5—91no—
116Dic5C22×C3⋊D311yescharacteristic
117C2×C32—52no—
118C2×C32C22×AGL(1,𝔽5)11yescharacteristic
119C3⋊D3—52no—
120C3⋊D3D5⋊C812yesdirect product factor
121C22×C4—451no—
122C2×C8—51no—
123C2×C8—452no—
124C2×C8—452no—
125C2×C8—451no—
126C3×C5C2×D3×C814yescomplemented
127C22×C3—54no—
128C2×D3—34no—
129C2×D3—1516no—
130C2×D3—154no—
131C3×C4—54no—
132C3×C4D3×AGL(1,𝔽5)14yes—
133Dic3—34no—
134Dic3—154no—
135C2×C5—92no—
136C2×C5C2×C4×C3⋊D311yescharacteristic
137D5—92no—
138D5C8×C3⋊D312yescomplemented
139C32C2×D5⋊C811yescharacteristic, complemented, Sylow
140C23—451no—
141C2×C4—51no—
142C2×C4—91no—
143C2×C4—451no—
144C2×C4—451no—
145C2×C4—451no—
146C2×C4—451no—
147C8—52no—
148C8—452no—
149C2×C3—58no—
150C2×C3C2×D3×AGL(1,𝔽5)14yes—
151D3—38no—
152D3—158no—
153C5C2×C8×C3⋊D311yescharacteristic, complemented, Sylow
154C22—51no—
155C22—91no—
156C22—454no—
157C22—451no—
158C4—51no—
159C4—91no—
160C4—451no—
161C4C3⋊D3×AGL(1,𝔽5)11yescharacteristic
162C3D3×D5⋊C814yescomplemented
163C2—52no—
164C2—92no—
165C2—452no—
166C2C2×C3⋊D3×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, hypercenterC4C3⋊D3×AGL(1,𝔽5)
commutator, hypocenterC32×C5C22×C8
FrattiniC2C2×C3⋊D3×AGL(1,𝔽5)
FittingC32×C4×C5C2×C4
socleC2×C32×C5C22×C4
prime radicalC2×D5×C3⋊D3C4
cosocleC32×Dic5C23
LCSG ▷ C32×C5
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. D5⋊(C3⋊(C3⋊C8))C2semidirect
3. C32×D5⋊C8C2semidirect
4. #10623967C2semidirect
5. C3⋊D3×#170C2semidirect
14. C3⋊(C3⋊#170)C22semidirect
15. C32×#170C22semidirect
19. C3×D5⋊C8D3semidirect
25. D5×C3⋊D3C8semidirect
44. C3×#170C2×D3semidirect
47. C3⋊D15C2×C8semidirect
48. C5×C3⋊D3C2×C8semidirect
49. C32×D5C2×C8semidirect
54. D5⋊C8C3⋊D3direct (N × H)
77. C32×C5C22×C8semidirect
86. #170C2×C3⋊D3semidirect
98. C3×D5D3×C8semidirect
120. C3⋊D3D5⋊C8direct (N × H)
126. C3×C5C2×D3×C8semidirect
138. D5C8×C3⋊D3semidirect
139. C32C2×D5⋊C8semidirect
153. C5C2×C8×C3⋊D3semidirect
162. C3D3×D5⋊C8semidirect

Maximal subgroups

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

subgroupindex
C4×D5×C3⋊D32
D5⋊(C3⋊(C3⋊C8))2
C32×D5⋊C82
#106239672
C3⋊D3×#1702
D3×D5⋊C83
C2×C8×C3⋊D35