Finite Group Databasebeta

← C3⋊D3×C4⋊Dic5 #13086886

Subgroups — C3⋊D3×C4⋊Dic5 #13086886

Order 1440.

552 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 160 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
1C2×C4×C5×C3⋊D3C211yesmaximal, characteristic
2C2×C3⋊D3×Dic5C212yesmaximal
3C4⋊(C3⋊Dic15)C211yesmaximal, characteristic, complemented
4C32×C4⋊Dic5C211yesmaximal, characteristic, complemented
5#10623775C212yesmaximal, complemented
6D3×C4⋊Dic5—34nomaximal
7C22×C5×C3⋊D3C2211yescharacteristic
8C2×C32×C4×C5C2211yescharacteristic
9C2×C3⋊Dic15C2212yes—
10C2×C5×C3⋊Dic3C2211yescharacteristic
11C4×C5×C3⋊D3C414yescomplemented
12C2×C32×Dic5C2212yes—
13C3⋊D3×Dic5—24no—
14C4⋊C4×C3⋊D3—51nomaximal, Hall
15C2×C4×C5×D3—34no—
16C2×D3×Dic5—38no—
17C4⋊Dic15—34no—
18C3×C4⋊Dic5D314yescomplemented
19Dic3⋊Dic5—38no—
20C22×C32×C5C2311yescharacteristic
21C2×C5×C3⋊D3C2×C412yes—
22C2×C5×C3⋊D3D412yes—
23C2×C5×C3⋊D3Q812yes—
24C32×C4×C5C2×C412yescomplemented
25C3⋊Dic15—22no—
26C5×C3⋊Dic3C2×C412yescomplemented
27C32×Dic5—22no—
28C2×C4⋊Dic5—91noHall
29C2×C4×C3⋊D3—52no—
30C2×C4×C3⋊D3D511yescharacteristic
31C32×C4⋊C4—51no—
32C4⋊(C3⋊Dic3)—51no—
33#3750—52no—
34C22×C5×D3—34no—
35C2×C3×C4×C5C2×D314yes—
36C2×Dic15—38no—
37C2×C5×Dic3—34no—
38C4×C5×D3—316no—
39C2×C3×Dic5C2×D318yes—
40D3×Dic5—616no—
41D3×C4⋊C4—154no—
42C2×C32×C5C22×C411yescharacteristic
43C2×C32×C5C2×D411yescharacteristic
44C2×C32×C5C2×Q811yescharacteristic
45C5×C3⋊D3C4⋊C414yescomplemented
46C22×C4×C5—91no—
47C22×Dic5—92no—
48C4⋊Dic5—91no—
49C4⋊Dic5—92no—
50C4⋊Dic5C3⋊D311yescharacteristic, direct product factor
51C22×C3⋊D3C2×D511yescharacteristic
52C2×C32×C4—52no—
53C2×C32×C4C2×D511yescharacteristic
54C2×C3⋊Dic3—52no—
55C2×C3⋊Dic3C2×D511yescharacteristic
56C4×C3⋊D3—104no—
57C4×C3⋊D3Dic514yescomplemented
58C22×C3×C5C22×D314yes—
59C2×C5×D3—38no—
60C2×C5×D3—38no—
61C2×C5×D3—38no—
62C3×C4×C5C4×D318yescomplemented
63Dic15—68no—
64C3×Dic5—28no—
65C5×Dic3—38no—
66C2×C4×D3—34no—
67C2×C4×D3—158no—
68C3×C4⋊C4—54no—
69C4⋊Dic3—154no—
70Dic3⋊C4—158no—
71C32×C5C2×C4⋊C411yescharacteristic, complemented, Hall
72C23×C5—91no—
73C2×C4×C5—91no—
74C2×C4×C5—94no—
75C2×C4×C5C2×C3⋊D311yescharacteristic
76C2×Dic5—92no—
77C2×Dic5—184no—
78C2×Dic5C2×C3⋊D312yes—
79C22×C32C22×D511yescharacteristic
80C2×C3⋊D3Dic1012yes—
81C2×C3⋊D3D2012yes—
82C2×C3⋊D3C2×Dic512yes—
83C32×C4—102no—
84C32×C4C2×Dic512yescomplemented
85C3⋊Dic3—102no—
86C3⋊Dic3C2×Dic512yescomplemented
87C2×C4⋊C4—451noSylow
88C2×C3×C5C2×C4×D314yes—
89C2×C3×C5D3×D414yes—
90C2×C3×C5D3×Q814yes—
91C5×D3—316no—
92C22×D3—34no—
93C2×C3×C4—58no—
94C2×C3×C4D3×D514yes—
95C2×Dic3—34no—
96C2×Dic3—158no—
97C4×D3—316no—
98C4×D3—3016no—
99C22×C5—92no—
100C22×C5—92no—
101C22×C5—92no—
102C22×C5C22×C3⋊D311yescharacteristic
103C4×C5—92no—
104C4×C5C4×C3⋊D312yescomplemented
105Dic5—22no—
106Dic5—182no—
107C2×C32C2×Dic1011yescharacteristic
108C2×C32C2×D2011yescharacteristic
109C2×C32C22×Dic511yescharacteristic
110C3⋊D3C4⋊Dic514yesdirect product factor
111C22×C4—91no—
112C22×C4—452no—
113C4⋊C4—51no—
114C4⋊C4—452no—
115C4⋊C4—451no—
116C3×C5D3×C4⋊C414yescomplemented
117C22×C3C2×D3×D514yes—
118C2×D3—38no—
119C2×D3—38no—
120C2×D3—38no—
121C3×C4—108no—
122C3×C4D3×Dic518yescomplemented
123Dic3—38no—
124Dic3—308no—
125C2×C5—94no—
126C2×C5C2×C4×C3⋊D311yescharacteristic
127C2×C5D4×C3⋊D311yescharacteristic
128C2×C5Q8×C3⋊D311yescharacteristic
129C32C2×C4⋊Dic511yescharacteristic, complemented, Sylow
130C23—91no—
131C2×C4—52no—
132C2×C4—91no—
133C2×C4—94no—
134C2×C4—452no—
135C2×C4—904no—
136C2×C4D5×C3⋊D311yescharacteristic
137C2×C3D3×Dic1014yes—
138C2×C3D3×D2014yes—
139C2×C3C2×D3×Dic514yes—
140D3—316no—
141C5C4⋊C4×C3⋊D311yescharacteristic, complemented, Sylow
142C22—92no—
143C22—92no—
144C22—92no—
145C22C2×D5×C3⋊D311yescharacteristic
146C4—92no—
147C4—102no—
148C4—902no—
149C4C3⋊D3×Dic512yescomplemented
150C3D3×C4⋊Dic514yescomplemented
151C2—94no—
152C2C3⋊D3×Dic1011yescharacteristic
153C2C3⋊D3×D2011yescharacteristic
154C2C2×C3⋊D3×Dic511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×C3⋊D3
commutatorC2×C32×C5C22×C4
FittingC2×C32×C4×C5C22
socle, cosocleC22×C32×C5C23
prime radicalC22×C5×C3⋊D3C22
hypercenterC2×C4D5×C3⋊D3
hypocenterC32×C5C2×C4⋊C4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
3. C4⋊(C3⋊Dic15)C2semidirect
4. C32×C4⋊Dic5C2semidirect
5. #10623775C2semidirect
11. C4×C5×C3⋊D3C4semidirect
18. C3×C4⋊Dic5D3semidirect
24. C32×C4×C5C2×C4semidirect
26. C5×C3⋊Dic3C2×C4semidirect
45. C5×C3⋊D3C4⋊C4semidirect
50. C4⋊Dic5C3⋊D3direct (N × H)
57. C4×C3⋊D3Dic5semidirect
62. C3×C4×C5C4×D3semidirect
71. C32×C5C2×C4⋊C4semidirect
84. C32×C4C2×Dic5semidirect
86. C3⋊Dic3C2×Dic5semidirect
104. C4×C5C4×C3⋊D3semidirect
110. C3⋊D3C4⋊Dic5direct (N × H)
116. C3×C5D3×C4⋊C4semidirect
122. C3×C4D3×Dic5semidirect
129. C32C2×C4⋊Dic5semidirect
141. C5C4⋊C4×C3⋊D3semidirect
149. C4C3⋊D3×Dic5semidirect
150. C3D3×C4⋊Dic5semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C5×C3⋊D32
C2×C3⋊D3×Dic52
C4⋊(C3⋊Dic15)2
C32×C4⋊Dic52
#106237752
D3×C4⋊Dic53
C4⋊C4×C3⋊D35