Finite Group Databasebeta

← C5×D4×C3⋊Dic3 #13088114

Subgroups — C5×D4×C3⋊Dic3 #13088114

Order 1440.

564 conjugacy classes of subgroups; only the 254 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 254 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×C32×C5×D4C211yesmaximal, characteristic
2C22×C5×C3⋊Dic3C212yesmaximal, complemented
3C5×#3757C212yesmaximal, complemented
4C5×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
5C4×C5×C3⋊Dic3C211yesmaximal, characteristic, complemented
6C5×D4×Dic3—34nomaximal
7C23×C32×C5C2212yes—
8C32×C5×D4C414yescomplemented
9C2×C32×C4×C5C2211yescharacteristic
10C2×C5×C3⋊Dic3—24no—
11C2×C5×C3⋊Dic3C2212yes—
12C2×C5×C3⋊Dic3C2211yescharacteristic
13C2×C5×C3⋊Dic3C2211yescharacteristic
14D4×C3⋊Dic3C511yesmaximal, characteristic, direct product factor, Hall
15C2×C3×C5×D4D314yes—
16C22×C5×Dic3—38no—
17C5×#217—38no—
18C5×C4⋊Dic3—34no—
19C4×C5×Dic3—34no—
20C22×C32×C5—22no—
21C22×C32×C5—22no—
22C22×C32×C5C2×C414yescomplemented
23C22×C32×C5C2311yescharacteristic
24C32×C4×C5C2×C412yescomplemented
25C5×C3⋊Dic3—22no—
26C5×C3⋊Dic3—21no—
27C5×C3⋊Dic3D412yesdirect product factor
28C4×C5×D4—91noHall
29C2×C32×D4C2×C511yescharacteristic
30C22×C3⋊Dic3C2×C512yescomplemented
31#3757C2×C512yescomplemented
32C4⋊(C3⋊Dic3)C2×C511yescharacteristic, complemented
33C4×C3⋊Dic3C2×C511yescharacteristic, complemented
34C23×C3×C5C2×D318yes—
35C3×C5×D4Dic3116yescomplemented
36C2×C3×C4×C5C2×D314yes—
37C2×C5×Dic3—34no—
38C2×C5×Dic3—34no—
39C2×C5×Dic3—38no—
40C2×C5×Dic3—616no—
41D4×Dic3—34no—
42C2×C32×C5—24no—
43C2×C32×C5C22×C411yescharacteristic
44C2×C32×C5C2×D411yescharacteristic
45C2×C32×C5#4111yescharacteristic
46C2×C5×D4C3⋊D311yescharacteristic
47C22×C4×C5—92no—
48C5×C4⋊C4—91no—
49C5×C22⋊C4—92no—
50C42×C5—91no—
51C23×C32C22×C512yes—
52C32×D4C4×C514yescomplemented
53C2×C32×C4C22×C511yescharacteristic
54C2×C3⋊Dic3—24no—
55C2×C3⋊Dic3C22×C511yescharacteristic
56C2×C3⋊Dic3C22×C512yes—
57C2×C3⋊Dic3C22×C511yescharacteristic
58C22×C3×C5—28no—
59C22×C3×C5—28no—
60C22×C3×C5C2×Dic3116yescomplemented
61C22×C3×C5C22×D314yes—
62C3×C4×C5C2×Dic318yescomplemented
63C5×Dic3—38no—
64C5×Dic3—68no—
65C5×Dic3—64no—
66C2×C3×D4C5×D314yes—
67C22×Dic3—38no—
68#217—38no—
69C4⋊Dic3—34no—
70C4×Dic3—34no—
71C32×C5C4×D411yescharacteristic, complemented, Hall
72C23×C5C2×C3⋊D312yes—
73C5×D4C3⋊Dic314yesdirect product factor
74C2×C4×C5—91no—
75C2×C4×C5—91no—
76C2×C4×C5—92no—
77C2×C4×C5—184no—
78C2×C4×C5C2×C3⋊D311yescharacteristic
79C22×C32—22no—
80C22×C32—22no—
81C22×C32C2×C4×C514yescomplemented
82C22×C32C23×C511yescharacteristic
83C32×C4C2×C4×C512yescomplemented
84C3⋊Dic3—22no—
85C3⋊Dic3—21no—
86C3⋊Dic3C5×D412yesdirect product factor
87C4×D4—91noSylow
88C2×C3×C5—216no—
89C2×C3×C5D3×D414yes—
90C2×C3×C5#23714yes—
91C2×C3×C5C22×Dic314yes—
92C23×C3C2×C5×D318yes—
93C3×D4C5×Dic3116yescomplemented
94C2×C3×C4C2×C5×D314yes—
95C2×Dic3—34no—
96C2×Dic3—34no—
97C2×Dic3—38no—
98C2×Dic3—616no—
99C22×C5—22no—
100C22×C5—22no—
101C22×C5C2×C3⋊Dic314yescomplemented
102C22×C5C22×C3⋊D311yescharacteristic
103C4×C5—92no—
104C4×C5—182no—
105C4×C5—181no—
106C4×C5C2×C3⋊Dic312yescomplemented
107C2×C32—24no—
108C2×C32C22×C4×C511yescharacteristic
109C2×C32C2×C5×D411yescharacteristic
110C2×C32C5×#4111yescharacteristic
111C2×D4C5×C3⋊D311yescharacteristic
112C22×C4—92no—
113C4⋊C4—91no—
114C22⋊C4—92no—
115C42—91no—
116C3×C5D4×Dic314yescomplemented
117C22×C3—28no—
118C22×C3—28no—
119C22×C3C2×C5×Dic3116yescomplemented
120C22×C3C22×C5×D314yes—
121C3×C4C2×C5×Dic318yescomplemented
122Dic3—38no—
123Dic3—68no—
124Dic3—64no—
125C2×C5—24no—
126C2×C5D4×C3⋊D311yescharacteristic
127C2×C5#383011yescharacteristic
128C2×C5C22×C3⋊Dic311yescharacteristic
129C32C4×C5×D411yescharacteristic, complemented, Sylow
130C23C2×C5×C3⋊D312yes—
131D4C5×C3⋊Dic314yesdirect product factor
132C2×C4—91no—
133C2×C4—91no—
134C2×C4—92no—
135C2×C4—184no—
136C2×C4C2×C5×C3⋊D311yescharacteristic
137C2×C3—216no—
138C2×C3C5×D3×D414yes—
139C2×C3C5×#23714yes—
140C2×C3C22×C5×Dic314yes—
141C5D4×C3⋊Dic311yescharacteristic, direct product factor, Sylow
142C22—22no—
143C22—22no—
144C22C2×C5×C3⋊Dic314yescomplemented
145C22C22×C5×C3⋊D311yescharacteristic
146C4—92no—
147C4—182no—
148C4—181no—
149C4C2×C5×C3⋊Dic312yescomplemented
150C3C5×D4×Dic314yescomplemented
151C2—24no—
152C2C5×D4×C3⋊D311yescharacteristic
153C2C5×#383011yescharacteristic
154C2C22×C5×C3⋊Dic311yescharacteristic
subgroupG/H
centerC22×C5C22×C3⋊D3
commutatorC2×C32C22×C4×C5
FrattiniC22C22×C5×C3⋊D3
Fitting, prime radicalC2×C32×C5×D4C2
socleC22×C32×C5C23
cosocleC22×C32C23×C5
hypercenterC2×C5×D4C3⋊D3
hypocenterC32C4×C5×D4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C5 ◁ C2×C5×D4

Complements

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

NH ≅ G/Ntype
2. C22×C5×C3⋊Dic3C2semidirect
3. C5×#3757C2semidirect
4. C5×C4⋊(C3⋊Dic3)C2semidirect
5. C4×C5×C3⋊Dic3C2semidirect
8. C32×C5×D4C4semidirect
14. D4×C3⋊Dic3C5direct (N × H)
22. C22×C32×C5C2×C4semidirect
24. C32×C4×C5C2×C4semidirect
27. C5×C3⋊Dic3D4direct (N × H)
30. C22×C3⋊Dic3C2×C5semidirect
31. #3757C2×C5semidirect
32. C4⋊(C3⋊Dic3)C2×C5semidirect
33. C4×C3⋊Dic3C2×C5semidirect
35. C3×C5×D4Dic3semidirect
52. C32×D4C4×C5semidirect
60. C22×C3×C5C2×Dic3semidirect
62. C3×C4×C5C2×Dic3semidirect
71. C32×C5C4×D4semidirect
73. C5×D4C3⋊Dic3direct (N × H)
81. C22×C32C2×C4×C5semidirect
83. C32×C4C2×C4×C5semidirect
86. C3⋊Dic3C5×D4direct (N × H)
93. C3×D4C5×Dic3semidirect
101. C22×C5C2×C3⋊Dic3semidirect
106. C4×C5C2×C3⋊Dic3semidirect
116. C3×C5D4×Dic3semidirect
119. C22×C3C2×C5×Dic3semidirect
121. C3×C4C2×C5×Dic3semidirect
129. C32C4×C5×D4semidirect
131. D4C5×C3⋊Dic3direct (N × H)
141. C5D4×C3⋊Dic3direct (N × H)
144. C22C2×C5×C3⋊Dic3semidirect
149. C4C2×C5×C3⋊Dic3semidirect
150. C3C5×D4×Dic3semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C5×D42
C22×C5×C3⋊Dic32
C5×#37572
C5×C4⋊(C3⋊Dic3)2
C4×C5×C3⋊Dic32
C5×D4×Dic33
D4×C3⋊Dic35