Finite Group Databasebeta

← C4×C5×C4⋊(C3⋊D3) #13088056

Subgroups — C4×C5×C4⋊(C3⋊D3) #13088056

Order 1440.

564 conjugacy classes of subgroups; only the 194 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 194 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×C5×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2C2×C4×C5×C3⋊D3C212yesmaximal, complemented
3C32×C42×C5C211yesmaximal, characteristic, complemented
4C5×#3752C212yesmaximal, complemented
5C5×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
6C4×C5×D12—34nomaximal
7C22×C5×C3⋊D3C2212yes—
8C2×C32×C4×C5C2211yescharacteristic
9C2×C32×C4×C5C2211yescharacteristic
10C2×C32×C4×C5C2211yescharacteristic
11C2×C5×C3⋊Dic3C2212yes—
12C5×C4⋊(C3⋊D3)C414yesdirect product factor
13C4×C5×C3⋊D3—24no—
14C4×C4⋊(C3⋊D3)C511yesmaximal, characteristic, direct product factor, Hall
15C2×C5×D12—34no—
16C2×C4×C5×D3—38no—
17C3×C42×C5D314yescomplemented
18C5×(C2×D3)⋊C4—38no—
19C5×C4⋊Dic3—34no—
20C22×C32×C5C2311yescharacteristic
21C2×C5×C3⋊D3—22no—
22C2×C5×C3⋊D3—22no—
23C2×C5×C3⋊D3C2×C414yescomplemented
24C32×C4×C5—21no—
25C32×C4×C5C2×C412yescomplemented
26C32×C4×C5D412yescomplemented
27C5×C3⋊Dic3—22no—
28C4×C5×D4—91noHall
29C2×C4⋊(C3⋊D3)C2×C511yescharacteristic
30C2×C4×C3⋊D3C2×C512yescomplemented
31C32×C42C2×C511yescharacteristic, complemented
32#3752C2×C512yescomplemented
33C4⋊(C3⋊Dic3)C2×C511yescharacteristic, complemented
34C22×C5×D3—38no—
35C2×C3×C4×C5C2×D314yes—
36C2×C3×C4×C5C2×D314yes—
37C2×C3×C4×C5C2×D314yes—
38C2×C5×Dic3—38no—
39C5×D12—316no—
40C4×C5×D3—616no—
41C4×D12—34no—
42C2×C32×C5C22×C411yescharacteristic
43C2×C32×C5C2×D411yescharacteristic
44C2×C32×C5#4111yescharacteristic
45C5×C3⋊D3—24no—
46C2×C5×D4—91no—
47C22×C4×C5—92no—
48C5×C4⋊C4—91no—
49C5×C22⋊C4—92no—
50C42×C5C3⋊D311yescharacteristic, complemented
51C22×C3⋊D3C22×C512yes—
52C2×C32×C4C22×C511yescharacteristic
53C2×C32×C4C22×C511yescharacteristic
54C2×C32×C4C22×C511yescharacteristic
55C2×C3⋊Dic3C22×C512yes—
56C4⋊(C3⋊D3)C4×C514yesdirect product factor
57C4×C3⋊D3—24no—
58C22×C3×C5C22×D314yes—
59C2×C5×D3—316no—
60C2×C5×D3—68no—
61C2×C5×D3—68no—
62C3×C4×C5—24no—
63C3×C4×C5C4×D318yescomplemented
64C3×C4×C5D1218yescomplemented
65C5×Dic3—68no—
66C2×D12—34no—
67C2×C4×D3—38no—
68C3×C42C5×D314yescomplemented
69(C2×D3)⋊C4—38no—
70C4⋊Dic3—34no—
71C32×C5C4×D411yescharacteristic, complemented, Hall
72C23×C5—92no—
73C5×D4—94no—
74C2×C4×C5—92no—
75C2×C4×C5—184no—
76C2×C4×C5C2×C3⋊D311yescharacteristic
77C2×C4×C5C2×C3⋊D311yescharacteristic
78C2×C4×C5C2×C3⋊D311yescharacteristic
79C22×C32C23×C511yescharacteristic
80C2×C3⋊D3—22no—
81C2×C3⋊D3—22no—
82C2×C3⋊D3C2×C4×C514yescomplemented
83C32×C4—21no—
84C32×C4C2×C4×C512yescomplemented
85C32×C4C5×D412yescomplemented
86C3⋊Dic3—22no—
87C4×D4—91noSylow
88C2×C3×C5C2×C4×D314yes—
89C2×C3×C5C2×D1214yes—
90C2×C3×C5#23514yes—
91C5×D3—616no—
92C22×D3—38no—
93C2×C3×C4C2×C5×D314yes—
94C2×C3×C4C2×C5×D314yes—
95C2×C3×C4C2×C5×D314yes—
96C2×Dic3—38no—
97D12—316no—
98C4×D3—616no—
99C22×C5—94no—
100C22×C5—182no—
101C22×C5—182no—
102C22×C5C22×C3⋊D311yescharacteristic
103C4×C5—21no—
104C4×C5—182no—
105C4×C5C4×C3⋊D312yescomplemented
106C4×C5C4⋊(C3⋊D3)12yesdirect product factor
107C2×C32C22×C4×C511yescharacteristic
108C2×C32C2×C5×D411yescharacteristic
109C2×C32C5×#4111yescharacteristic
110C3⋊D3—24no—
111C2×D4—91no—
112C22×C4—92no—
113C4⋊C4—91no—
114C22⋊C4—92no—
115C42C5×C3⋊D311yescharacteristic, complemented
116C3×C5C4×D1214yescomplemented
117C22×C3C22×C5×D314yes—
118C2×D3—316no—
119C2×D3—68no—
120C2×D3—68no—
121C3×C4—24no—
122C3×C4C4×C5×D318yescomplemented
123C3×C4C5×D1218yescomplemented
124Dic3—68no—
125C2×C5—184no—
126C2×C5C2×C4×C3⋊D311yescharacteristic
127C2×C5C2×C4⋊(C3⋊D3)11yescharacteristic
128C2×C5#382811yescharacteristic
129C32C4×C5×D411yescharacteristic, complemented, Sylow
130C23—92no—
131D4—94no—
132C2×C4—92no—
133C2×C4—184no—
134C2×C4C2×C5×C3⋊D311yescharacteristic
135C2×C4C2×C5×C3⋊D311yescharacteristic
136C2×C4C2×C5×C3⋊D311yescharacteristic
137C2×C3C2×C4×C5×D314yes—
138C2×C3C2×C5×D1214yes—
139C2×C3C5×#23514yes—
140D3—616no—
141C5C4×C4⋊(C3⋊D3)11yescharacteristic, direct product factor, Sylow
142C22—94no—
143C22—182no—
144C22—182no—
145C22C22×C5×C3⋊D311yescharacteristic
146C4—21no—
147C4—182no—
148C4C4×C5×C3⋊D312yescomplemented
149C4C5×C4⋊(C3⋊D3)12yesdirect product factor
150C3C4×C5×D1214yescomplemented
151C2—184no—
152C2C2×C4×C5×C3⋊D311yescharacteristic
153C2C2×C5×C4⋊(C3⋊D3)11yescharacteristic
154C2C5×#382811yescharacteristic
subgroupG/H
centerC2×C4×C5C2×C3⋊D3
commutatorC2×C32C22×C4×C5
FrattiniC22C22×C5×C3⋊D3
FittingC32×C42×C5C2
socleC22×C32×C5C23
prime radicalC2×C5×C4⋊(C3⋊D3)C2
cosocleC22×C32C23×C5
hypercenterC42×C5C3⋊D3
hypocenterC32C4×C5×D4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4×C5 ◁ C42×C5

Complements

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

NH ≅ G/Ntype
2. C2×C4×C5×C3⋊D3C2semidirect
3. C32×C42×C5C2semidirect
4. C5×#3752C2semidirect
5. C5×C4⋊(C3⋊Dic3)C2semidirect
12. C5×C4⋊(C3⋊D3)C4direct (N × H)
14. C4×C4⋊(C3⋊D3)C5direct (N × H)
17. C3×C42×C5D3semidirect
23. C2×C5×C3⋊D3C2×C4semidirect
25. C32×C4×C5C2×C4semidirect
26. C32×C4×C5D4semidirect
30. C2×C4×C3⋊D3C2×C5semidirect
31. C32×C42C2×C5semidirect
32. #3752C2×C5semidirect
33. C4⋊(C3⋊Dic3)C2×C5semidirect
50. C42×C5C3⋊D3semidirect
56. C4⋊(C3⋊D3)C4×C5direct (N × H)
63. C3×C4×C5C4×D3semidirect
64. C3×C4×C5D12semidirect
68. C3×C42C5×D3semidirect
71. C32×C5C4×D4semidirect
82. C2×C3⋊D3C2×C4×C5semidirect
84. C32×C4C2×C4×C5semidirect
85. C32×C4C5×D4semidirect
105. C4×C5C4×C3⋊D3semidirect
106. C4×C5C4⋊(C3⋊D3)direct (N × H)
115. C42C5×C3⋊D3semidirect
116. C3×C5C4×D12semidirect
122. C3×C4C4×C5×D3semidirect
123. C3×C4C5×D12semidirect
129. C32C4×C5×D4semidirect
141. C5C4×C4⋊(C3⋊D3)direct (N × H)
148. C4C4×C5×C3⋊D3semidirect
149. C4C5×C4⋊(C3⋊D3)direct (N × H)
150. C3C4×C5×D12semidirect

Maximal subgroups

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

subgroupindex
C2×C5×C4⋊(C3⋊D3)2
C2×C4×C5×C3⋊D32
C32×C42×C52
C5×#37522
C5×C4⋊(C3⋊Dic3)2
C4×C5×D123
C4×C4⋊(C3⋊D3)5