Finite Group Databasebeta

← C5×C4⋊C4×C3⋊D3 #13088075

Subgroups — C5×C4⋊C4×C3⋊D3 #13088075

Order 1440.

552 conjugacy classes of subgroups; only the 186 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 186 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⋊D3C212yesmaximal
2C2×C4×C5×C3⋊D3C211yesmaximal, characteristic
3C32×C5×C4⋊C4C211yesmaximal, characteristic, complemented
4C5×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
5C5×#3750C212yesmaximal, complemented
6C5×D3×C4⋊C4—34nomaximal
7C22×C5×C3⋊D3C2211yescharacteristic
8C2×C32×C4×C5C2212yes—
9C2×C32×C4×C5C2211yescharacteristic
10C2×C5×C3⋊Dic3C2212yes—
11C2×C5×C3⋊Dic3C2211yescharacteristic
12C4×C5×C3⋊D3—24no—
13C4×C5×C3⋊D3C414yescomplemented
14C4⋊C4×C3⋊D3C511yesmaximal, characteristic, direct product factor, Hall
15C2×C4×C5×D3—34no—
16C2×C4×C5×D3—38no—
17C3×C5×C4⋊C4D314yescomplemented
18C5×C4⋊Dic3—34no—
19C5×Dic3⋊C4—38no—
20C22×C32×C5C2311yescharacteristic
21C2×C5×C3⋊D3C2×C412yes—
22C2×C5×C3⋊D3D412yes—
23C2×C5×C3⋊D3Q812yes—
24C32×C4×C5—22no—
25C32×C4×C5C2×C412yescomplemented
26C5×C3⋊Dic3—22no—
27C5×C3⋊Dic3C2×C412yescomplemented
28C2×C5×C4⋊C4—91noHall
29C2×C4×C3⋊D3C2×C512yes—
30C2×C4×C3⋊D3C2×C511yescharacteristic
31C32×C4⋊C4C2×C511yescharacteristic, complemented
32C4⋊(C3⋊Dic3)C2×C511yescharacteristic, complemented
33#3750C2×C512yescomplemented
34C22×C5×D3—34no—
35C2×C3×C4×C5C2×D318yes—
36C2×C3×C4×C5C2×D314yes—
37C2×C5×Dic3—34no—
38C2×C5×Dic3—38no—
39C4×C5×D3—316no—
40C4×C5×D3—616no—
41D3×C4⋊C4—34no—
42C2×C32×C5C22×C411yescharacteristic
43C2×C32×C5C2×D411yescharacteristic
44C2×C32×C5C2×Q811yescharacteristic
45C5×C3⋊D3C4⋊C414yesdirect product factor
46C22×C4×C5—91no—
47C22×C4×C5—92no—
48C5×C4⋊C4—92no—
49C5×C4⋊C4—91no—
50C5×C4⋊C4C3⋊D311yescharacteristic, direct product factor
51C22×C3⋊D3C22×C511yescharacteristic
52C2×C32×C4C22×C512yes—
53C2×C32×C4C22×C511yescharacteristic
54C2×C3⋊Dic3C22×C512yes—
55C2×C3⋊Dic3C22×C511yescharacteristic
56C4×C3⋊D3—24no—
57C4×C3⋊D3C4×C514yescomplemented
58C22×C3×C5C22×D314yes—
59C2×C5×D3—38no—
60C2×C5×D3—38no—
61C2×C5×D3—38no—
62C3×C4×C5—28no—
63C3×C4×C5C4×D318yescomplemented
64C5×Dic3—38no—
65C5×Dic3—68no—
66C2×C4×D3—34no—
67C2×C4×D3—38no—
68C3×C4⋊C4C5×D314yescomplemented
69C4⋊Dic3—34no—
70Dic3⋊C4—38no—
71C32×C5C2×C4⋊C411yescharacteristic, complemented, Hall
72C23×C5—91no—
73C2×C4×C5—91no—
74C2×C4×C5—94no—
75C2×C4×C5—92no—
76C2×C4×C5—184no—
77C2×C4×C5C2×C3⋊D312yes—
78C2×C4×C5C2×C3⋊D311yescharacteristic
79C22×C32C23×C511yescharacteristic
80C2×C3⋊D3C2×C4×C512yes—
81C2×C3⋊D3C5×D412yes—
82C2×C3⋊D3C5×Q812yes—
83C32×C4—22no—
84C32×C4C2×C4×C512yescomplemented
85C3⋊Dic3—22no—
86C3⋊Dic3C2×C4×C512yescomplemented
87C2×C4⋊C4—91noSylow
88C2×C3×C5C2×C4×D314yes—
89C2×C3×C5D3×D414yes—
90C2×C3×C5D3×Q814yes—
91C5×D3—316no—
92C22×D3—34no—
93C2×C3×C4C2×C5×D318yes—
94C2×C3×C4C2×C5×D314yes—
95C2×Dic3—34no—
96C2×Dic3—38no—
97C4×D3—316no—
98C4×D3—616no—
99C22×C5—92no—
100C22×C5—92no—
101C22×C5—92no—
102C22×C5C22×C3⋊D311yescharacteristic
103C4×C5—22no—
104C4×C5—92no—
105C4×C5—182no—
106C4×C5C4×C3⋊D312yescomplemented
107C2×C32C22×C4×C511yescharacteristic
108C2×C32C2×C5×D411yescharacteristic
109C2×C32C2×C5×Q811yescharacteristic
110C3⋊D3C5×C4⋊C414yesdirect product factor
111C22×C4—91no—
112C22×C4—92no—
113C4⋊C4—92no—
114C4⋊C4—91no—
115C4⋊C4C5×C3⋊D311yescharacteristic, direct product factor
116C3×C5D3×C4⋊C414yescomplemented
117C22×C3C22×C5×D314yes—
118C2×D3—38no—
119C2×D3—38no—
120C2×D3—38no—
121C3×C4—28no—
122C3×C4C4×C5×D318yescomplemented
123Dic3—38no—
124Dic3—68no—
125C2×C5—94no—
126C2×C5C2×C4×C3⋊D311yescharacteristic
127C2×C5D4×C3⋊D311yescharacteristic
128C2×C5Q8×C3⋊D311yescharacteristic
129C32C2×C5×C4⋊C411yescharacteristic, complemented, Sylow
130C23—91no—
131C2×C4—91no—
132C2×C4—94no—
133C2×C4—92no—
134C2×C4—184no—
135C2×C4C2×C5×C3⋊D312yes—
136C2×C4C2×C5×C3⋊D311yescharacteristic
137C2×C3C2×C4×C5×D314yes—
138C2×C3C5×D3×D414yes—
139C2×C3C5×D3×Q814yes—
140D3—316no—
141C5C4⋊C4×C3⋊D311yescharacteristic, direct product factor, Sylow
142C22—92no—
143C22—92no—
144C22—92no—
145C22C22×C5×C3⋊D311yescharacteristic
146C4—22no—
147C4—92no—
148C4—182no—
149C4C4×C5×C3⋊D312yescomplemented
150C3C5×D3×C4⋊C414yescomplemented
151C2—94no—
152C2C2×C4×C5×C3⋊D311yescharacteristic
153C2C5×D4×C3⋊D311yescharacteristic
154C2C5×Q8×C3⋊D311yescharacteristic
subgroupG/H
centerC22×C5C22×C3⋊D3
commutatorC2×C32C22×C4×C5
FrattiniC22C22×C5×C3⋊D3
FittingC32×C5×C4⋊C4C2
socleC22×C32×C5C23
prime radicalC22×C5×C3⋊D3C22
cosocleC22×C32C23×C5
hypercenterC5×C4⋊C4C3⋊D3
hypocenterC32C2×C5×C4⋊C4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C5 ◁ C5×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C32×C5×C4⋊C4C2semidirect
4. C5×C4⋊(C3⋊Dic3)C2semidirect
5. C5×#3750C2semidirect
13. C4×C5×C3⋊D3C4semidirect
14. C4⋊C4×C3⋊D3C5direct (N × H)
17. C3×C5×C4⋊C4D3semidirect
25. C32×C4×C5C2×C4semidirect
27. C5×C3⋊Dic3C2×C4semidirect
31. C32×C4⋊C4C2×C5semidirect
32. C4⋊(C3⋊Dic3)C2×C5semidirect
33. #3750C2×C5semidirect
45. C5×C3⋊D3C4⋊C4direct (N × H)
50. C5×C4⋊C4C3⋊D3direct (N × H)
57. C4×C3⋊D3C4×C5semidirect
63. C3×C4×C5C4×D3semidirect
68. C3×C4⋊C4C5×D3semidirect
71. C32×C5C2×C4⋊C4semidirect
84. C32×C4C2×C4×C5semidirect
86. C3⋊Dic3C2×C4×C5semidirect
106. C4×C5C4×C3⋊D3semidirect
110. C3⋊D3C5×C4⋊C4direct (N × H)
115. C4⋊C4C5×C3⋊D3direct (N × H)
116. C3×C5D3×C4⋊C4semidirect
122. C3×C4C4×C5×D3semidirect
129. C32C2×C5×C4⋊C4semidirect
141. C5C4⋊C4×C3⋊D3direct (N × H)
149. C4C4×C5×C3⋊D3semidirect
150. C3C5×D3×C4⋊C4semidirect

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
C32×C5×C4⋊C42
C5×C4⋊(C3⋊Dic3)2
C5×#37502
C5×D3×C4⋊C43
C4⋊C4×C3⋊D35