Finite Group Databasebeta

← #13086897

Subgroups — #13086897

Order 1440.

552 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 144 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×C3⋊D15C211yesmaximal, characteristic
2C2×#67137C212yesmaximal
3C5×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
4C32×C4⋊Dic5C211yesmaximal, characteristic, complemented
5#10623774C212yesmaximal, complemented
6#91437—34nomaximal
7C22×C3⋊D15C2211yescharacteristic
8C2×C32×C4×C5C2211yescharacteristic
9C2×C3⋊Dic15C2211yescharacteristic
10C4×C3⋊D15C414yescomplemented
11C2×C5×C3⋊Dic3C2212yes—
12C2×C32×Dic5C2212yes—
13#67137—24no—
14C4⋊C4×C3⋊D3—51nomaximal, Hall
15C2×C4×D15—34no—
16C2×#1200—38no—
17C5×C4⋊Dic3—34no—
18C3×C4⋊Dic5D314yescomplemented
19#6669—38no—
20C22×C32×C5C2311yescharacteristic
21C2×C3⋊D15C2×C412yes—
22C2×C3⋊D15D412yes—
23C2×C3⋊D15Q812yes—
24C32×C4×C5C2×C412yescomplemented
25C3⋊Dic15C2×C412yescomplemented
26C5×C3⋊Dic3—22no—
27C32×Dic5—22no—
28D5×C4⋊C4—91noHall
29C2×C4×C3⋊D3—51no—
30C2×C4×C3⋊D3—52no—
31C32×C4⋊C4—51no—
32C4⋊(C3⋊Dic3)D511yescharacteristic, complemented
33#3750—52no—
34C22×D15—34no—
35C2×C3×C4×C5C2×D314yes—
36C2×Dic15—34no—
37C4×D15—316no—
38C2×C5×Dic3—38no—
39C2×C3×Dic5C2×D318yes—
40#1200—616no—
41D3×C4⋊C4—154no—
42C2×C32×C5C22×C411yescharacteristic
43C2×C32×C5C2×D411yescharacteristic
44C2×C32×C5C2×Q811yescharacteristic
45C3⋊D15C4⋊C414yescomplemented
46C2×C4×D5—91no—
47C2×C4×D5—92no—
48C5×C4⋊C4—91no—
49C4⋊Dic5C3⋊D311yescharacteristic, complemented
50#683—92no—
51C22×C3⋊D3—51no—
52C2×C32×C4—52no—
53C2×C32×C4C2×D511yescharacteristic
54C2×C3⋊Dic3—51no—
55C2×C3⋊Dic3C2×D512yes—
56C4×C3⋊D3—54no—
57C4×C3⋊D3—104no—
58C22×C3×C5C22×D314yes—
59C2×D15—38no—
60C2×D15—38no—
61C2×D15—38no—
62C3×C4×C5C4×D318yescomplemented
63Dic15—38no—
64C3×Dic5—28no—
65C5×Dic3—68no—
66C2×C4×D3—154no—
67C2×C4×D3—158no—
68C3×C4⋊C4—54no—
69C4⋊Dic3—34no—
70Dic3⋊C4—158no—
71C32×C5C2×C4⋊C411yescharacteristic, complemented, Hall
72C22×D5—91no—
73C2×C4×C5—92no—
74C2×C4×C5C2×C3⋊D311yescharacteristic
75C2×Dic5—91no—
76C2×Dic5C2×C3⋊D312yes—
77C4×D5—94no—
78C4×D5—184no—
79C22×C32C22×D511yescharacteristic
80C2×C3⋊D3—52no—
81C2×C3⋊D3—52no—
82C2×C3⋊D3—52no—
83C32×C4—102no—
84C32×C4C4×D512yescomplemented
85C3⋊Dic3—22no—
86C3⋊Dic3—52no—
87C2×C4⋊C4—451noSylow
88C2×C3×C5C2×C4×D314yes—
89C2×C3×C5D3×D414yes—
90C2×C3×C5D3×Q814yes—
91D15—316no—
92C22×D3—154no—
93C2×C3×C4—58no—
94C2×C3×C4D3×D514yes—
95C2×Dic3—38no—
96C2×Dic3—154no—
97C4×D3—1516no—
98C4×D3—3016no—
99C22×C5C22×C3⋊D311yescharacteristic
100C2×D5—92no—
101C2×D5—92no—
102C2×D5—92no—
103C4×C5—182no—
104C4×C5C4×C3⋊D312yescomplemented
105Dic5—22no—
106Dic5—92no—
107C2×C32C2×C4×D511yescharacteristic
108C2×C32D4×D511yescharacteristic
109C2×C32Q8×D511yescharacteristic
110C3⋊D3—54no—
111C22×C4—452no—
112C22×C4—451no—
113C4⋊C4—51no—
114C4⋊C4—91no—
115C4⋊C4—452no—
116C3×C5D3×C4⋊C414yescomplemented
117C22×C3C2×D3×D514yes—
118C2×D3—158no—
119C2×D3—158no—
120C2×D3—158no—
121C3×C4—108no—
122C3×C4#120018yescomplemented
123Dic3—68no—
124Dic3—158no—
125C2×C5C2×C4×C3⋊D311yescharacteristic
126C2×C5D4×C3⋊D311yescharacteristic
127C2×C5Q8×C3⋊D311yescharacteristic
128D5—94no—
129C32D5×C4⋊C411yescharacteristic, complemented, Sylow
130C23—451no—
131C2×C4—52no—
132C2×C4—92no—
133C2×C4—451no—
134C2×C4—454no—
135C2×C4—904no—
136C2×C4D5×C3⋊D311yescharacteristic
137C2×C3D15⋊Q814yes—
138C2×C3#677714yes—
139C2×C3C2×#120014yes—
140D3—1516no—
141C5C4⋊C4×C3⋊D311yescharacteristic, complemented, Sylow
142C22—452no—
143C22—452no—
144C22—452no—
145C22C2×D5×C3⋊D311yescharacteristic
146C4—102no—
147C4—182no—
148C4—452no—
149C4#6713712yescomplemented
150C3#9143714yescomplemented
151C2—454no—
152C2#1062415311yescharacteristic
153C2#1062416011yescharacteristic
154C2C2×#6713711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×C3⋊D3
commutatorC2×C32×C5C22×C4
FittingC2×C32×C4×C5C22
socle, cosocleC22×C32×C5C23
prime radicalC22×C3⋊D15C22
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. C5×C4⋊(C3⋊Dic3)C2semidirect
4. C32×C4⋊Dic5C2semidirect
5. #10623774C2semidirect
10. C4×C3⋊D15C4semidirect
18. C3×C4⋊Dic5D3semidirect
24. C32×C4×C5C2×C4semidirect
25. C3⋊Dic15C2×C4semidirect
32. C4⋊(C3⋊Dic3)D5semidirect
45. C3⋊D15C4⋊C4semidirect
49. C4⋊Dic5C3⋊D3semidirect
62. C3×C4×C5C4×D3semidirect
71. C32×C5C2×C4⋊C4semidirect
84. C32×C4C4×D5semidirect
104. C4×C5C4×C3⋊D3semidirect
116. C3×C5D3×C4⋊C4semidirect
122. C3×C4#1200semidirect
129. C32D5×C4⋊C4semidirect
141. C5C4⋊C4×C3⋊D3semidirect
149. C4#67137semidirect
150. C3#91437semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C3⋊D152
C2×#671372
C5×C4⋊(C3⋊Dic3)2
C32×C4⋊Dic52
#106237742
#914373
C4⋊C4×C3⋊D35