Finite Group Databasebeta

← #13088209

Subgroups — #13088209

Order 1440.

564 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 145 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, complemented
2C2×#67184C212yesmaximal, complemented
3C2×C4×C3⋊D15C211yesmaximal, characteristic, complemented
4#10623913C212yesmaximal, complemented
5C4⋊(C3⋊Dic15)C211yesmaximal, characteristic, complemented
6#91827—34nomaximal
7C23×C32×C5C2212yes—
8C22×C3⋊D15C2211yescharacteristic
9C32×C5×D4—22no—
10C2×C32×C4×C5C2211yescharacteristic
11#67184—24no—
12C2×C3⋊Dic15C2211yescharacteristic
13C2×C3⋊Dic15C2212yes—
14C4×C3⋊D15—22no—
15#64147—51nomaximal, Hall
16C2×C3×C5×D4D314yescomplemented
17C2×#1220—38no—
18C2×C4×D15—34no—
19#6719—38no—
20C4⋊Dic15—34no—
21C22×C32×C5—22no—
22C22×C32×C5—22no—
23C22×C32×C5—22no—
24C22×C32×C5C2311yescharacteristic
25C2×C3⋊D15—21no—
26C2×C3⋊D15—21no—
27C2×C3⋊D15D412yescomplemented
28C32×C4×C5D412yescomplemented
29C3⋊Dic15—21no—
30C3⋊Dic15—22no—
31#4084—91noHall
32C2×C32×D4D511yescharacteristic, complemented
33C2×#638—52no—
34C2×C4×C3⋊D3—51no—
35#3757—52no—
36C4⋊(C3⋊Dic3)—51no—
37C23×C3×C5C2×D318yes—
38C22×D15—34no—
39C3×C5×D4—28no—
40C2×C3×C4×C5C2×D314yes—
41#1220—616no—
42C2×Dic15—38no—
43C2×Dic15—34no—
44C4×D15—68no—
45#938—154no—
46C2×C32×C5—42no—
47C2×C32×C5C2×D411yescharacteristic
48C2×C32×C5C2×D411yescharacteristic
49C2×C32×C5#4111yescharacteristic
50C3⋊D15—22no—
51C2×C5×D4C3⋊D311yescharacteristic, complemented
52C2×C22⋊D5—92no—
53C2×C4×D5—91no—
54C22⋊Dic5—92no—
55C4⋊Dic5—91no—
56C23×C32C2×D512yes—
57C22×C3⋊D3—51no—
58C32×D4—22no—
59C2×C32×C4C2×D511yescharacteristic
60#638—104no—
61C2×C3⋊Dic3—52no—
62C2×C3⋊Dic3—51no—
63C4×C3⋊D3—102no—
64C22×C3×C5—28no—
65C22×C3×C5—28no—
66C22×C3×C5—28no—
67C22×C3×C5C22×D314yes—
68C2×D15—38no—
69C2×D15—64no—
70C2×D15—64no—
71C3×C4×C5#6718yescomplemented
72Dic15—68no—
73Dic15—64no—
74C2×C3×D4D1514yescomplemented
75C2×#67—158no—
76C2×C4×D3—154no—
77#217—158no—
78C4⋊Dic3—154no—
79C32×C5#12111yescharacteristic, complemented, Hall
80C23×C5C2×C3⋊D312yes—
81C22×D5—91no—
82C5×D4—22no—
83C2×C4×C5C2×C3⋊D311yescharacteristic
84C22⋊D5—184no—
85C2×Dic5—92no—
86C2×Dic5—91no—
87C4×D5—182no—
88C22×C32—22no—
89C22×C32—22no—
90C22×C32—22no—
91C22×C32C22×D511yescharacteristic
92C2×C3⋊D3—52no—
93C2×C3⋊D3—101no—
94C2×C3⋊D3—101no—
95C32×C4C22⋊D512yescomplemented
96C3⋊Dic3—102no—
97C3⋊Dic3—101no—
98#121—451noSylow
99C2×C3×C5—48no—
100C2×C3×C5D3×D414yes—
101C2×C3×C5#23714yes—
102C2×C3×C5C2×#6714yes—
103D15—68no—
104C23×C3C2×D1518yes—
105C22×D3—154no—
106C3×D4—28no—
107C2×C3×C4C2×D1514yes—
108#67—3016no—
109C2×Dic3—158no—
110C2×Dic3—154no—
111C4×D3—308no—
112C22×C5—22no—
113C22×C5—22no—
114C22×C5—22no—
115C22×C5C22×C3⋊D311yescharacteristic
116C2×D5—92no—
117C2×D5—181no—
118C2×D5—181no—
119C4×C5#63812yescomplemented
120Dic5—182no—
121Dic5—181no—
122C2×C32—42no—
123C2×C32D4×D511yescharacteristic
124C2×C32#71111yescharacteristic
125C2×C32C2×C22⋊D511yescharacteristic
126C3⋊D3—102no—
127C2×D4—452no—
128C2×D4C3⋊D1511yescharacteristic, complemented
129C22×C4—451no—
130C4⋊C4—451no—
131C22⋊C4—452no—
132C3×C5#93814yescomplemented
133C22×C3—28no—
134C22×C3—28no—
135C22×C3—28no—
136C22×C3C22×D1514yes—
137C2×D3—158no—
138C2×D3—304no—
139C2×D3—304no—
140C3×C4#122018yescomplemented
141Dic3—308no—
142Dic3—304no—
143C2×C5—42no—
144C2×C5D4×C3⋊D311yescharacteristic
145C2×C5#383011yescharacteristic
146C2×C5C2×#63811yescharacteristic
147D5—182no—
148C32#408411yescharacteristic, complemented, Sylow
149C23—451no—
150C23C2×C3⋊D1512yes—
151D4—22no—
152D4—904no—
153C2×C4—451no—
154C2×C4—452no—
155C2×C4—902no—
156C2×C4C2×C3⋊D1511yescharacteristic
157C2×C3—48no—
158C2×C3D4×D1514yes—
159C2×C3#681914yes—
160C2×C3C2×#122014yes—
161D3—308no—
162C5#6414711yescharacteristic, complemented, Sylow
163C22—22no—
164C22—22no—
165C22—22no—
166C22—452no—
167C22—901no—
168C22—901no—
169C22C22×C3⋊D1511yescharacteristic
170C4—902no—
171C4—901no—
172C4#6718412yescomplemented
173C3#9182714yescomplemented
174C2—42no—
175C2—902no—
176C2D4×C3⋊D1511yescharacteristic
177C2#1062428511yescharacteristic
178C2C2×#6718411yescharacteristic
subgroupG/H
center, FrattiniC22C22×C3⋊D15
commutator, socle, cosocleC22×C32×C5C23
FittingC2×C32×C5×D4C2
hypercenterC2×D4C3⋊D15
hypocenterC32×C5#121
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C5×D4C2semidirect
2. C2×#67184C2semidirect
3. C2×C4×C3⋊D15C2semidirect
4. #10623913C2semidirect
5. C4⋊(C3⋊Dic15)C2semidirect
16. C2×C3×C5×D4D3semidirect
27. C2×C3⋊D15D4semidirect
28. C32×C4×C5D4semidirect
32. C2×C32×D4D5semidirect
51. C2×C5×D4C3⋊D3semidirect
71. C3×C4×C5#67semidirect
74. C2×C3×D4D15semidirect
79. C32×C5#121semidirect
95. C32×C4C22⋊D5semidirect
119. C4×C5#638semidirect
128. C2×D4C3⋊D15semidirect
132. C3×C5#938semidirect
140. C3×C4#1220semidirect
148. C32#4084semidirect
162. C5#64147semidirect
172. C4#67184semidirect
173. C3#91827semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C5×D42
C2×#671842
C2×C4×C3⋊D152
#106239132
C4⋊(C3⋊Dic15)2
#918273
#641475