Finite Group Databasebeta

← #13086905

Subgroups — #13086905

Order 1440.

564 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 130 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×#67139C211yesmaximal, characteristic
2C2×#67137C211yesmaximal, characteristic, complemented
3C2×D5×C3⋊Dic3C211yesmaximal, characteristic, complemented
4#10623908C211yesmaximal, characteristic, complemented
5C4×C5×C3⋊Dic3C211yesmaximal, characteristic, complemented
6C32×#685C211yesmaximal, characteristic, complemented
7#10623775C211yesmaximal, characteristic, complemented
8#91395—34nomaximal
9C22×C3⋊D15C2211yescharacteristic
10C22×C32×D5C2211yescharacteristic
11C2×C32×C4×C5C2211yescharacteristic
12C2×C3⋊Dic15C2211yescharacteristic
13C2×C5×C3⋊Dic3C2211yescharacteristic
14C2×C5×C3⋊Dic3C2211yescharacteristic
15C2×C32×Dic5C2211yescharacteristic
16#67139C414yescomplemented
17#67137—22no—
18D5×C3⋊Dic3—22no—
19#64090—51nomaximal, Hall
20C2×#1202—34no—
21C2×#1200—34no—
22C2×D5×Dic3—34no—
23#6714—34no—
24C4×C5×Dic3—34no—
25C3×#685D314yescomplemented
26Dic3⋊Dic5—34no—
27C22×C32×C5C2311yescharacteristic
28C2×C3⋊D15—21no—
29C2×C3⋊D15—21no—
30C2×C3⋊D15C2×C412yescomplemented
31C2×C32×D5—21no—
32C2×C32×D5—21no—
33C2×C32×D5C2×C412yescomplemented
34C32×C4×C5—21no—
35C3⋊Dic15—21no—
36C5×C3⋊Dic3C2×C412yescomplemented
37C5×C3⋊Dic3D412yescomplemented
38C32×Dic5—21no—
39C4×D20—91noHall
40C2×#638—51no—
41C22×C3⋊Dic3—51no—
42C2×C4×C3⋊D3—51no—
43C32×C22⋊C4—51no—
44#3752—51no—
45#3750—51no—
46C4×C3⋊Dic3D511yescharacteristic, complemented
47C22×D15—34no—
48C22×C3×D5C2×D314yes—
49C2×C3×C4×C5C2×D314yes—
50C2×Dic15—34no—
51C2×C5×Dic3—34no—
52C2×C5×Dic3—34no—
53C2×C3×Dic5C2×D314yes—
54#1202—316no—
55#1200—68no—
56D5×Dic3—68no—
57#67⋊C4—154no—
58C2×C32×C5C22×C411yescharacteristic
59C2×C32×C5C2×D411yescharacteristic
60C2×C32×C5#4111yescharacteristic
61C3⋊D15—22no—
62C32×D5—22no—
63C2×D20—91no—
64C2×C4×D5—91no—
65C2×C4×D5—91no—
66C42×C5—91no—
67#685—91no—
68#685C3⋊D311yescharacteristic, complemented
69C4⋊Dic5—91no—
70C23×C32—51no—
71C22×C3⋊D3—51no—
72C2×C32×C4—51no—
73C2×C32×C4C2×D511yescharacteristic
74#638—54no—
75C2×C3⋊Dic3—51no—
76C2×C3⋊Dic3—102no—
77C2×C3⋊Dic3C2×D511yescharacteristic
78C2×C3⋊Dic3C2×D511yescharacteristic
79C4×C3⋊D3—102no—
80C22×C3×C5C22×D314yes—
81C2×D15—38no—
82C2×D15—64no—
83C2×D15—64no—
84C2×C3×D5—24no—
85C2×C3×D5—24no—
86C2×C3×D5C4×D318yescomplemented
87C3×C4×C5—24no—
88Dic15—64no—
89C3×Dic5—24no—
90C5×Dic3—38no—
91C5×Dic3—38no—
92C2×#67—154no—
93C22×Dic3—154no—
94C2×C4×D3—154no—
95C3×C22⋊C4—54no—
96(C2×D3)⋊C4—154no—
97Dic3⋊C4—154no—
98C4×Dic3—34no—
99C32×C5C4×D411yescharacteristic, complemented, Hall
100C22×D5—91no—
101C22×D5C2×C3⋊D311yescharacteristic
102C2×C4×C5—91no—
103C2×C4×C5—91no—
104C2×C4×C5C2×C3⋊D311yescharacteristic
105C2×Dic5—91no—
106C2×Dic5C2×C3⋊D311yescharacteristic
107D20—94no—
108C4×D5—182no—
109C4×D5—182no—
110C22×C32—52no—
111C22×C32—101no—
112C22×C32—101no—
113C22×C32C22×D511yescharacteristic
114C2×C3⋊D3—52no—
115C2×C3⋊D3—101no—
116C2×C3⋊D3—101no—
117C32×C4—21no—
118C32×C4—101no—
119C3⋊Dic3—101no—
120C3⋊Dic3C4×D512yescomplemented
121C3⋊Dic3D2012yescomplemented
122C4×D4—451noSylow
123C2×C3×C5C2×C4×D314yes—
124C2×C3×C5D3×D414yes—
125C2×C3×C5#23714yes—
126D15—68no—
127C3×D5—28no—
128C23×C3—54no—
129C22×D3—154no—
130C2×C3×C4—54no—
131C2×C3×C4D3×D514yes—
132#67—1516no—
133C2×Dic3—34no—
134C2×Dic3—34no—
135C2×Dic3—154no—
136C2×Dic3—308no—
137C4×D3—308no—
138C22×C5C22×C3⋊D311yescharacteristic
139C2×D5—21no—
140C2×D5—21no—
141C2×D5—92no—
142C2×D5—181no—
143C2×D5—181no—
144C2×D5C4×C3⋊D312yescomplemented
145C4×C5—21no—
146C4×C5—92no—
147C4×C5—92no—
148Dic5—21no—
149Dic5—181no—
150C2×C32—102no—
151C2×C32C2×C4×D511yescharacteristic
152C2×C32C2×D2011yescharacteristic
153C2×C32#70911yescharacteristic
154C3⋊D3—102no—
155C2×D4—451no—
156C22×C4—451no—
157C22×C4—451no—
158C4⋊C4—451no—
159C22⋊C4—51no—
160C22⋊C4—451no—
161C42—91no—
162C3×C5#67⋊C414yescomplemented
163C22×C3—58no—
164C22×C3—104no—
165C22×C3—104no—
166C22×C3C2×D3×D514yes—
167C2×D3—158no—
168C2×D3—304no—
169C2×D3—304no—
170C3×C4—24no—
171C3×C4—104no—
172Dic3—38no—
173Dic3—38no—
174Dic3—304no—
175C2×C5C2×C4×C3⋊D311yescharacteristic
176C2×C5D4×C3⋊D311yescharacteristic
177C2×C5#383011yescharacteristic
178D5—22no—
179D5—182no—
180C32C4×D2011yescharacteristic, complemented, Sylow
181C23—51no—
182C23—451no—
183D4—454no—
184C2×C4—51no—
185C2×C4—91no—
186C2×C4—91no—
187C2×C4—451no—
188C2×C4—902no—
189C2×C4—902no—
190C2×C4D5×C3⋊D311yescharacteristic
191C2×C3—108no—
192C2×C3C4×D3×D514yes—
193C2×C3D3×D2014yes—
194C2×C3#677914yes—
195D3—308no—
196C5#6409011yescharacteristic, complemented, Sylow
197C22—52no—
198C22—101no—
199C22—101no—
200C22—452no—
201C22—901no—
202C22—901no—
203C22C2×D5×C3⋊D311yescharacteristic
204C4—21no—
205C4—92no—
206C4—92no—
207C4—101no—
208C4—901no—
209C3#9139514yescomplemented
210C2—102no—
211C2—902no—
212C2C4×D5×C3⋊D311yescharacteristic
213C2C3⋊D3×D2011yescharacteristic
214C2#1062416211yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×C3⋊D3
commutatorC2×C32×C5C22×C4
FittingC2×C32×C4×C5C22
socle, cosocleC22×C32×C5C23
prime radicalC2×#67139C2
hypercenterC2×C4D5×C3⋊D3
hypocenterC32×C5C4×D4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×#67137C2semidirect
3. C2×D5×C3⋊Dic3C2semidirect
4. #10623908C2semidirect
5. C4×C5×C3⋊Dic3C2semidirect
6. C32×#685C2semidirect
7. #10623775C2semidirect
16. #67139C4semidirect
25. C3×#685D3semidirect
30. C2×C3⋊D15C2×C4semidirect
33. C2×C32×D5C2×C4semidirect
36. C5×C3⋊Dic3C2×C4semidirect
37. C5×C3⋊Dic3D4semidirect
46. C4×C3⋊Dic3D5semidirect
68. #685C3⋊D3semidirect
86. C2×C3×D5C4×D3semidirect
99. C32×C5C4×D4semidirect
120. C3⋊Dic3C4×D5semidirect
121. C3⋊Dic3D20semidirect
144. C2×D5C4×C3⋊D3semidirect
162. C3×C5#67⋊C4semidirect
180. C32C4×D20semidirect
196. C5#64090semidirect
209. C3#91395semidirect

Maximal subgroups

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

subgroupindex
C2×#671392
C2×#671372
C2×D5×C3⋊Dic32
#106239082
C4×C5×C3⋊Dic32
C32×#6852
#106237752
#913953
#640905