Finite Group Databasebeta

← C4×#67149 #13087395

Subgroups — C4×#67149 #13087395

Order 1440.

486 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 138 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×#67149C212yesmaximal
3C3×C4×Dic15C211yesmaximal, characteristic, complemented
4C3×C4×C5×Dic3C211yesmaximal, characteristic, complemented
5Dic3×Dic15C212yesmaximal, complemented
6C42×D15—31nomaximal
7C4×#1200—31nomaximal
8C22×C3⋊D15C2211yescharacteristic
9C2×C32×C4×C5C2211yescharacteristic
10C2×C3⋊Dic15C2211yescharacteristic
11C4×C3⋊D15C414yescomplemented
12C2×C3×Dic15C2212yes—
13C2×C3×C5×Dic3C2212yes—
14#67149C418yesdirect product factor
15C4×#624—51nomaximal, Hall
16C2×C4×D15—31no—
17C2×C4×D15—31no—
18C2×C4×D15—32no—
19C2×C4×D15—61no—
20C2×#1200—32no—
21C3×C42×C5—31no—
22C4×Dic15—32no—
23C4×Dic15D311yescharacteristic, complemented
24C4×C5×Dic3D311yescharacteristic, complemented
25C3×C4×Dic5—31no—
26Dic3×Dic5—32no—
27C22×C32×C5C2311yescharacteristic
28C2×C3⋊D15C2×C414yes—
29C2×C3⋊D15C2×C412yes—
30C32×C4×C5C2×C412yescomplemented
31C3⋊Dic15C2×C412yescomplemented
32C3×Dic15C2×C414yescomplemented
33C3×C5×Dic3C2×C414yescomplemented
34C42×D5—91noHall
35C2×C4×C3⋊D3—51no—
36C2×#624—52no—
37C3×C4×Dic3—51no—
38C3×C4×Dic3D511yescharacteristic, complemented
39Dic32—52no—
40C22×D15—31no—
41C22×D15—31no—
42C22×D15—61no—
43C2×C3×C4×C5—21no—
44C2×C3×C4×C5—32no—
45C2×C3×C4×C5C2×D311yescharacteristic
46C2×C3×C4×C5C2×D311yescharacteristic
47C2×Dic15—31no—
48C2×Dic15—31no—
49C2×Dic15—61no—
50C2×Dic15C2×D312yes—
51C4×D15—34no—
52C4×D15—34no—
53C4×D15—38no—
54C4×D15—64no—
55C2×C5×Dic3C2×D312yes—
56C2×C3×Dic5—32no—
57#1200—38no—
58C42×D3—151no—
59C42×D3—151no—
60C2×C32×C5C22×C412yes—
61C2×C32×C5C22×C411yescharacteristic
62C3⋊D15C4214yescomplemented
63C2×C4×D5—92no—
64C2×C4×D5—91no—
65C42×C5—31no—
66C4×Dic5—31no—
67C4×Dic5—92no—
68C22×C3⋊D3—51no—
69C2×C32×C4C2×D511yescharacteristic
70C2×C3⋊Dic3—51no—
71C4×C3⋊D3—54no—
72C2×C3×Dic3—52no—
73C2×C3×Dic3C2×D512yes—
74#624—58no—
75C22×C3×C5—21no—
76C22×C3×C5C22×D311yescharacteristic
77C22×C3×C5C22×D311yescharacteristic
78C2×D15—34no—
79C2×D15—34no—
80C2×D15—32no—
81C2×D15—32no—
82C2×D15—62no—
83C2×D15—64no—
84C3×C4×C5—22no—
85C3×C4×C5—34no—
86C3×C4×C5C4×D312yescomplemented
87C3×C4×C5C4×D312yescomplemented
88Dic15—32no—
89Dic15—32no—
90Dic15—62no—
91Dic15C4×D314yescomplemented
92C3×Dic5—34no—
93C5×Dic3C4×D314yescomplemented
94C2×C4×D3—152no—
95C2×C4×D3—151no—
96C2×C4×D3—151no—
97C2×C4×D3—152no—
98C2×C4×D3—301no—
99C3×C42—31no—
100C3×C42—151no—
101C4×Dic3—51no—
102C4×Dic3—152no—
103C4×Dic3—152no—
104C4×Dic3D1511yescharacteristic, complemented
105C32×C5C2×C4211yescharacteristic, complemented, Hall
106C22×D5—91no—
107C2×C4×C5—32no—
108C2×C4×C5D3211yescharacteristic
109C2×Dic5—32no—
110C2×Dic5—91no—
111C4×D5—98no—
112C4×D5—94no—
113C22×C32C22×D511yescharacteristic
114C2×C3⋊D3—54no—
115C2×C3⋊D3—52no—
116C32×C4C4×D512yescomplemented
117C3⋊Dic3—52no—
118C3×Dic3—54no—
119C3×Dic3C4×D514yescomplemented
120C2×C42—451noSylow
121C2×C3×C5—22no—
122C2×C3×C5—21no—
123C2×C3×C5C2×C4×D312yes—
124C2×C3×C5C2×C4×D311yescharacteristic
125C2×C3×C5C2×C4×D312yes—
126C2×C3×C5C2×C4×D311yescharacteristic
127D15—34no—
128D15—34no—
129D15—64no—
130C22×D3—151no—
131C22×D3—151no—
132C22×D3—301no—
133C2×C3×C4—21no—
134C2×C3×C4—32no—
135C2×C3×C4—152no—
136C2×C3×C4D3×D511yescharacteristic
137C2×C3×C4C2×D1511yescharacteristic
138C2×Dic3—52no—
139C2×Dic3—151no—
140C2×Dic3—151no—
141C2×Dic3—301no—
142C2×Dic3C2×D1512yes—
143C4×D3—158no—
144C4×D3—154no—
145C4×D3—154no—
146C4×D3—158no—
147C4×D3—304no—
148C22×C5C2×D3211yescharacteristic
149C2×D5—94no—
150C2×D5—92no—
151C4×C5—34no—
152C4×C5#62412yescomplemented
153Dic5—34no—
154Dic5—92no—
155C2×C32C2×C4×D512yes—
156C2×C32C2×C4×D511yescharacteristic
157C3⋊D3—54no—
158C22×C4—452no—
159C22×C4—451no—
160C42—31no—
161C42—151no—
162C42—452no—
163C3×C5—21no—
164C3×C5C42×D311yescharacteristic, complemented
165C3×C5C42×D311yescharacteristic, complemented
166C22×C3—21no—
167C22×C3C2×D3×D511yescharacteristic
168C22×C3C22×D1511yescharacteristic
169C2×D3—154no—
170C2×D3—152no—
171C2×D3—154no—
172C2×D3—152no—
173C2×D3—302no—
174C2×D3—304no—
175C3×C4—22no—
176C3×C4—34no—
177C3×C4—154no—
178C3×C4#120012yescomplemented
179C3×C4C4×D1512yescomplemented
180Dic3—54no—
181Dic3—152no—
182Dic3—152no—
183Dic3—302no—
184Dic3C4×D1514yescomplemented
185C2×C5C4×D3212yes—
186C2×C5C2×#62411yescharacteristic
187D5—94no—
188C32C42×D511yescharacteristic, complemented, Sylow
189C23—451no—
190C2×C4—32no—
191C2×C4—152no—
192C2×C4—458no—
193C2×C4—451no—
194C2×C4—454no—
195C2×C4D3×D1511yescharacteristic
196C2×C3—22no—
197C2×C3—21no—
198C2×C3C4×D3×D512yes—
199C2×C3C2×#120011yescharacteristic
200C2×C3C2×C4×D1512yes—
201C2×C3C2×C4×D1511yescharacteristic
202D3—154no—
203D3—154no—
204D3—304no—
205C5C4×#62411yescharacteristic, complemented, Sylow
206C22—454no—
207C22—452no—
208C22C2×D3×D1511yescharacteristic
209C4—34no—
210C4—154no—
211C4—452no—
212C4#6714912yesdirect product factor
213C3—21no—
214C3C4×#120011yescharacteristic, complemented
215C3C42×D1511yescharacteristic, complemented
216C2—454no—
217C2C4×D3×D1512yes—
218C2C2×#6714911yescharacteristic
subgroupG/H
center, hypercenterC2×C4D3×D15
commutator, hypocenterC32×C5C2×C42
FrattiniC22C2×D3×D15
FittingC2×C32×C4×C5C22
socle, cosocleC22×C32×C5C23
prime radicalC22×C3⋊D15C22
LCSG ▷ C32×C5
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
3. C3×C4×Dic15C2semidirect
4. C3×C4×C5×Dic3C2semidirect
5. Dic3×Dic15C2semidirect
11. C4×C3⋊D15C4semidirect
14. #67149C4direct (N × H)
23. C4×Dic15D3semidirect
24. C4×C5×Dic3D3semidirect
30. C32×C4×C5C2×C4semidirect
31. C3⋊Dic15C2×C4semidirect
32. C3×Dic15C2×C4semidirect
33. C3×C5×Dic3C2×C4semidirect
38. C3×C4×Dic3D5semidirect
62. C3⋊D15C42semidirect
86. C3×C4×C5C4×D3semidirect
87. C3×C4×C5C4×D3semidirect
91. Dic15C4×D3semidirect
93. C5×Dic3C4×D3semidirect
104. C4×Dic3D15semidirect
105. C32×C5C2×C42semidirect
116. C32×C4C4×D5semidirect
119. C3×Dic3C4×D5semidirect
152. C4×C5#624semidirect
164. C3×C5C42×D3semidirect
165. C3×C5C42×D3semidirect
178. C3×C4#1200semidirect
179. C3×C4C4×D15semidirect
184. Dic3C4×D15semidirect
188. C32C42×D5semidirect
205. C5C4×#624semidirect
212. C4#67149direct (N × H)
214. C3C4×#1200semidirect
215. C3C42×D15semidirect

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×#671492
C3×C4×Dic152
C3×C4×C5×Dic32
Dic3×Dic152
C42×D153
C4×#12003
C4×#6245