Finite Group Databasebeta

← C4×#67157 #13087693

Subgroups — C4×#67157 #13087693

Order 1440.

406 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 103 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×C3×C4×D15C212yesmaximal, complemented
2C2×#67157C211yesmaximal, characteristic
3C4×C5×C3⋊Dic3C211yesmaximal, characteristic, complemented
4#10623832C211yesmaximal, characteristic, complemented
5#10623829C212yesmaximal, complemented
6C4×#1202—32nomaximal
7C22×C3×D15C2212yes—
8C2×C32×C4×C5C2211yescharacteristic
9C2×C5×C3⋊Dic3C2211yescharacteristic
10C2×C5×C3⋊Dic3C2211yescharacteristic
11C2×C3×Dic15C2212yes—
12C3×C4×D15—24no—
13#67157C414yesdirect product factor
14C4×#625—51nomaximal, Hall
15C2×C4×D15D312yescomplemented
16C2×C3×C4×D5—32no—
17C2×#1202—32no—
18C4×C5×Dic3—32no—
19C4×C5×Dic3—61no—
20Dic3⋊Dic5—32no—
21#6667—32no—
22#6665—32no—
23C22×C32×C5C2311yescharacteristic
24C2×C3×D15—22no—
25C2×C3×D15—22no—
26C2×C3×D15C2×C414yescomplemented
27C32×C4×C5D412yescomplemented
28C5×C3⋊Dic3—21no—
29C5×C3⋊Dic3C2×C412yescomplemented
30C3×Dic15—22no—
31C4×D20—91noHall
32C2×C3×C4×D3—52no—
33C2×#625—51no—
34C4×C3⋊Dic3D511yescharacteristic, complemented
35#3724—51no—
36(C2×D3)⋊Dic3—52no—
37C22×D15C2×D312yes—
38C22×C3×D5—32no—
39C2×C3×C4×C5—21no—
40C2×C3×C4×C5C2×D312yes—
41C2×Dic15C2×D312yes—
42C4×D15—24no—
43C2×C5×Dic3—32no—
44C2×C5×Dic3—32no—
45C2×C5×Dic3—61no—
46C2×C5×Dic3—61no—
47C2×C3×Dic5—32no—
48C3×C4×D5—64no—
49#1202—38no—
50C4×#67—152no—
51C2×C32×C5C22×C411yescharacteristic
52C2×C32×C5C2×D411yescharacteristic
53C2×C32×C5#4111yescharacteristic
54C3×D15—24no—
55C2×D20—91no—
56C2×C4×D5—32no—
57C42×C5—91no—
58#685—92no—
59C4⋊Dic5—91no—
60C22×C3×D3—52no—
61C2×C32×C4C2×D511yescharacteristic
62C2×C3⋊Dic3C2×D511yescharacteristic
63C2×C3⋊Dic3C2×D511yescharacteristic
64C2×C3×Dic3—52no—
65C3×C4×D3—104no—
66#625—54no—
67C22×C3×C5—21no—
68C22×C3×C5C22×D312yes—
69C2×D15—22no—
70C2×D15—22no—
71C2×D15C4×D314yescomplemented
72C2×C3×D5—34no—
73C2×C3×D5—62no—
74C2×C3×D5—62no—
75C3×C4×C5—22no—
76C3×C4×C5#6714yescomplemented
77Dic15—22no—
78C3×Dic5—62no—
79C5×Dic3—34no—
80C5×Dic3—62no—
81C5×Dic3—62no—
82C5×Dic3—62no—
83C22×C3×C4—152no—
84C2×#67—152no—
85C2×C4×D3—52no—
86#217—152no—
87(C2×D3)⋊C4—152no—
88Dic3⋊C4—152no—
89C4×Dic3—32no—
90C4×Dic3—61no—
91C32×C5C4×D411yescharacteristic, complemented, Hall
92C22×D5—32no—
93C2×C4×C5—91no—
94C2×C4×C5—91no—
95C2×C4×C5D3211yescharacteristic
96C2×Dic5—32no—
97D20—94no—
98C4×D5—64no—
99C22×C32C22×D511yescharacteristic
100C2×C3×D3—54no—
101C2×C3×D3—102no—
102C2×C3×D3—102no—
103C32×C4D2012yescomplemented
104C3⋊Dic3—21no—
105C3⋊Dic3C4×D512yescomplemented
106C3×Dic3—102no—
107C4×D4—451noSylow
108C2×C3×C5—21no—
109C2×C3×C5—21no—
110C2×C3×C5—21no—
111C2×C3×C5C2×C4×D312yes—
112C2×C3×C5#23512yes—
113C2×C3×C5C2×#6712yes—
114D15—24no—
115C3×D5—64no—
116C23×C3—152no—
117C22×D3—52no—
118C2×C3×C4—21no—
119C2×C3×C4—152no—
120C2×C3×C4—304no—
121C2×C3×C4D3×D512yes—
122#67—158no—
123C2×Dic3—32no—
124C2×Dic3—32no—
125C2×Dic3—52no—
126C2×Dic3—61no—
127C2×Dic3—61no—
128C4×D3—104no—
129C22×C5C2×D3211yescharacteristic
130C2×D5—34no—
131C2×D5—62no—
132C2×D5—62no—
133C4×C5—92no—
134C4×C5—181no—
135C4×C5#62512yescomplemented
136Dic5—62no—
137C2×C32C2×C4×D511yescharacteristic
138C2×C32C2×D2011yescharacteristic
139C2×C32#70911yescharacteristic
140C3×D3—104no—
141C2×D4—451no—
142C22×C4—152no—
143C4⋊C4—451no—
144C22⋊C4—452no—
145C42—91no—
146C3×C5—21no—
147C3×C5C4×#6712yescomplemented
148C22×C3—21no—
149C22×C3—154no—
150C22×C3—302no—
151C22×C3—302no—
152C22×C3C2×D3×D512yes—
153C2×D3—54no—
154C2×D3—102no—
155C2×D3—102no—
156C3×C4—22no—
157C3×C4—302no—
158C3×C4#120214yescomplemented
159Dic3—34no—
160Dic3—62no—
161Dic3—62no—
162Dic3—62no—
163Dic3—102no—
164C2×C5#379811yescharacteristic
165C2×C5C4×D3211yescharacteristic
166C2×C5C2×#62511yescharacteristic
167D5—64no—
168C32C4×D2011yescharacteristic, complemented, Sylow
169C23—152no—
170D4—454no—
171C2×C4—91no—
172C2×C4—91no—
173C2×C4—152no—
174C2×C4—304no—
175C2×C4(C3⋊D3)⋊D511yescharacteristic
176C2×C3—21no—
177C2×C3—21no—
178C2×C3—21no—
179C2×C3—304no—
180C2×C3#677112yes—
181C2×C3C4×D3×D512yes—
182C2×C3C2×#120212yes—
183D3—104no—
184C5C4×#62511yescharacteristic, complemented, Sylow
185C22—154no—
186C22—302no—
187C22—302no—
188C22C2×(C3⋊D3)⋊D511yescharacteristic
189C4—92no—
190C4—181no—
191C4—302no—
192C4#6715712yesdirect product factor
193C3—21no—
194C3C4×#120212yescomplemented
195C2—304no—
196C2#1062422311yescharacteristic
197C2C4×(C3⋊D3)⋊D511yescharacteristic
198C2C2×#6715711yescharacteristic
subgroupG/H
center, hypercenterC2×C4(C3⋊D3)⋊D5
commutatorC2×C32×C5C22×C4
FrattiniC22C2×(C3⋊D3)⋊D5
FittingC2×C32×C4×C5C22
socle, cosocleC22×C32×C5C23
prime radicalC2×#67157C2
hypocenterC32×C5C4×D4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×D15C2semidirect
3. C4×C5×C3⋊Dic3C2semidirect
4. #10623832C2semidirect
5. #10623829C2semidirect
13. #67157C4direct (N × H)
15. C2×C4×D15D3semidirect
26. C2×C3×D15C2×C4semidirect
27. C32×C4×C5D4semidirect
29. C5×C3⋊Dic3C2×C4semidirect
34. C4×C3⋊Dic3D5semidirect
71. C2×D15C4×D3semidirect
76. C3×C4×C5#67semidirect
91. C32×C5C4×D4semidirect
103. C32×C4D20semidirect
105. C3⋊Dic3C4×D5semidirect
135. C4×C5#625semidirect
147. C3×C5C4×#67semidirect
158. C3×C4#1202semidirect
168. C32C4×D20semidirect
184. C5C4×#625semidirect
192. C4#67157direct (N × H)
194. C3C4×#1202semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×D152
C2×#671572
C4×C5×C3⋊Dic32
#106238322
#106238292
C4×#12023
C4×#6255