Finite Group Databasebeta

← C3⋊Dic3×C22⋊D5 #13087032

Subgroups — C3⋊Dic3×C22⋊D5 #13087032

Order 1440.

564 conjugacy classes of subgroups; only the 180 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 180 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
1C22×C5×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C2×C32×C22⋊D5C211yesmaximal, characteristic
3C2×D5×C3⋊Dic3C211yesmaximal, characteristic, complemented
4#10623913C211yesmaximal, characteristic, complemented
5#10623773C211yesmaximal, characteristic, complemented
6#10623770C211yesmaximal, characteristic, complemented
7Dic5×C3⋊Dic3C211yesmaximal, characteristic, complemented
8Dic3×C22⋊D5—34nomaximal
9C23×C32×C5C2211yescharacteristic
10C22×C32×D5C2211yescharacteristic
11C2×C3⋊Dic15C2211yescharacteristic
12C2×C3⋊Dic15C2211yescharacteristic
13C2×C5×C3⋊Dic3—22no—
14C2×C5×C3⋊Dic3C2211yescharacteristic
15C2×C5×C3⋊Dic3C2211yescharacteristic
16C32×C22⋊D5C414yescomplemented
17C2×C32×Dic5C2211yescharacteristic
18D5×C3⋊Dic3—22no—
19D4×C3⋊Dic3—51nomaximal, Hall
20C22×C5×Dic3—34no—
21C2×C3×C22⋊D5D314yes—
22C2×D5×Dic3—34no—
23#6719—34no—
24#6668—34no—
25#6665—34no—
26Dic3×Dic5—34no—
27C22×C32×C5—21no—
28C22×C32×C5—21no—
29C22×C32×C5C2×C412yescomplemented
30C22×C32×C5C2311yescharacteristic
31C2×C32×D5—21no—
32C2×C32×D5—21no—
33C2×C32×D5C2×C412yescomplemented
34C3⋊Dic15—21no—
35C3⋊Dic15—21no—
36C5×C3⋊Dic3—21no—
37C5×C3⋊Dic3D412yescomplemented
38C32×Dic5C2×C412yescomplemented
39C4×C22⋊D5—91noHall
40C2×C32×D4—51no—
41C22×C3⋊Dic3—51no—
42C22×C3⋊Dic3D511yescharacteristic, complemented
43#3757—51no—
44#3757—51no—
45C4⋊(C3⋊Dic3)—51no—
46C4×C3⋊Dic3—51no—
47C23×C3×C5C2×D314yes—
48C22×C3×D5C2×D314yes—
49C2×Dic15—34no—
50C2×Dic15—34no—
51C2×C5×Dic3—34no—
52C2×C5×Dic3—34no—
53C2×C5×Dic3—68no—
54C3×C22⋊D5Dic3116yescomplemented
55C2×C3×Dic5C2×D314yes—
56D5×Dic3—68no—
57D4×Dic3—154no—
58C2×C32×C5—22no—
59C2×C32×C5C22×C411yescharacteristic
60C2×C32×C5C2×D411yescharacteristic
61C2×C32×C5#4111yescharacteristic
62C32×D5—22no—
63C22×C4×C5—91no—
64C2×C22⋊D5C3⋊D311yescharacteristic
65C2×C4×D5—91no—
66C22⋊Dic5—91no—
67#685—91no—
68#683—91no—
69C4×Dic5—91no—
70C23×C32—51no—
71C23×C32C2×D511yescharacteristic
72C32×D4—54no—
73C2×C32×C4—51no—
74C2×C3⋊Dic3—22no—
75C2×C3⋊Dic3—51no—
76C2×C3⋊Dic3—51no—
77C2×C3⋊Dic3—102no—
78C2×C3⋊Dic3C2×D511yescharacteristic
79C2×C3⋊Dic3C2×D511yescharacteristic
80C22×C3×C5—24no—
81C22×C3×C5—24no—
82C22×C3×C5C2×Dic318yescomplemented
83C22×C3×C5C22×D314yes—
84C2×C3×D5—24no—
85C2×C3×D5—24no—
86C2×C3×D5C2×Dic318yescomplemented
87Dic15—64no—
88Dic15—64no—
89C3×Dic5C2×Dic318yescomplemented
90C5×Dic3—38no—
91C5×Dic3—64no—
92C2×C3×D4—54no—
93C22×Dic3—34no—
94C22×Dic3—154no—
95#217—154no—
96#217—154no—
97C4⋊Dic3—154no—
98C4×Dic3—154no—
99C32×C5C4×D411yescharacteristic, complemented, Hall
100C23×C5C2×C3⋊D311yescharacteristic
101C22×D5C2×C3⋊D311yescharacteristic
102C2×C4×C5—91no—
103C2×C4×C5—91no—
104C2×C4×C5—182no—
105C22⋊D5C3⋊Dic314yesdirect product factor
106C2×Dic5—91no—
107C2×Dic5—91no—
108C2×Dic5C2×C3⋊D311yescharacteristic
109C4×D5—182no—
110C22×C32—21no—
111C22×C32—21no—
112C22×C32—52no—
113C22×C32—101no—
114C22×C32—101no—
115C22×C32C4×D512yescomplemented
116C22×C32C22×D511yescharacteristic
117C32×C4—52no—
118C3⋊Dic3—21no—
119C3⋊Dic3—101no—
120C3⋊Dic3—101no—
121C3⋊Dic3C22⋊D512yesdirect product factor
122C4×D4—451noSylow
123C2×C3×C5—28no—
124C2×C3×C5D3×D414yes—
125C2×C3×C5#23714yes—
126C2×C3×C5C22×Dic314yes—
127C3×D5—28no—
128C23×C3—54no—
129C23×C3D3×D514yes—
130C3×D4—516no—
131C2×C3×C4—54no—
132C2×Dic3—34no—
133C2×Dic3—34no—
134C2×Dic3—68no—
135C2×Dic3—154no—
136C2×Dic3—154no—
137C2×Dic3—308no—
138C22×C5—21no—
139C22×C5—21no—
140C22×C5C2×C3⋊Dic312yescomplemented
141C22×C5C22×C3⋊D311yescharacteristic
142C2×D5—21no—
143C2×D5—21no—
144C2×D5C2×C3⋊Dic312yescomplemented
145C4×C5—92no—
146C4×C5—181no—
147Dic5—181no—
148Dic5—181no—
149Dic5C2×C3⋊Dic312yescomplemented
150C2×C32—22no—
151C2×C32—102no—
152C2×C32C2×C4×D511yescharacteristic
153C2×C32#70911yescharacteristic
154C2×C32C2×C22⋊D511yescharacteristic
155C2×D4—51no—
156C22×C4—91no—
157C22×C4—451no—
158C4⋊C4—451no—
159C22⋊C4—451no—
160C22⋊C4—451no—
161C42—451no—
162C3×C5D4×Dic314yescomplemented
163C22×C3—24no—
164C22×C3—24no—
165C22×C3—58no—
166C22×C3—104no—
167C22×C3—104no—
168C22×C3D5×Dic318yescomplemented
169C22×C3C2×D3×D514yes—
170C3×C4—58no—
171Dic3—38no—
172Dic3—64no—
173Dic3—304no—
174Dic3—304no—
175C2×C5—22no—
176C2×C5D4×C3⋊D311yescharacteristic
177C2×C5#383011yescharacteristic
178C2×C5C22×C3⋊Dic311yescharacteristic
179D5—22no—
180C32C4×C22⋊D511yescharacteristic, complemented, Sylow
181C23—51no—
182C23D5×C3⋊D311yescharacteristic
183D4—54no—
184C2×C4—51no—
185C2×C4—91no—
186C2×C4—91no—
187C2×C4—182no—
188C2×C4—451no—
189C2×C4—451no—
190C2×C4—902no—
191C2×C3—28no—
192C2×C3—108no—
193C2×C3C2×D5×Dic314yes—
194C2×C3#677914yes—
195C2×C3D3×C22⋊D514yes—
196C5D4×C3⋊Dic311yescharacteristic, complemented, Sylow
197C22—21no—
198C22—21no—
199C22—52no—
200C22—101no—
201C22—101no—
202C22D5×C3⋊Dic312yescomplemented
203C22C2×D5×C3⋊D311yescharacteristic
204C4—52no—
205C4—92no—
206C4—181no—
207C4—901no—
208C4—901no—
209C3Dic3×C22⋊D514yescomplemented
210C2—22no—
211C2—102no—
212C2C2×D5×C3⋊Dic311yescharacteristic
213C2#1062416211yescharacteristic
214C2C3⋊D3×C22⋊D511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×C3⋊D3
commutatorC2×C32×C5C22×C4
FittingC23×C32×C5C22
socle, cosocleC22×C32×C5C23
prime radicalC2×C32×C22⋊D5C2
hypercenterC23D5×C3⋊D3
hypocenterC32×C5C4×D4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C22×C5×C3⋊Dic3C2semidirect
3. C2×D5×C3⋊Dic3C2semidirect
4. #10623913C2semidirect
5. #10623773C2semidirect
6. #10623770C2semidirect
7. Dic5×C3⋊Dic3C2semidirect
16. C32×C22⋊D5C4semidirect
29. C22×C32×C5C2×C4semidirect
33. C2×C32×D5C2×C4semidirect
37. C5×C3⋊Dic3D4semidirect
38. C32×Dic5C2×C4semidirect
42. C22×C3⋊Dic3D5semidirect
54. C3×C22⋊D5Dic3semidirect
82. C22×C3×C5C2×Dic3semidirect
86. C2×C3×D5C2×Dic3semidirect
89. C3×Dic5C2×Dic3semidirect
99. C32×C5C4×D4semidirect
105. C22⋊D5C3⋊Dic3direct (N × H)
115. C22×C32C4×D5semidirect
121. C3⋊Dic3C22⋊D5direct (N × H)
140. C22×C5C2×C3⋊Dic3semidirect
144. C2×D5C2×C3⋊Dic3semidirect
149. Dic5C2×C3⋊Dic3semidirect
162. C3×C5D4×Dic3semidirect
168. C22×C3D5×Dic3semidirect
180. C32C4×C22⋊D5semidirect
196. C5D4×C3⋊Dic3semidirect
202. C22D5×C3⋊Dic3semidirect
209. C3Dic3×C22⋊D5semidirect

Maximal subgroups

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

subgroupindex
C22×C5×C3⋊Dic32
C2×C32×C22⋊D52
C2×D5×C3⋊Dic32
#106239132
#106237732
#106237702
Dic5×C3⋊Dic32
Dic3×C22⋊D53
D4×C3⋊Dic35