Finite Group Databasebeta

← C3⋊D3×C22⋊Dic5 #13087033

Subgroups — C3⋊D3×C22⋊Dic5 #13087033

Order 1440.

792 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 792 conjugacy classes of subgroups — too many to draw. Only its 160 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
1C23×C5×C3⋊D3C211yesmaximal, characteristic
2C2×C3⋊D3×Dic5C212yesmaximal, complemented
3#10623913C211yesmaximal, characteristic, complemented
4C32×C22⋊Dic5C211yesmaximal, characteristic, complemented
5#10623771C212yesmaximal, complemented
6D3×C22⋊Dic5—34nomaximal
7C23×C32×C5C2211yescharacteristic
8C22×C5×C3⋊D3—24no—
9C22×C5×C3⋊D3C414yescomplemented
10C22×C5×C3⋊D3C2211yescharacteristic
11C22×C5×C3⋊D3C2211yescharacteristic
12C2×C3⋊Dic15C2212yescomplemented
13C2×C32×Dic5C2212yescomplemented
14C3⋊D3×Dic5—24no—
15C22⋊C4×C3⋊D3—51nomaximal, Hall
16C23×C5×D3—34no—
17C2×D3×Dic5—38no—
18#6719—34no—
19C3×C22⋊Dic5D314yescomplemented
20(C2×D3)⋊Dic5—38no—
21C22×C32×C5—22no—
22C22×C32×C5C2×C412yescomplemented
23C22×C32×C5C2311yescharacteristic
24C2×C5×C3⋊D3—22no—
25C2×C5×C3⋊D3—28no—
26C2×C5×C3⋊D3C2×C412yes—
27C2×C5×C3⋊D3C2×C412yescomplemented
28C2×C5×C3⋊D3D414yes—
29C3⋊Dic15—22no—
30C32×Dic5—22no—
31C2×C22⋊Dic5—91noHall
32C23×C3⋊D3D511yescharacteristic
33C2×C4×C3⋊D3—52no—
34C32×C22⋊C4—51no—
35#3757—51no—
36#3752—52no—
37C23×C3×C5C2×D314yes—
38C22×C5×D3—34no—
39C22×C5×D3—316no—
40C22×C5×D3—34no—
41C22×C5×D3—616no—
42C2×Dic15—38no—
43C2×C3×Dic5C2×D318yescomplemented
44D3×Dic5—616no—
45D3×C22⋊C4—154no—
46C2×C32×C5—22no—
47C2×C32×C5C22×C411yescharacteristic
48C2×C32×C5C2×D412yes—
49C5×C3⋊D3—22no—
50C5×C3⋊D3C22⋊C414yescomplemented
51C24×C5—91no—
52C22×Dic5—92no—
53C22⋊Dic5—91no—
54C22⋊Dic5—92no—
55C22⋊Dic5C3⋊D311yescharacteristic, direct product factor
56C23×C32C2×D511yescharacteristic
57C22×C3⋊D3—24no—
58C22×C3⋊D3Dic514yescomplemented
59C22×C3⋊D3C2×D511yescharacteristic
60C22×C3⋊D3C2×D511yescharacteristic
61C2×C32×C4—52no—
62C2×C3⋊Dic3—52no—
63C4×C3⋊D3—104no—
64C22×C3×C5—28no—
65C22×C3×C5C4×D318yescomplemented
66C22×C3×C5C22×D314yes—
67C2×C5×D3—38no—
68C2×C5×D3—316no—
69C2×C5×D3—38no—
70C2×C5×D3—632no—
71C2×C5×D3—68no—
72Dic15—68no—
73C3×Dic5—28no—
74C23×D3—34no—
75C2×C4×D3—158no—
76C3×C22⋊C4—54no—
77#217—154no—
78(C2×D3)⋊C4—158no—
79C32×C5C2×C22⋊C411yescharacteristic, complemented, Hall
80C23×C5—91no—
81C23×C5—94no—
82C23×C5—91no—
83C23×C5—184no—
84C23×C5C2×C3⋊D311yescharacteristic
85C2×Dic5—92no—
86C2×Dic5—184no—
87C2×Dic5C2×C3⋊D312yescomplemented
88C22×C32—22no—
89C22×C32C2×Dic512yescomplemented
90C22×C32C22×D511yescharacteristic
91C2×C3⋊D3—22no—
92C2×C3⋊D3—28no—
93C2×C3⋊D3C2×Dic512yes—
94C2×C3⋊D3C2×Dic512yescomplemented
95C2×C3⋊D3C22⋊D514yes—
96C32×C4—102no—
97C3⋊Dic3—102no—
98C2×C22⋊C4—451noSylow
99C2×C3×C5—28no—
100C2×C3×C5C2×C4×D314yes—
101C2×C3×C5D3×D418yes—
102C5×D3—316no—
103C5×D3—68no—
104C23×C3D3×D514yes—
105C22×D3—34no—
106C22×D3—316no—
107C22×D3—34no—
108C22×D3—616no—
109C2×C3×C4—58no—
110C2×Dic3—158no—
111C4×D3—3016no—
112C22×C5—22no—
113C22×C5—92no—
114C22×C5—94no—
115C22×C5—92no—
116C22×C5—188no—
117C22×C5—182no—
118C22×C5C4×C3⋊D312yescomplemented
119C22×C5C22×C3⋊D311yescharacteristic
120Dic5—22no—
121Dic5—182no—
122C2×C32—22no—
123C2×C32C22×Dic511yescharacteristic
124C2×C32C2×C22⋊D512yes—
125C3⋊D3—22no—
126C3⋊D3C22⋊Dic514yesdirect product factor
127C24—91no—
128C22×C4—452no—
129C22⋊C4—51no—
130C22⋊C4—452no—
131C22⋊C4—451no—
132C3×C5D3×C22⋊C414yescomplemented
133C22×C3—28no—
134C22×C3D3×Dic518yescomplemented
135C22×C3C2×D3×D514yes—
136C2×D3—38no—
137C2×D3—316no—
138C2×D3—38no—
139C2×D3—632no—
140C2×D3—68no—
141C3×C4—108no—
142Dic3—308no—
143C2×C5—22no—
144C2×C5—94no—
145C2×C5—182no—
146C2×C5C2×C4×C3⋊D311yescharacteristic
147C2×C5D4×C3⋊D312yes—
148C32C2×C22⋊Dic511yescharacteristic, complemented, Sylow
149C23—91no—
150C23—94no—
151C23—91no—
152C23—184no—
153C23D5×C3⋊D311yescharacteristic
154C2×C4—52no—
155C2×C4—452no—
156C2×C4—904no—
157C2×C3—28no—
158C2×C3C2×D3×Dic514yes—
159C2×C3D3×C22⋊D518yes—
160D3—316no—
161D3—68no—
162C5C22⋊C4×C3⋊D311yescharacteristic, complemented, Sylow
163C22—22no—
164C22—92no—
165C22—94no—
166C22—92no—
167C22—188no—
168C22—182no—
169C22C3⋊D3×Dic512yescomplemented
170C22C2×D5×C3⋊D311yescharacteristic
171C4—102no—
172C4—902no—
173C3D3×C22⋊Dic514yescomplemented
174C2—22no—
175C2—94no—
176C2—182no—
177C2C2×C3⋊D3×Dic511yescharacteristic
178C2C3⋊D3×C22⋊D512yes—
subgroupG/H
center, FrattiniC22C2×D5×C3⋊D3
commutatorC2×C32×C5C22×C4
FittingC23×C32×C5C22
socle, cosocleC22×C32×C5C23
prime radicalC23×C5×C3⋊D3C2
hypercenterC23D5×C3⋊D3
hypocenterC32×C5C2×C22⋊C4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
2. C2×C3⋊D3×Dic5C2semidirect
3. #10623913C2semidirect
4. C32×C22⋊Dic5C2semidirect
5. #10623771C2semidirect
9. C22×C5×C3⋊D3C4semidirect
12. C2×C3⋊Dic15C22semidirect
13. C2×C32×Dic5C22semidirect
19. C3×C22⋊Dic5D3semidirect
22. C22×C32×C5C2×C4semidirect
27. C2×C5×C3⋊D3C2×C4semidirect
43. C2×C3×Dic5C2×D3semidirect
50. C5×C3⋊D3C22⋊C4semidirect
55. C22⋊Dic5C3⋊D3direct (N × H)
58. C22×C3⋊D3Dic5semidirect
65. C22×C3×C5C4×D3semidirect
79. C32×C5C2×C22⋊C4semidirect
87. C2×Dic5C2×C3⋊D3semidirect
89. C22×C32C2×Dic5semidirect
94. C2×C3⋊D3C2×Dic5semidirect
118. C22×C5C4×C3⋊D3semidirect
126. C3⋊D3C22⋊Dic5direct (N × H)
132. C3×C5D3×C22⋊C4semidirect
134. C22×C3D3×Dic5semidirect
148. C32C2×C22⋊Dic5semidirect
162. C5C22⋊C4×C3⋊D3semidirect
169. C22C3⋊D3×Dic5semidirect
173. C3D3×C22⋊Dic5semidirect

Maximal subgroups

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

subgroupindex
C23×C5×C3⋊D32
C2×C3⋊D3×Dic52
#106239132
C32×C22⋊Dic52
#106237712
D3×C22⋊Dic53
C22⋊C4×C3⋊D35