Finite Group Databasebeta

← #13087771

Subgroups — #13087771

Order 1440.

662 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 119 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×#67155C212yesmaximal, complemented
3C3×#6719C212yesmaximal, complemented
4#10623830C212yesmaximal, complemented
5D3×C22⋊Dic5—32nomaximal
6C23×C32×C5C2211yescharacteristic
7C22×C5×C3⋊D3—24no—
8C22×C5×C3⋊D3C414yescomplemented
9C22×C5×C3⋊D3C2211yescharacteristic
10C22×C5×C3⋊D3C2211yescharacteristic
11C2×C3×Dic15C2214yescomplemented
12#67155—24no—
13#63974—51nomaximal, Hall
14C23×C5×D3—32no—
15C23×C5×D3—61no—
16C2×D3×Dic5—34no—
17#6719D312yescomplemented
18C3×C22⋊Dic5—32no—
19(C2×D3)⋊Dic5—34no—
20C22×C32×C5—22no—
21C22×C32×C5C2×C412yescomplemented
22C22×C32×C5C2311yescharacteristic
23C2×C5×C3⋊D3—22no—
24C2×C5×C3⋊D3—28no—
25C2×C5×C3⋊D3C2×C412yes—
26C2×C5×C3⋊D3C2×C412yescomplemented
27C2×C5×C3⋊D3D414yes—
28C3×Dic15—24no—
29C2×C22⋊Dic5—91noHall
30C23×C3⋊D3D511yescharacteristic
31C2×#624—52no—
32C3×#217—52no—
33#3722—52no—
34C23×C3×C5—21no—
35C23×C3×C5C2×D312yes—
36C22×C5×D3—32no—
37C22×C5×D3—38no—
38C22×C5×D3—32no—
39C22×C5×D3—68no—
40C22×C5×D3—64no—
41C22×C5×D3—61no—
42C22×C5×D3—61no—
43C22×C5×D3—68no—
44C2×Dic15C2×D314yescomplemented
45C2×C3×Dic5—34no—
46D3×Dic5—68no—
47D3×C22⋊C4—152no—
48C2×C32×C5—22no—
49C2×C32×C5C22×C411yescharacteristic
50C2×C32×C5C2×D412yes—
51C5×C3⋊D3—22no—
52C5×C3⋊D3C22⋊C414yescomplemented
53C24×C5—91no—
54C22×Dic5—92no—
55C22⋊Dic5—32no—
56C22⋊Dic5—92no—
57C23×C32C2×D511yescharacteristic
58C22×C3⋊D3—24no—
59C22×C3⋊D3Dic514yescomplemented
60C22×C3⋊D3C2×D511yescharacteristic
61C22×C3⋊D3C2×D511yescharacteristic
62C2×C3×Dic3—54no—
63#624—104no—
64C22×C3×C5—24no—
65C22×C3×C5—24no—
66C22×C3×C5—22no—
67C22×C3×C5—21no—
68C22×C3×C5C4×D314yescomplemented
69C22×C3×C5C22×D312yes—
70C2×C5×D3—34no—
71C2×C5×D3—38no—
72C2×C5×D3—34no—
73C2×C5×D3—62no—
74C2×C5×D3—62no—
75C2×C5×D3—64no—
76C2×C5×D3—616no—
77C2×C5×D3—616no—
78C2×C5×D3—64no—
79C2×C5×D3—64no—
80Dic15—24no—
81C3×Dic5—64no—
82C23×D3—32no—
83C23×D3—61no—
84C2×C4×D3—154no—
85C3×C22⋊C4—152no—
86#217—52no—
87(C2×D3)⋊C4—154no—
88C32×C5C2×C22⋊C411yescharacteristic, complemented, Hall
89C23×C5—91no—
90C23×C5—94no—
91C23×C5—91no—
92C23×C5—184no—
93C23×C5D3211yescharacteristic
94C2×Dic5—34no—
95C2×Dic5—184no—
96C22×C32—22no—
97C22×C32C2×Dic512yescomplemented
98C22×C32C22×D511yescharacteristic
99C2×C3⋊D3—22no—
100C2×C3⋊D3—28no—
101C2×C3⋊D3C2×Dic512yes—
102C2×C3⋊D3C2×Dic512yescomplemented
103C2×C3⋊D3C22⋊D514yes—
104C3×Dic3—104no—
105C2×C22⋊C4—451noSylow
106C2×C3×C5—24no—
107C2×C3×C5—24no—
108C2×C3×C5—21no—
109C2×C3×C5—22no—
110C2×C3×C5C2×C4×D312yes—
111C2×C3×C5D3×D414yes—
112C5×D3—38no—
113C5×D3—64no—
114C5×D3—64no—
115C5×D3—64no—
116C23×C3—21no—
117C23×C3D3×D512yes—
118C22×D3—32no—
119C22×D3—38no—
120C22×D3—32no—
121C22×D3—64no—
122C22×D3—61no—
123C22×D3—61no—
124C22×D3—68no—
125C22×D3—68no—
126C2×C3×C4—154no—
127C2×Dic3—54no—
128C4×D3—308no—
129C22×C5—22no—
130C22×C5—92no—
131C22×C5—94no—
132C22×C5—92no—
133C22×C5—188no—
134C22×C5—182no—
135C22×C5#62412yescomplemented
136C22×C5C2×D3211yescharacteristic
137Dic5—64no—
138C2×C32—22no—
139C2×C32C22×Dic511yescharacteristic
140C2×C32C2×C22⋊D512yes—
141C3⋊D3—22no—
142C3⋊D3C22⋊Dic514yescomplemented
143C24—91no—
144C22×C4—452no—
145C22⋊C4—152no—
146C22⋊C4—452no—
147C3×C5—21no—
148C3×C5D3×C22⋊C412yescomplemented
149C22×C3—24no—
150C22×C3—24no—
151C22×C3—22no—
152C22×C3—21no—
153C22×C3D3×Dic514yescomplemented
154C22×C3C2×D3×D512yes—
155C2×D3—34no—
156C2×D3—38no—
157C2×D3—34no—
158C2×D3—62no—
159C2×D3—62no—
160C2×D3—64no—
161C2×D3—616no—
162C2×D3—616no—
163C2×D3—64no—
164C2×D3—64no—
165C3×C4—304no—
166Dic3—104no—
167C2×C5—22no—
168C2×C5—94no—
169C2×C5—182no—
170C2×C5C2×#62411yescharacteristic
171C2×C5#381112yes—
172C32C2×C22⋊Dic511yescharacteristic, complemented, Sylow
173C23—91no—
174C23—94no—
175C23—91no—
176C23—184no—
177C23(C3⋊D3)⋊D511yescharacteristic
178C2×C4—154no—
179C2×C4—904no—
180C2×C3—24no—
181C2×C3—24no—
182C2×C3—21no—
183C2×C3—22no—
184C2×C3C2×D3×Dic512yes—
185C2×C3D3×C22⋊D514yes—
186D3—38no—
187D3—64no—
188D3—64no—
189D3—64no—
190C5#6397411yescharacteristic, complemented, Sylow
191C22—22no—
192C22—92no—
193C22—94no—
194C22—92no—
195C22—188no—
196C22—182no—
197C22#6715512yescomplemented
198C22C2×(C3⋊D3)⋊D511yescharacteristic
199C4—304no—
200C3—21no—
201C3D3×C22⋊Dic512yescomplemented
202C2—22no—
203C2—94no—
204C2—182no—
205C2C2×#6715511yescharacteristic
206C2#1062423612yes—
subgroupG/H
center, FrattiniC22C2×(C3⋊D3)⋊D5
commutatorC2×C32×C5C22×C4
FittingC23×C32×C5C22
socle, cosocleC22×C32×C5C23
prime radicalC23×C5×C3⋊D3C2
hypercenterC23(C3⋊D3)⋊D5
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×#67155C2semidirect
3. C3×#6719C2semidirect
4. #10623830C2semidirect
8. C22×C5×C3⋊D3C4semidirect
11. C2×C3×Dic15C22semidirect
17. #6719D3semidirect
21. C22×C32×C5C2×C4semidirect
26. C2×C5×C3⋊D3C2×C4semidirect
44. C2×Dic15C2×D3semidirect
52. C5×C3⋊D3C22⋊C4semidirect
59. C22×C3⋊D3Dic5semidirect
68. C22×C3×C5C4×D3semidirect
88. C32×C5C2×C22⋊C4semidirect
97. C22×C32C2×Dic5semidirect
102. C2×C3⋊D3C2×Dic5semidirect
135. C22×C5#624semidirect
142. C3⋊D3C22⋊Dic5semidirect
148. C3×C5D3×C22⋊C4semidirect
153. C22×C3D3×Dic5semidirect
172. C32C2×C22⋊Dic5semidirect
190. C5#63974semidirect
197. C22#67155semidirect
201. 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×#671552
C3×#67192
#106238302
D3×C22⋊Dic53
#639745