Finite Group Databasebeta

← #13086189

Subgroups — #13086189

Order 1440.

486 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 90 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×#67157C211yesmaximal, characteristic, complemented
2C2×#67151C212yesmaximal, complemented
3C2×#67139C211yesmaximal, characteristic, complemented
4C2×C3×#1202C212yesmaximal, complemented
5C5×Dic32C211yesmaximal, characteristic, complemented
6#91458—32nomaximal
7C22×C3⋊D15C2211yescharacteristic
8C22×C3×D15C2212yes—
9C22×C32×D5C2211yescharacteristic
10C2×C5×C3⋊Dic3C2211yescharacteristic
11C2×C3×C5×Dic3C2212yes—
12#67157—22no—
13#67151—24no—
14#67139—22no—
15C3×#1202—24no—
16#63979—51nomaximal, Hall
17C2×D60—32no—
18C2×C3×D20—32no—
19C2×#1202—32no—
20C2×#1202—32no—
21C2×#1202—32no—
22C2×#1202—61no—
23C2×#1202D312yescomplemented
24C4×C5×Dic3—32no—
25C22×C32×C5C2311yescharacteristic
26C2×C3⋊D15—21no—
27C2×C3⋊D15—22no—
28C2×C3×D15—22no—
29C2×C3×D15—22no—
30C2×C3×D15—22no—
31C2×C32×D5—21no—
32C2×C32×D5—22no—
33C5×C3⋊Dic3D412yescomplemented
34C3×C5×Dic3D414yescomplemented
35#4020—91noHall
36C2×#638—51no—
37C2×C3×#67—52no—
38C2×#626—52no—
39C2×#625—51no—
40Dic32D511yescharacteristic, complemented
41C22×D15—32no—
42C22×D15—61no—
43C22×D15C2×D312yes—
44C22×C3×D5—21no—
45C22×C3×D5—32no—
46C22×C3×D5C2×D312yes—
47C2×C3×C4×C5—32no—
48D60—64no—
49C2×C5×Dic3—32no—
50C2×C5×Dic3—61no—
51C2×C5×Dic3C2×D312yes—
52C3×D20—64no—
53#1202—24no—
54#1202—64no—
55#1202—64no—
56#1202—64no—
57#1202—64no—
58#940—152no—
59C2×C32×C5C2×D411yescharacteristic
60C2×C32×C5C2×D412yes—
61C3⋊D15—41no—
62C3×D15—42no—
63C32×D5—41no—
64C2×D20—32no—
65C2×D20—92no—
66C2×D20—91no—
67C2×D20—91no—
68C42×C5—91no—
69C23×C32—51no—
70C22×C3⋊D3—51no—
71C22×C3×D3—52no—
72#638—102no—
73C2×C3⋊Dic3C2×D511yescharacteristic
74C3×#67—104no—
75C2×C3×Dic3C2×D512yes—
76#626—104no—
77#625—102no—
78C22×C3×C5—21no—
79C22×C3×C5C22×D312yes—
80C2×D15—22no—
81C2×D15—22no—
82C2×D15—22no—
83C2×D15—62no—
84C2×D15—62no—
85C2×D15—62no—
86C2×D15—62no—
87C2×D15—122no—
88C2×C3×D5—22no—
89C2×C3×D5—22no—
90C2×C3×D5—22no—
91C2×C3×D5—22no—
92C2×C3×D5—42no—
93C2×C3×D5—62no—
94C2×C3×D5—62no—
95C2×C3×D5—62no—
96C3×C4×C5—34no—
97C5×Dic3—34no—
98C5×Dic3—62no—
99C5×Dic3#6714yescomplemented
100C2×C3×D4—152no—
101C2×#67—52no—
102C2×#67—152no—
103C2×#67—152no—
104C2×#67—152no—
105C2×#67—301no—
106C2×D12—152no—
107C4×Dic3—32no—
108C32×C5#12711yescharacteristic, complemented, Hall
109C22×D5—32no—
110C22×D5—91no—
111C22×D5D3211yescharacteristic
112C2×C4×C5—32no—
113C2×C4×C5—91no—
114D20—64no—
115D20—184no—
116D20—182no—
117D20—182no—
118C22×C32—101no—
119C22×C32—102no—
120C22×C32C22×D511yescharacteristic
121C2×C3⋊D3—101no—
122C2×C3⋊D3—102no—
123C2×C3×D3—102no—
124C2×C3×D3—102no—
125C2×C3×D3—102no—
126C3⋊Dic3D2012yescomplemented
127C3×Dic3D2014yescomplemented
128#127—451noSylow
129C2×C3×C5—22no—
130C2×C3×C5—21no—
131C2×C3×C5D3×D412yes—
132C2×C3×C5D3×D412yes—
133C2×C3×C5C2×#6712yes—
134D15—42no—
135D15—122no—
136D15—122no—
137C3×D5—42no—
138C3×D5—42no—
139C3×D5—122no—
140C23×C3—52no—
141C23×C3—101no—
142C23×C3—152no—
143C22×D3—52no—
144C22×D3—152no—
145C22×D3—301no—
146C3×D4—304no—
147C2×C3×C4—32no—
148#67—104no—
149#67—304no—
150#67—304no—
151#67—304no—
152#67—304no—
153C2×Dic3—32no—
154C2×Dic3—61no—
155C2×Dic3D3×D512yes—
156D12—304no—
157C22×C5C2×D3211yescharacteristic
158C2×D5—22no—
159C2×D5—21no—
160C2×D5—62no—
161C2×D5—62no—
162C2×D5—62no—
163C2×D5—182no—
164C2×D5—181no—
165C4×C5—34no—
166C4×C5—92no—
167C2×C32—201no—
168C2×C32C2×D2011yescharacteristic
169C2×C32C2×D2012yes—
170C3⋊D3—201no—
171C3×D3—202no—
172C2×D4—152no—
173C2×D4—452no—
174C2×D4—451no—
175C2×D4—451no—
176C42—91no—
177C3×C5—21no—
178C3×C5#94012yescomplemented
179C22×C3—21no—
180C22×C3—102no—
181C22×C3—102no—
182C22×C3—102no—
183C22×C3—102no—
184C22×C3—202no—
185C22×C3—302no—
186C22×C3—302no—
187C22×C3—302no—
188C22×C3C2×D3×D512yes—
189C2×D3—102no—
190C2×D3—102no—
191C2×D3—102no—
192C2×D3—302no—
193C2×D3—302no—
194C2×D3—302no—
195C2×D3—302no—
196C2×D3—602no—
197C3×C4—34no—
198Dic3—34no—
199Dic3—62no—
200Dic3#120214yescomplemented
201C2×C5D3×#6712yes—
202C2×C5#381111yescharacteristic
203D5—41no—
204D5—122no—
205D5—361no—
206C32#402011yescharacteristic, complemented, Sylow
207C23—51no—
208C23—152no—
209C23—451no—
210D4—304no—
211D4—904no—
212D4—902no—
213D4—902no—
214C2×C4—32no—
215C2×C4—91no—
216C2×C3—22no—
217C2×C3—21no—
218C2×C3—202no—
219C2×C3—202no—
220C2×C3—602no—
221C2×C3D3×D2012yes—
222C2×C3D3×D2012yes—
223C2×C3C2×#120212yes—
224D3—202no—
225D3—602no—
226D3—602no—
227C5#6397911yescharacteristic, complemented, Sylow
228C22—102no—
229C22—101no—
230C22—302no—
231C22—302no—
232C22—302no—
233C22—902no—
234C22—901no—
235C22D32×D511yescharacteristic
236C4—34no—
237C4—92no—
238C3—21no—
239C3#9145812yescomplemented
240C2—201no—
241C2—602no—
242C2—1801no—
243C2D3×#120212yes—
244C2#1062403111yescharacteristic
subgroupG/H
center, Frattini, hypercenterC22D32×D5
commutator, Fitting, socle, cosocleC22×C32×C5C23
hypocenterC32×C5#127
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C2×#67157C2semidirect
2. C2×#67151C2semidirect
3. C2×#67139C2semidirect
4. C2×C3×#1202C2semidirect
5. C5×Dic32C2semidirect
23. C2×#1202D3semidirect
33. C5×C3⋊Dic3D4semidirect
34. C3×C5×Dic3D4semidirect
40. Dic32D5semidirect
99. C5×Dic3#67semidirect
108. C32×C5#127semidirect
126. C3⋊Dic3D20semidirect
127. C3×Dic3D20semidirect
178. C3×C5#940semidirect
200. Dic3#1202semidirect
206. C32#4020semidirect
227. C5#63979semidirect
239. C3#91458semidirect

Maximal subgroups

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

subgroupindex
C2×#671572
C2×#671512
C2×#671392
C2×C3×#12022
C5×Dic322
#914583
#639795