Finite Group Databasebeta

← #13086190

Subgroups — #13086190

Order 1440.

486 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 82 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×#67152C212yesmaximal, complemented
2C2×C5×#625C211yesmaximal, characteristic, complemented
3C2×#67139C211yesmaximal, characteristic, complemented
4C2×C3×#1201C212yesmaximal, complemented
5#10623828C211yesmaximal, characteristic, complemented
6#91567—32nomaximal
7C22×C3⋊D15C2211yescharacteristic
8C22×C3×C5×D3C2212yes—
9C22×C32×D5C2211yescharacteristic
10C2×C5×C3⋊Dic3C2211yescharacteristic
11C2×C3×Dic15C2212yes—
12#67152—24no—
13C5×#625—22no—
14#67139—22no—
15C3×#1201—24no—
16#63979—51nomaximal, Hall
17C2×#1220—32no—
18C2×C5×#67—32no—
19C2×C3×C22⋊D5—32no—
20C2×#1203—32no—
21C2×#1202—32no—
22C2×#1202—61no—
23C2×#1201D312yescomplemented
24Dic3×Dic5—32no—
25C22×C32×C5C2311yescharacteristic
26C2×C3⋊D15—21no—
27C2×C3⋊D15—22no—
28C2×C3×C5×D3—22no—
29C2×C3×C5×D3—22no—
30C2×C3×C5×D3—22no—
31C2×C32×D5—21no—
32C2×C32×D5—22no—
33C5×C3⋊Dic3D412yescomplemented
34C3×Dic15D414yescomplemented
35#4086—91noHall
36C2×#638—51no—
37C2×C3×#67—52no—
38C2×#626—52no—
39C2×#625D511yescharacteristic, complemented
40Dic32—51no—
41C23×C3×C5—32no—
42C22×D15—32no—
43C22×D15—61no—
44C22×C5×D3C2×D312yes—
45C22×C3×D5—21no—
46C22×C3×D5C2×D312yes—
47#1220—64no—
48C2×Dic15C2×D312yes—
49C5×#67—64no—
50C2×C5×Dic3—32no—
51C2×C5×Dic3—61no—
52C3×C22⋊D5—64no—
53C2×C3×Dic5—32no—
54#1203—64no—
55#1202—64no—
56#1202—64no—
57#1201—24no—
58#940—152no—
59C2×C32×C5C2×D412yes—
60C2×C32×C5C2×D411yescharacteristic
61C3⋊D15—41no—
62C3×C5×D3—42no—
63C32×D5—41no—
64C2×C5×D4—91no—
65C2×C22⋊D5—32no—
66C2×C22⋊D5—92no—
67C2×D20—91no—
68C4×Dic5—91no—
69C23×C32—51no—
70C22×C3⋊D3—51no—
71C22×C3×D3C2×D512yes—
72#638—102no—
73C2×C3⋊Dic3C2×D511yescharacteristic
74C3×#67—104no—
75C2×C3×Dic3—52no—
76#626—104no—
77#625—22no—
78C22×C3×C5—21no—
79C22×C3×C5—62no—
80C22×C3×C5—62no—
81C22×C3×C5—62no—
82C22×C3×C5C22×D312yes—
83C2×D15—62no—
84C2×D15—62no—
85C2×D15—62no—
86C2×D15—62no—
87C2×D15—122no—
88C2×C5×D3—22no—
89C2×C5×D3—22no—
90C2×C5×D3—22no—
91C2×C3×D5—22no—
92C2×C3×D5—22no—
93C2×C3×D5—22no—
94C2×C3×D5—22no—
95C2×C3×D5—42no—
96Dic15#6714yescomplemented
97C3×Dic5—34no—
98C5×Dic3—34no—
99C5×Dic3—62no—
100C2×C3×D4—152no—
101C2×#67—32no—
102C2×#67—52no—
103C2×#67—152no—
104C2×#67—152no—
105C2×#67—301no—
106C2×D12—152no—
107C4×Dic3—152no—
108C32×C5#12711yescharacteristic, complemented, Hall
109C23×C5—32no—
110C22×D5—91no—
111C22×D5D3211yescharacteristic
112C5×D4—182no—
113C2×C4×C5—91no—
114C22⋊D5—64no—
115C22⋊D5—184no—
116C2×Dic5—32no—
117D20—182no—
118C22×C32—101no—
119C22×C32—102no—
120C22×C32C22×D511yescharacteristic
121C2×C3⋊D3—101no—
122C2×C3⋊D3—102no—
123C2×C3×D3—22no—
124C2×C3×D3—22no—
125C2×C3×D3—22no—
126C3⋊Dic3C22⋊D512yescomplemented
127C3×Dic3—54no—
128#127—451noSylow
129C2×C3×C5—22no—
130C2×C3×C5—21no—
131C2×C3×C5—122no—
132C2×C3×C5D3×D412yes—
133C2×C3×C5D3×D412yes—
134C2×C3×C5C2×#6712yes—
135D15—122no—
136D15—122no—
137C3×D5—42no—
138C3×D5—42no—
139C5×D3—42no—
140C23×C3—32no—
141C23×C3—52no—
142C23×C3—101no—
143C22×D3—152no—
144C22×D3—301no—
145C22×D3D3×D512yes—
146C3×D4—304no—
147C2×C3×C4—152no—
148#67—64no—
149#67—104no—
150#67—304no—
151#67—304no—
152#67—304no—
153C2×Dic3—32no—
154C2×Dic3—52no—
155C2×Dic3—61no—
156D12—304no—
157C22×C5—62no—
158C22×C5—62no—
159C22×C5—62no—
160C22×C5C2×D3211yescharacteristic
161C2×D5—22no—
162C2×D5—21no—
163C2×D5—182no—
164C2×D5—181no—
165C4×C5—92no—
166Dic5—34no—
167C2×C32—201no—
168C2×C32D4×D512yes—
169C2×C32C2×C22⋊D511yescharacteristic
170C3⋊D3—201no—
171C3×D3—42no—
172C2×D4—91no—
173C2×D4—152no—
174C2×D4—451no—
175C2×D4—452no—
176C42—451no—
177C3×C5—21no—
178C3×C5#94012yescomplemented
179C22×C3—21no—
180C22×C3—62no—
181C22×C3—62no—
182C22×C3—62no—
183C22×C3—102no—
184C22×C3—102no—
185C22×C3—102no—
186C22×C3—102no—
187C22×C3—202no—
188C22×C3C2×D3×D512yes—
189C2×D3—22no—
190C2×D3—22no—
191C2×D3—22no—
192C2×D3—302no—
193C2×D3—302no—
194C2×D3—302no—
195C2×D3—302no—
196C2×D3—602no—
197C3×C4—154no—
198Dic3—34no—
199Dic3—54no—
200Dic3—62no—
201C2×C5—122no—
202C2×C5D3×#6712yes—
203C2×C5#381111yescharacteristic
204D5—41no—
205D5—361no—
206C32#408611yescharacteristic, complemented, Sylow
207C23—32no—
208C23—51no—
209C23—451no—
210D4—182no—
211D4—304no—
212D4—902no—
213D4—904no—
214C2×C4—91no—
215C2×C4—152no—
216C2×C3—22no—
217C2×C3—21no—
218C2×C3—122no—
219C2×C3—202no—
220C2×C3—202no—
221C2×C3D5×#6712yes—
222C2×C3D3×C22⋊D512yes—
223C2×C3#679012yes—
224D3—42no—
225D3—602no—
226D3—602no—
227C5#6397911yescharacteristic, complemented, Sylow
228C22—62no—
229C22—62no—
230C22—62no—
231C22—102no—
232C22—101no—
233C22—902no—
234C22—901no—
235C22D32×D511yescharacteristic
236C4—92no—
237C4—154no—
238C3—21no—
239C3#9156712yescomplemented
240C2—122no—
241C2—201no—
242C2—1801no—
243C2#1062402712yes—
244C2#1062402911yescharacteristic
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×#67152C2semidirect
2. C2×C5×#625C2semidirect
3. C2×#67139C2semidirect
4. C2×C3×#1201C2semidirect
5. #10623828C2semidirect
23. C2×#1201D3semidirect
33. C5×C3⋊Dic3D4semidirect
34. C3×Dic15D4semidirect
39. C2×#625D5semidirect
96. Dic15#67semidirect
108. C32×C5#127semidirect
126. C3⋊Dic3C22⋊D5semidirect
178. C3×C5#940semidirect
206. C32#4086semidirect
227. C5#63979semidirect
239. C3#91567semidirect

Maximal subgroups

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

subgroupindex
C2×#671522
C2×C5×#6252
C2×#671392
C2×C3×#12012
#106238282
#915673
#639795