Finite Group Databasebeta

← #11756425

Subgroups — #11756425

Order 960.

504 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 131 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
1C3×C5×#123C211yesmaximal, characteristic, complemented
2#91829C211yesmaximal, characteristic, complemented
3#91826C211yesmaximal, characteristic, complemented
4#91819C212yesmaximal, complemented
5#91787C212yesmaximal, complemented
6#91784C212yesmaximal, complemented
7#91773C212yesmaximal, complemented
8#91772C212yesmaximal, complemented
9#91771C212yesmaximal, complemented
10#66000—31nomaximal, Hall
11C23×D15C2211yescharacteristic
12C2×C3×C5×D4C2211yescharacteristic
13C22×C3×C4×C5C2211yescharacteristic, complemented
14C2×#1220C2212yes—
15C2×#1220C2212yes—
16C2×#1220C2212yescomplemented
17C2×D60C2212yes—
18C2×D60C2212yes—
19C2×D60C2211yescharacteristic, complemented
20C2×C4×D15C2212yescomplemented
21C3×C5×C4⋊C4C2212yescomplemented
22C3×C5×C22⋊C4C2212yes—
23C3×C5×C22⋊C4C2211yescharacteristic, complemented
24#6719C2211yescharacteristic
25#6714C2212yes—
26#6714C2212yes—
27#6714C2212yes—
28#6714C2212yescomplemented
29C4⋊Dic15C2212yescomplemented
30#6712C2212yescomplemented
31C4×Dic15C2211yescharacteristic, complemented
32#5666—51nomaximal, Hall
33C5×#123D311yescharacteristic, complemented
34#4086—31no—
35#4083—31no—
36#4076—32no—
37#4044—32no—
38#4041—32no—
39#4030—32no—
40#4029—32no—
41#4028—32no—
42C23×C3×C5C2311yescharacteristic
43C23×C3×C5C2311yescharacteristic
44C22×D15—41no—
45C22×D15—42no—
46C22×D15C2312yes—
47C22×D15C2312yes—
48C3×C5×D4—41no—
49C2×C3×C4×C5—41no—
50C2×C3×C4×C5C2311yescharacteristic
51C2×C3×C4×C5C2312yes—
52C2×C3×C4×C5C2312yes—
53#1220—42no—
54#1220—42no—
55#1220—42no—
56C2×Dic15C2312yes—
57C2×Dic15C2312yes—
58D60—42no—
59D60—42no—
60D60—41no—
61C4×D15—42no—
62C3×#123D511yescharacteristic, complemented
63#940—51no—
64#937—51no—
65#930—52no—
66#898—52no—
67#895—52no—
68#884—52no—
69#883—52no—
70#882—52no—
71C23×D5—31no—
72C2×C5×D4C2×D311yescharacteristic
73C22×C4×C5C2×D311yescharacteristic, complemented
74C2×C22⋊D5—32no—
75C2×C22⋊D5—32no—
76C2×C22⋊D5—32no—
77C2×D20—32no—
78C2×D20—32no—
79C2×D20—31no—
80C2×C4×D5—32no—
81C5×C4⋊C4C2×D312yescomplemented
82C5×C22⋊C4C2×D312yes—
83C5×C22⋊C4C2×D311yescharacteristic, complemented
84C22⋊Dic5—31no—
85#685—32no—
86#685—32no—
87#685—32no—
88#685—32no—
89C4⋊Dic5—32no—
90#683—32no—
91C4×Dic5—31no—
92#560—151noSylow
93C22×C3×C5—22no—
94C22×C3×C5—22no—
95C22×C3×C5—21no—
96C22×C3×C5—21no—
97C22×C3×C5C2411yescharacteristic
98C2×D15—22no—
99C2×D15—22no—
100C2×D15—22no—
101C2×D15—22no—
102C2×D15—22no—
103C2×D15—22no—
104C2×D15—44no—
105C3×C4×C5—22no—
106C3×C4×C5—22no—
107C3×C4×C5—21no—
108Dic15—22no—
109Dic15—22no—
110C23×D3—51no—
111C2×C3×D4C2×D511yescharacteristic
112C22×C3×C4C2×D511yescharacteristic, complemented
113C2×#67—52no—
114C2×#67—52no—
115C2×#67—52no—
116C2×D12—52no—
117C2×D12—52no—
118C2×D12—51no—
119C2×C4×D3—52no—
120C3×C4⋊C4C2×D512yescomplemented
121C3×C22⋊C4C2×D512yes—
122C3×C22⋊C4C2×D511yescharacteristic, complemented
123#217—51no—
124(C2×D3)⋊C4—52no—
125(C2×D3)⋊C4—52no—
126(C2×D3)⋊C4—52no—
127(C2×D3)⋊C4—52no—
128C4⋊Dic3—52no—
129Dic3⋊C4—52no—
130C4×Dic3—51no—
131C23×C5C22×D311yescharacteristic
132C23×C5C22×D311yescharacteristic
133C22×D5—32no—
134C22×D5—32no—
135C22×D5—121no—
136C22×D5—122no—
137C5×D4—41no—
138C2×C4×C5—41no—
139C2×C4×C5C22×D311yescharacteristic
140C2×C4×C5C22×D312yes—
141C2×C4×C5C22×D312yes—
142C22⋊D5—122no—
143C22⋊D5—122no—
144C22⋊D5—122no—
145C2×Dic5—32no—
146C2×Dic5—32no—
147D20—122no—
148D20—121no—
149D20—122no—
150C4×D5—122no—
151#127—151no—
152#126—152no—
153#123—152no—
154#123D1511yescharacteristic, complemented
155#121—152no—
156#121—152no—
157#121—152no—
158#120—151no—
159#120—152no—
160C2×C3×C5—41no—
161C2×C3×C5—41no—
162C2×C3×C5H(5,𝔽2)11yescharacteristic
163C2×C3×C5H(5,𝔽2)12yes—
164D15—42no—
165D15—42no—
166C23×C3C22×D511yescharacteristic
167C23×C3C22×D511yescharacteristic
168C22×D3—52no—
169C22×D3—52no—
170C22×D3—201no—
171C22×D3—202no—
172C3×D4—41no—
173C2×C3×C4—41no—
174C2×C3×C4C22×D511yescharacteristic
175C2×C3×C4C22×D512yes—
176C2×C3×C4C22×D512yes—
177#67—202no—
178#67—202no—
179#67—202no—
180C2×Dic3—52no—
181C2×Dic3—52no—
182D12—202no—
183D12—201no—
184D12—202no—
185C4×D3—202no—
186C22×C5—21no—
187C22×C5—21no—
188C22×C5—22no—
189C22×C5—22no—
190C22×C5C23×D311yescharacteristic
191C2×D5—62no—
192C2×D5—62no—
193C2×D5—62no—
194C2×D5—62no—
195C2×D5—62no—
196C2×D5—62no—
197C2×D5—124no—
198C4×C5—22no—
199C4×C5—21no—
200C4×C5—22no—
201Dic5—62no—
202Dic5—62no—
203C24—151no—
204C2×D4—152no—
205C2×D4—152no—
206C2×D4—152no—
207C2×D4—152no—
208C2×D4—152no—
209C2×D4—151no—
210C2×D4C2×D1511yescharacteristic
211C22×C4—152no—
212C22×C4C2×D1511yescharacteristic, complemented
213C4⋊C4—152no—
214C4⋊C4—152no—
215C4⋊C4C2×D1512yescomplemented
216C22⋊C4—151no—
217C22⋊C4—152no—
218C22⋊C4—152no—
219C22⋊C4—152no—
220C22⋊C4—152no—
221C22⋊C4C2×D1512yes—
222C22⋊C4C2×D1511yescharacteristic, complemented
223C42—151no—
224C3×C5#56011yescharacteristic, complemented, Hall
225C22×C3—21no—
226C22×C3—21no—
227C22×C3—22no—
228C22×C3—22no—
229C22×C3C23×D511yescharacteristic
230C2×D3—102no—
231C2×D3—102no—
232C2×D3—102no—
233C2×D3—102no—
234C2×D3—102no—
235C2×D3—102no—
236C2×D3—204no—
237C3×C4—22no—
238C3×C4—21no—
239C3×C4—22no—
240Dic3—102no—
241Dic3—102no—
242C2×C5—41no—
243C2×C5—41no—
244C2×C5#100411yescharacteristic
245C2×C5#100912yes—
246D5—122no—
247D5—122no—
248C23—152no—
249C23—152no—
250C23—601no—
251C23—602no—
252C23C22×D1511yescharacteristic
253C23C22×D1511yescharacteristic
254D4—41no—
255D4—602no—
256D4—601no—
257D4—602no—
258D4—602no—
259D4—602no—
260D4—602no—
261C2×C4—41no—
262C2×C4—152no—
263C2×C4—152no—
264C2×C4—602no—
265C2×C4C22×D1511yescharacteristic
266C2×C4C22×D1512yes—
267C2×C4C22×D1512yes—
268C2×C3—41no—
269C2×C3—41no—
270C2×C3#414411yescharacteristic
271C2×C3#414912yes—
272D3—202no—
273D3—202no—
274C5#566611yescharacteristic, complemented, Sylow
275C22—21no—
276C22—21no—
277C22—22no—
278C22—22no—
279C22—302no—
280C22—302no—
281C22—302no—
282C22—302no—
283C22—302no—
284C22—302no—
285C22—604no—
286C22C23×D1511yescharacteristic
287C4—22no—
288C4—21no—
289C4—22no—
290C4—302no—
291C4—302no—
292C3#6600011yescharacteristic, complemented, Sylow
293C2—41no—
294C2—41no—
295C2—602no—
296C2—602no—
297C2#9209511yescharacteristic
298C2#9210012yes—
subgroupG/H
center, FrattiniC22C23×D15
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×#123C2
hypercenter#123D15
hypocenterC3×C5#560
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C3×C5×#123C2semidirect
2. #91829C2semidirect
3. #91826C2semidirect
4. #91819C2semidirect
5. #91787C2semidirect
6. #91784C2semidirect
7. #91773C2semidirect
8. #91772C2semidirect
9. #91771C2semidirect
13. C22×C3×C4×C5C22semidirect
16. C2×#1220C22semidirect
19. C2×D60C22semidirect
20. C2×C4×D15C22semidirect
21. C3×C5×C4⋊C4C22semidirect
23. C3×C5×C22⋊C4C22semidirect
28. #6714C22semidirect
29. C4⋊Dic15C22semidirect
30. #6712C22semidirect
31. C4×Dic15C22semidirect
33. C5×#123D3semidirect
62. C3×#123D5semidirect
73. C22×C4×C5C2×D3semidirect
81. C5×C4⋊C4C2×D3semidirect
83. C5×C22⋊C4C2×D3semidirect
112. C22×C3×C4C2×D5semidirect
120. C3×C4⋊C4C2×D5semidirect
122. C3×C22⋊C4C2×D5semidirect
154. #123D15semidirect
212. C22×C4C2×D15semidirect
215. C4⋊C4C2×D15semidirect
222. C22⋊C4C2×D15semidirect
224. C3×C5#560semidirect
274. C5#5666semidirect
292. C3#66000semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#1232
#918292
#918262
#918192
#917872
#917842
#917732
#917722
#917712
#660003
#56665