Finite Group Databasebeta

← #11752638

Subgroups — #11752638

Order 960.

440 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 120 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
1#91764C211yesmaximal, characteristic, complemented
2C5×#870C211yesmaximal, characteristic, complemented
3C3×#4021C211yesmaximal, characteristic, complemented
4#91459C212yesmaximal, complemented
5#91431C212yesmaximal, complemented
6#91413C212yesmaximal, complemented
7#91411C212yesmaximal, complemented
8#91409C212yesmaximal, complemented
9#91356C212yesmaximal, complemented
10#66034—31nomaximal, Hall
11C2×D60C2211yescharacteristic
12C2×Dic30C2211yescharacteristic
13C2×C3×D20C2211yescharacteristic
14C2×C3×Dic10C2211yescharacteristic
15C2×#1202C2212yes—
16C2×#1202C2212yes—
17C2×#1200C2212yes—
18C2×D5×Dic3C2212yes—
19C3×C42×C5C2211yescharacteristic
20#6714C2212yes—
21#6714C2212yes—
22C5×C4⋊Dic3C2211yescharacteristic
23C5×C4⋊Dic3C2211yescharacteristic
24C5×Dic3⋊C4C2212yes—
25C5×Dic3⋊C4C2212yes—
26C3×#685C2212yes—
27C3×#685C2212yes—
28#6669C2212yes—
29#6668C2212yes—
30#6667C2212yes—
31#6665C2212yes—
32#5684—51nomaximal, Hall
33C5×#125—31no—
34#4042—32no—
35#4042—32no—
36#4041—32no—
37#4041—32no—
38#4040—32no—
39#4040—32no—
40#4021—31no—
41#4021D311yescharacteristic, complemented
42C22×D15C2312yes—
43C22×C3×D5C2312yes—
44C2×C3×C4×C5C2311yescharacteristic
45C2×C3×C4×C5C2311yescharacteristic
46C2×C3×C4×C5C2311yescharacteristic
47C2×Dic15C2312yes—
48D60—41no—
49Dic30—41no—
50C2×C5×Dic3C2312yes—
51C2×C5×Dic3C2312yes—
52C2×C3×Dic5C2312yes—
53C3×D20—41no—
54C3×Dic10—41no—
55#1202—42no—
56#1202—42no—
57#1200—42no—
58D5×Dic3—42no—
59C3×#124—51no—
60#946—52no—
61#939—52no—
62#886—52no—
63#884—52no—
64#883—52no—
65#878—52no—
66#875—51no—
67#870D511yescharacteristic, complemented
68C2×D20—32no—
69C2×D20—32no—
70C2×D20—31no—
71C2×D20C2×D311yescharacteristic
72C2×C4×D5—32no—
73C2×C4×D5—32no—
74C2×Dic10—31no—
75C2×Dic10C2×D311yescharacteristic
76C5×C4⋊C4—32no—
77C5×C4⋊C4—32no—
78C5×C4⋊C4—31no—
79C5×C4⋊C4—31no—
80C42×C5C2×D311yescharacteristic
81#685—32no—
82#685—32no—
83#685—32no—
84#685—32no—
85#685C2×D312yes—
86#685C2×D312yes—
87#683—32no—
88#683—32no—
89#562—151noSylow
90C22×C3×C5C2411yescharacteristic
91C2×D15—22no—
92C2×D15—22no—
93C2×D15—22no—
94C2×C3×D5—22no—
95C2×C3×D5—22no—
96C2×C3×D5—22no—
97C3×C4×C5—21no—
98C3×C4×C5—21no—
99C3×C4×C5—21no—
100Dic15—22no—
101C3×Dic5—22no—
102C5×Dic3—22no—
103C5×Dic3—22no—
104C2×C3×Q8—51no—
105C2×C3×D4—51no—
106C2×#67—52no—
107C2×#67—52no—
108C22×Dic3—52no—
109C2×D12—51no—
110C2×C4×D3—52no—
111C2×Dic6—51no—
112C3×C22⋊C4—52no—
113C3×C22⋊C4—52no—
114C3×C42C2×D511yescharacteristic
115#217—52no—
116(C2×D3)⋊C4—52no—
117(C2×D3)⋊C4—52no—
118(C2×D3)⋊C4—52no—
119C4⋊Dic3—52no—
120C4⋊Dic3C2×D511yescharacteristic
121C4⋊Dic3C2×D511yescharacteristic
122Dic3⋊C4—52no—
123Dic3⋊C4C2×D512yes—
124Dic3⋊C4C2×D512yes—
125C22×D5—32no—
126C22×D5C22×D312yes—
127C2×C4×C5—32no—
128C2×C4×C5—32no—
129C2×C4×C5C22×D311yescharacteristic
130C2×C4×C5C22×D311yescharacteristic
131C2×C4×C5C22×D311yescharacteristic
132C2×Dic5—32no—
133C2×Dic5C22×D312yes—
134D20—41no—
135D20—121no—
136D20—122no—
137D20—122no—
138C4×D5—122no—
139C4×D5—122no—
140Dic10—41no—
141Dic10—121no—
142#125—31no—
143#124—51no—
144#124—151no—
145#123—152no—
146#123—152no—
147C22⋊Q8—152no—
148C22⋊Q8—152no—
149#121—152no—
150#121—152no—
151C2×C3×C5H(5,𝔽2)11yescharacteristic
152C2×C3×C5H(5,𝔽2)11yescharacteristic
153C2×C3×C52−1+411yescharacteristic
154D15—42no—
155C3×D5—42no—
156C23×C3—52no—
157C22×D3—52no—
158C3×Q8—201no—
159C3×D4—201no—
160C2×C3×C4—52no—
161C2×C3×C4C22×D511yescharacteristic
162C2×C3×C4C22×D511yescharacteristic
163C2×C3×C4C22×D511yescharacteristic
164#67—202no—
165#67—202no—
166C2×Dic3—52no—
167C2×Dic3—202no—
168C2×Dic3C22×D512yes—
169C2×Dic3C22×D512yes—
170D12—201no—
171C4×D3—202no—
172Dic6—201no—
173C22×C5C23×D311yescharacteristic
174C2×D5—22no—
175C2×D5—22no—
176C2×D5—22no—
177C2×D5—62no—
178C2×D5—62no—
179C2×D5—62no—
180C4×C5—21no—
181C4×C5—21no—
182C4×C5—21no—
183C4×C5—62no—
184C4×C5—62no—
185Dic5—22no—
186Dic5—62no—
187C2×Q8—51no—
188C2×Q8—151no—
189C2×D4—51no—
190C2×D4—152no—
191C2×D4—152no—
192C2×D4—151no—
193C22×C4—152no—
194C22×C4—152no—
195C4⋊C4—32no—
196C4⋊C4—32no—
197C4⋊C4—31no—
198C4⋊C4—31no—
199C4⋊C4—152no—
200C4⋊C4—152no—
201C22⋊C4—52no—
202C22⋊C4—52no—
203C22⋊C4—152no—
204C22⋊C4—152no—
205C22⋊C4—152no—
206C22⋊C4—152no—
207C42D3×D511yescharacteristic
208C3×C5#56211yescharacteristic, complemented, Hall
209C22×C3—102no—
210C22×C3—102no—
211C22×C3—102no—
212C22×C3C23×D511yescharacteristic
213C2×D3—102no—
214C2×D3—102no—
215C2×D3—102no—
216C3×C4—21no—
217C3×C4—21no—
218C3×C4—21no—
219C3×C4—102no—
220Dic3—22no—
221Dic3—22no—
222Dic3—102no—
223C2×C5#100411yescharacteristic
224C2×C5#100911yescharacteristic
225C2×C5#101011yescharacteristic
226D5—42no—
227D5—122no—
228C23—52no—
229C23—152no—
230Q8—201no—
231Q8—601no—
232D4—201no—
233D4—601no—
234D4—602no—
235D4—602no—
236C2×C4—32no—
237C2×C4—32no—
238C2×C4—52no—
239C2×C4—152no—
240C2×C4—602no—
241C2×C4—602no—
242C2×C4C2×D3×D511yescharacteristic
243C2×C4C2×D3×D511yescharacteristic
244C2×C4C2×D3×D511yescharacteristic
245C2×C3—202no—
246C2×C3#414711yescharacteristic
247C2×C3#414911yescharacteristic
248C2×C3#414911yescharacteristic
249D3—202no—
250C5#568411yescharacteristic, complemented, Sylow
251C22—102no—
252C22—102no—
253C22—102no—
254C22—302no—
255C22—302no—
256C22—302no—
257C22C22×D3×D511yescharacteristic
258C4—21no—
259C4—21no—
260C4—21no—
261C4—62no—
262C4—62no—
263C4—102no—
264C4—302no—
265C3#6603411yescharacteristic, complemented, Sylow
266C2—202no—
267C2—602no—
268C2#9200011yescharacteristic
269C2#9201711yescharacteristic
270C2#9201911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C42×C5C22
hypercenterC42D3×D5
hypocenterC3×C5#562
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. #91764C2semidirect
2. C5×#870C2semidirect
3. C3×#4021C2semidirect
4. #91459C2semidirect
5. #91431C2semidirect
6. #91413C2semidirect
7. #91411C2semidirect
8. #91409C2semidirect
9. #91356C2semidirect
41. #4021D3semidirect
67. #870D5semidirect
208. C3×C5#562semidirect
250. C5#5684semidirect
265. C3#66034semidirect

Maximal subgroups

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

subgroupindex
#917642
C5×#8702
C3×#40212
#914592
#914312
#914132
#914112
#914092
#913562
#660343
#56845