Finite Group Databasebeta

← #11752656

Subgroups — #11752656

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×#875C211yesmaximal, characteristic, complemented
3C3×#4016C211yesmaximal, characteristic, complemented
4#91438C212yesmaximal, complemented
5#91432C212yesmaximal, complemented
6#91427C212yesmaximal, complemented
7#91424C212yesmaximal, complemented
8#91420C212yesmaximal, complemented
9#91416C212yesmaximal, complemented
10#66018—31nomaximal, Hall
11C2×D60C2211yescharacteristic
12C2×Dic30C2211yescharacteristic
13C2×C5×D12C2211yescharacteristic
14C2×C5×Dic6C2211yescharacteristic
15C2×#1203C2212yes—
16C2×#1203C2212yes—
17C2×#1200C2212yes—
18C2×D3×Dic5C2212yes—
19C3×C42×C5C2211yescharacteristic
20#6714C2212yes—
21#6714C2212yes—
22C5×(C2×D3)⋊C4C2212yes—
23C5×(C2×D3)⋊C4C2212yes—
24C3×C4⋊Dic5C2211yescharacteristic
25C3×C4⋊Dic5C2211yescharacteristic
26C3×#683C2212yes—
27C3×#683C2212yes—
28Dic3⋊Dic5C2212yes—
29#6669C2212yes—
30#6667C2212yes—
31(C2×D3)⋊Dic5C2212yes—
32#5700—51nomaximal, Hall
33C5×#124—31no—
34#4092—32no—
35#4085—32no—
36#4032—32no—
37#4030—32no—
38#4029—32no—
39#4024—32no—
40#4021—31no—
41#4016D311yescharacteristic, complemented
42C22×D15C2312yes—
43C22×C5×D3C2312yes—
44C2×C3×C4×C5C2311yescharacteristic
45C2×C3×C4×C5C2311yescharacteristic
46C2×C3×C4×C5C2311yescharacteristic
47C2×Dic15C2312yes—
48D60—41no—
49Dic30—41no—
50C2×C5×Dic3C2312yes—
51C5×D12—41no—
52C5×Dic6—41no—
53C2×C3×Dic5C2312yes—
54C2×C3×Dic5C2312yes—
55#1203—42no—
56#1203—42no—
57#1200—42no—
58D3×Dic5—42no—
59C3×#125—51no—
60#896—52no—
61#896—52no—
62#895—52no—
63#895—52no—
64#894—52no—
65#894—52no—
66#875—51no—
67#875D511yescharacteristic, complemented
68C2×C5×Q8—31no—
69C2×C5×D4—31no—
70C2×C22⋊D5—32no—
71C2×C22⋊D5—32no—
72C22×Dic5—32no—
73C2×D20—31no—
74C2×C4×D5—32no—
75C2×Dic10—31no—
76C5×C22⋊C4—32no—
77C5×C22⋊C4—32no—
78C42×C5C2×D311yescharacteristic
79C22⋊Dic5—32no—
80#685—32no—
81#685—32no—
82#685—32no—
83C4⋊Dic5—32no—
84C4⋊Dic5C2×D311yescharacteristic
85C4⋊Dic5C2×D311yescharacteristic
86#683—32no—
87#683C2×D312yes—
88#683C2×D312yes—
89#562—151noSylow
90C22×C3×C5C2411yescharacteristic
91C2×D15—22no—
92C2×D15—22no—
93C2×D15—22no—
94C2×C5×D3—22no—
95C2×C5×D3—22no—
96C2×C5×D3—22no—
97C3×C4×C5—21no—
98C3×C4×C5—21no—
99C3×C4×C5—21no—
100Dic15—22no—
101C3×Dic5—22no—
102C3×Dic5—22no—
103C5×Dic3—22no—
104C2×D12—52no—
105C2×D12—52no—
106C2×D12—51no—
107C2×D12C2×D511yescharacteristic
108C2×C4×D3—52no—
109C2×C4×D3—52no—
110C2×Dic6—51no—
111C2×Dic6C2×D511yescharacteristic
112C3×C4⋊C4—52no—
113C3×C4⋊C4—52no—
114C3×C4⋊C4—51no—
115C3×C4⋊C4—51no—
116C3×C42C2×D511yescharacteristic
117(C2×D3)⋊C4—52no—
118(C2×D3)⋊C4—52no—
119(C2×D3)⋊C4—52no—
120(C2×D3)⋊C4—52no—
121(C2×D3)⋊C4C2×D512yes—
122(C2×D3)⋊C4C2×D512yes—
123Dic3⋊C4—52no—
124Dic3⋊C4—52no—
125C23×C5—32no—
126C22×D5—32no—
127C5×Q8—121no—
128C5×D4—121no—
129C2×C4×C5—32no—
130C2×C4×C5C22×D311yescharacteristic
131C2×C4×C5C22×D311yescharacteristic
132C2×C4×C5C22×D311yescharacteristic
133C22⋊D5—122no—
134C22⋊D5—122no—
135C2×Dic5—32no—
136C2×Dic5—122no—
137C2×Dic5C22×D312yes—
138C2×Dic5C22×D312yes—
139D20—121no—
140C4×D5—122no—
141Dic10—121no—
142#125—51no—
143#124—31no—
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—
155C5×D3—42no—
156C22×D3—52no—
157C22×D3C22×D512yes—
158C2×C3×C4—52no—
159C2×C3×C4—52no—
160C2×C3×C4C22×D511yescharacteristic
161C2×C3×C4C22×D511yescharacteristic
162C2×C3×C4C22×D511yescharacteristic
163C2×Dic3—52no—
164C2×Dic3C22×D512yes—
165D12—41no—
166D12—201no—
167D12—202no—
168D12—202no—
169C4×D3—202no—
170C4×D3—202no—
171Dic6—41no—
172Dic6—201no—
173C22×C5—62no—
174C22×C5—62no—
175C22×C5—62no—
176C22×C5C23×D311yescharacteristic
177C2×D5—62no—
178C2×D5—62no—
179C2×D5—62no—
180C4×C5—21no—
181C4×C5—21no—
182C4×C5—21no—
183C4×C5—62no—
184Dic5—22no—
185Dic5—22no—
186Dic5—62no—
187C2×Q8—31no—
188C2×Q8—151no—
189C2×D4—31no—
190C2×D4—152no—
191C2×D4—152no—
192C2×D4—151no—
193C22×C4—152no—
194C22×C4—152no—
195C4⋊C4—52no—
196C4⋊C4—52no—
197C4⋊C4—51no—
198C4⋊C4—51no—
199C4⋊C4—152no—
200C4⋊C4—152no—
201C22⋊C4—32no—
202C22⋊C4—32no—
203C22⋊C4—152no—
204C22⋊C4—152no—
205C22⋊C4—152no—
206C22⋊C4—152no—
207C42D3×D511yescharacteristic
208C3×C5#56211yescharacteristic, complemented, Hall
209C22×C3C23×D511yescharacteristic
210C2×D3—22no—
211C2×D3—22no—
212C2×D3—22no—
213C2×D3—102no—
214C2×D3—102no—
215C2×D3—102no—
216C3×C4—21no—
217C3×C4—21no—
218C3×C4—21no—
219C3×C4—102no—
220C3×C4—102no—
221Dic3—22no—
222Dic3—102no—
223C2×C5—122no—
224C2×C5#100711yescharacteristic
225C2×C5#100911yescharacteristic
226C2×C5#100911yescharacteristic
227D5—122no—
228C23—32no—
229C23—152no—
230Q8—121no—
231Q8—601no—
232D4—121no—
233D4—601no—
234D4—602no—
235D4—602no—
236C2×C4—32no—
237C2×C4—52no—
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#414411yescharacteristic
246C2×C3#414911yescharacteristic
247C2×C3#415011yescharacteristic
248D3—42no—
249D3—202no—
250C5#570011yescharacteristic, complemented, Sylow
251C22—62no—
252C22—62no—
253C22—62no—
254C22—302no—
255C22—302no—
256C22—302no—
257C22C22×D3×D511yescharacteristic
258C4—21no—
259C4—21no—
260C4—21no—
261C4—62no—
262C4—102no—
263C4—102no—
264C4—302no—
265C3#6601811yescharacteristic, complemented, Sylow
266C2—122no—
267C2—602no—
268C2#9200411yescharacteristic
269C2#9201811yescharacteristic
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×#875C2semidirect
3. C3×#4016C2semidirect
4. #91438C2semidirect
5. #91432C2semidirect
6. #91427C2semidirect
7. #91424C2semidirect
8. #91420C2semidirect
9. #91416C2semidirect
41. #4016D3semidirect
67. #875D5semidirect
208. C3×C5#562semidirect
250. C5#5700semidirect
265. C3#66018semidirect

Maximal subgroups

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

subgroupindex
#917642
C5×#8752
C3×#40162
#914382
#914322
#914272
#914242
#914202
#914162
#660183
#57005