Finite Group Databasebeta

← #11755017

Subgroups — #11755017

Order 960.

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

normal subgroups only

This group has 392 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#91824C211yesmaximal, characteristic
2C5×#935C211yesmaximal, characteristic
3C3×#4082C211yesmaximal, characteristic
4#91576C212yesmaximal, complemented
5#91575C212yesmaximal, complemented
6#91531C212yesmaximal, complemented
7#91530C212yesmaximal, complemented
8#91378C212yesmaximal, complemented
9#91327C212yesmaximal, complemented
10#65985—31nomaximal, Hall
11C2×C3×C5×D4C2211yescharacteristic
12C22×Dic15C2211yescharacteristic
13C22×C5×Dic3C2211yescharacteristic
14C2×C3×Dic10C2211yescharacteristic
15C2×#1204C2212yes—
16#6719C2212yes—
17#6719C2211yescharacteristic
18#6712C2212yes—
19C5×#217C2211yescharacteristic
20C5×#217C2212yes—
21C5×Dic3⋊C4C2212yes—
22C3×C22⋊Dic5C2212yes—
23C3×C22⋊Dic5C2212yes—
24C3×C4×Dic5C2211yescharacteristic
25Dic3⋊Dic5C2212yes—
26Dic3⋊Dic5C2212yes—
27#6669C2212yes—
28#6669C2212yes—
29#6668C2212yes—
30#6668C2212yes—
31Dic3×Dic5C2212yes—
32#5672—51nomaximal, Hall
33C5×#123—31no—
34#4082D311yescharacteristic
35#4081—31no—
36#4070—32no—
37#4035—32no—
38#4034—32no—
39#4025—32no—
40#4025—32no—
41#4024—32no—
42C23×C3×C5C2311yescharacteristic
43C23×C3×C5C2311yescharacteristic
44C3×C5×D4—41no—
45C2×C3×C4×C5C2311yescharacteristic
46C2×Dic15—41no—
47C2×Dic15C2312yes—
48C2×Dic15C2312yes—
49C2×C5×Dic3—41no—
50C2×C5×Dic3C2312yes—
51C2×C5×Dic3C2312yes—
52C2×C3×Dic5C2312yes—
53C2×C3×Dic5C2312yes—
54C3×Dic10—41no—
55#1204—42no—
56C3×#124—51no—
57#944—52no—
58#935—51no—
59#935D511yescharacteristic
60#879—52no—
61#879—52no—
62#878—52no—
63#878—52no—
64#870—52no—
65C2×C5×D4C2×D311yescharacteristic
66C22×C4×C5—31no—
67C22×Dic5—31no—
68C2×Dic10—32no—
69C2×Dic10C2×D311yescharacteristic
70C5×C4⋊C4—32no—
71C5×C22⋊C4—32no—
72C5×C22⋊C4—31no—
73C22⋊Dic5—31no—
74C22⋊Dic5—32no—
75C22⋊Dic5C2×D312yes—
76C22⋊Dic5C2×D312yes—
77C4⋊Dic5—32no—
78C4⋊Dic5—32no—
79#683—32no—
80#683—32no—
81#683—32no—
82#683—32no—
83#683—32no—
84C4×Dic5—32no—
85C4×Dic5C2×D311yescharacteristic
86#563—151noSylow
87C22×C3×C5—21no—
88C22×C3×C5—21no—
89C22×C3×C5—22no—
90C22×C3×C5—22no—
91C22×C3×C5C2411yescharacteristic
92C3×C4×C5—21no—
93Dic15—22no—
94Dic15—22no—
95C3×Dic5—22no—
96C3×Dic5—22no—
97C5×Dic3—22no—
98C5×Dic3—22no—
99C2×C3×Q8—51no—
100C2×C3×D4C2×D511yescharacteristic
101C22×Dic3—51no—
102C22×Dic3C2×D511yescharacteristic
103C2×Dic6—52no—
104C3×C22⋊C4—52no—
105C3×C22⋊C4—52no—
106C3×C42—51no—
107#217—52no—
108#217—51no—
109#217C2×D512yes—
110#217C2×D511yescharacteristic
111C4⋊Dic3—52no—
112C4⋊Dic3—52no—
113Dic3⋊C4—52no—
114Dic3⋊C4—52no—
115Dic3⋊C4—52no—
116Dic3⋊C4—52no—
117Dic3⋊C4—52no—
118Dic3⋊C4C2×D512yes—
119C4×Dic3—52no—
120C23×C5C22×D311yescharacteristic
121C23×C5C22×D311yescharacteristic
122C5×D4—41no—
123C2×C4×C5—32no—
124C2×C4×C5—32no—
125C2×C4×C5—121no—
126C2×C4×C5C22×D311yescharacteristic
127C2×Dic5—32no—
128C2×Dic5—32no—
129C2×Dic5—121no—
130C2×Dic5C22×D312yes—
131C2×Dic5C22×D312yes—
132Dic10—41no—
133Dic10—122no—
134C4⋊Q8—152no—
135#126—152no—
136#126—152no—
137#125—152no—
138#124—51no—
139#123—31no—
140#123—151no—
141C22⋊Q8—152no—
142C22⋊Q8—152no—
143C2×C3×C5—41no—
144C2×C3×C5—41no—
145C2×C3×C5H(5,𝔽2)11yescharacteristic
146C2×C3×C52−1+412yes—
147C23×C3C22×D511yescharacteristic
148C23×C3C22×D511yescharacteristic
149C3×Q8—201no—
150C3×D4—41no—
151C2×C3×C4—52no—
152C2×C3×C4—52no—
153C2×C3×C4C22×D511yescharacteristic
154C2×Dic3—41no—
155C2×Dic3—52no—
156C2×Dic3—52no—
157C2×Dic3—201no—
158C2×Dic3C22×D512yes—
159C2×Dic3C22×D512yes—
160Dic6—202no—
161C22×C5—21no—
162C22×C5—21no—
163C22×C5—22no—
164C22×C5—22no—
165C22×C5C23×D311yescharacteristic
166C4×C5—21no—
167C4×C5—62no—
168C4×C5—62no—
169Dic5—22no—
170Dic5—22no—
171Dic5—62no—
172Dic5—62no—
173C2×Q8—51no—
174C2×Q8—152no—
175C2×D4D3×D511yescharacteristic
176C22×C4—31no—
177C22×C4—151no—
178C4⋊C4—32no—
179C4⋊C4—152no—
180C4⋊C4—152no—
181C4⋊C4—152no—
182C4⋊C4—152no—
183C4⋊C4—152no—
184C4⋊C4—152no—
185C4⋊C4—152no—
186C22⋊C4—32no—
187C22⋊C4—31no—
188C22⋊C4—52no—
189C22⋊C4—52no—
190C22⋊C4—152no—
191C22⋊C4—151no—
192C42—51no—
193C42—152no—
194C3×C5#56311yescharacteristic, complemented, Hall
195C22×C3—21no—
196C22×C3—21no—
197C22×C3—22no—
198C22×C3—22no—
199C22×C3C23×D511yescharacteristic
200C3×C4—21no—
201C3×C4—102no—
202C3×C4—102no—
203Dic3—22no—
204Dic3—22no—
205Dic3—102no—
206Dic3—102no—
207C2×C5—41no—
208C2×C5—41no—
209C2×C5#100411yescharacteristic
210C2×C5#101012yes—
211C23C2×D3×D511yescharacteristic
212C23C2×D3×D511yescharacteristic
213Q8—201no—
214Q8—602no—
215D4—41no—
216C2×C4—32no—
217C2×C4—32no—
218C2×C4—52no—
219C2×C4—52no—
220C2×C4—121no—
221C2×C4—152no—
222C2×C4—152no—
223C2×C4—601no—
224C2×C4C2×D3×D511yescharacteristic
225C2×C3—41no—
226C2×C3—41no—
227C2×C3#414411yescharacteristic
228C2×C3#415012yes—
229C5#567211yescharacteristic, complemented, Sylow
230C22—22no—
231C22—22no—
232C22—21no—
233C22—21no—
234C22C22×D3×D511yescharacteristic
235C4—21no—
236C4—62no—
237C4—62no—
238C4—102no—
239C4—102no—
240C4—302no—
241C4—302no—
242C3#6598511yescharacteristic, complemented, Sylow
243C2—41no—
244C2—41no—
245C2#9202012yes—
246C2#9204911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
Fitting, prime radicalC2×C3×C5×D4C22
hypercenterC2×D4D3×D5
hypocenterC3×C5#563
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
4. #91576C2semidirect
5. #91575C2semidirect
6. #91531C2semidirect
7. #91530C2semidirect
8. #91378C2semidirect
9. #91327C2semidirect
194. C3×C5#563semidirect
229. C5#5672semidirect
242. C3#65985semidirect

Maximal subgroups

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

subgroupindex
#918242
C5×#9352
C3×#40822
#915762
#915752
#915312
#915302
#913782
#913272
#659853
#56725