Finite Group Databasebeta

← #11756494

Subgroups — #11756494

Order 960.

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

normal subgroups only

This group has 392 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×C4⋊Q8C211yesmaximal, characteristic, complemented
2#91836C211yesmaximal, characteristic
3#91835C212yesmaximal, complemented
4#91833C211yesmaximal, characteristic, complemented
5#91787C212yesmaximal, complemented
6#91785C212yesmaximal, complemented
7#91783C212yesmaximal
8#91778C212yesmaximal, complemented
9#91765C212yesmaximal, complemented
10#66069—31nomaximal, Hall
11C2×C3×C5×Q8C2211yescharacteristic
12C2×C3×C5×Q8C2211yescharacteristic
13C2×D60C2211yescharacteristic
14C2×C4×D15C2212yes—
15C2×Dic30C2211yescharacteristic
16C3×C5×C4⋊C4C2212yes—
17C3×C5×C4⋊C4C2212yes—
18C3×C42×C5C2211yescharacteristic
19#6714C2212yes—
20#6714C2212yes—
21#6714C2212yes—
22#6714C2212yes—
23#6714C2212yes—
24C4⋊Dic15C2212yes—
25#6712C2212yes—
26#6712C2212yes—
27#6712C2212yes—
28#6712C2212yes—
29#6712C2212yes—
30C4×Dic15C2211yescharacteristic
31C4×Dic15C2211yescharacteristic
32#5735—51nomaximal, Hall
33C5×C4⋊Q8D311yescharacteristic, complemented
34#4093—31no—
35#4092—32no—
36#4090—31no—
37#4044—32no—
38#4042—32no—
39#4040—32no—
40#4035—32no—
41#4022—32no—
42C22×D15C2312yes—
43C3×C5×Q8—41no—
44C3×C5×Q8—41no—
45C2×C3×C4×C5C2311yescharacteristic
46C2×C3×C4×C5C2311yescharacteristic
47C2×C3×C4×C5C2312yes—
48C2×C3×C4×C5C2311yescharacteristic
49C2×C3×C4×C5C2312yes—
50C2×Dic15C2312yes—
51C2×Dic15C2312yes—
52C2×Dic15C2312yes—
53D60—41no—
54C4×D15—42no—
55Dic30—41no—
56C3×C4⋊Q8D511yescharacteristic, complemented
57#947—51no—
58#946—52no—
59#944—51no—
60#898—52no—
61#896—52no—
62#894—52no—
63#889—52no—
64#876—52no—
65C2×C5×Q8C2×D311yescharacteristic
66C2×C5×Q8C2×D311yescharacteristic
67C2×D20—31no—
68C2×C4×D5—32no—
69C2×Dic10—31no—
70C5×C4⋊C4C2×D312yes—
71C5×C4⋊C4C2×D312yes—
72C42×C5C2×D311yescharacteristic
73#685—32no—
74#685—32no—
75#685—32no—
76#685—32no—
77#685—32no—
78C4⋊Dic5—32no—
79#683—32no—
80#683—32no—
81#683—32no—
82#683—32no—
83#683—32no—
84C4×Dic5—31no—
85C4×Dic5—31no—
86#563—151noSylow
87C22×C3×C5C2411yescharacteristic
88C2×D15—22no—
89C2×D15—24no—
90C3×C4×C5—21no—
91C3×C4×C5—22no—
92C3×C4×C5—21no—
93C3×C4×C5—21no—
94C3×C4×C5—22no—
95Dic15—22no—
96Dic15—22no—
97Dic15—22no—
98C2×C3×Q8C2×D511yescharacteristic
99C2×C3×Q8C2×D511yescharacteristic
100C2×D12—51no—
101C2×C4×D3—52no—
102C2×Dic6—51no—
103C3×C4⋊C4C2×D512yes—
104C3×C4⋊C4C2×D512yes—
105C3×C42C2×D511yescharacteristic
106(C2×D3)⋊C4—52no—
107(C2×D3)⋊C4—52no—
108(C2×D3)⋊C4—52no—
109(C2×D3)⋊C4—52no—
110(C2×D3)⋊C4—52no—
111C4⋊Dic3—52no—
112Dic3⋊C4—52no—
113Dic3⋊C4—52no—
114Dic3⋊C4—52no—
115Dic3⋊C4—52no—
116Dic3⋊C4—52no—
117C4×Dic3—51no—
118C4×Dic3—51no—
119C22×D5—32no—
120C5×Q8—41no—
121C5×Q8—41no—
122C2×C4×C5C22×D311yescharacteristic
123C2×C4×C5C22×D311yescharacteristic
124C2×C4×C5C22×D312yes—
125C2×C4×C5C22×D311yescharacteristic
126C2×C4×C5C22×D312yes—
127C2×Dic5—32no—
128C2×Dic5—32no—
129C2×Dic5—32no—
130D20—121no—
131C4×D5—122no—
132Dic10—121no—
133C4⋊Q8—151no—
134C4⋊Q8D1511yescharacteristic, complemented
135#126—152no—
136#126—152no—
137#125—152no—
138#124—151no—
139#123—152no—
140C22⋊Q8—152no—
141C22⋊Q8—152no—
142C2×C3×C5H(5,𝔽2)11yescharacteristic
143C2×C3×C52−1+412yes—
144D15—42no—
145C22×D3—52no—
146C3×Q8—41no—
147C3×Q8—41no—
148C2×C3×C4C22×D511yescharacteristic
149C2×C3×C4C22×D511yescharacteristic
150C2×C3×C4C22×D512yes—
151C2×C3×C4C22×D511yescharacteristic
152C2×C3×C4C22×D512yes—
153C2×Dic3—52no—
154C2×Dic3—52no—
155C2×Dic3—52no—
156D12—201no—
157C4×D3—202no—
158Dic6—201no—
159C22×C5C23×D311yescharacteristic
160C2×D5—62no—
161C2×D5—64no—
162C4×C5—21no—
163C4×C5—22no—
164C4×C5—21no—
165C4×C5—21no—
166C4×C5—22no—
167Dic5—62no—
168Dic5—62no—
169Dic5—62no—
170C2×Q8—151no—
171C2×Q8C2×D1511yescharacteristic
172C2×Q8C2×D1511yescharacteristic
173C2×D4—151no—
174C22×C4—152no—
175C4⋊C4—152no—
176C4⋊C4—152no—
177C4⋊C4—152no—
178C4⋊C4—152no—
179C4⋊C4—152no—
180C4⋊C4—152no—
181C4⋊C4C2×D1512yes—
182C4⋊C4C2×D1512yes—
183C22⋊C4—152no—
184C22⋊C4—152no—
185C22⋊C4—152no—
186C22⋊C4—152no—
187C22⋊C4—152no—
188C42—151no—
189C42—151no—
190C42C2×D1511yescharacteristic
191C3×C5#56311yescharacteristic, complemented, Hall
192C22×C3C23×D511yescharacteristic
193C2×D3—102no—
194C2×D3—104no—
195C3×C4—21no—
196C3×C4—22no—
197C3×C4—21no—
198C3×C4—21no—
199C3×C4—22no—
200Dic3—102no—
201Dic3—102no—
202Dic3—102no—
203C2×C5#100411yescharacteristic
204C2×C5#100712yes—
205D5—122no—
206C23—152no—
207Q8—41no—
208Q8—41no—
209Q8—601no—
210D4—601no—
211C2×C4—152no—
212C2×C4—152no—
213C2×C4—152no—
214C2×C4—602no—
215C2×C4C22×D1511yescharacteristic
216C2×C4C22×D1511yescharacteristic
217C2×C4C22×D1512yes—
218C2×C4C22×D1511yescharacteristic
219C2×C4C22×D1512yes—
220C2×C3#414411yescharacteristic
221C2×C3#414712yes—
222D3—202no—
223C5#573511yescharacteristic, complemented, Sylow
224C22—302no—
225C22—304no—
226C22C23×D1511yescharacteristic
227C4—22no—
228C4—21no—
229C4—21no—
230C4—21no—
231C4—22no—
232C4—302no—
233C4—302no—
234C4—302no—
235C3#6606911yescharacteristic, complemented, Sylow
236C2—602no—
237C2#9209511yescharacteristic
238C2#9209812yes—
subgroupG/H
center, FrattiniC22C23×D15
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C4⋊Q8C2
prime radicalC2×D60C22
hypercenterC4⋊Q8D15
hypocenterC3×C5#563
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×C5×C4⋊Q8C2semidirect
3. #91835C2semidirect
4. #91833C2semidirect
5. #91787C2semidirect
6. #91785C2semidirect
8. #91778C2semidirect
9. #91765C2semidirect
33. C5×C4⋊Q8D3semidirect
56. C3×C4⋊Q8D5semidirect
134. C4⋊Q8D15semidirect
191. C3×C5#563semidirect
223. C5#5735semidirect
235. C3#66069semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C4⋊Q82
#918362
#918352
#918332
#917872
#917852
#917832
#917782
#917652
#660693
#57355