Finite Group Databasebeta

← #11755125

Subgroups — #11755125

Order 960.

540 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 144 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
1C2×C3×Q8×D5C211yesmaximal, characteristic, complemented
2C2×#6773C211yesmaximal, characteristic
3#91836C211yesmaximal, characteristic, complemented
4C5×#944C211yesmaximal, characteristic, complemented
5#91411C214yesmaximal, complemented
6#91385C211yesmaximal, characteristic, complemented
7#91374C211yesmaximal, characteristic, complemented
8#91357C211yesmaximal, characteristic, complemented
9#91348C214yesmaximal, complemented
10#66058—31nomaximal, Hall
11C2×C3×C5×Q8C2211yescharacteristic
12C2×D60C2211yescharacteristic
13C2×C5×Dic6C2211yescharacteristic
14C3×Q8×D5—24no—
15C2×C3×C4×D5C2212yes—
16C2×C3×C4×D5C2211yescharacteristic
17C2×C3×Dic10C2212yes—
18C2×C3×Dic10C2211yescharacteristic
19C2×#1202C2212yes—
20C2×#1200C2212yes—
21#6773—24no—
22#6714C2214yes—
23C4×Dic15C2211yescharacteristic
24C5×Dic3⋊C4C2214yes—
25C4×C5×Dic3C2211yescharacteristic
26#6669C2214yes—
27#6668C2212yes—
28#6667C2214yes—
29#6665C2212yes—
30#5816—51nomaximal, Hall
31C2×#713—31no—
32C2×Q8×D5D311yescharacteristic, complemented
33C5×C4⋊Q8—31no—
34#4093—31no—
35#4090—31no—
36#4042—34no—
37#4040—34no—
38#4021—31no—
39#4018—31no—
40C22×D15C2312yes—
41C22×C3×D5C2311yescharacteristic
42C3×C5×Q8—22no—
43C2×C3×C4×C5C2312yes—
44C2×C3×C4×C5C2311yescharacteristic
45C2×Dic15C2312yes—
46D60—22no—
47C2×C5×Dic3C2312yes—
48C2×C5×Dic3C2312yes—
49C5×Dic6—22no—
50C2×C3×Dic5C2312yes—
51C2×C3×Dic5C2311yescharacteristic
52C3×C4×D5—24no—
53C3×C4×D5D414yes—
54C3×Dic10—22no—
55C3×Dic10—24no—
56#1202—24no—
57#1200—24no—
58C22×C3×Q8—51no—
59C2×#235—51no—
60#947—51no—
61#947—51no—
62#946—54no—
63#944—51no—
64#944D511yescharacteristic, complemented
65#929—54no—
66#926—51no—
67C2×C5×Q8—31no—
68C2×C5×Q8C2×D311yescharacteristic
69#713—64no—
70Q8×D5—24no—
71C2×D20—32no—
72C2×D20—31no—
73C2×C4×D5—32no—
74C2×C4×D5C2×D312yes—
75C2×C4×D5C2×D311yescharacteristic
76C2×Dic10C2×D311yescharacteristic
77C2×Dic10C2×D312yes—
78C5×C4⋊C4—34no—
79C42×C5—31no—
80#685—32no—
81#685—34no—
82#685—34no—
83#683—32no—
84#683—34no—
85C4×Dic5—31no—
86#536—151noSylow
87C22×C3×C5C2411yescharacteristic
88C2×D15—22no—
89C2×D15—24no—
90C2×C3×D5—22no—
91C2×C3×D5C2×D412yes—
92C3×C4×C5—22no—
93C3×C4×C5C2×D412yes—
94Dic15—22no—
95C3×Dic5—22no—
96C3×Dic5C2×D412yes—
97C5×Dic3—22no—
98C5×Dic3—22no—
99C2×C3×Q8—51no—
100C2×C3×Q8—52no—
101C2×C3×Q8—104no—
102C2×C3×Q8C2×D511yescharacteristic
103C22×C3×C4—51no—
104C22×C3×C4—52no—
105C2×#67—52no—
106#235—104no—
107C2×D12—51no—
108C2×C4×D3—52no—
109C2×Dic6C2×D511yescharacteristic
110#217—52no—
111(C2×D3)⋊C4—54no—
112(C2×D3)⋊C4—54no—
113C4⋊Dic3—52no—
114Dic3⋊C4—54no—
115Dic3⋊C4C2×D514yes—
116C4×Dic3—51no—
117C4×Dic3C2×D511yescharacteristic
118C22×D5—32no—
119C22×D5C22×D311yescharacteristic
120C5×Q8—22no—
121C5×Q8—62no—
122C2×C4×C5—32no—
123C2×C4×C5—32no—
124C2×C4×C5C22×D312yes—
125C2×C4×C5C22×D311yescharacteristic
126C2×Dic5—32no—
127C2×Dic5C22×D312yes—
128C2×Dic5C22×D311yescharacteristic
129D20—64no—
130D20—62no—
131C4×D5—24no—
132C4×D5—64no—
133C4×D5#6714yes—
134Dic10—22no—
135Dic10—24no—
136C2×#41—151no—
137C22×Q8—51no—
138C4⋊Q8—31no—
139C4⋊Q8—151no—
140#124—151no—
141#124—151no—
142#123—154no—
143C22⋊Q8—154no—
144#117—151no—
145C2×C3×C5C22×D411yescharacteristic
146C2×C3×C52−1+412yes—
147D15—42no—
148C3×D5—22no—
149C23×C3—51no—
150C22×D3—52no—
151C3×Q8—22no—
152C3×Q8—104no—
153C3×Q8—102no—
154C2×C3×C4—51no—
155C2×C3×C4—54no—
156C2×C3×C4—52no—
157C2×C3×C4—104no—
158C2×C3×C4C22×D512yes—
159C2×C3×C4C22×D511yescharacteristic
160#67—104no—
161C2×Dic3—52no—
162C2×Dic3C22×D512yes—
163C2×Dic3C22×D512yes—
164D12—102no—
165C4×D3—104no—
166Dic6—22no—
167C22×C5C23×D311yescharacteristic
168C2×D5—22no—
169C2×D5—64no—
170C2×D5—62no—
171C2×D5C2×#6712yes—
172C4×C5—22no—
173C4×C5—62no—
174C4×C5—62no—
175C4×C5C2×#6712yes—
176Dic5—22no—
177Dic5—62no—
178Dic5C2×#6712yes—
179#41—304no—
180C2×Q8—31no—
181C2×Q8—52no—
182C2×Q8—51no—
183C2×Q8—104no—
184C2×Q8D3×D511yescharacteristic
185C2×D4—152no—
186C2×D4—151no—
187C22×C4—51no—
188C22×C4—52no—
189C22×C4—152no—
190C4⋊C4—34no—
191C4⋊C4—152no—
192C4⋊C4—154no—
193C22⋊C4—154no—
194C22⋊C4—152no—
195C22⋊C4—154no—
196C42—31no—
197C42—151no—
198C3×C5#53611yescharacteristic, complemented, Hall
199C22×C3—52no—
200C22×C3—102no—
201C22×C3C23×D511yescharacteristic
202C2×D3—102no—
203C2×D3—104no—
204C3×C4—22no—
205C3×C4—52no—
206C3×C4—102no—
207C3×C4D4×D512yes—
208Dic3—22no—
209Dic3—22no—
210Dic3—102no—
211C2×C5#100712yes—
212C2×C5C22×#6711yescharacteristic
213D5—22no—
214D5—122no—
215C23—51no—
216C23—152no—
217Q8—22no—
218Q8—62no—
219Q8—104no—
220Q8—102no—
221D4—304no—
222D4—302no—
223C2×C4—32no—
224C2×C4—32no—
225C2×C4—51no—
226C2×C4—54no—
227C2×C4—52no—
228C2×C4—104no—
229C2×C4—152no—
230C2×C4—304no—
231C2×C4C2×D3×D512yes—
232C2×C4C2×D3×D511yescharacteristic
233C2×C3—102no—
234C2×C3C2×D4×D511yescharacteristic
235C2×C3#414712yes—
236D3—202no—
237C5#581611yescharacteristic, complemented, Sylow
238C22—52no—
239C22—102no—
240C22—304no—
241C22—302no—
242C22C22×D3×D511yescharacteristic
243C4—22no—
244C4—52no—
245C4—62no—
246C4—62no—
247C4—102no—
248C4—302no—
249C4D5×#6712yes—
250C3#6605811yescharacteristic, complemented, Sylow
251C2—102no—
252C2—602no—
253C2#9202912yes—
254C2C2×D5×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC2×C3×C5×Q8C22
prime radicalC2×#6773C2
hypercenterC2×Q8D3×D5
hypocenterC3×C5#536
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×Q8×D5C2semidirect
3. #91836C2semidirect
4. C5×#944C2semidirect
5. #91411C2semidirect
6. #91385C2semidirect
7. #91374C2semidirect
8. #91357C2semidirect
9. #91348C2semidirect
32. C2×Q8×D5D3semidirect
64. #944D5semidirect
198. C3×C5#536semidirect
237. C5#5816semidirect
250. C3#66058semidirect

Maximal subgroups

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

subgroupindex
C2×C3×Q8×D52
C2×#67732
#918362
C5×#9442
#914112
#913852
#913742
#913572
#913482
#660583
#58165