Finite Group Databasebeta

← #11754794

Subgroups — #11754794

Order 960.

620 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 148 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×#711C211yesmaximal, characteristic, complemented
2C2×#6773C211yesmaximal, characteristic, complemented
3#91829C211yesmaximal, characteristic, complemented
4C5×#936C211yesmaximal, characteristic, complemented
5#91552C214yesmaximal, complemented
6#91550C214yesmaximal, complemented
7C4×D5×Dic3C211yesmaximal, characteristic, complemented
8#91385C211yesmaximal, characteristic, complemented
9#91374C211yesmaximal, characteristic, complemented
10#66002—31nomaximal, Hall
11C2×C3×C5×D4C2211yescharacteristic
12C2×#1220C2214yes—
13C2×D60C2211yescharacteristic
14C2×C5×Dic6C2211yescharacteristic
15C2×C3×C22⋊D5C2212yes—
16C22×C3×Dic5C2212yes—
17C3×#711—24no—
18C2×C3×C4×D5C2211yescharacteristic
19C2×C3×Dic10C2211yescharacteristic
20C2×#1202C2212yes—
21C2×#1200C2212yes—
22C2×D5×Dic3C2212yes—
23#6773—24no—
24C4×Dic15C2211yescharacteristic
25C5×#217C2214yes—
26C4×C5×Dic3C2211yescharacteristic
27#6669C2214yes—
28#6667C2214yes—
29Dic3×Dic5C2212yes—
30#5832—51nomaximal, Hall
31C2×#713—31no—
32C2×#711D311yescharacteristic, complemented
33C5×#124—31no—
34#4090—31no—
35#4086—31no—
36#4030—34no—
37#4027—34no—
38#4021—31no—
39C42×D5—31no—
40C23×C3×C5C2312yes—
41C22×D15C2312yes—
42C22×C3×D5C2311yescharacteristic
43C3×C5×D4—22no—
44C2×C3×C4×C5C2311yescharacteristic
45#1220—28no—
46C2×Dic15C2312yes—
47D60—22no—
48C2×C5×Dic3C2312yes—
49C2×C5×Dic3C2312yes—
50C5×Dic6—22no—
51C3×C22⋊D5—24no—
52C2×C3×Dic5—24no—
53C2×C3×Dic5C2312yes—
54C2×C3×Dic5C2311yescharacteristic
55C3×C4×D5D414yescomplemented
56C3×Dic10—22no—
57#1202—24no—
58#1200—24no—
59D5×Dic3—24no—
60C2×C3×#41—51no—
61C2×#235—51no—
62#947—51no—
63#944—51no—
64#940—51no—
65#939—54no—
66#936D511yescharacteristic, complemented
67C4×#67—54no—
68C2×C4×Dic3—51no—
69C2×C5×Q8—31no—
70C2×C5×D4C2×D311yescharacteristic
71C2×C22⋊D5—34no—
72C2×C22⋊D5C2×D312yes—
73C22×Dic5C2×D312yes—
74#713—64no—
75#711—24no—
76C2×D20—32no—
77C2×D20—31no—
78C2×C4×D5—32no—
79C2×C4×D5—32no—
80C2×C4×D5C2×D311yescharacteristic
81C2×Dic10C2×D311yescharacteristic
82C5×C22⋊C4—34no—
83C42×C5—31no—
84#685—34no—
85#683—34no—
86C4×Dic5—31no—
87C4×Dic5—32no—
88#532—151noSylow
89C22×C3×C5—22no—
90C22×C3×C5—24no—
91C22×C3×C5C2411yescharacteristic
92C2×D15—22no—
93C2×D15—24no—
94C2×C3×D5—22no—
95C2×C3×D5C2×D412yes—
96C3×C4×C5C2×D412yes—
97Dic15#4114yescomplemented
98C3×Dic5—22no—
99C3×Dic5C2×D412yes—
100C5×Dic3—22no—
101C5×Dic3—22no—
102C3×#41—104no—
103C2×C3×Q8—51no—
104C2×C3×D4—52no—
105C2×C3×D4C2×D511yescharacteristic
106C22×C3×C4—51no—
107C22×C3×C4—52no—
108C2×#67—54no—
109C2×#67—52no—
110C22×Dic3—52no—
111#235—104no—
112C2×D12—51no—
113C2×C4×D3—52no—
114C2×Dic6C2×D511yescharacteristic
115#217C2×D514yes—
116(C2×D3)⋊C4—54no—
117Dic3⋊C4—54no—
118C4×Dic3—51no—
119C4×Dic3—52no—
120C4×Dic3C2×D511yescharacteristic
121C23×C5C22×D312yes—
122C22×D5—32no—
123C22×D5C22×D311yescharacteristic
124C5×Q8—62no—
125C5×D4—22no—
126C2×C4×C5—32no—
127C2×C4×C5—32no—
128C2×C4×C5C22×D311yescharacteristic
129C22⋊D5—24no—
130C22⋊D5—68no—
131C2×Dic5—24no—
132C2×Dic5—32no—
133C2×Dic5C22×D312yes—
134C2×Dic5C22×D311yescharacteristic
135D20—64no—
136D20—62no—
137C4×D5—64no—
138C4×D5—64no—
139C4×D5#6714yescomplemented
140Dic10—22no—
141C2×#41—51no—
142C2×#41—151no—
143C4⋊Q8—151no—
144#127—151no—
145#124—31no—
146#124—151no—
147#121—154no—
148C4×D4—154no—
149C2×C42—151no—
150C2×C3×C5—42no—
151C2×C3×C5C22×D411yescharacteristic
152C2×C3×C5C2×#4112yes—
153D15—42no—
154C3×D5—22no—
155C23×C3—51no—
156C23×C3C22×D512yes—
157C22×D3—52no—
158C3×Q8—102no—
159C3×D4—22no—
160C3×D4—104no—
161C2×C3×C4—51no—
162C2×C3×C4—54no—
163C2×C3×C4—52no—
164C2×C3×C4—104no—
165C2×C3×C4C22×D511yescharacteristic
166#67—104no—
167#67—108no—
168C2×Dic3—52no—
169C2×Dic3—104no—
170C2×Dic3C22×D512yes—
171C2×Dic3C22×D512yes—
172D12—102no—
173C4×D3—104no—
174Dic6—22no—
175C22×C5—24no—
176C22×C5—22no—
177C22×C5C23×D311yescharacteristic
178C2×D5—22no—
179C2×D5—64no—
180C2×D5—62no—
181C2×D5C2×#6712yes—
182C4×C5—62no—
183C4×C5—62no—
184C4×C5C2×#6712yes—
185Dic5—22no—
186Dic5—34no—
187Dic5C2×#6712yes—
188#41—104no—
189#41—304no—
190C2×Q8—31no—
191C2×Q8—51no—
192C2×D4—52no—
193C2×D4—152no—
194C2×D4—154no—
195C2×D4—151no—
196C2×D4D3×D511yescharacteristic
197C22×C4—51no—
198C22×C4—52no—
199C22×C4—152no—
200C22×C4—152no—
201C4⋊C4—154no—
202C22⋊C4—34no—
203C22⋊C4—154no—
204C42—31no—
205C42—152no—
206C42—151no—
207C3×C5#53211yescharacteristic, complemented, Hall
208C22×C3—22no—
209C22×C3—24no—
210C22×C3—52no—
211C22×C3—102no—
212C22×C3C23×D511yescharacteristic
213C2×D3—102no—
214C2×D3—104no—
215C3×C4—52no—
216C3×C4—102no—
217C3×C4D4×D512yes—
218Dic3—22no—
219Dic3—22no—
220Dic3—54no—
221C2×C5—42no—
222C2×C5D3×#4112yes—
223C2×C5C22×#6711yescharacteristic
224D5—22no—
225D5—122no—
226C23—51no—
227C23—152no—
228C23C2×D3×D512yes—
229Q8—62no—
230Q8—102no—
231D4—22no—
232D4—104no—
233D4—304no—
234D4—308no—
235D4—302no—
236C2×C4—32no—
237C2×C4—32no—
238C2×C4—51no—
239C2×C4—54no—
240C2×C4—52no—
241C2×C4—104no—
242C2×C4—152no—
243C2×C4—304no—
244C2×C4—304no—
245C2×C4C2×D3×D511yescharacteristic
246C2×C3—42no—
247C2×C3—102no—
248C2×C3C2×D4×D511yescharacteristic
249C2×C3D5×#4112yes—
250D3—202no—
251C5#583211yescharacteristic, complemented, Sylow
252C22—24no—
253C22—22no—
254C22—52no—
255C22—102no—
256C22—304no—
257C22—302no—
258C22C22×D3×D511yescharacteristic
259C4—52no—
260C4—62no—
261C4—62no—
262C4—102no—
263C4—154no—
264C4D5×#6712yes—
265C3#6600211yescharacteristic, complemented, Sylow
266C2—42no—
267C2—102no—
268C2—602no—
269C2#9202412yes—
270C2C2×D5×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC2×C3×C5×D4C22
hypercenterC2×D4D3×D5
hypocenterC3×C5#532
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#711C2semidirect
2. C2×#6773C2semidirect
3. #91829C2semidirect
4. C5×#936C2semidirect
5. #91552C2semidirect
6. #91550C2semidirect
7. C4×D5×Dic3C2semidirect
8. #91385C2semidirect
9. #91374C2semidirect
32. C2×#711D3semidirect
55. C3×C4×D5D4semidirect
66. #936D5semidirect
97. Dic15#41semidirect
139. C4×D5#67semidirect
207. C3×C5#532semidirect
251. C5#5832semidirect
265. C3#66002semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#7112
C2×#67732
#918292
C5×#9362
#915522
#915502
C4×D5×Dic32
#913852
#913742
#660023
#58325