Finite Group Databasebeta

← #11754831

Subgroups — #11754831

Order 960.

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

normal subgroups only

This group has 660 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×D4×D15C211yesmaximal, characteristic
2C2×D15⋊Q8C211yesmaximal, characteristic, complemented
3C5×#936C211yesmaximal, characteristic, complemented
4C3×#4082C211yesmaximal, characteristic, complemented
5#91561C214yesmaximal, complemented
6#91526C214yesmaximal, complemented
7C4×#1200C211yesmaximal, characteristic, complemented
8#91375C211yesmaximal, characteristic, complemented
9#91374C211yesmaximal, characteristic, complemented
10D5×#124—31nomaximal, Hall
11C23×D15C2212yes—
12C2×C3×C5×D4C2211yescharacteristic
13C2×#1220C2212yes—
14D4×D15—24no—
15C2×D60C2211yescharacteristic
16C2×C4×D15C2211yescharacteristic
17C2×C5×Dic6C2211yescharacteristic, complemented
18C2×C3×Dic10C2211yescharacteristic, complemented
19C2×#1204C2212yescomplemented
20C2×#1200C2212yes—
21C2×#1200C2212yes—
22D15⋊Q8—24no—
23C5×#217C2214yescomplemented
24C4×C5×Dic3C2211yescharacteristic, complemented
25C3×C22⋊Dic5C2214yescomplemented
26C3×C4×Dic5C2211yescharacteristic, complemented
27#6667C2214yescomplemented
28#6667C2214yescomplemented
29Dic3×Dic5C2212yescomplemented
30D3×#124—51nomaximal, Hall
31C2×Q8×D5—31no—
32C2×D4×D5—31no—
33C5×#124—31no—
34#4093—31no—
35#4082D311yescharacteristic, complemented
36#4031—34no—
37D5×C22⋊C4—34no—
38#4021—31no—
39C42×D5—31no—
40C23×C3×C5C2312yes—
41C22×D15—24no—
42C22×D15—28no—
43C22×D15C2312yes—
44C22×D15C2311yescharacteristic
45C3×C5×D4—22no—
46C2×C3×C4×C5C2311yescharacteristic
47#1220—24no—
48C2×Dic15C2311yescharacteristic
49D60—22no—
50C4×D15D414yes—
51C2×C5×Dic3C2312yes—
52C2×C5×Dic3C2312yes—
53C5×Dic6—22no—
54C2×C3×Dic5C2312yes—
55C2×C3×Dic5C2312yes—
56C3×Dic10—22no—
57#1204—24no—
58#1200—24no—
59#1200—24no—
60C2×D3×Q8—51no—
61C2×D3×D4—51no—
62C3×#124—51no—
63#947—51no—
64#936D511yescharacteristic, complemented
65#885—54no—
66D3×C22⋊C4—54no—
67#875—51no—
68C42×D3—51no—
69C23×D5—32no—
70C2×C5×Q8—31no—
71C2×C5×D4C2×D311yescharacteristic
72C2×C22⋊D5—32no—
73Q8×D5—64no—
74D4×D5—64no—
75C2×D20—31no—
76C2×C4×D5—31no—
77C2×C4×D5—32no—
78C2×C4×D5—32no—
79C2×Dic10—32no—
80C2×Dic10C2×D311yescharacteristic, complemented
81C5×C22⋊C4—34no—
82C42×C5—31no—
83C22⋊Dic5C2×D314yescomplemented
84#685—34no—
85#685—34no—
86C4×Dic5—32no—
87C4×Dic5C2×D311yescharacteristic, complemented
88C2×#124—151noSylow
89C22×C3×C5—22no—
90C22×C3×C5—24no—
91C22×C3×C5C2411yescharacteristic
92C2×D15—22no—
93C2×D15—24no—
94C2×D15—48no—
95C2×D15C2×D412yes—
96C2×D15#4114yes—
97C3×C4×C5C2×D412yes—
98Dic15C2×D412yes—
99C3×Dic5—22no—
100C3×Dic5—22no—
101C5×Dic3—22no—
102C5×Dic3—22no—
103C23×D3—52no—
104C2×C3×Q8—51no—
105C2×C3×D4C2×D511yescharacteristic
106C2×#67—52no—
107D3×Q8—104no—
108D3×D4—104no—
109C2×D12—51no—
110C2×C4×D3—51no—
111C2×C4×D3—52no—
112C2×C4×D3—52no—
113C2×Dic6—52no—
114C2×Dic6C2×D511yescharacteristic, complemented
115C3×C22⋊C4—54no—
116C3×C42—51no—
117#217C2×D514yescomplemented
118(C2×D3)⋊C4—54no—
119(C2×D3)⋊C4—54no—
120C4×Dic3—52no—
121C4×Dic3C2×D511yescharacteristic, complemented
122C23×C5C22×D312yes—
123C22×D5—31no—
124C22×D5—32no—
125C22×D5—64no—
126C22×D5—68no—
127C5×Q8—62no—
128C5×D4—22no—
129C2×C4×C5—32no—
130C2×C4×C5—32no—
131C2×C4×C5C22×D311yescharacteristic
132C22⋊D5—64no—
133C2×Dic5—31no—
134C2×Dic5C22×D312yes—
135C2×Dic5C22×D312yes—
136D20—62no—
137C4×D5—34no—
138C4×D5—64no—
139C4×D5—64no—
140Dic10—22no—
141Dic10—64no—
142C22×Q8—151no—
143C22×D4—151no—
144#124—31no—
145#124—51no—
146#124—151no—
147#124—151no—
148#124—154no—
149C2×C22⋊C4—154no—
150C2×C42—151no—
151C2×C3×C5—42no—
152C2×C3×C5C22×D411yescharacteristic
153C2×C3×C5C2×#4112yes—
154D15—42no—
155D15#12414yescomplemented
156C23×C3C22×D512yes—
157C22×D3—51no—
158C22×D3—52no—
159C22×D3—104no—
160C22×D3—108no—
161C3×Q8—102no—
162C3×D4—22no—
163C2×C3×C4—52no—
164C2×C3×C4—52no—
165C2×C3×C4C22×D511yescharacteristic
166#67—104no—
167C2×Dic3—51no—
168C2×Dic3C22×D512yes—
169C2×Dic3C22×D512yes—
170D12—102no—
171C4×D3—54no—
172C4×D3—104no—
173C4×D3—104no—
174Dic6—22no—
175Dic6—104no—
176C22×C5—22no—
177C22×C5—24no—
178C22×C5C23×D311yescharacteristic
179C2×D5—32no—
180C2×D5—34no—
181C2×D5—62no—
182C2×D5—64no—
183C2×D5—128no—
184C4×C5—62no—
185C4×C5—62no—
186C4×C5D3×D412yes—
187Dic5—22no—
188Dic5—22no—
189Dic5—32no—
190C24—152no—
191C2×Q8—31no—
192C2×Q8—51no—
193C2×Q8—152no—
194C2×Q8—304no—
195C2×D4—152no—
196C2×D4—151no—
197C2×D4—304no—
198C2×D4D3×D511yescharacteristic
199C22×C4—152no—
200C22×C4—152no—
201C22×C4—151no—
202C22⋊C4—34no—
203C22⋊C4—54no—
204C22⋊C4—154no—
205C22⋊C4—154no—
206C42—31no—
207C42—51no—
208C42—152no—
209C3×C5C2×#12411yescharacteristic, complemented, Hall
210C22×C3—22no—
211C22×C3—24no—
212C22×C3C23×D511yescharacteristic
213C2×D3—52no—
214C2×D3—54no—
215C2×D3—102no—
216C2×D3—104no—
217C2×D3—208no—
218C3×C4—102no—
219C3×C4—102no—
220C3×C4D4×D512yes—
221Dic3—22no—
222Dic3—22no—
223Dic3—52no—
224C2×C5—42no—
225C2×C5C2×D3×D411yescharacteristic
226C2×C5D3×#4112yes—
227D5—34no—
228D5—122no—
229C23—151no—
230C23—152no—
231C23—304no—
232C23—308no—
233C23C2×D3×D512yes—
234Q8—62no—
235Q8—102no—
236Q8—304no—
237D4—22no—
238D4—304no—
239D4—302no—
240C2×C4—32no—
241C2×C4—32no—
242C2×C4—52no—
243C2×C4—52no—
244C2×C4—151no—
245C2×C4—154no—
246C2×C4—304no—
247C2×C4—304no—
248C2×C4C2×D3×D511yescharacteristic
249C2×C3—42no—
250C2×C3C2×D4×D511yescharacteristic
251C2×C3D5×#4112yes—
252D3—54no—
253D3—202no—
254C5D3×#12411yescharacteristic, complemented, Sylow
255C22—24no—
256C22—22no—
257C22—154no—
258C22—152no—
259C22—304no—
260C22—302no—
261C22—608no—
262C22C22×D3×D511yescharacteristic
263C4—62no—
264C4—62no—
265C4—102no—
266C4—102no—
267C4—152no—
268C4#679012yes—
269C3D5×#12411yescharacteristic, complemented, Sylow
270C2—42no—
271C2—154no—
272C2—602no—
273C2#9202412yes—
274C2C2×#679011yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC2×C3×C5×D4C22
prime radicalC2×D4×D15C2
hypercenterC2×D4D3×D5
hypocenterC3×C5C2×#124
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C2×D15⋊Q8C2semidirect
3. C5×#936C2semidirect
4. C3×#4082C2semidirect
5. #91561C2semidirect
6. #91526C2semidirect
7. C4×#1200C2semidirect
8. #91375C2semidirect
9. #91374C2semidirect
17. C2×C5×Dic6C22semidirect
18. C2×C3×Dic10C22semidirect
19. C2×#1204C22semidirect
23. C5×#217C22semidirect
24. C4×C5×Dic3C22semidirect
25. C3×C22⋊Dic5C22semidirect
26. C3×C4×Dic5C22semidirect
27. #6667C22semidirect
28. #6667C22semidirect
29. Dic3×Dic5C22semidirect
35. #4082D3semidirect
64. #936D5semidirect
80. C2×Dic10C2×D3semidirect
83. C22⋊Dic5C2×D3semidirect
87. C4×Dic5C2×D3semidirect
114. C2×Dic6C2×D5semidirect
117. #217C2×D5semidirect
121. C4×Dic3C2×D5semidirect
155. D15#124semidirect
209. C3×C5C2×#124semidirect
254. C5D3×#124semidirect
269. C3D5×#124semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D152
C2×D15⋊Q82
C5×#9362
C3×#40822
#915612
#915262
C4×#12002
#913752
#913742
D5×#1243
D3×#1245