Finite Group Databasebeta

← #11755426

Subgroups — #11755426

Order 960.

692 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 692 conjugacy classes of subgroups — too many to draw. Only its 160 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
1C22×C5×#67C211yesmaximal, characteristic, complemented
2C22×C3×C22⋊D5C211yesmaximal, characteristic, complemented
3C2×#6719C211yesmaximal, characteristic, complemented
4#91571C214yesmaximal, complemented
5#91568C212yesmaximal, complemented
6#91563C212yesmaximal, complemented
7#91539C212yesmaximal, complemented
8#91536C212yesmaximal, complemented
9#66138—31nomaximal, Hall
10C24×C3×C5C2211yescharacteristic
11C23×C5×D3C2211yescharacteristic, complemented
12C23×C3×D5C2211yescharacteristic, complemented
13C22×Dic15C2212yescomplemented
14C2×C5×#67—24no—
15C2×C5×#67C2212yes—
16C2×C5×#67C2212yescomplemented
17C22×C5×Dic3C2211yescharacteristic, complemented
18C2×C3×C22⋊D5—24no—
19C2×C3×C22⋊D5C2212yes—
20C2×C3×C22⋊D5C2212yescomplemented
21C22×C3×Dic5C2211yescharacteristic, complemented
22C2×#1201C2214yescomplemented
23#6719C2212yescomplemented
24#6719C2212yescomplemented
25#6669C2214yescomplemented
26(C2×D3)⋊Dic5C2214yescomplemented
27#6665C2214yescomplemented
28#5804—51nomaximal, Hall
29C22×C5×D4—31no—
30C22×C22⋊D5D311yescharacteristic, complemented
31#4099—32no—
32C2×C22⋊Dic5—31no—
33#4085—34no—
34#4083—32no—
35#4081—32no—
36#4075—32no—
37C23×C3×C5—42no—
38C23×C3×C5D414yescomplemented
39C23×C3×C5C2311yescharacteristic
40C23×C3×C5C2311yescharacteristic
41C23×C3×C5C2311yescharacteristic
42C22×C5×D3—22no—
43C22×C5×D3—42no—
44C22×C5×D3C2312yes—
45C22×C3×D5—22no—
46C22×C3×D5—42no—
47C22×C3×D5C2312yes—
48C2×Dic15—42no—
49C2×Dic15C2314yes—
50C5×#67—24no—
51C5×#67—24no—
52C2×C5×Dic3—22no—
53C2×C5×Dic3C2312yes—
54C3×C22⋊D5—24no—
55C3×C22⋊D5—24no—
56C2×C3×Dic5—22no—
57C2×C3×Dic5C2312yes—
58#1201—44no—
59C22×C3×D4—51no—
60C22×#67D511yescharacteristic, complemented
61#953—52no—
62C2×#217—51no—
63#939—54no—
64#937—52no—
65#935—52no—
66#929—52no—
67C24×C5—31no—
68C24×C5C2×D311yescharacteristic
69C23×D5C2×D311yescharacteristic, complemented
70C2×C5×D4—32no—
71C2×C5×D4—32no—
72C2×C5×D4—64no—
73C22×C4×C5—31no—
74C2×C22⋊D5—24no—
75C2×C22⋊D5—34no—
76C2×C22⋊D5C2×D312yes—
77C2×C22⋊D5C2×D312yescomplemented
78C22×Dic5—32no—
79C22×Dic5C2×D311yescharacteristic, complemented
80C22⋊Dic5—32no—
81C22⋊Dic5—32no—
82C22⋊Dic5—34no—
83#685—34no—
84#683—34no—
85#534—151noSylow
86C22×C3×C5—22no—
87C22×C3×C5—22no—
88C22×C3×C5—22no—
89C22×C3×C5—44no—
90C22×C3×C5C2×D412yes—
91C22×C3×C5C2×D412yes—
92C22×C3×C5C2×D412yes—
93C22×C3×C5C2411yescharacteristic
94C2×C5×D3—22no—
95C2×C5×D3—24no—
96C2×C5×D3—44no—
97C2×C3×D5—22no—
98C2×C3×D5—24no—
99C2×C3×D5—44no—
100Dic15—24no—
101C3×Dic5—22no—
102C5×Dic3—22no—
103C24×C3—51no—
104C24×C3C2×D511yescharacteristic
105C23×D3C2×D511yescharacteristic, complemented
106C2×C3×D4—52no—
107C2×C3×D4—52no—
108C2×C3×D4—104no—
109C22×C3×C4—51no—
110C2×#67—24no—
111C2×#67—54no—
112C2×#67C2×D512yes—
113C2×#67C2×D512yescomplemented
114C22×Dic3—52no—
115C22×Dic3C2×D511yescharacteristic, complemented
116#217—52no—
117#217—52no—
118#217—54no—
119(C2×D3)⋊C4—54no—
120Dic3⋊C4—54no—
121C23×C5—32no—
122C23×C5—42no—
123C23×C5—62no—
124C23×C5—122no—
125C23×C5#6714yescomplemented
126C23×C5C22×D311yescharacteristic
127C23×C5C22×D311yescharacteristic
128C23×C5C22×D311yescharacteristic
129C22×D5—22no—
130C22×D5—42no—
131C22×D5C22×D312yes—
132C5×D4—64no—
133C5×D4—64no—
134C2×C4×C5—32no—
135C2×C4×C5—62no—
136C22⋊D5—24no—
137C22⋊D5—24no—
138C22⋊D5—124no—
139C2×Dic5—22no—
140C2×Dic5—34no—
141C2×Dic5—122no—
142C2×Dic5C22×D312yes—
143C22×D4—31no—
144C22×D4—51no—
145#123—152no—
146#123—152no—
147#121—154no—
148#120—152no—
149#120—152no—
150C2×C22⋊C4—151no—
151C2×C3×C5—22no—
152C2×C3×C5—22no—
153C2×C3×C5—22no—
154C2×C3×C5C22×D411yescharacteristic
155C2×C3×C5H(5,𝔽2)12yes—
156C3×D5—42no—
157C5×D3—42no—
158C23×C3—42no—
159C23×C3—52no—
160C23×C3—102no—
161C23×C3—202no—
162C23×C3C22⋊D514yescomplemented
163C23×C3C22×D511yescharacteristic
164C23×C3C22×D511yescharacteristic
165C23×C3C22×D511yescharacteristic
166C22×D3—22no—
167C22×D3—42no—
168C22×D3C22×D512yes—
169C3×D4—104no—
170C3×D4—104no—
171C2×C3×C4—52no—
172C2×C3×C4—102no—
173#67—24no—
174#67—24no—
175#67—204no—
176C2×Dic3—22no—
177C2×Dic3—54no—
178C2×Dic3—202no—
179C2×Dic3C22×D512yes—
180C22×C5—22no—
181C22×C5—22no—
182C22×C5—22no—
183C22×C5—44no—
184C22×C5—64no—
185C22×C5—62no—
186C22×C5—124no—
187C22×C5C2×#6712yes—
188C22×C5C2×#6712yes—
189C22×C5C2×#6712yes—
190C22×C5C23×D311yescharacteristic
191C2×D5—24no—
192C2×D5—22no—
193C2×D5—44no—
194C4×C5—62no—
195Dic5—22no—
196Dic5—64no—
197C24—31no—
198C24—51no—
199C24D3×D511yescharacteristic
200C2×D4—32no—
201C2×D4—32no—
202C2×D4—52no—
203C2×D4—52no—
204C2×D4—64no—
205C2×D4—104no—
206C2×D4—154no—
207C22×C4—31no—
208C22×C4—51no—
209C22×C4—152no—
210C4⋊C4—154no—
211C22⋊C4—154no—
212C22⋊C4—154no—
213C22⋊C4—152no—
214C22⋊C4—152no—
215C3×C5#53411yescharacteristic, complemented, Hall
216C22×C3—22no—
217C22×C3—22no—
218C22×C3—22no—
219C22×C3—44no—
220C22×C3—104no—
221C22×C3—102no—
222C22×C3—204no—
223C22×C3C2×C22⋊D512yes—
224C22×C3C2×C22⋊D512yes—
225C22×C3C2×C22⋊D512yes—
226C22×C3C23×D511yescharacteristic
227C2×D3—24no—
228C2×D3—22no—
229C2×D3—44no—
230C3×C4—102no—
231Dic3—22no—
232Dic3—104no—
233C2×C5—22no—
234C2×C5—22no—
235C2×C5—22no—
236C2×C5—122no—
237C2×C5#100412yes—
238C2×C5C22×#6711yescharacteristic
239D5—42no—
240C23—32no—
241C23—42no—
242C23—52no—
243C23—62no—
244C23—102no—
245C23—122no—
246C23—202no—
247C23#120114yescomplemented
248C23C2×D3×D511yescharacteristic
249C23C2×D3×D511yescharacteristic
250C23C2×D3×D511yescharacteristic
251D4—64no—
252D4—64no—
253D4—104no—
254D4—104no—
255D4—604no—
256C2×C4—32no—
257C2×C4—52no—
258C2×C4—62no—
259C2×C4—102no—
260C2×C4—154no—
261C2×C4—602no—
262C2×C3—22no—
263C2×C3—22no—
264C2×C3—22no—
265C2×C3—202no—
266C2×C3#414412yes—
267C2×C3C22×C22⋊D511yescharacteristic
268D3—42no—
269C5#580411yescharacteristic, complemented, Sylow
270C22—22no—
271C22—22no—
272C22—22no—
273C22—44no—
274C22—62no—
275C22—64no—
276C22—102no—
277C22—104no—
278C22—124no—
279C22—204no—
280C22C2×#120112yes—
281C22C2×#120112yes—
282C22C2×#120112yes—
283C22C22×D3×D511yescharacteristic
284C4—62no—
285C4—102no—
286C4—304no—
287C3#6613811yescharacteristic, complemented, Sylow
288C2—22no—
289C2—22no—
290C2—22no—
291C2—122no—
292C2—202no—
293C2C22×#120111yescharacteristic
294C2#9204912yes—
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC24×C3×C5C22
hypercenterC24D3×D5
hypocenterC3×C5#534
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
1. C22×C5×#67C2semidirect
2. C22×C3×C22⋊D5C2semidirect
3. C2×#6719C2semidirect
4. #91571C2semidirect
5. #91568C2semidirect
6. #91563C2semidirect
7. #91539C2semidirect
8. #91536C2semidirect
11. C23×C5×D3C22semidirect
12. C23×C3×D5C22semidirect
13. C22×Dic15C22semidirect
16. C2×C5×#67C22semidirect
17. C22×C5×Dic3C22semidirect
20. C2×C3×C22⋊D5C22semidirect
21. C22×C3×Dic5C22semidirect
22. C2×#1201C22semidirect
23. #6719C22semidirect
24. #6719C22semidirect
25. #6669C22semidirect
26. (C2×D3)⋊Dic5C22semidirect
27. #6665C22semidirect
30. C22×C22⋊D5D3semidirect
38. C23×C3×C5D4semidirect
60. C22×#67D5semidirect
69. C23×D5C2×D3semidirect
77. C2×C22⋊D5C2×D3semidirect
79. C22×Dic5C2×D3semidirect
105. C23×D3C2×D5semidirect
113. C2×#67C2×D5semidirect
115. C22×Dic3C2×D5semidirect
125. C23×C5#67semidirect
162. C23×C3C22⋊D5semidirect
215. C3×C5#534semidirect
247. C23#1201semidirect
269. C5#5804semidirect
287. C3#66138semidirect

Maximal subgroups

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

subgroupindex
C22×C5×#672
C22×C3×C22⋊D52
C2×#67192
#915712
#915682
#915632
#915392
#915362
#661383
#58045