Finite Group Databasebeta

← #11755294

Subgroups — #11755294

Order 960.

520 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 120 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
1#91836C211yesmaximal, characteristic, complemented
2C5×#947C211yesmaximal, characteristic, complemented
3C3×#4093C211yesmaximal, characteristic, complemented
4#91476C212yesmaximal, complemented
5#91475C212yesmaximal, complemented
6#91474C212yesmaximal, complemented
7#91464C212yesmaximal, complemented
8#91353C212yesmaximal, complemented
9#91350C212yesmaximal, complemented
10#66017—31nomaximal, Hall
11C22×D3×D5C2212yescomplemented
12C2×C3×C5×Q8C2211yescharacteristic, complemented
13C2×D60C2211yescharacteristic
14C2×C5×D12C2211yescharacteristic
15C2×C3×D20C2211yescharacteristic
16C2×#1204C2212yescomplemented
17C2×#1203C2212yes—
18C2×#1202C2212yes—
19C2×#1201C2212yes—
20#6714C2212yescomplemented
21#6714C2212yescomplemented
22C4×Dic15C2211yescharacteristic, complemented
23C5×(C2×D3)⋊C4C2212yescomplemented
24C5×(C2×D3)⋊C4C2212yescomplemented
25C4×C5×Dic3C2211yescharacteristic, complemented
26C3×#685C2212yescomplemented
27C3×#685C2212yescomplemented
28C3×C4×Dic5C2211yescharacteristic, complemented
29#6667C2212yescomplemented
30(C2×D3)⋊Dic5C2212yescomplemented
31#6665C2212yescomplemented
32#5683—51nomaximal, Hall
33C5×#124—31no—
34#4093—31no—
35#4093D311yescharacteristic, complemented
36#4083—32no—
37#4031—32no—
38#4031—32no—
39#4028—32no—
40#4028—32no—
41#4021—32no—
42C22×D15C2312yes—
43C22×C5×D3C2312yes—
44C22×C3×D5C2312yes—
45C2×D3×D5—42no—
46C2×D3×D5—42no—
47C2×D3×D5—42no—
48C3×C5×Q8—41no—
49C2×C3×C4×C5C2311yescharacteristic
50C2×C3×C4×C5C2311yescharacteristic
51C2×C3×C4×C5C2311yescharacteristic
52C2×Dic15C2312yes—
53D60—41no—
54C2×C5×Dic3C2312yes—
55C5×D12—41no—
56C2×C3×Dic5C2312yes—
57C3×D20—41no—
58#1204—42no—
59#1203—42no—
60#1202—42no—
61#1201—42no—
62C3×#124—51no—
63#947—51no—
64#947D511yescharacteristic, complemented
65#937—52no—
66#885—52no—
67#885—52no—
68#882—52no—
69#882—52no—
70#875—52no—
71C23×D5—32no—
72C2×C5×Q8C2×D311yescharacteristic, complemented
73C2×C5×D4—31no—
74C2×C22⋊D5—32no—
75C2×C22⋊D5—32no—
76C2×D20—32no—
77C2×D20—31no—
78C2×D20C2×D311yescharacteristic
79C2×Dic10—32no—
80C5×C22⋊C4—32no—
81C5×C22⋊C4—32no—
82C42×C5—31no—
83C22⋊Dic5—32no—
84#685—32no—
85#685—32no—
86#685—32no—
87#685—32no—
88#685C2×D312yescomplemented
89#685C2×D312yescomplemented
90C4×Dic5—31no—
91C4×Dic5C2×D311yescharacteristic, complemented
92H(3,𝔽4)—151noSylow
93C22×C3×C5C2411yescharacteristic
94C2×D15—22no—
95C2×D15—22no—
96C2×D15—22no—
97C2×C5×D3—22no—
98C2×C5×D3—22no—
99C2×C5×D3—22no—
100C2×C3×D5—22no—
101C2×C3×D5—22no—
102C2×C3×D5—22no—
103D3×D5—48no—
104C3×C4×C5—21no—
105C3×C4×C5—21no—
106C3×C4×C5—21no—
107Dic15—22no—
108C3×Dic5—22no—
109C5×Dic3—22no—
110C23×D3—52no—
111C2×C3×Q8C2×D511yescharacteristic, complemented
112C2×C3×D4—51no—
113C2×#67—52no—
114C2×#67—52no—
115C2×D12—52no—
116C2×D12—51no—
117C2×D12C2×D511yescharacteristic
118C2×Dic6—52no—
119C3×C22⋊C4—52no—
120C3×C22⋊C4—52no—
121C3×C42—51no—
122#217—52no—
123(C2×D3)⋊C4—52no—
124(C2×D3)⋊C4—52no—
125(C2×D3)⋊C4—52no—
126(C2×D3)⋊C4—52no—
127(C2×D3)⋊C4C2×D512yescomplemented
128(C2×D3)⋊C4C2×D512yescomplemented
129C4×Dic3—51no—
130C4×Dic3C2×D511yescharacteristic, complemented
131C23×C5—32no—
132C22×D5—32no—
133C22×D5—122no—
134C22×D5—122no—
135C22×D5—122no—
136C22×D5C22×D312yes—
137C5×Q8—41no—
138C5×D4—121no—
139C2×C4×C5—32no—
140C2×C4×C5C22×D311yescharacteristic
141C2×C4×C5C22×D311yescharacteristic
142C2×C4×C5C22×D311yescharacteristic
143C22⋊D5—122no—
144C22⋊D5—122no—
145C2×Dic5—32no—
146C2×Dic5C22×D312yes—
147D20—41no—
148D20—121no—
149D20—122no—
150Dic10—122no—
151#124—31no—
152#124—51no—
153#124—152no—
154#124—152no—
155#124—152no—
156#124—151no—
157#120—152no—
158#120—152no—
159#120—152no—
160C2×C3×C5H(5,𝔽2)11yescharacteristic
161C2×C3×C5H(5,𝔽2)12yes—
162D15—42no—
163C3×D5—42no—
164C5×D3—42no—
165C23×C3—52no—
166C22×D3—52no—
167C22×D3—202no—
168C22×D3—202no—
169C22×D3—202no—
170C22×D3C22×D512yes—
171C3×Q8—41no—
172C3×D4—201no—
173C2×C3×C4—52no—
174C2×C3×C4C22×D511yescharacteristic
175C2×C3×C4C22×D511yescharacteristic
176C2×C3×C4C22×D511yescharacteristic
177#67—202no—
178#67—202no—
179C2×Dic3—52no—
180C2×Dic3C22×D512yes—
181D12—41no—
182D12—201no—
183D12—202no—
184Dic6—202no—
185C22×C5—62no—
186C22×C5—62no—
187C22×C5—62no—
188C22×C5C23×D311yescharacteristic
189C2×D5—22no—
190C2×D5—22no—
191C2×D5—22no—
192C2×D5—62no—
193C2×D5—62no—
194C2×D5—62no—
195C2×D5—128no—
196C4×C5—21no—
197C4×C5—21no—
198C4×C5—21no—
199C4×C5—62no—
200Dic5—22no—
201Dic5—62no—
202C24—152no—
203C2×Q8—152no—
204C2×Q8D3×D511yescharacteristic, complemented
205C2×D4—31no—
206C2×D4—51no—
207C2×D4—152no—
208C2×D4—152no—
209C2×D4—152no—
210C2×D4—151no—
211C22⋊C4—32no—
212C22⋊C4—32no—
213C22⋊C4—52no—
214C22⋊C4—52no—
215C22⋊C4—152no—
216C22⋊C4—152no—
217C22⋊C4—152no—
218C22⋊C4—152no—
219C22⋊C4—152no—
220C42—31no—
221C42—51no—
222C42—151no—
223C3×C5H(3,𝔽4)11yescharacteristic, complemented, Hall
224C22×C3—102no—
225C22×C3—102no—
226C22×C3—102no—
227C22×C3C23×D511yescharacteristic
228C2×D3—22no—
229C2×D3—22no—
230C2×D3—22no—
231C2×D3—102no—
232C2×D3—102no—
233C2×D3—102no—
234C2×D3—208no—
235C3×C4—21no—
236C3×C4—21no—
237C3×C4—21no—
238C3×C4—102no—
239Dic3—22no—
240Dic3—102no—
241C2×C5—122no—
242C2×C5#100411yescharacteristic
243C2×C5#100912yes—
244D5—42no—
245D5—122no—
246C23—32no—
247C23—52no—
248C23—152no—
249C23—602no—
250C23—602no—
251C23—602no—
252Q8—41no—
253Q8—602no—
254D4—121no—
255D4—201no—
256D4—601no—
257D4—602no—
258D4—602no—
259D4—602no—
260C2×C4—32no—
261C2×C4—52no—
262C2×C4—152no—
263C2×C4C2×D3×D511yescharacteristic
264C2×C4C2×D3×D511yescharacteristic
265C2×C4C2×D3×D511yescharacteristic
266C2×C3—202no—
267C2×C3#414411yescharacteristic
268C2×C3#414912yes—
269D3—42no—
270D3—202no—
271C5#568311yescharacteristic, complemented, Sylow
272C22—62no—
273C22—62no—
274C22—62no—
275C22—102no—
276C22—102no—
277C22—102no—
278C22—302no—
279C22—302no—
280C22—302no—
281C22—608no—
282C22C22×D3×D511yescharacteristic
283C4—21no—
284C4—21no—
285C4—21no—
286C4—62no—
287C4—102no—
288C4—302no—
289C3#6601711yescharacteristic, complemented, Sylow
290C2—122no—
291C2—202no—
292C2—602no—
293C2#9203512yes—
294C2#9204911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC2×C3×C5×Q8C22
hypercenterC2×Q8D3×D5
hypocenterC3×C5H(3,𝔽4)
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. #91836C2semidirect
2. C5×#947C2semidirect
3. C3×#4093C2semidirect
4. #91476C2semidirect
5. #91475C2semidirect
6. #91474C2semidirect
7. #91464C2semidirect
8. #91353C2semidirect
9. #91350C2semidirect
11. C22×D3×D5C22semidirect
12. C2×C3×C5×Q8C22semidirect
16. C2×#1204C22semidirect
20. #6714C22semidirect
21. #6714C22semidirect
22. C4×Dic15C22semidirect
23. C5×(C2×D3)⋊C4C22semidirect
24. C5×(C2×D3)⋊C4C22semidirect
25. C4×C5×Dic3C22semidirect
26. C3×#685C22semidirect
27. C3×#685C22semidirect
28. C3×C4×Dic5C22semidirect
29. #6667C22semidirect
30. (C2×D3)⋊Dic5C22semidirect
31. #6665C22semidirect
35. #4093D3semidirect
64. #947D5semidirect
72. C2×C5×Q8C2×D3semidirect
88. #685C2×D3semidirect
89. #685C2×D3semidirect
91. C4×Dic5C2×D3semidirect
111. C2×C3×Q8C2×D5semidirect
127. (C2×D3)⋊C4C2×D5semidirect
128. (C2×D3)⋊C4C2×D5semidirect
130. C4×Dic3C2×D5semidirect
204. C2×Q8D3×D5semidirect
223. C3×C5H(3,𝔽4)semidirect
271. C5#5683semidirect
289. C3#66017semidirect

Maximal subgroups

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

subgroupindex
#918362
C5×#9472
C3×#40932
#914762
#914752
#914742
#914642
#913532
#913502
#660173
#56835