Finite Group Databasebeta

← #11752704

Subgroups — #11752704

Order 960.

472 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 130 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
1C4×Dic30C211yesmaximal, characteristic, complemented
2C5×#875C211yesmaximal, characteristic, complemented
3C3×C4×D20C211yesmaximal, characteristic, complemented
4#91463C211yesmaximal, characteristic
5#91462C212yesmaximal, complemented
6#91457C212yesmaximal, complemented
7#91447C212yesmaximal, complemented
8#91440C212yesmaximal, complemented
9#91435C211yesmaximal, characteristic, complemented
10#91368C211yesmaximal, characteristic, complemented
11#91344C211yesmaximal, characteristic, complemented
12#66015—31nomaximal, Hall
13C2×Dic30C2211yescharacteristic
14C2×C5×D12C2211yescharacteristic
15C2×C5×Dic6C2211yescharacteristic
16C2×C3×D20C2211yescharacteristic
17C2×C3×C4×D5C2212yes—
18C2×#1201C2212yes—
19C2×#1201C2212yes—
20C2×D3×Dic5C2212yes—
21C3×C42×C5C2211yescharacteristic
22C4⋊Dic15C2211yescharacteristic
23#6712C2211yescharacteristic
24#6712C2211yescharacteristic
25C4×Dic15C2211yescharacteristic
26C4×Dic15C2211yescharacteristic
27C5×(C2×D3)⋊C4C2212yes—
28C5×(C2×D3)⋊C4C2212yes—
29C3×#685C2212yes—
30C3×C4⋊Dic5C2211yescharacteristic
31Dic3⋊Dic5C2212yes—
32(C2×D3)⋊Dic5C2212yes—
33#6665C2212yes—
34#6665C2212yes—
35Dic3×Dic5C2212yes—
36#5559—51nomaximal, Hall
37C5×#124—31no—
38#4093—31no—
39Q8×Dic5—31no—
40#4086—31no—
41D4×Dic5—31no—
42#4032—32no—
43#4031—32no—
44#4029—32no—
45#4027—32no—
46C4×D20D311yescharacteristic, complemented
47C4×Dic10—31no—
48C22×C5×D3C2312yes—
49C22×C3×D5C2312yes—
50C2×C3×C4×C5C2311yescharacteristic
51C2×C3×C4×C5C2311yescharacteristic
52C2×C3×C4×C5C2311yescharacteristic
53C2×Dic15C2311yescharacteristic
54C2×Dic15C2311yescharacteristic
55C2×Dic15C2311yescharacteristic
56C2×Dic15C2311yescharacteristic
57Dic30—22no—
58C2×C5×Dic3C2312yes—
59C5×D12—22no—
60C5×Dic6—22no—
61C2×C3×Dic5C2312yes—
62C3×D20—22no—
63C3×C4×D5—42no—
64#1201—24no—
65#1201—42no—
66D3×Dic5—42no—
67C3×C4×D4—51no—
68#940—51no—
69#936—51no—
70#929—52no—
71C4×#67—52no—
72#893—51no—
73#887—51no—
74#885—52no—
75#883—52no—
76#875D511yescharacteristic, complemented
77C4×Dic6—51no—
78C2×C5×Q8—31no—
79C2×C5×D4—31no—
80C2×C22⋊D5—32no—
81C2×C22⋊D5—32no—
82C22×Dic5—32no—
83C2×D20C2×D311yescharacteristic
84C2×C4×D5C2×D312yes—
85C2×Dic10—31no—
86C5×C22⋊C4—32no—
87C5×C22⋊C4—32no—
88C42×C5C2×D311yescharacteristic
89C22⋊Dic5—32no—
90#685—32no—
91#685—32no—
92#685C2×D312yes—
93C4⋊Dic5—31no—
94C4⋊Dic5—32no—
95C4⋊Dic5C2×D311yescharacteristic
96#683—31no—
97#683—31no—
98C4×Dic5—31no—
99C4×Dic5—31no—
100C4×Dic5—32no—
101#559—151noSylow
102C22×C3×C5C2411yescharacteristic
103C2×C5×D3—22no—
104C2×C5×D3—22no—
105C2×C5×D3—22no—
106C2×C3×D5—22no—
107C2×C3×D5—22no—
108C2×C3×D5—22no—
109C3×C4×C5—21no—
110C3×C4×C5—21no—
111C3×C4×C5#4112yes—
112Dic15—21no—
113Dic15—21no—
114Dic15—21no—
115Dic15#4112yes—
116C3×Dic5—22no—
117C5×Dic3—22no—
118C2×C3×D4—51no—
119C22×C3×C4—52no—
120C2×#67—52no—
121C2×#67—52no—
122C2×D12C2×D511yescharacteristic
123C2×C4×D3—52no—
124C2×Dic6—51no—
125C2×Dic6C2×D511yescharacteristic
126C3×C4⋊C4—51no—
127C3×C22⋊C4—52no—
128C3×C42C2×D511yescharacteristic
129#217—52no—
130#217—52no—
131(C2×D3)⋊C4—52no—
132(C2×D3)⋊C4C2×D512yes—
133(C2×D3)⋊C4C2×D512yes—
134C4⋊Dic3—51no—
135Dic3⋊C4—51no—
136Dic3⋊C4—51no—
137Dic3⋊C4—52no—
138C4×Dic3—51no—
139C4×Dic3—51no—
140C4×Dic3—52no—
141C23×C5—32no—
142C22×D5C22×D312yes—
143C5×Q8—62no—
144C5×D4—62no—
145C2×C4×C5—32no—
146C2×C4×C5C22×D311yescharacteristic
147C2×C4×C5C22×D311yescharacteristic
148C2×C4×C5C22×D311yescharacteristic
149C22⋊D5—64no—
150C22⋊D5—122no—
151C2×Dic5—31no—
152C2×Dic5—31no—
153C2×Dic5—31no—
154C2×Dic5—31no—
155C2×Dic5—122no—
156C2×Dic5C22×D312yes—
157D20—22no—
158C4×D5—42no—
159Dic10—62no—
160#127—151no—
161#124—31no—
162#124—152no—
163#124—151no—
164#123—152no—
165#123—152no—
166C4×Q8—151no—
167C4×Q8—151no—
168C4×D4—51no—
169C4×D4—152no—
170C4×D4—151no—
171C2×C3×C5C2×#4111yescharacteristic
172C2×C3×C5C2×#4111yescharacteristic
173C2×C3×C5H(5,𝔽2)11yescharacteristic
174C3×D5—42no—
175C5×D3—42no—
176C23×C3—52no—
177C22×D3C22×D512yes—
178C3×D4—102no—
179C2×C3×C4—52no—
180C2×C3×C4—202no—
181C2×C3×C4C22×D511yescharacteristic
182C2×C3×C4C22×D511yescharacteristic
183C2×C3×C4C22×D511yescharacteristic
184#67—104no—
185#67—202no—
186C2×Dic3—51no—
187C2×Dic3—51no—
188C2×Dic3—51no—
189C2×Dic3—51no—
190C2×Dic3C22×D512yes—
191D12—22no—
192C4×D3—202no—
193Dic6—22no—
194Dic6—102no—
195C22×C5—62no—
196C22×C5—62no—
197C22×C5—62no—
198C22×C5C23×D311yescharacteristic
199C2×D5—22no—
200C2×D5—22no—
201C2×D5—22no—
202C4×C5—21no—
203C4×C5—21no—
204C4×C5—62no—
205C4×C5#23512yes—
206Dic5—22no—
207Dic5—32no—
208Dic5—61no—
209Dic5—61no—
210Dic5—61no—
211C2×Q8—31no—
212C2×Q8—151no—
213C2×D4—31no—
214C2×D4—51no—
215C2×D4—152no—
216C2×D4—152no—
217C22×C4—52no—
218C22×C4—152no—
219C4⋊C4—51no—
220C4⋊C4—152no—
221C4⋊C4—151no—
222C4⋊C4—151no—
223C4⋊C4—151no—
224C22⋊C4—32no—
225C22⋊C4—32no—
226C22⋊C4—52no—
227C22⋊C4—152no—
228C22⋊C4—152no—
229C22⋊C4—152no—
230C42—152no—
231C42—151no—
232C42—151no—
233C42D3×D511yescharacteristic
234C3×C5#55911yescharacteristic, complemented, Hall
235C22×C3—102no—
236C22×C3—102no—
237C22×C3—102no—
238C22×C3C23×D511yescharacteristic
239C2×D3—22no—
240C2×D3—22no—
241C2×D3—22no—
242C3×C4—21no—
243C3×C4—21no—
244C3×C4—102no—
245C3×C4#71112yes—
246Dic3—22no—
247Dic3—52no—
248Dic3—101no—
249Dic3—101no—
250Dic3—101no—
251C2×C5—122no—
252C2×C5C2×#23511yescharacteristic
253C2×C5#100411yescharacteristic
254C2×C5D3×#4111yescharacteristic
255D5—42no—
256C23—32no—
257C23—52no—
258Q8—62no—
259Q8—302no—
260D4—62no—
261D4—102no—
262D4—304no—
263D4—602no—
264C2×C4—32no—
265C2×C4—52no—
266C2×C4—151no—
267C2×C4—151no—
268C2×C4—151no—
269C2×C4—151no—
270C2×C4—202no—
271C2×C4—602no—
272C2×C4C2×D3×D511yescharacteristic
273C2×C4C2×D3×D511yescharacteristic
274C2×C4C2×D3×D511yescharacteristic
275C2×C3—202no—
276C2×C3C2×#71111yescharacteristic
277C2×C3D5×#4111yescharacteristic
278C2×C3#414911yescharacteristic
279D3—42no—
280C5#555911yescharacteristic, complemented, Sylow
281C22—62no—
282C22—62no—
283C22—62no—
284C22—102no—
285C22—102no—
286C22—102no—
287C22C22×D3×D511yescharacteristic
288C4—21no—
289C4—21no—
290C4—62no—
291C4—102no—
292C4—152no—
293C4—301no—
294C4—301no—
295C4—301no—
296C4#677212yes—
297C3#6601511yescharacteristic, complemented, Sylow
298C2—122no—
299C2—202no—
300C2C2×#677211yescharacteristic
301C2#9201611yescharacteristic
302C2#9201711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C42×C5C22
prime radical#91463C2
hypercenterC42D3×D5
hypocenterC3×C5#559
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C4×Dic30C2semidirect
2. C5×#875C2semidirect
3. C3×C4×D20C2semidirect
5. #91462C2semidirect
6. #91457C2semidirect
7. #91447C2semidirect
8. #91440C2semidirect
9. #91435C2semidirect
10. #91368C2semidirect
11. #91344C2semidirect
46. C4×D20D3semidirect
76. #875D5semidirect
234. C3×C5#559semidirect
280. C5#5559semidirect
297. C3#66015semidirect

Maximal subgroups

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

subgroupindex
C4×Dic302
C5×#8752
C3×C4×D202
#914632
#914622
#914572
#914472
#914402
#914352
#913682
#913442
#660153
#55595