Finite Group Databasebeta

← #11753764

Subgroups — #11753764

Order 960.

428 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 132 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#91779C211yesmaximal, characteristic, complemented
2C5×D3×C4⋊C4C211yesmaximal, characteristic, complemented
3C3×#4043C211yesmaximal, characteristic, complemented
4#91452C212yesmaximal
5C4×#1201C211yesmaximal, characteristic
6#91369C211yesmaximal, characteristic, complemented
7#91362C212yesmaximal, complemented
8#91358C211yesmaximal, characteristic, complemented
9#91339C212yesmaximal, complemented
10#91338C212yesmaximal, complemented
11#91331C211yesmaximal, characteristic, complemented
12#65847—31nomaximal, Hall
13C2×C4×C5×D3C2211yescharacteristic
14C2×C4×C5×D3C2212yes—
15C2×C3×C4×D5C2211yescharacteristic
16C2×C3×Dic10C2211yescharacteristic
17C2×#1201C2211yescharacteristic
18C3×C5×C4⋊C4C2211yescharacteristic
19C4⋊Dic15C2212yes—
20C4⋊Dic15C2211yescharacteristic
21#6712C2212yes—
22C4×Dic15C2211yescharacteristic
23C5×C4⋊Dic3C2211yescharacteristic
24C5×Dic3⋊C4C2212yes—
25C3×#685C2212yes—
26C3×C4⋊Dic5C2212yes—
27#6669C2211yescharacteristic
28#6669C2212yes—
29#6668C2212yes—
30(C2×D3)⋊Dic5C2211yescharacteristic
31(C2×D3)⋊Dic5C2212yes—
32#6665C2211yescharacteristic
33#6665C2212yes—
34Dic3×Dic5C2212yes—
35Dic3×Dic5C2212yes—
36#5639—51nomaximal, Hall
37C2×C5×C4⋊C4—31no—
38#4075—32no—
39C4×C22⋊D5—31no—
40#4072—32no—
41#4070—31no—
42#4044—32no—
43#4043D311yescharacteristic, complemented
44#4038—31no—
45#4036—31no—
46#4035—32no—
47#4033—31no—
48C22×C5×D3C2311yescharacteristic
49C22×C3×D5C2311yescharacteristic
50C2×C3×C4×C5C2312yes—
51C2×C3×C4×C5C2311yescharacteristic
52C2×Dic15C2311yescharacteristic
53C2×Dic15C2312yes—
54C2×Dic15C2311yescharacteristic
55C2×C5×Dic3C2312yes—
56C2×C5×Dic3C2311yescharacteristic
57C4×C5×D3—24no—
58C4×C5×D3—22no—
59C2×C3×Dic5C2311yescharacteristic
60C2×C3×Dic5C2312yes—
61C3×C4×D5—22no—
62C3×Dic10—22no—
63#1201—22no—
64C3×C22⋊Q8—51no—
65#946—51no—
66Q8×Dic3—51no—
67C4×#67—51no—
68#926—51no—
69#892—52no—
70D3×C4⋊C4D511yescharacteristic, complemented
71#890—51no—
72#889—52no—
73#883—52no—
74#879—52no—
75C22×C4×C5—31no—
76C22×C4×C5—32no—
77C2×C22⋊D5—31no—
78C2×C4×D5C2×D311yescharacteristic
79C2×Dic10C2×D311yescharacteristic
80C5×C4⋊C4—32no—
81C5×C4⋊C4—31no—
82C5×C4⋊C4C2×D311yescharacteristic
83C22⋊Dic5—32no—
84C22⋊Dic5—31no—
85#685—32no—
86#685—31no—
87#685C2×D312yes—
88C4⋊Dic5—31no—
89C4⋊Dic5—32no—
90C4⋊Dic5C2×D312yes—
91#683—32no—
92#683—32no—
93#683—31no—
94#683—32no—
95C4×Dic5—31no—
96C4×Dic5—32no—
97C4×Dic5—32no—
98#552—151noSylow
99C22×C3×C5C2411yescharacteristic
100C2×C5×D3—21no—
101C2×C5×D3—21no—
102C2×C5×D3#4112yes—
103C2×C3×D5—21no—
104C2×C3×D5—21no—
105C2×C3×D5—21no—
106C3×C4×C5—22no—
107C3×C4×C5#4112yes—
108Dic15—21no—
109Dic15—21no—
110Dic15—22no—
111C3×Dic5—22no—
112C3×Dic5—21no—
113C5×Dic3—21no—
114C5×Dic3—22no—
115C2×C3×Q8—51no—
116C22×C3×C4—51no—
117C2×#67—51no—
118C2×C4×D3C2×D512yes—
119C2×C4×D3C2×D511yescharacteristic
120C3×C4⋊C4—52no—
121C3×C4⋊C4C2×D511yescharacteristic
122C3×C22⋊C4—52no—
123#217—51no—
124#217—52no—
125(C2×D3)⋊C4—52no—
126(C2×D3)⋊C4—51no—
127C4⋊Dic3—52no—
128C4⋊Dic3—51no—
129C4⋊Dic3—52no—
130C4⋊Dic3C2×D511yescharacteristic
131Dic3⋊C4—52no—
132Dic3⋊C4—52no—
133Dic3⋊C4—51no—
134Dic3⋊C4C2×D512yes—
135C4×Dic3—51no—
136C4×Dic3—52no—
137C4×Dic3—52no—
138C23×C5—31no—
139C22×D5C22×D311yescharacteristic
140C2×C4×C5—32no—
141C2×C4×C5—31no—
142C2×C4×C5—64no—
143C2×C4×C5—62no—
144C2×C4×C5C22×D312yes—
145C2×C4×C5C22×D311yescharacteristic
146C22⋊D5—62no—
147C2×Dic5—31no—
148C2×Dic5—31no—
149C2×Dic5—32no—
150C2×Dic5C22×D311yescharacteristic
151C2×Dic5C22×D312yes—
152C4×D5—22no—
153Dic10—22no—
154#126—152no—
155#125—152no—
156#125—151no—
157#123—152no—
158C22⋊Q8—51no—
159C22⋊Q8—151no—
160C4×Q8—151no—
161C4×D4—151no—
162#117—151no—
163#117—152no—
164C2×C4⋊C4—31no—
165C2×C3×C5C2×#4111yescharacteristic
166C2×C3×C5C2×#4111yescharacteristic
167C2×C3×C52−1+411yescharacteristic
168C3×D5—41no—
169C5×D3—22no—
170C23×C3—51no—
171C22×D3C22×D511yescharacteristic
172C3×Q8—102no—
173C2×C3×C4—51no—
174C2×C3×C4—52no—
175C2×C3×C4—102no—
176C2×C3×C4C22×D512yes—
177C2×C3×C4C22×D511yescharacteristic
178#67—102no—
179C2×Dic3—51no—
180C2×Dic3—51no—
181C2×Dic3—52no—
182C2×Dic3C22×D512yes—
183C2×Dic3C22×D511yescharacteristic
184C4×D3—24no—
185C4×D3—22no—
186C22×C5—32no—
187C22×C5—61no—
188C22×C5—61no—
189C22×C5C23×D311yescharacteristic
190C2×D5—21no—
191C2×D5—21no—
192C2×D5—21no—
193C4×C5—22no—
194C4×C5—61no—
195C4×C5—62no—
196C4×C5#23712yes—
197Dic5—22no—
198Dic5—21no—
199Dic5—61no—
200Dic5—62no—
201Dic5—61no—
202C2×Q8—51no—
203C2×D4—151no—
204C22×C4—32no—
205C22×C4—31no—
206C22×C4—51no—
207C4⋊C4—31no—
208C4⋊C4—32no—
209C4⋊C4—52no—
210C4⋊C4—151no—
211C4⋊C4—152no—
212C4⋊C4—152no—
213C4⋊C4—151no—
214C4⋊C4—152no—
215C4⋊C4—152no—
216C4⋊C4D3×D511yescharacteristic
217C22⋊C4—52no—
218C22⋊C4—152no—
219C22⋊C4—151no—
220C22⋊C4—151no—
221C22⋊C4—152no—
222C42—152no—
223C42—152no—
224C42—151no—
225C3×C5#55211yescharacteristic, complemented, Hall
226C22×C3—101no—
227C22×C3—101no—
228C22×C3—101no—
229C22×C3C23×D511yescharacteristic
230C2×D3—21no—
231C2×D3—21no—
232C2×D3#71112yes—
233C3×C4—22no—
234C3×C4—101no—
235C3×C4—102no—
236C3×C4#70912yes—
237Dic3—21no—
238Dic3—22no—
239Dic3—101no—
240Dic3—101no—
241Dic3—102no—
242C2×C5—62no—
243C2×C5C2×#23711yescharacteristic
244C2×C5#100711yescharacteristic
245C2×C5D3×#4111yescharacteristic
246D5—41no—
247C23—31no—
248C23—51no—
249Q8—102no—
250D4—302no—
251C2×C4—32no—
252C2×C4—31no—
253C2×C4—51no—
254C2×C4—52no—
255C2×C4—64no—
256C2×C4—62no—
257C2×C4—102no—
258C2×C4—151no—
259C2×C4—152no—
260C2×C4—151no—
261C2×C4C2×D3×D512yes—
262C2×C4C2×D3×D511yescharacteristic
263C2×C3—201no—
264C2×C3C2×#70911yescharacteristic
265C2×C3C2×#71111yescharacteristic
266C2×C3#414711yescharacteristic
267D3—22no—
268C5#563911yescharacteristic, complemented, Sylow
269C22—32no—
270C22—61no—
271C22—61no—
272C22—101no—
273C22—101no—
274C22—101no—
275C22C22×D3×D511yescharacteristic
276C4—22no—
277C4—61no—
278C4—62no—
279C4—101no—
280C4—102no—
281C4—301no—
282C4—301no—
283C4—302no—
284C4#676512yes—
285C3#6584711yescharacteristic, complemented, Sylow
286C2—62no—
287C2—201no—
288C2C2×#676511yescharacteristic
289C2D3×#71111yescharacteristic
290C2#9202911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C4⋊C4C22
prime radicalC2×#1201C22
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#552
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #91779C2semidirect
2. C5×D3×C4⋊C4C2semidirect
3. C3×#4043C2semidirect
6. #91369C2semidirect
7. #91362C2semidirect
8. #91358C2semidirect
9. #91339C2semidirect
10. #91338C2semidirect
11. #91331C2semidirect
43. #4043D3semidirect
70. D3×C4⋊C4D5semidirect
225. C3×C5#552semidirect
268. C5#5639semidirect
285. C3#65847semidirect

Maximal subgroups

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

subgroupindex
#917792
C5×D3×C4⋊C42
C3×#40432
#914522
C4×#12012
#913692
#913622
#913582
#913392
#913382
#913312
#658473
#56395