Finite Group Databasebeta

← #11753332

Subgroups — #11753332

Order 960.

412 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 136 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⋊C4×D15C211yesmaximal, characteristic
2C5×#888C211yesmaximal, characteristic, complemented
3C3×#4036C211yesmaximal, characteristic, complemented
4#91468C211yesmaximal, characteristic, complemented
5#91386C211yesmaximal, characteristic
6#91383C212yesmaximal
7#91381C211yesmaximal, characteristic, complemented
8#91377C212yesmaximal
9#91347C211yesmaximal, characteristic
10#91339C212yesmaximal, complemented
11#91329C212yesmaximal, complemented
12#66063—31nomaximal, Hall
13C2×C4×D15C2212yes—
14C2×C4×D15C2211yescharacteristic
15C2×C5×Dic6C2212yes—
16C2×#1204C2212yes—
17C3×C5×C4⋊C4C2211yescharacteristic
18C4⋊Dic15C2211yescharacteristic
19#6712C2212yes—
20C5×C4⋊Dic3C2211yescharacteristic
21C5×Dic3⋊C4C2212yes—
22C4×C5×Dic3C2211yescharacteristic
23C3×C4⋊Dic5C2212yes—
24C3×C4⋊Dic5C2211yescharacteristic
25C3×#683C2212yes—
26C3×C4×Dic5C2211yescharacteristic
27#6669C2211yescharacteristic
28#6669C2211yescharacteristic
29#6669C2212yes—
30#6668C2212yes—
31#6668C2212yes—
32#6667C2212yes—
33#6667C2211yescharacteristic
34#6667C2211yescharacteristic
35Dic3×Dic5C2212yes—
36#5689—51nomaximal, Hall
37C5×C4⋊Q8—31no—
38#4092—32no—
39#4090—32no—
40#4042—32no—
41#4038—31no—
42D5×C4⋊C4—31no—
43#4036D311yescharacteristic, complemented
44#4035—32no—
45#4034—31no—
46#4018—31no—
47#4016—31no—
48C22×D15C2311yescharacteristic
49C2×C3×C4×C5C2312yes—
50C2×C3×C4×C5C2311yescharacteristic
51C2×Dic15C2312yes—
52C2×Dic15C2311yescharacteristic
53C4×D15—42no—
54C4×D15Q814yescomplemented
55C2×C5×Dic3C2312yes—
56C2×C5×Dic3C2311yescharacteristic
57C2×C5×Dic3C2311yescharacteristic
58C5×Dic6—42no—
59C2×C3×Dic5C2312yes—
60C2×C3×Dic5C2311yescharacteristic
61C2×C3×Dic5C2311yescharacteristic
62#1204—42no—
63C3×#125—51no—
64#897—52no—
65#896—52no—
66#892—51no—
67D3×C4⋊C4—51no—
68#890—51no—
69#889—52no—
70#888—52no—
71#888D511yescharacteristic, complemented
72#872—51no—
73#869—51no—
74C2×C5×Q8—32no—
75C2×C4×D5—31no—
76C2×C4×D5—32no—
77C2×Dic10—32no—
78C5×C4⋊C4—32no—
79C5×C4⋊C4—31no—
80C5×C4⋊C4C2×D311yescharacteristic
81C42×C5—31no—
82#685—31no—
83#685—31no—
84#685—32no—
85C4⋊Dic5—31no—
86C4⋊Dic5C2×D311yescharacteristic
87C4⋊Dic5C2×D312yes—
88#683—32no—
89#683—32no—
90#683—32no—
91#683—32no—
92#683—31no—
93#683—31no—
94#683C2×D312yes—
95C4×Dic5—32no—
96C4×Dic5C2×D311yescharacteristic
97#544—151noSylow
98C22×C3×C5C2411yescharacteristic
99C2×D15—21no—
100C2×D15—21no—
101C2×D15C2×Q812yes—
102C3×C4×C5—22no—
103C3×C4×C5C2×Q812yes—
104Dic15—22no—
105Dic15C2×Q812yes—
106C3×Dic5—21no—
107C3×Dic5—22no—
108C3×Dic5—21no—
109C5×Dic3—22no—
110C5×Dic3—21no—
111C5×Dic3—21no—
112C2×C4×D3—51no—
113C2×C4×D3—52no—
114C2×Dic6—52no—
115C2×Dic6C2×D512yes—
116C3×C4⋊C4—52no—
117C3×C4⋊C4—52no—
118C3×C4⋊C4—51no—
119C3×C4⋊C4C2×D511yescharacteristic
120C3×C42—51no—
121(C2×D3)⋊C4—51no—
122(C2×D3)⋊C4—51no—
123(C2×D3)⋊C4—52no—
124C4⋊Dic3—51no—
125C4⋊Dic3—52no—
126C4⋊Dic3—52no—
127C4⋊Dic3C2×D511yescharacteristic
128Dic3⋊C4—52no—
129Dic3⋊C4—51no—
130Dic3⋊C4—51no—
131Dic3⋊C4—52no—
132Dic3⋊C4C2×D512yes—
133C4×Dic3—52no—
134C4×Dic3C2×D511yescharacteristic
135C22×D5—31no—
136C5×Q8—122no—
137C2×C4×C5—32no—
138C2×C4×C5—31no—
139C2×C4×C5—31no—
140C2×C4×C5C22×D312yes—
141C2×C4×C5C22×D311yescharacteristic
142C2×Dic5—31no—
143C2×Dic5—32no—
144C2×Dic5C22×D312yes—
145C2×Dic5C22×D311yescharacteristic
146C2×Dic5C22×D311yescharacteristic
147C4×D5—34no—
148C4×D5—122no—
149Dic10—122no—
150C4⋊Q8—31no—
151C4⋊Q8—151no—
152C4⋊Q8—152no—
153#125—51no—
154#125—151no—
155#125—152no—
156C22⋊Q8—152no—
157C22⋊Q8—152no—
158#117—151no—
159#117—151no—
160C2×C4⋊C4—151no—
161C2×C3×C5C22×Q811yescharacteristic
162C2×C3×C5H(5,𝔽2)11yescharacteristic
163C2×C3×C52−1+411yescharacteristic
164D15—22no—
165C22×D3—51no—
166C2×C3×C4—52no—
167C2×C3×C4—51no—
168C2×C3×C4—51no—
169C2×C3×C4C22×D512yes—
170C2×C3×C4C22×D511yescharacteristic
171C2×Dic3—51no—
172C2×Dic3—52no—
173C2×Dic3C22×D512yes—
174C2×Dic3C22×D511yescharacteristic
175C2×Dic3C22×D511yescharacteristic
176C4×D3—54no—
177C4×D3—202no—
178Dic6—42no—
179Dic6—202no—
180C22×C5C23×D311yescharacteristic
181C2×D5—32no—
182C2×D5—61no—
183C2×D5—61no—
184C4×C5—22no—
185C4×C5—62no—
186C4×C5—61no—
187C4×C5—61no—
188C4×C5D3×Q812yes—
189Dic5—21no—
190Dic5—22no—
191Dic5—21no—
192Dic5—32no—
193Dic5—62no—
194C2×Q8—32no—
195C2×Q8—152no—
196C22×C4—151no—
197C22×C4—152no—
198C4⋊C4—31no—
199C4⋊C4—32no—
200C4⋊C4—51no—
201C4⋊C4—52no—
202C4⋊C4—52no—
203C4⋊C4—151no—
204C4⋊C4—151no—
205C4⋊C4—152no—
206C4⋊C4—152no—
207C4⋊C4—152no—
208C4⋊C4—152no—
209C4⋊C4—151no—
210C4⋊C4D3×D511yescharacteristic
211C22⋊C4—151no—
212C22⋊C4—151no—
213C22⋊C4—152no—
214C42—31no—
215C42—51no—
216C42—152no—
217C3×C5#54411yescharacteristic, complemented, Hall
218C22×C3C23×D511yescharacteristic
219C2×D3—52no—
220C2×D3—101no—
221C2×D3—101no—
222C3×C4—22no—
223C3×C4—101no—
224C3×C4—102no—
225C3×C4—101no—
226C3×C4Q8×D512yes—
227Dic3—21no—
228Dic3—22no—
229Dic3—21no—
230Dic3—52no—
231Dic3—102no—
232C2×C5C2×D3×Q811yescharacteristic
233C2×C5#100911yescharacteristic
234C2×C5#101011yescharacteristic
235D5—62no—
236C23—151no—
237Q8—122no—
238Q8—602no—
239C2×C4—31no—
240C2×C4—31no—
241C2×C4—32no—
242C2×C4—51no—
243C2×C4—51no—
244C2×C4—52no—
245C2×C4—151no—
246C2×C4—154no—
247C2×C4—152no—
248C2×C4—602no—
249C2×C4C2×D3×D512yes—
250C2×C4C2×D3×D511yescharacteristic
251C2×C3#414411yescharacteristic
252C2×C3C2×Q8×D511yescharacteristic
253C2×C3#414711yescharacteristic
254D3—102no—
255C5#568911yescharacteristic, complemented, Sylow
256C22—152no—
257C22—301no—
258C22—301no—
259C22C22×D3×D511yescharacteristic
260C4—22no—
261C4—61no—
262C4—62no—
263C4—61no—
264C4—101no—
265C4—101no—
266C4—102no—
267C4—152no—
268C4—302no—
269C4D15⋊Q812yes—
270C3#6606311yescharacteristic, complemented, Sylow
271C2—302no—
272C2C2×D15⋊Q811yescharacteristic
273C2#9202711yescharacteristic
274C2#9202811yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C4⋊C4C22
prime radicalC22×D15C23
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#544
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C5×#888C2semidirect
3. C3×#4036C2semidirect
4. #91468C2semidirect
7. #91381C2semidirect
10. #91339C2semidirect
11. #91329C2semidirect
43. #4036D3semidirect
54. C4×D15Q8semidirect
71. #888D5semidirect
217. C3×C5#544semidirect
255. C5#5689semidirect
270. C3#66063semidirect

Maximal subgroups

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

subgroupindex
C4⋊C4×D152
C5×#8882
C3×#40362
#914682
#913862
#913832
#913812
#913772
#913472
#913392
#913292
#660633
#56895