Finite Group Databasebeta

← #11755189

Subgroups — #11755189

Order 960.

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

normal subgroups only

This group has 468 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
1#91836C211yesmaximal, characteristic, complemented
2C5×Q8×Dic3C211yesmaximal, characteristic, complemented
3C3×#4092C211yesmaximal, characteristic, complemented
4#91450C211yesmaximal, characteristic
5#91428C211yesmaximal, characteristic, complemented
6#91413C212yesmaximal, complemented
7#91403C212yesmaximal, complemented
8#91395C212yesmaximal, complemented
9C4×D5×Dic3C211yesmaximal, characteristic, complemented
10#91384C211yesmaximal, characteristic, complemented
11#91337C212yesmaximal, complemented
12#65914—31nomaximal, Hall
13C2×C3×C5×Q8C2211yescharacteristic
14C2×D60C2211yescharacteristic
15C2×C3×C4×D5C2211yescharacteristic
16C2×#1202C2212yes—
17C2×#1200C2212yes—
18C2×D5×Dic3C2211yescharacteristic
19C2×D5×Dic3C2211yescharacteristic
20#6714C2212yes—
21#6714C2212yes—
22C4×Dic15C2211yescharacteristic
23C5×C4⋊Dic3C2212yes—
24C5×C4⋊Dic3C2211yescharacteristic
25C4×C5×Dic3C2212yes—
26C4×C5×Dic3C2211yescharacteristic
27C3×#685C2212yes—
28C3×C4⋊Dic5C2211yescharacteristic
29C3×#683C2212yes—
30Dic3⋊Dic5C2212yes—
31#6668C2212yes—
32#6667C2212yes—
33#6667C2212yes—
34Dic3×Dic5C2211yescharacteristic
35Dic3×Dic5C2211yescharacteristic
36#5624—51nomaximal, Hall
37C4×C5×Q8—31no—
38#4093—31no—
39#4092D311yescharacteristic, complemented
40#4044—32no—
41#4041—31no—
42#4040—32no—
43#4036—31no—
44C4×D20—32no—
45C4×D20—31no—
46#4018—32no—
47C42×D5—31no—
48C22×D15C2312yes—
49C22×C3×D5C2311yescharacteristic
50C3×C5×Q8—22no—
51C2×C3×C4×C5C2312yes—
52C2×C3×C4×C5C2311yescharacteristic
53C2×Dic15C2311yescharacteristic
54C2×Dic15C2311yescharacteristic
55D60—22no—
56C2×C5×Dic3C2311yescharacteristic
57C2×C5×Dic3C2312yes—
58C2×C5×Dic3C2311yescharacteristic
59C2×C3×Dic5C2311yescharacteristic
60C2×C3×Dic5C2312yes—
61C3×C4×D5—22no—
62#1202—24no—
63#1200—24no—
64D5×Dic3—22no—
65D5×Dic3—22no—
66C3×C22⋊Q8—51no—
67#947—51no—
68Q8×Dic3D511yescharacteristic, complemented
69#930—51no—
70C2×C4×Dic3—51no—
71#898—52no—
72#893—51no—
73#892—52no—
74#890—51no—
75#886—52no—
76#67⋊C4—52no—
77C2×C5×Q8C2×D311yescharacteristic
78C2×D20—32no—
79C2×D20—31no—
80C2×C4×D5—31no—
81C2×C4×D5—31no—
82C2×C4×D5—32no—
83C2×C4×D5C2×D311yescharacteristic
84C5×C4⋊C4—31no—
85C5×C4⋊C4—32no—
86C42×C5—31no—
87C42×C5—32no—
88#685—32no—
89#685—32no—
90#685—32no—
91#685—32no—
92#685C2×D312yes—
93C4⋊Dic5—32no—
94C4⋊Dic5C2×D311yescharacteristic
95#683—32no—
96#683C2×D312yes—
97C4×Dic5—31no—
98C4×Dic5—31no—
99C4×Dic5—31no—
100#529—151noSylow
101C22×C3×C5C2411yescharacteristic
102C2×D15—22no—
103C2×D15—22no—
104C2×D15—22no—
105C2×C3×D5—21no—
106C2×C3×D5—21no—
107C2×C3×D5#4112yes—
108C3×C4×C5—22no—
109C3×C4×C5#4112yes—
110Dic15—21no—
111Dic15—21no—
112C3×Dic5—22no—
113C3×Dic5—21no—
114C5×Dic3—21no—
115C5×Dic3—22no—
116C5×Dic3#4112yes—
117C2×C3×Q8C2×D511yescharacteristic
118C22×C3×C4—51no—
119C2×#67—52no—
120C22×Dic3—51no—
121C22×Dic3—51no—
122C2×D12—51no—
123C2×C4×D3—52no—
124C3×C4⋊C4—52no—
125C3×C4⋊C4—51no—
126C3×C22⋊C4—52no—
127(C2×D3)⋊C4—52no—
128(C2×D3)⋊C4—52no—
129(C2×D3)⋊C4—52no—
130(C2×D3)⋊C4—52no—
131C4⋊Dic3—52no—
132C4⋊Dic3C2×D512yes—
133C4⋊Dic3C2×D511yescharacteristic
134Dic3⋊C4—52no—
135C4×Dic3—51no—
136C4×Dic3—51no—
137C4×Dic3—51no—
138C4×Dic3C2×D512yes—
139C4×Dic3C2×D511yescharacteristic
140C22×D5—32no—
141C22×D5C22×D311yescharacteristic
142C5×Q8—22no—
143C2×C4×C5—31no—
144C2×C4×C5—31no—
145C2×C4×C5—32no—
146C2×C4×C5C22×D312yes—
147C2×C4×C5C22×D311yescharacteristic
148C2×Dic5—31no—
149C2×Dic5—31no—
150C2×Dic5C22×D311yescharacteristic
151C2×Dic5C22×D312yes—
152D20—64no—
153D20—62no—
154C4×D5—22no—
155C4×D5—64no—
156C4×D5—62no—
157C4×D5—62no—
158#126—152no—
159#125—151no—
160#124—151no—
161#123—152no—
162C22⋊Q8—51no—
163#121—151no—
164C4×Q8—31no—
165C4×D4—152no—
166C4×D4—151no—
167#117—152no—
168C2×C42—151no—
169C2×C3×C5C2×#4111yescharacteristic
170C2×C3×C5C2×#4111yescharacteristic
171C2×C3×C5C2×#4111yescharacteristic
172D15—42no—
173C3×D5—22no—
174C23×C3—51no—
175C22×D3—52no—
176C3×Q8—22no—
177C2×C3×C4—51no—
178C2×C3×C4—52no—
179C2×C3×C4—102no—
180C2×C3×C4C22×D512yes—
181C2×C3×C4C22×D511yescharacteristic
182#67—104no—
183C2×Dic3—51no—
184C2×Dic3—51no—
185C2×Dic3—102no—
186C2×Dic3—102no—
187C2×Dic3C22×D511yescharacteristic
188C2×Dic3C22×D512yes—
189C2×Dic3C22×D511yescharacteristic
190D12—102no—
191C4×D3—104no—
192C22×C5C23×D311yescharacteristic
193C2×D5—21no—
194C2×D5—21no—
195C2×D5—62no—
196C2×D5—62no—
197C2×D5—62no—
198C2×D5#23912yes—
199C4×C5—22no—
200C4×C5—32no—
201C4×C5—61no—
202C4×C5—62no—
203C4×C5#23712yes—
204Dic5—21no—
205Dic5—22no—
206Dic5—61no—
207Dic5—61no—
208C2×Q8D3×D511yescharacteristic
209C2×D4—152no—
210C2×D4—151no—
211C22×C4—51no—
212C22×C4—152no—
213C22×C4—151no—
214C22×C4—151no—
215C4⋊C4—31no—
216C4⋊C4—32no—
217C4⋊C4—52no—
218C4⋊C4—51no—
219C4⋊C4—152no—
220C4⋊C4—152no—
221C22⋊C4—52no—
222C22⋊C4—152no—
223C22⋊C4—152no—
224C22⋊C4—152no—
225C22⋊C4—152no—
226C42—31no—
227C42—32no—
228C42—151no—
229C42—151no—
230C42—151no—
231C3×C5#52911yescharacteristic, complemented, Hall
232C22×C3—52no—
233C22×C3—101no—
234C22×C3—101no—
235C22×C3C23×D511yescharacteristic
236C2×D3—102no—
237C2×D3—102no—
238C2×D3—102no—
239C3×C4—22no—
240C3×C4—101no—
241C3×C4—102no—
242C3×C4#70912yes—
243Dic3—21no—
244Dic3—22no—
245Dic3—101no—
246Dic3—101no—
247Dic3#71312yes—
248C2×C5C2×#23711yescharacteristic
249C2×C5C2×#23911yescharacteristic
250C2×C5D3×#4111yescharacteristic
251D5—22no—
252D5—122no—
253C23—51no—
254C23—152no—
255Q8—22no—
256D4—304no—
257D4—302no—
258C2×C4—31no—
259C2×C4—31no—
260C2×C4—32no—
261C2×C4—51no—
262C2×C4—52no—
263C2×C4—102no—
264C2×C4—151no—
265C2×C4—151no—
266C2×C4—304no—
267C2×C4—302no—
268C2×C4—302no—
269C2×C4C2×D3×D512yes—
270C2×C4C2×D3×D511yescharacteristic
271C2×C3—102no—
272C2×C3C2×#70911yescharacteristic
273C2×C3C2×#71311yescharacteristic
274C2×C3D5×#4111yescharacteristic
275D3—202no—
276C5#562411yescharacteristic, complemented, Sylow
277C22—52no—
278C22—101no—
279C22—101no—
280C22—302no—
281C22—302no—
282C22—302no—
283C22C22×D3×D511yescharacteristic
284C4—22no—
285C4—32no—
286C4—61no—
287C4—62no—
288C4—102no—
289C4—101no—
290C4—301no—
291C4—301no—
292C4#677912yes—
293C3#6591411yescharacteristic, complemented, Sylow
294C2—102no—
295C2—602no—
296C2D5×#23911yescharacteristic
297C2D3×#71311yescharacteristic
298C2C2×#677911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC2×C3×C5×Q8C22
prime radical#91450C2
hypercenterC2×Q8D3×D5
hypocenterC3×C5#529
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×Q8×Dic3C2semidirect
3. C3×#4092C2semidirect
5. #91428C2semidirect
6. #91413C2semidirect
7. #91403C2semidirect
8. #91395C2semidirect
9. C4×D5×Dic3C2semidirect
10. #91384C2semidirect
11. #91337C2semidirect
39. #4092D3semidirect
68. Q8×Dic3D5semidirect
231. C3×C5#529semidirect
276. C5#5624semidirect
293. C3#65914semidirect

Maximal subgroups

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

subgroupindex
#918362
C5×Q8×Dic32
C3×#40922
#914502
#914282
#914132
#914032
#913952
C4×D5×Dic32
#913842
#913372
#659143
#56245