Finite Group Databasebeta

← #11753703

Subgroups — #11753703

Order 960.

580 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 140 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
1C2×#6772C211yesmaximal, characteristic, complemented
2C2×D3×Dic10C211yesmaximal, characteristic, complemented
3#91776C211yesmaximal, characteristic, complemented
4C5×#895C211yesmaximal, characteristic, complemented
5C3×#4043C211yesmaximal, characteristic, complemented
6#91464C212yesmaximal, complemented
7#91453C212yesmaximal, complemented
8C4×#1201C211yesmaximal, characteristic, complemented
9#91436C212yesmaximal, complemented
10#91435C212yesmaximal, complemented
11#91370C211yesmaximal, characteristic, complemented
12#65932—31nomaximal, Hall
13C2×Dic30C2211yescharacteristic
14C2×C5×D12C2212yes—
15C2×C5×D12C2211yescharacteristic
16C2×C4×C5×D3C2211yescharacteristic
17C2×C3×C4×D5C2211yescharacteristic
18C2×C3×Dic10C2211yescharacteristic
19C2×#1204C2212yes—
20C2×#1201C2211yescharacteristic
21C2×#1201C2212yes—
22C2×D3×Dic5C2212yes—
23C2×D3×Dic5C2212yes—
24#6772—24no—
25D3×Dic10—24no—
26C3×C5×C4⋊C4C2211yescharacteristic
27#6712C2212yes—
28C4×Dic15C2212yes—
29C4×Dic15C2211yescharacteristic
30C5×(C2×D3)⋊C4C2212yes—
31C3×#685C2212yes—
32C3×C4⋊Dic5C2212yes—
33#6669C2211yescharacteristic
34(C2×D3)⋊Dic5C2211yescharacteristic
35(C2×D3)⋊Dic5C2212yes—
36(C2×D3)⋊Dic5C2212yes—
37#6665C2211yescharacteristic
38#5633—51nomaximal, Hall
39C2×#711—31no—
40C22×Dic10—31no—
41C5×#121—31no—
42#4085—32no—
43#4082—31no—
44D4×Dic5—32no—
45C4×C22⋊D5—31no—
46#4043D311yescharacteristic, complemented
47#4033—31no—
48#4031—32no—
49#4024—32no—
50C22×C5×D3C2312yes—
51C22×C5×D3C2311yescharacteristic
52C22×C3×D5C2311yescharacteristic
53C2×C3×C4×C5C2312yes—
54C2×C3×C4×C5C2311yescharacteristic
55C2×Dic15C2311yescharacteristic
56C2×Dic15C2311yescharacteristic
57C2×Dic15C2312yes—
58Dic30D414yescomplemented
59C2×C5×Dic3C2311yescharacteristic
60C5×D12—24no—
61C5×D12—22no—
62C4×C5×D3—22no—
63C2×C3×Dic5C2312yes—
64C2×C3×Dic5C2311yescharacteristic
65C3×C4×D5—22no—
66C3×Dic10—22no—
67#1204—24no—
68#1201—22no—
69#1201—24no—
70D3×Dic5—24no—
71D3×Dic5—24no—
72C2×D3×Q8—51no—
73C2×#235—51no—
74C3×C22⋊Q8—51no—
75#947—51no—
76C4×#67—51no—
77#896—52no—
78#895D511yescharacteristic, complemented
79#893—52no—
80#887—51no—
81#885—52no—
82#884—52no—
83C2×C5×D4—31no—
84C2×C5×D4—32no—
85C22×C4×C5—31no—
86C2×C22⋊D5—32no—
87C2×C22⋊D5—31no—
88C22×Dic5—32no—
89C22×Dic5—32no—
90#711—64no—
91C2×C4×D5C2×D311yescharacteristic
92C2×Dic10—31no—
93C2×Dic10—32no—
94C2×Dic10—64no—
95C2×Dic10C2×D311yescharacteristic
96C5×C4⋊C4C2×D311yescharacteristic
97C5×C22⋊C4—32no—
98C22⋊Dic5—32no—
99C22⋊Dic5—32no—
100C22⋊Dic5—31no—
101#685—31no—
102#685C2×D312yes—
103C4⋊Dic5C2×D312yes—
104#683—32no—
105#683—31no—
106C4×Dic5—32no—
107C4×Dic5—31no—
108#548—151noSylow
109C22×C3×C5C2411yescharacteristic
110C2×C5×D3—21no—
111C2×C5×D3—21no—
112C2×C5×D3—22no—
113C2×C5×D3—22no—
114C2×C5×D3—22no—
115C2×C5×D3#4112yescomplemented
116C2×C3×D5—21no—
117C2×C3×D5—21no—
118C2×C3×D5—21no—
119C3×C4×C5—22no—
120C3×C4×C5C2×D412yes—
121Dic15—21no—
122Dic15—21no—
123Dic15C2×D414yes—
124C3×Dic5—21no—
125C3×Dic5—22no—
126C5×Dic3—21no—
127C2×C3×Q8—51no—
128C22×C3×C4—51no—
129C2×#67—51no—
130C2×#67—52no—
131D3×Q8—104no—
132#235—104no—
133C2×D12C2×D512yes—
134C2×D12C2×D511yescharacteristic
135C2×C4×D3—52no—
136C2×C4×D3—52no—
137C2×C4×D3C2×D511yescharacteristic
138C2×Dic6—51no—
139C2×Dic6—52no—
140C3×C4⋊C4—52no—
141C3×C4⋊C4C2×D511yescharacteristic
142C3×C22⋊C4—52no—
143#217—51no—
144(C2×D3)⋊C4—52no—
145(C2×D3)⋊C4—52no—
146(C2×D3)⋊C4—51no—
147(C2×D3)⋊C4C2×D512yes—
148Dic3⋊C4—52no—
149Dic3⋊C4—51no—
150C4×Dic3—52no—
151C4×Dic3—51no—
152C23×C5—31no—
153C23×C5—32no—
154C22×D5C22×D311yescharacteristic
155C5×D4—64no—
156C5×D4—62no—
157C2×C4×C5—31no—
158C2×C4×C5—62no—
159C2×C4×C5C22×D312yes—
160C2×C4×C5C22×D311yescharacteristic
161C22⋊D5—64no—
162C22⋊D5—62no—
163C2×Dic5—32no—
164C2×Dic5—31no—
165C2×Dic5—31no—
166C2×Dic5—64no—
167C2×Dic5—64no—
168C2×Dic5C22×D311yescharacteristic
169C2×Dic5C22×D312yes—
170C4×D5—22no—
171Dic10—22no—
172Dic10—34no—
173Dic10—64no—
174C2×#41—151no—
175C22×Q8—151no—
176#124—152no—
177#124—151no—
178C22⋊Q8—51no—
179C22⋊Q8—152no—
180#121—31no—
181#121—152no—
182C4×Q8—151no—
183C4×D4—152no—
184C4×D4—151no—
185C2×C3×C5C22×D411yescharacteristic
186C2×C3×C5C2×#4111yescharacteristic
187C2×C3×C52−1+411yescharacteristic
188C3×D5—41no—
189C5×D3—22no—
190C5×D3—42no—
191C23×C3—51no—
192C22×D3C22×D512yes—
193C22×D3C22×D511yescharacteristic
194C3×Q8—102no—
195C2×C3×C4—51no—
196C2×C3×C4—52no—
197C2×C3×C4—102no—
198C2×C3×C4C22×D512yes—
199C2×C3×C4C22×D511yescharacteristic
200#67—104no—
201#67—102no—
202C2×Dic3—52no—
203C2×Dic3—51no—
204C2×Dic3—51no—
205C2×Dic3C22×D511yescharacteristic
206D12—24no—
207D12—22no—
208C4×D3—22no—
209C4×D3—104no—
210C4×D3—104no—
211Dic6—54no—
212Dic6—104no—
213C22×C5—32no—
214C22×C5—61no—
215C22×C5—61no—
216C22×C5—62no—
217C22×C5—62no—
218C22×C5—62no—
219C22×C5C23×D311yescharacteristic
220C2×D5—21no—
221C2×D5—21no—
222C2×D5—21no—
223C4×C5—22no—
224C4×C5—61no—
225C4×C5D3×D412yes—
226Dic5—22no—
227Dic5—21no—
228Dic5—34no—
229Dic5—61no—
230Dic5—61no—
231#41—304no—
232C2×Q8—51no—
233C2×Q8—152no—
234C2×Q8—151no—
235C2×Q8—304no—
236C2×D4—32no—
237C2×D4—31no—
238C2×D4—151no—
239C2×D4—152no—
240C22×C4—31no—
241C22×C4—51no—
242C22×C4—152no—
243C22×C4—152no—
244C4⋊C4—52no—
245C4⋊C4—151no—
246C4⋊C4—152no—
247C4⋊C4D3×D511yescharacteristic
248C22⋊C4—32no—
249C22⋊C4—52no—
250C22⋊C4—151no—
251C22⋊C4—151no—
252C22⋊C4—152no—
253C22⋊C4—152no—
254C42—152no—
255C42—151no—
256C3×C5#54811yescharacteristic, complemented, Hall
257C22×C3—101no—
258C22×C3—101no—
259C22×C3—101no—
260C22×C3C23×D511yescharacteristic
261C2×D3—21no—
262C2×D3—21no—
263C2×D3—22no—
264C2×D3—22no—
265C2×D3—22no—
266C2×D3#71112yescomplemented
267C3×C4—22no—
268C3×C4—102no—
269C3×C4—101no—
270C3×C4D4×D512yes—
271Dic3—21no—
272Dic3—54no—
273Dic3—101no—
274Dic3—101no—
275C2×C5—62no—
276C2×C5—122no—
277C2×C5C2×D3×D411yescharacteristic
278C2×C5#100711yescharacteristic
279C2×C5D3×#4111yescharacteristic
280D5—41no—
281C23—31no—
282C23—32no—
283C23—51no—
284Q8—102no—
285Q8—154no—
286Q8—304no—
287D4—64no—
288D4—62no—
289D4—304no—
290D4—302no—
291C2×C4—31no—
292C2×C4—52no—
293C2×C4—51no—
294C2×C4—62no—
295C2×C4—102no—
296C2×C4—152no—
297C2×C4—151no—
298C2×C4—151no—
299C2×C4—304no—
300C2×C4—304no—
301C2×C4C2×D3×D512yes—
302C2×C4C2×D3×D511yescharacteristic
303C2×C3—201no—
304C2×C3C2×D4×D511yescharacteristic
305C2×C3C2×#71111yescharacteristic
306C2×C3#415011yescharacteristic
307D3—22no—
308D3—42no—
309C5#563311yescharacteristic, complemented, Sylow
310C22—32no—
311C22—61no—
312C22—61no—
313C22—62no—
314C22—62no—
315C22—62no—
316C22—101no—
317C22—101no—
318C22—101no—
319C22C22×D3×D511yescharacteristic
320C4—22no—
321C4—61no—
322C4—101no—
323C4—102no—
324C4—154no—
325C4—301no—
326C4—301no—
327C4#677712yes—
328C3#6593211yescharacteristic, complemented, Sylow
329C2—62no—
330C2—122no—
331C2—201no—
332C2C2×#677711yescharacteristic
333C2D3×#71111yescharacteristic
334C2#9203011yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C4⋊C4C22
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#548
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. C2×#6772C2semidirect
2. C2×D3×Dic10C2semidirect
3. #91776C2semidirect
4. C5×#895C2semidirect
5. C3×#4043C2semidirect
6. #91464C2semidirect
7. #91453C2semidirect
8. C4×#1201C2semidirect
9. #91436C2semidirect
10. #91435C2semidirect
11. #91370C2semidirect
46. #4043D3semidirect
58. Dic30D4semidirect
78. #895D5semidirect
115. C2×C5×D3#41semidirect
256. C3×C5#548semidirect
266. C2×D3#711semidirect
309. C5#5633semidirect
328. C3#65932semidirect

Maximal subgroups

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

subgroupindex
C2×#67722
C2×D3×Dic102
#917762
C5×#8952
C3×#40432
#914642
#914532
C4×#12012
#914362
#914352
#913702
#659323
#56335