Finite Group Databasebeta

← #11754816

Subgroups — #11754816

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×#6819C211yesmaximal, characteristic, complemented
2C2×D5×Dic6C211yesmaximal, characteristic, complemented
3C5×#936C211yesmaximal, characteristic, complemented
4C3×#4084C211yesmaximal, characteristic, complemented
5#91576C212yesmaximal, complemented
6#91559C212yesmaximal, complemented
7#91550C212yesmaximal, complemented
8#91526C212yesmaximal, complemented
9C4×#1202C211yesmaximal, characteristic, complemented
10#91383C211yesmaximal, characteristic, complemented
11#91340C211yesmaximal, characteristic, complemented
12#66011—31nomaximal, Hall
13C2×C3×C5×D4C2211yescharacteristic
14C2×#1220C2212yes—
15C22×Dic15C2212yes—
16#6819—24no—
17C2×C4×D15C2211yescharacteristic
18C2×Dic30C2211yescharacteristic
19C2×C5×Dic6C2211yescharacteristic
20C2×C3×C22⋊D5C2212yes—
21C2×C3×C4×D5C2211yescharacteristic
22C2×#1204C2212yes—
23C2×#1202C2211yescharacteristic
24C2×D5×Dic3C2212yes—
25D5×Dic6—24no—
26C5×#217C2212yes—
27C5×#217C2212yes—
28C4×C5×Dic3C2211yescharacteristic
29C3×C22⋊Dic5C2212yes—
30C3×C4⋊Dic5C2211yescharacteristic
31Dic3⋊Dic5C2211yescharacteristic
32#6669C2212yes—
33#6668C2212yes—
34#6667C2211yescharacteristic
35#6667C2212yes—
36#6665C2211yescharacteristic
37Dic3×Dic5C2212yes—
38#5598—51nomaximal, Hall
39C2×Q8×D5—31no—
40C2×#711—31no—
41C5×#124—31no—
42#4092—31no—
43#4084D311yescharacteristic, complemented
44#4031—32no—
45#4030—32no—
46#4027—32no—
47#4024—32no—
48C4×D20—31no—
49C4×Dic10—31no—
50C23×C3×C5C2312yes—
51C22×D15C2311yescharacteristic
52C22×C3×D5C2311yescharacteristic
53C3×C5×D4—22no—
54C2×C3×C4×C5C2311yescharacteristic
55#1220—24no—
56C2×Dic15—24no—
57C2×Dic15C2311yescharacteristic
58C2×Dic15C2312yes—
59C4×D15—22no—
60Dic30D414yescomplemented
61C2×C5×Dic3C2311yescharacteristic
62C2×C5×Dic3C2312yes—
63C2×C5×Dic3C2311yescharacteristic
64C5×Dic6—22no—
65C3×C22⋊D5—24no—
66C2×C3×Dic5C2312yes—
67C2×C3×Dic5C2311yescharacteristic
68C3×C4×D5—22no—
69#1204—24no—
70#1202—22no—
71D5×Dic3—24no—
72C2×#237—51no—
73C22×Dic6—51no—
74C3×#121—51no—
75#939—52no—
76#936D511yescharacteristic, complemented
77D4×Dic3—52no—
78C4×#67—51no—
79#897—51no—
80#887—51no—
81#885—52no—
82#878—52no—
83C2×C5×Q8—31no—
84C2×C5×D4C2×D311yescharacteristic
85C2×C22⋊D5—32no—
86C2×C22⋊D5C2×D312yes—
87C22×Dic5—32no—
88Q8×D5—64no—
89#711—64no—
90C2×D20—31no—
91C2×C4×D5—32no—
92C2×C4×D5—31no—
93C2×C4×D5C2×D311yescharacteristic
94C2×Dic10—31no—
95C2×Dic10—32no—
96C5×C22⋊C4—32no—
97C5×C22⋊C4—32no—
98C42×C5—31no—
99C22⋊Dic5C2×D312yes—
100#685—31no—
101#685—31no—
102#685—32no—
103C4⋊Dic5—31no—
104C4⋊Dic5C2×D311yescharacteristic
105#683—32no—
106#683—32no—
107C4×Dic5—32no—
108#548—151noSylow
109C22×C3×C5—22no—
110C22×C3×C5—22no—
111C22×C3×C5—22no—
112C22×C3×C5C2411yescharacteristic
113C2×D15—21no—
114C2×D15—21no—
115C2×D15—21no—
116C2×C3×D5—21no—
117C2×C3×D5—21no—
118C2×C3×D5#4112yescomplemented
119C3×C4×C5C2×D412yes—
120Dic15—21no—
121Dic15C2×D414yes—
122C3×Dic5—21no—
123C3×Dic5—22no—
124C5×Dic3—22no—
125C5×Dic3—21no—
126C5×Dic3—21no—
127C2×C3×D4—52no—
128C2×C3×D4C2×D511yescharacteristic
129C22×C3×C4—51no—
130C2×#67—52no—
131C2×#67—51no—
132C22×Dic3—52no—
133C22×Dic3—52no—
134#237—104no—
135C2×C4×D3—51no—
136C2×Dic6—51no—
137C2×Dic6—52no—
138C2×Dic6—104no—
139C2×Dic6C2×D511yescharacteristic
140C3×C4⋊C4—51no—
141C3×C22⋊C4—52no—
142#217—51no—
143#217C2×D512yes—
144#217C2×D512yes—
145(C2×D3)⋊C4—51no—
146(C2×D3)⋊C4—52no—
147C4⋊Dic3—52no—
148Dic3⋊C4—52no—
149Dic3⋊C4—51no—
150C4×Dic3—52no—
151C4×Dic3C2×D511yescharacteristic
152C23×C5C22×D312yes—
153C22×D5—31no—
154C22×D5C22×D311yescharacteristic
155C5×Q8—62no—
156C5×D4—22no—
157C2×C4×C5—31no—
158C2×C4×C5—31no—
159C2×C4×C5—32no—
160C2×C4×C5C22×D311yescharacteristic
161C22⋊D5—24no—
162C22⋊D5—64no—
163C2×Dic5—32no—
164C2×Dic5—31no—
165C2×Dic5—64no—
166C2×Dic5C22×D312yes—
167C2×Dic5C22×D311yescharacteristic
168D20—62no—
169C4×D5—22no—
170C4×D5—64no—
171C4×D5—62no—
172Dic10—34no—
173Dic10—64no—
174C2×#41—151no—
175C22×Q8—151no—
176#124—31no—
177#124—152no—
178C22⋊Q8—152no—
179C22⋊Q8—151no—
180#121—51no—
181#121—152no—
182C4×Q8—151no—
183C4×D4—151no—
184C4×D4—152no—
185C2×C3×C5—42no—
186C2×C3×C5C22×D411yescharacteristic
187C2×C3×C5C2×#4111yescharacteristic
188C2×C3×C52−1+411yescharacteristic
189D15—41no—
190C3×D5—22no—
191C23×C3—51no—
192C23×C3C22×D512yes—
193C22×D3—51no—
194C3×D4—22no—
195C3×D4—104no—
196C2×C3×C4—52no—
197C2×C3×C4—51no—
198C2×C3×C4—102no—
199C2×C3×C4C22×D511yescharacteristic
200#67—102no—
201#67—104no—
202C2×Dic3—52no—
203C2×Dic3—51no—
204C2×Dic3—104no—
205C2×Dic3—104no—
206C2×Dic3C22×D511yescharacteristic
207C2×Dic3C22×D511yescharacteristic
208C2×Dic3C22×D512yes—
209C4×D3—102no—
210Dic6—22no—
211Dic6—54no—
212Dic6—104no—
213C22×C5—22no—
214C22×C5—22no—
215C22×C5—22no—
216C22×C5C23×D311yescharacteristic
217C2×D5—21no—
218C2×D5—21no—
219C2×D5—61no—
220C2×D5—61no—
221C2×D5—61no—
222C2×D5#23712yescomplemented
223C4×C5—62no—
224C4×C5—61no—
225C4×C5—61no—
226C4×C5D3×D412yes—
227Dic5—21no—
228Dic5—22no—
229Dic5—34no—
230Dic5—61no—
231#41—304no—
232C2×Q8—31no—
233C2×Q8—152no—
234C2×Q8—151no—
235C2×Q8—304no—
236C2×D4—52no—
237C2×D4—151no—
238C2×D4—152no—
239C2×D4D3×D511yescharacteristic
240C22×C4—51no—
241C22×C4—152no—
242C22×C4—152no—
243C22×C4—151no—
244C4⋊C4—51no—
245C4⋊C4—152no—
246C4⋊C4—151no—
247C4⋊C4—152no—
248C22⋊C4—32no—
249C22⋊C4—32no—
250C22⋊C4—52no—
251C22⋊C4—151no—
252C22⋊C4—152no—
253C22⋊C4—151no—
254C42—31no—
255C42—152no—
256C3×C5#54811yescharacteristic, complemented, Hall
257C22×C3—22no—
258C22×C3—22no—
259C22×C3—22no—
260C22×C3—52no—
261C22×C3—101no—
262C22×C3—101no—
263C22×C3C23×D511yescharacteristic
264C2×D3—101no—
265C2×D3—101no—
266C2×D3—101no—
267C3×C4—101no—
268C3×C4—102no—
269C3×C4D4×D512yes—
270Dic3—22no—
271Dic3—21no—
272Dic3—21no—
273Dic3—54no—
274Dic3—101no—
275C2×C5—42no—
276C2×C5C2×D3×D411yescharacteristic
277C2×C5C2×#23711yescharacteristic
278C2×C5#101011yescharacteristic
279D5—22no—
280D5—121no—
281C23—51no—
282C23—151no—
283C23C2×D3×D512yes—
284Q8—62no—
285Q8—154no—
286Q8—304no—
287D4—22no—
288D4—104no—
289D4—302no—
290D4—304no—
291C2×C4—31no—
292C2×C4—31no—
293C2×C4—32no—
294C2×C4—52no—
295C2×C4—51no—
296C2×C4—102no—
297C2×C4—152no—
298C2×C4—151no—
299C2×C4—304no—
300C2×C4—304no—
301C2×C4—302no—
302C2×C4C2×D3×D511yescharacteristic
303C2×C3—42no—
304C2×C3—102no—
305C2×C3C2×D4×D511yescharacteristic
306C2×C3D5×#4111yescharacteristic
307C2×C3#415011yescharacteristic
308D3—201no—
309C5#559811yescharacteristic, complemented, Sylow
310C22—22no—
311C22—22no—
312C22—22no—
313C22—52no—
314C22—101no—
315C22—101no—
316C22—301no—
317C22—301no—
318C22—301no—
319C22C22×D3×D511yescharacteristic
320C4—61no—
321C4—61no—
322C4—62no—
323C4—102no—
324C4—101no—
325C4—154no—
326C4—301no—
327C4#679012yes—
328C3#6601111yescharacteristic, complemented, Sylow
329C2—42no—
330C2—102no—
331C2—601no—
332C2#9202011yescharacteristic
333C2D5×#23711yescharacteristic
334C2C2×#679011yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC2×C3×C5×D4C22
hypercenterC2×D4D3×D5
hypocenterC3×C5#548
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×#6819C2semidirect
2. C2×D5×Dic6C2semidirect
3. C5×#936C2semidirect
4. C3×#4084C2semidirect
5. #91576C2semidirect
6. #91559C2semidirect
7. #91550C2semidirect
8. #91526C2semidirect
9. C4×#1202C2semidirect
10. #91383C2semidirect
11. #91340C2semidirect
43. #4084D3semidirect
60. Dic30D4semidirect
76. #936D5semidirect
118. C2×C3×D5#41semidirect
222. C2×D5#237semidirect
256. C3×C5#548semidirect
309. C5#5598semidirect
328. C3#66011semidirect

Maximal subgroups

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

subgroupindex
C2×#68192
C2×D5×Dic62
C5×#9362
C3×#40842
#915762
#915592
#915502
#915262
C4×#12022
#913832
#913402
#660113
#55985