Finite Group Databasebeta

← #11752960

Subgroups — #11752960

Order 960.

424 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#91766C211yesmaximal, characteristic, complemented
2C5×#879C211yesmaximal, characteristic, complemented
3C3×#4031C211yesmaximal, characteristic
4#91576C211yesmaximal, characteristic, complemented
5#91559C211yesmaximal, characteristic
6#91534C211yesmaximal, characteristic
7#91530C211yesmaximal, characteristic, complemented
8C4×#1204C211yesmaximal, characteristic, complemented
9#91430C211yesmaximal, characteristic, complemented
10#91393C211yesmaximal, characteristic, complemented
11#91366C211yesmaximal, characteristic, complemented
12#91366C211yesmaximal, characteristic, complemented
13#91331C211yesmaximal, characteristic, complemented
14#91327C211yesmaximal, characteristic, complemented
15#91323C211yesmaximal, characteristic, complemented
16#66036—31nomaximal, Hall
17C22×Dic15C2211yescharacteristic
18C2×C3×C22⋊D5C2211yescharacteristic
19C2×C3×Dic10C2211yescharacteristic
20C2×#1204C2211yescharacteristic
21C2×#1204C2211yescharacteristic
22C2×D5×Dic3C2211yescharacteristic
23C3×C5×C22⋊C4C2211yescharacteristic
24#6719C2211yescharacteristic
25#6712C2211yescharacteristic
26#6712C2211yescharacteristic
27C4×Dic15C2211yescharacteristic
28C4×Dic15C2211yescharacteristic
29C5×#217C2211yescharacteristic
30C5×#217C2211yescharacteristic
31C5×C4⋊Dic3C2211yescharacteristic
32C5×Dic3⋊C4C2211yescharacteristic
33C5×Dic3⋊C4C2211yescharacteristic
34C4×C5×Dic3C2211yescharacteristic
35C3×C22⋊Dic5C2211yescharacteristic
36C3×#685C2211yescharacteristic
37C3×#685C2211yescharacteristic
38C3×C4×Dic5C2211yescharacteristic
39Dic3⋊Dic5C2211yescharacteristic
40Dic3⋊Dic5C2211yescharacteristic
41#6669C2211yescharacteristic
42#6669C2211yescharacteristic
43#6668C2211yescharacteristic
44#6668C2211yescharacteristic
45#6668C2211yescharacteristic
46#6665C2211yescharacteristic
47#6665C2211yescharacteristic
48#6665C2211yescharacteristic
49Dic3×Dic5C2211yescharacteristic
50Dic3×Dic5C2211yescharacteristic
51Dic3×Dic5C2211yescharacteristic
52#5671—51nomaximal, Hall
53C5×#126—31no—
54#4044—31no—
55#4044—31no—
56#4042—31no—
57#4034—31no—
58#4033—31no—
59#4033—31no—
60#4031—31no—
61#4031D311yescharacteristic
62#4027—31no—
63#4025—31no—
64#4024—31no—
65#4023—31no—
66#4018—31no—
67C4×Dic10—31no—
68C23×C3×C5C2311yescharacteristic
69C22×C3×D5C2311yescharacteristic
70C2×C3×C4×C5C2311yescharacteristic
71C2×C3×C4×C5C2311yescharacteristic
72C2×Dic15—22no—
73C2×Dic15C2311yescharacteristic
74C2×Dic15C2311yescharacteristic
75C2×Dic15C2311yescharacteristic
76C2×Dic15C2311yescharacteristic
77C2×C5×Dic3C2311yescharacteristic
78C2×C5×Dic3C2311yescharacteristic
79C2×C5×Dic3C2311yescharacteristic
80C2×C5×Dic3C2311yescharacteristic
81C3×C22⋊D5—22no—
82C2×C3×Dic5C2311yescharacteristic
83C2×C3×Dic5C2311yescharacteristic
84C2×C3×Dic5C2311yescharacteristic
85C3×Dic10—22no—
86#1204—22no—
87#1204—22no—
88D5×Dic3—22no—
89C3×#124—51no—
90Q8×Dic3—51no—
91#944—51no—
92#936—51no—
93D4×Dic3—51no—
94#879—51no—
95#879—51no—
96#879—51no—
97#879D511yescharacteristic, complemented
98#878—51no—
99#878—51no—
100#877—51no—
101#877—51no—
102C4×Dic6—51no—
103C4×Dic6—51no—
104C2×C22⋊D5C2×D311yescharacteristic
105C22×Dic5—31no—
106C2×C4×D5—31no—
107C2×Dic10—31no—
108C2×Dic10—31no—
109C2×Dic10C2×D311yescharacteristic
110C5×C4⋊C4—31no—
111C5×C4⋊C4—31no—
112C5×C4⋊C4—31no—
113C5×C22⋊C4—31no—
114C5×C22⋊C4—31no—
115C5×C22⋊C4C2×D311yescharacteristic
116C42×C5—31no—
117C22⋊Dic5—31no—
118C22⋊Dic5C2×D311yescharacteristic
119#685—31no—
120#685—31no—
121#685—31no—
122#685C2×D311yescharacteristic
123#685C2×D311yescharacteristic
124C4⋊Dic5—31no—
125C4⋊Dic5—31no—
126#683—31no—
127#683—31no—
128#683—31no—
129#683—31no—
130#683—31no—
131#683—31no—
132#683—31no—
133C4×Dic5—31no—
134C4×Dic5—31no—
135C4×Dic5—31no—
136C4×Dic5—31no—
137C4×Dic5—31no—
138C4×Dic5C2×D311yescharacteristic
139#556—151noSylow
140C22×C3×C5—21no—
141C22×C3×C5—21no—
142C22×C3×C5—21no—
143C22×C3×C5C2411yescharacteristic
144C2×C3×D5—21no—
145C2×C3×D5—21no—
146C2×C3×D5—21no—
147C3×C4×C5—21no—
148C3×C4×C5—21no—
149Dic15—21no—
150Dic15—21no—
151Dic15—21no—
152Dic15#4112yes—
153C3×Dic5—21no—
154C3×Dic5—21no—
155C3×Dic5#4112yes—
156C5×Dic3—21no—
157C5×Dic3—21no—
158C5×Dic3—21no—
159C5×Dic3—21no—
160C2×C3×Q8—51no—
161C2×C3×D4—51no—
162C22×Dic3—51no—
163C22×Dic3—51no—
164C2×Dic6—51no—
165C2×Dic6—51no—
166C3×C22⋊C4—51no—
167C3×C22⋊C4—51no—
168C3×C22⋊C4—51no—
169C3×C22⋊C4C2×D511yescharacteristic
170C3×C42—51no—
171#217—51no—
172#217—51no—
173#217—51no—
174#217—51no—
175#217C2×D511yescharacteristic
176#217C2×D511yescharacteristic
177C4⋊Dic3—51no—
178C4⋊Dic3—51no—
179C4⋊Dic3—51no—
180C4⋊Dic3C2×D511yescharacteristic
181Dic3⋊C4—51no—
182Dic3⋊C4—51no—
183Dic3⋊C4—51no—
184Dic3⋊C4—51no—
185Dic3⋊C4—51no—
186Dic3⋊C4—51no—
187Dic3⋊C4C2×D511yescharacteristic
188Dic3⋊C4C2×D511yescharacteristic
189C4×Dic3—51no—
190C4×Dic3—51no—
191C4×Dic3—51no—
192C4×Dic3—51no—
193C4×Dic3—51no—
194C4×Dic3C2×D511yescharacteristic
195C23×C5C22×D311yescharacteristic
196C22×D5C22×D311yescharacteristic
197C2×C4×C5—31no—
198C2×C4×C5—31no—
199C2×C4×C5—31no—
200C2×C4×C5—31no—
201C2×C4×C5C22×D311yescharacteristic
202C2×C4×C5C22×D311yescharacteristic
203C22⋊D5—22no—
204C2×Dic5—31no—
205C2×Dic5—31no—
206C2×Dic5—31no—
207C2×Dic5—31no—
208C2×Dic5—62no—
209C2×Dic5C22×D311yescharacteristic
210C2×Dic5C22×D311yescharacteristic
211C2×Dic5C22×D311yescharacteristic
212C4×D5—62no—
213Dic10—22no—
214Dic10—62no—
215Dic10—62no—
216C4⋊Q8—151no—
217#126—31no—
218#126—151no—
219#126—151no—
220#126—151no—
221#124—51no—
222#124—151no—
223C22⋊Q8—151no—
224C22⋊Q8—151no—
225C4×Q8—151no—
226C4×Q8—151no—
227C4×Q8—151no—
228C4×D4—151no—
229#117—151no—
230#117—151no—
231C2×C3×C5—41no—
232C2×C3×C5C2×#4111yescharacteristic
233C2×C3×C5C2×#4111yescharacteristic
234C2×C3×C52−1+411yescharacteristic
235C3×D5—41no—
236C23×C3—51no—
237C23×C3C22×D511yescharacteristic
238C3×Q8—102no—
239C3×D4—102no—
240C2×C3×C4—51no—
241C2×C3×C4—51no—
242C2×C3×C4—51no—
243C2×C3×C4C22×D511yescharacteristic
244C2×C3×C4C22×D511yescharacteristic
245C2×Dic3—51no—
246C2×Dic3—51no—
247C2×Dic3—51no—
248C2×Dic3—51no—
249C2×Dic3—102no—
250C2×Dic3—102no—
251C2×Dic3C22×D511yescharacteristic
252C2×Dic3C22×D511yescharacteristic
253C2×Dic3C22×D511yescharacteristic
254C2×Dic3C22×D511yescharacteristic
255Dic6—102no—
256Dic6—102no—
257C22×C5—21no—
258C22×C5—21no—
259C22×C5—21no—
260C22×C5C23×D311yescharacteristic
261C2×D5—21no—
262C2×D5—21no—
263C2×D5—21no—
264C4×C5—21no—
265C4×C5—21no—
266C4×C5—61no—
267C4×C5—61no—
268C4×C5—61no—
269C4×C5—61no—
270Dic5—21no—
271Dic5—21no—
272Dic5—32no—
273Dic5—61no—
274Dic5—61no—
275Dic5—61no—
276Dic5#23712yes—
277C2×Q8—51no—
278C2×Q8—151no—
279C2×Q8—151no—
280C2×D4—51no—
281C22×C4—151no—
282C22×C4—151no—
283C4⋊C4—31no—
284C4⋊C4—31no—
285C4⋊C4—31no—
286C4⋊C4—151no—
287C4⋊C4—151no—
288C4⋊C4—151no—
289C4⋊C4—151no—
290C4⋊C4—151no—
291C4⋊C4—151no—
292C4⋊C4—151no—
293C4⋊C4—151no—
294C4⋊C4—151no—
295C22⋊C4—31no—
296C22⋊C4—31no—
297C22⋊C4—51no—
298C22⋊C4—51no—
299C22⋊C4—51no—
300C22⋊C4—151no—
301C22⋊C4—151no—
302C22⋊C4—151no—
303C22⋊C4—151no—
304C22⋊C4D3×D511yescharacteristic
305C42—31no—
306C42—51no—
307C42—151no—
308C42—151no—
309C42—151no—
310C42—151no—
311C42—151no—
312C3×C5#55611yescharacteristic, complemented, Hall
313C22×C3—21no—
314C22×C3—21no—
315C22×C3—21no—
316C22×C3—101no—
317C22×C3—101no—
318C22×C3—101no—
319C22×C3C23×D511yescharacteristic
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—52no—
323C3×C4—101no—
324C3×C4—101no—
325Dic3—21no—
326Dic3—21no—
327Dic3—21no—
328Dic3—21no—
329Dic3—52no—
330Dic3—101no—
331Dic3—101no—
332Dic3—101no—
333C2×C5—41no—
334C2×C5C2×#23711yescharacteristic
335C2×C5D3×#4111yescharacteristic
336C2×C5#101011yescharacteristic
337D5—41no—
338C23—51no—
339C23C2×D3×D511yescharacteristic
340Q8—102no—
341Q8—302no—
342Q8—302no—
343D4—102no—
344C2×C4—31no—
345C2×C4—31no—
346C2×C4—31no—
347C2×C4—31no—
348C2×C4—51no—
349C2×C4—51no—
350C2×C4—51no—
351C2×C4—151no—
352C2×C4—151no—
353C2×C4—151no—
354C2×C4—151no—
355C2×C4—302no—
356C2×C4—302no—
357C2×C4C2×D3×D511yescharacteristic
358C2×C4C2×D3×D511yescharacteristic
359C2×C3—41no—
360C2×C3—201no—
361C2×C3D5×#4111yescharacteristic
362C2×C3D5×#4111yescharacteristic
363C2×C3#415011yescharacteristic
364C5#567111yescharacteristic, complemented, Sylow
365C22—21no—
366C22—21no—
367C22—21no—
368C22—101no—
369C22—101no—
370C22—101no—
371C22C22×D3×D511yescharacteristic
372C4—21no—
373C4—21no—
374C4—52no—
375C4—61no—
376C4—61no—
377C4—61no—
378C4—61no—
379C4—101no—
380C4—101no—
381C4—152no—
382C4—301no—
383C4—301no—
384C4—301no—
385C3#6603611yescharacteristic, complemented, Sylow
386C2—41no—
387C2—201no—
388C2#9201611yescharacteristic
389C2#9202011yescharacteristic
390C2D5×#23711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C22⋊C4C22
prime radicalC2×C3×C22⋊D5C22
hypercenterC22⋊C4D3×D5
hypocenterC3×C5#556
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #91766C2semidirect
2. C5×#879C2semidirect
4. #91576C2semidirect
7. #91530C2semidirect
8. C4×#1204C2semidirect
9. #91430C2semidirect
10. #91393C2semidirect
11. #91366C2semidirect
12. #91366C2semidirect
13. #91331C2semidirect
14. #91327C2semidirect
15. #91323C2semidirect
97. #879D5semidirect
312. C3×C5#556semidirect
364. C5#5671semidirect
385. C3#66036semidirect

Maximal subgroups

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

subgroupindex
#917662
C5×#8792
C3×#40312
#915762
#915592
#915342
#915302
C4×#12042
#914302
#913932
#913662
#913312
#913272
#913232
#660363
#56715