Finite Group Databasebeta

← #11753471

Subgroups — #11753471

Order 960.

412 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#91785C211yesmaximal, characteristic
2C5×#888C211yesmaximal, characteristic, complemented
3C3×#4035C211yesmaximal, characteristic, complemented
4#91424C211yesmaximal, characteristic
5#91419C211yesmaximal, characteristic
6#91404C211yesmaximal, characteristic
7#91403C211yesmaximal, characteristic
8#91402C211yesmaximal, characteristic
9#91383C211yesmaximal, characteristic
10#91379C211yesmaximal, characteristic, complemented
11#91376C211yesmaximal, characteristic, complemented
12#91346C211yesmaximal, characteristic, complemented
13#91335C211yesmaximal, characteristic, complemented
14#91329C211yesmaximal, characteristic, complemented
15#91328C211yesmaximal, characteristic, complemented
16#66063—31nomaximal, Hall
17C2×C4×D15C2211yescharacteristic
18C2×Dic30C2211yescharacteristic
19C2×C5×Dic6C2211yescharacteristic
20C2×C5×Dic6C2211yescharacteristic
21C2×#1204C2211yescharacteristic
22C2×#1200C2211yescharacteristic
23C2×#1200C2211yescharacteristic
24C3×C5×C4⋊C4C2211yescharacteristic
25#6714C2211yescharacteristic
26#6714C2211yescharacteristic
27#6712C2211yescharacteristic
28#6712C2211yescharacteristic
29C5×C4⋊Dic3C2211yescharacteristic
30C5×Dic3⋊C4C2211yescharacteristic
31C5×Dic3⋊C4C2211yescharacteristic
32C4×C5×Dic3C2211yescharacteristic
33C3×C4⋊Dic5C2211yescharacteristic
34C3×#683C2211yescharacteristic
35C3×#683C2211yescharacteristic
36C3×#683C2211yescharacteristic
37C3×#683C2211yescharacteristic
38C3×C4×Dic5C2211yescharacteristic
39Dic3⋊Dic5C2211yescharacteristic
40Dic3⋊Dic5C2211yescharacteristic
41Dic3⋊Dic5C2211yescharacteristic
42#6669C2211yescharacteristic
43#6668C2211yescharacteristic
44#6668C2211yescharacteristic
45#6668C2211yescharacteristic
46#6668C2211yescharacteristic
47#6668C2211yescharacteristic
48#6667C2211yescharacteristic
49#6667C2211yescharacteristic
50Dic3×Dic5C2211yescharacteristic
51Dic3×Dic5C2211yescharacteristic
52#5689—51nomaximal, Hall
53C5×C4⋊Q8—31no—
54#4092—31no—
55#4092—31no—
56#4090—31no—
57#4090—31no—
58#4042—31no—
59#4042—31no—
60#4038—31no—
61D5×C4⋊C4—31no—
62#4036—31no—
63#4035—31no—
64#4035D311yescharacteristic, complemented
65#4034—31no—
66#4018—31no—
67#4016—31no—
68C22×D15C2311yescharacteristic
69C2×C3×C4×C5C2311yescharacteristic
70C2×C3×C4×C5C2311yescharacteristic
71C2×C3×C4×C5C2311yescharacteristic
72C2×Dic15C2311yescharacteristic
73C2×Dic15C2311yescharacteristic
74C2×Dic15C2311yescharacteristic
75C4×D15—41no—
76Dic30—41no—
77C2×C5×Dic3C2311yescharacteristic
78C2×C5×Dic3C2311yescharacteristic
79C2×C5×Dic3C2311yescharacteristic
80C2×C5×Dic3C2311yescharacteristic
81C5×Dic6—41no—
82C5×Dic6—41no—
83C2×C3×Dic5C2311yescharacteristic
84C2×C3×Dic5C2311yescharacteristic
85C2×C3×Dic5C2311yescharacteristic
86C2×C3×Dic5C2311yescharacteristic
87#1204—41no—
88#1200—41no—
89#1200Q814yescomplemented
90C3×#125—51no—
91#897—51no—
92#897—51no—
93#896—51no—
94#896—51no—
95#892—51no—
96D3×C4⋊C4—51no—
97#890—51no—
98#889—51no—
99#889—51no—
100#888—51no—
101#888—51no—
102#888D511yescharacteristic, complemented
103#872—51no—
104#869—51no—
105C2×C5×Q8—31no—
106C2×C5×Q8—31no—
107C2×C4×D5—31no—
108C2×C4×D5—31no—
109C2×C4×D5—31no—
110C2×Dic10—31no—
111C2×Dic10—31no—
112C5×C4⋊C4—31no—
113C5×C4⋊C4—31no—
114C5×C4⋊C4—31no—
115C5×C4⋊C4C2×D311yescharacteristic
116C42×C5—31no—
117#685—31no—
118#685—31no—
119#685—31no—
120#685—31no—
121C4⋊Dic5—31no—
122C4⋊Dic5—31no—
123C4⋊Dic5—31no—
124C4⋊Dic5C2×D311yescharacteristic
125#683—31no—
126#683—31no—
127#683—31no—
128#683—31no—
129#683—31no—
130#683—31no—
131#683—31no—
132#683—31no—
133#683C2×D311yescharacteristic
134#683C2×D311yescharacteristic
135#683C2×D311yescharacteristic
136#683C2×D311yescharacteristic
137C4×Dic5—31no—
138C4×Dic5—31no—
139C4×Dic5C2×D311yescharacteristic
140#544—151noSylow
141C22×C3×C5C2411yescharacteristic
142C2×D15—21no—
143C2×D15—21no—
144C2×D15C2×Q812yes—
145C3×C4×C5—21no—
146C3×C4×C5—21no—
147C3×C4×C5—21no—
148Dic15—21no—
149Dic15—21no—
150Dic15—21no—
151C3×Dic5—21no—
152C3×Dic5—21no—
153C3×Dic5—21no—
154C3×Dic5C2×Q812yes—
155C5×Dic3—21no—
156C5×Dic3—21no—
157C5×Dic3—21no—
158C5×Dic3C2×Q812yes—
159C2×C4×D3—51no—
160C2×C4×D3—51no—
161C2×C4×D3—51no—
162C2×Dic6—51no—
163C2×Dic6—51no—
164C2×Dic6C2×D511yescharacteristic
165C2×Dic6C2×D511yescharacteristic
166C3×C4⋊C4—51no—
167C3×C4⋊C4—51no—
168C3×C4⋊C4—51no—
169C3×C4⋊C4—51no—
170C3×C4⋊C4—51no—
171C3×C4⋊C4C2×D511yescharacteristic
172C3×C42—51no—
173(C2×D3)⋊C4—51no—
174(C2×D3)⋊C4—51no—
175(C2×D3)⋊C4—51no—
176(C2×D3)⋊C4—51no—
177C4⋊Dic3—51no—
178C4⋊Dic3—51no—
179C4⋊Dic3—51no—
180C4⋊Dic3—51no—
181C4⋊Dic3—51no—
182C4⋊Dic3C2×D511yescharacteristic
183Dic3⋊C4—51no—
184Dic3⋊C4—51no—
185Dic3⋊C4—51no—
186Dic3⋊C4—51no—
187Dic3⋊C4—51no—
188Dic3⋊C4—51no—
189Dic3⋊C4C2×D511yescharacteristic
190Dic3⋊C4C2×D511yescharacteristic
191C4×Dic3—51no—
192C4×Dic3—51no—
193C4×Dic3C2×D511yescharacteristic
194C22×D5—31no—
195C5×Q8—121no—
196C5×Q8—121no—
197C2×C4×C5—31no—
198C2×C4×C5—31no—
199C2×C4×C5—31no—
200C2×C4×C5—31no—
201C2×C4×C5C22×D311yescharacteristic
202C2×C4×C5C22×D311yescharacteristic
203C2×C4×C5C22×D311yescharacteristic
204C2×Dic5—31no—
205C2×Dic5—31no—
206C2×Dic5—31no—
207C2×Dic5C22×D311yescharacteristic
208C2×Dic5C22×D311yescharacteristic
209C2×Dic5C22×D311yescharacteristic
210C2×Dic5C22×D311yescharacteristic
211C4×D5—34no—
212C4×D5—121no—
213C4×D5—121no—
214Dic10—121no—
215Dic10—121no—
216C4⋊Q8—31no—
217C4⋊Q8—151no—
218C4⋊Q8—151no—
219C4⋊Q8—151no—
220#125—51no—
221#125—151no—
222#125—151no—
223#125—151no—
224C22⋊Q8—151no—
225C22⋊Q8—151no—
226C22⋊Q8—151no—
227C22⋊Q8—151no—
228#117—151no—
229#117—151no—
230C2×C4⋊C4—151no—
231C2×C3×C5C22×Q811yescharacteristic
232C2×C3×C5H(5,𝔽2)11yescharacteristic
233C2×C3×C52−1+411yescharacteristic
234D15—22no—
235C22×D3—51no—
236C2×C3×C4—51no—
237C2×C3×C4—51no—
238C2×C3×C4—51no—
239C2×C3×C4—51no—
240C2×C3×C4C22×D511yescharacteristic
241C2×C3×C4C22×D511yescharacteristic
242C2×C3×C4C22×D511yescharacteristic
243C2×Dic3—51no—
244C2×Dic3—51no—
245C2×Dic3—51no—
246C2×Dic3C22×D511yescharacteristic
247C2×Dic3C22×D511yescharacteristic
248C2×Dic3C22×D511yescharacteristic
249C2×Dic3C22×D511yescharacteristic
250C4×D3—54no—
251C4×D3—201no—
252C4×D3—201no—
253Dic6—41no—
254Dic6—41no—
255Dic6—201no—
256Dic6—201no—
257C22×C5C23×D311yescharacteristic
258C2×D5—32no—
259C2×D5—61no—
260C2×D5—61no—
261C4×C5—21no—
262C4×C5—21no—
263C4×C5—21no—
264C4×C5—32no—
265C4×C5—61no—
266C4×C5—61no—
267C4×C5—61no—
268Dic5—21no—
269Dic5—21no—
270Dic5—21no—
271Dic5—61no—
272Dic5—61no—
273Dic5—61no—
274Dic5D3×Q812yes—
275C2×Q8—31no—
276C2×Q8—31no—
277C2×Q8—151no—
278C2×Q8—151no—
279C22×C4—151no—
280C22×C4—151no—
281C22×C4—151no—
282C4⋊C4—31no—
283C4⋊C4—31no—
284C4⋊C4—31no—
285C4⋊C4—51no—
286C4⋊C4—51no—
287C4⋊C4—51no—
288C4⋊C4—51no—
289C4⋊C4—51no—
290C4⋊C4—151no—
291C4⋊C4—151no—
292C4⋊C4—151no—
293C4⋊C4—151no—
294C4⋊C4—151no—
295C4⋊C4—151no—
296C4⋊C4—151no—
297C4⋊C4—151no—
298C4⋊C4—151no—
299C4⋊C4—151no—
300C4⋊C4—151no—
301C4⋊C4D3×D511yescharacteristic
302C22⋊C4—151no—
303C22⋊C4—151no—
304C22⋊C4—151no—
305C22⋊C4—151no—
306C42—31no—
307C42—51no—
308C42—151no—
309C42—151no—
310C3×C5#54411yescharacteristic, complemented, Hall
311C22×C3C23×D511yescharacteristic
312C2×D3—52no—
313C2×D3—101no—
314C2×D3—101no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—21no—
318C3×C4—52no—
319C3×C4—101no—
320C3×C4—101no—
321C3×C4—101no—
322Dic3—21no—
323Dic3—21no—
324Dic3—21no—
325Dic3—101no—
326Dic3—101no—
327Dic3—101no—
328Dic3Q8×D512yes—
329C2×C5C2×D3×Q811yescharacteristic
330C2×C5#100911yescharacteristic
331C2×C5#101011yescharacteristic
332D5—62no—
333C23—151no—
334Q8—121no—
335Q8—121no—
336Q8—601no—
337Q8—601no—
338C2×C4—31no—
339C2×C4—31no—
340C2×C4—31no—
341C2×C4—31no—
342C2×C4—51no—
343C2×C4—51no—
344C2×C4—51no—
345C2×C4—51no—
346C2×C4—154no—
347C2×C4—151no—
348C2×C4—151no—
349C2×C4—151no—
350C2×C4—601no—
351C2×C4—601no—
352C2×C4C2×D3×D511yescharacteristic
353C2×C4C2×D3×D511yescharacteristic
354C2×C4C2×D3×D511yescharacteristic
355C2×C3#414411yescharacteristic
356C2×C3C2×Q8×D511yescharacteristic
357C2×C3#414711yescharacteristic
358D3—102no—
359C5#568911yescharacteristic, complemented, Sylow
360C22—152no—
361C22—301no—
362C22—301no—
363C22C22×D3×D511yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—32no—
368C4—52no—
369C4—61no—
370C4—61no—
371C4—61no—
372C4—101no—
373C4—101no—
374C4—101no—
375C4—301no—
376C4—301no—
377C4—301no—
378C3#6606311yescharacteristic, complemented, Sylow
379C2—302no—
380C2#9200011yescharacteristic
381C2#9202711yescharacteristic
382C2D3×Q8×D511yescharacteristic
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×#4035C2semidirect
10. #91379C2semidirect
11. #91376C2semidirect
12. #91346C2semidirect
13. #91335C2semidirect
14. #91329C2semidirect
15. #91328C2semidirect
64. #4035D3semidirect
89. #1200Q8semidirect
102. #888D5semidirect
310. C3×C5#544semidirect
359. C5#5689semidirect
378. C3#66063semidirect

Maximal subgroups

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

subgroupindex
#917852
C5×#8882
C3×#40352
#914242
#914192
#914042
#914032
#914022
#913832
#913792
#913762
#913462
#913352
#913292
#913282
#660633
#56895