Finite Group Databasebeta

← #11753571

Subgroups — #11753571

Order 960.

428 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#91779C211yesmaximal, characteristic, complemented
2C5×#896C211yesmaximal, characteristic, complemented
3C3×#4044C211yesmaximal, characteristic, complemented
4#91457C211yesmaximal, characteristic
5#91457C211yesmaximal, characteristic
6#91441C211yesmaximal, characteristic
7D3×C4⋊Dic5C211yesmaximal, characteristic, complemented
8#91421C211yesmaximal, characteristic, complemented
9#91400C211yesmaximal, characteristic, complemented
10#91398C211yesmaximal, characteristic, complemented
11#91394C211yesmaximal, characteristic, complemented
12#91362C211yesmaximal, characteristic, complemented
13#91346C211yesmaximal, characteristic, complemented
14#91343C211yesmaximal, characteristic, complemented
15Dic5×Dic6C211yesmaximal, characteristic, complemented
16#65976—31nomaximal, Hall
17C2×C4×C5×D3C2211yescharacteristic
18C2×C5×Dic6C2211yescharacteristic
19C2×#1201C2211yescharacteristic
20C2×D3×Dic5C2211yescharacteristic
21C2×D3×Dic5C2211yescharacteristic
22C2×D5×Dic3C2211yescharacteristic
23C3×C5×C4⋊C4C2211yescharacteristic
24C4⋊Dic15C2211yescharacteristic
25C4⋊Dic15C2211yescharacteristic
26C4⋊Dic15C2211yescharacteristic
27#6712C2211yescharacteristic
28#6712C2211yescharacteristic
29C4×Dic15C2211yescharacteristic
30C5×(C2×D3)⋊C4C2211yescharacteristic
31C5×(C2×D3)⋊C4C2211yescharacteristic
32C5×Dic3⋊C4C2211yescharacteristic
33C5×Dic3⋊C4C2211yescharacteristic
34C3×#685C2211yescharacteristic
35C3×#685C2211yescharacteristic
36C3×#685C2211yescharacteristic
37C3×C4⋊Dic5C2211yescharacteristic
38C3×#683C2211yescharacteristic
39C3×C4×Dic5C2211yescharacteristic
40Dic3⋊Dic5C2211yescharacteristic
41Dic3⋊Dic5C2211yescharacteristic
42Dic3⋊Dic5C2211yescharacteristic
43Dic3⋊Dic5C2211yescharacteristic
44#6669C2211yescharacteristic
45#6668C2211yescharacteristic
46(C2×D3)⋊Dic5C2211yescharacteristic
47#6665C2211yescharacteristic
48#6665C2211yescharacteristic
49Dic3×Dic5C2211yescharacteristic
50Dic3×Dic5C2211yescharacteristic
51Dic3×Dic5C2211yescharacteristic
52#5708—51nomaximal, Hall
53C5×C22⋊Q8—31no—
54#4092—31no—
55Q8×Dic5—31no—
56C4×C22⋊D5—31no—
57C2×C4⋊Dic5—31no—
58#4044—31no—
59#4044D311yescharacteristic, complemented
60#4038—31no—
61#4036—31no—
62#4036—31no—
63#4036—31no—
64#4032—31no—
65#4032—31no—
66#4023—31no—
67#4023—31no—
68C22×C5×D3C2311yescharacteristic
69C22×C3×D5C2311yescharacteristic
70C2×C3×C4×C5C2311yescharacteristic
71C2×C3×C4×C5C2311yescharacteristic
72C2×C3×C4×C5C2311yescharacteristic
73C2×Dic15C2311yescharacteristic
74C2×Dic15C2311yescharacteristic
75C2×Dic15C2311yescharacteristic
76C2×Dic15C2311yescharacteristic
77C2×C5×Dic3C2311yescharacteristic
78C2×C5×Dic3C2311yescharacteristic
79C2×C5×Dic3C2311yescharacteristic
80C4×C5×D3—22no—
81C5×Dic6—22no—
82C2×C3×Dic5C2311yescharacteristic
83C2×C3×Dic5C2311yescharacteristic
84C2×C3×Dic5C2311yescharacteristic
85#1201—22no—
86D3×Dic5—22no—
87D3×Dic5—22no—
88D5×Dic3—22no—
89C3×#126—51no—
90#896D511yescharacteristic, complemented
91#892—51no—
92D3×C4⋊C4—51no—
93#890—51no—
94#889—51no—
95#889—51no—
96#883—51no—
97#883—51no—
98#67⋊C4—51no—
99#879—51no—
100#878—51no—
101#877—51no—
102#872—51no—
103C4×Dic6—51no—
104C2×C5×Q8—31no—
105C22×C4×C5—31no—
106C2×C22⋊D5—31no—
107C22×Dic5—31no—
108C22×Dic5—31no—
109C2×C4×D5—31no—
110C5×C4⋊C4—31no—
111C5×C4⋊C4—31no—
112C5×C4⋊C4C2×D311yescharacteristic
113C5×C22⋊C4—31no—
114C5×C22⋊C4—31no—
115C22⋊Dic5—31no—
116#685—31no—
117#685—31no—
118#685C2×D311yescharacteristic
119#685C2×D311yescharacteristic
120#685C2×D311yescharacteristic
121C4⋊Dic5—31no—
122C4⋊Dic5—31no—
123C4⋊Dic5—31no—
124C4⋊Dic5—31no—
125C4⋊Dic5—31no—
126C4⋊Dic5—31no—
127C4⋊Dic5—31no—
128C4⋊Dic5C2×D311yescharacteristic
129#683—31no—
130#683—31no—
131#683—31no—
132#683—31no—
133#683C2×D311yescharacteristic
134C4×Dic5—31no—
135C4×Dic5—31no—
136C4×Dic5—31no—
137C4×Dic5—31no—
138C4×Dic5C2×D311yescharacteristic
139#552—151noSylow
140C22×C3×C5C2411yescharacteristic
141C2×C5×D3—21no—
142C2×C5×D3—21no—
143C2×C5×D3#4112yes—
144C2×C3×D5—21no—
145C2×C3×D5—21no—
146C2×C3×D5—21no—
147C3×C4×C5—21no—
148C3×C4×C5—21no—
149C3×C4×C5—21no—
150Dic15—21no—
151Dic15—21no—
152Dic15—21no—
153Dic15—21no—
154C3×Dic5—21no—
155C3×Dic5—21no—
156C3×Dic5—21no—
157C5×Dic3—21no—
158C5×Dic3—21no—
159C5×Dic3#4112yes—
160C2×#67—51no—
161C22×Dic3—51no—
162C2×C4×D3—51no—
163C2×C4×D3—51no—
164C2×C4×D3C2×D511yescharacteristic
165C2×Dic6C2×D511yescharacteristic
166C3×C4⋊C4—51no—
167C3×C4⋊C4—51no—
168C3×C4⋊C4C2×D511yescharacteristic
169C3×C22⋊C4—51no—
170C3×C22⋊C4—51no—
171C3×C22⋊C4—51no—
172C3×C42—51no—
173#217—51no—
174#217—51no—
175(C2×D3)⋊C4—51no—
176(C2×D3)⋊C4C2×D511yescharacteristic
177(C2×D3)⋊C4C2×D511yescharacteristic
178C4⋊Dic3—51no—
179C4⋊Dic3—51no—
180C4⋊Dic3—51no—
181C4⋊Dic3—51no—
182Dic3⋊C4—51no—
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×Dic3—51no—
194C4×Dic3—51no—
195C23×C5—31no—
196C22×D5C22×D311yescharacteristic
197C5×Q8—62no—
198C2×C4×C5—31no—
199C2×C4×C5—31no—
200C2×C4×C5—31no—
201C2×C4×C5—62no—
202C2×C4×C5C22×D311yescharacteristic
203C2×C4×C5C22×D311yescharacteristic
204C2×C4×C5C22×D311yescharacteristic
205C22⋊D5—62no—
206C2×Dic5—31no—
207C2×Dic5—31no—
208C2×Dic5—31no—
209C2×Dic5—31no—
210C2×Dic5—62no—
211C2×Dic5—62no—
212C2×Dic5C22×D311yescharacteristic
213C2×Dic5C22×D311yescharacteristic
214C2×Dic5C22×D311yescharacteristic
215C4×D5—62no—
216#126—51no—
217#126—151no—
218#125—151no—
219#125—151no—
220#125—151no—
221#123—151no—
222#123—151no—
223C22⋊Q8—31no—
224C22⋊Q8—151no—
225C4×Q8—151no—
226C4×D4—151no—
227#117—151no—
228#117—151no—
229#117—151no—
230C2×C4⋊C4—151no—
231C2×C3×C5C2×#4111yescharacteristic
232C2×C3×C5C2×#4111yescharacteristic
233C2×C3×C52−1+411yescharacteristic
234C3×D5—41no—
235C5×D3—22no—
236C23×C3—51no—
237C22×D3C22×D511yescharacteristic
238C2×C3×C4—51no—
239C2×C3×C4—51no—
240C2×C3×C4—51no—
241C2×C3×C4C22×D511yescharacteristic
242C2×C3×C4C22×D511yescharacteristic
243C2×C3×C4C22×D511yescharacteristic
244#67—102no—
245C2×Dic3—51no—
246C2×Dic3—51no—
247C2×Dic3—51no—
248C2×Dic3—51no—
249C2×Dic3—102no—
250C2×Dic3C22×D511yescharacteristic
251C2×Dic3C22×D511yescharacteristic
252C2×Dic3C22×D511yescharacteristic
253C4×D3—22no—
254C4×D3—102no—
255C4×D3—102no—
256Dic6—22no—
257C22×C5—32no—
258C22×C5—61no—
259C22×C5—61no—
260C22×C5C23×D311yescharacteristic
261C2×D5—21no—
262C2×D5—21no—
263C2×D5—21no—
264C4×C5—21no—
265C4×C5—21no—
266C4×C5—21no—
267C4×C5—32no—
268C4×C5—61no—
269C4×C5—61no—
270Dic5—21no—
271Dic5—21no—
272Dic5—21no—
273Dic5—61no—
274Dic5—61no—
275Dic5—61no—
276Dic5—61no—
277C2×Q8—31no—
278C2×D4—151no—
279C22×C4—31no—
280C22×C4—151no—
281C22×C4—151no—
282C22×C4—151no—
283C4⋊C4—31no—
284C4⋊C4—31no—
285C4⋊C4—51no—
286C4⋊C4—51no—
287C4⋊C4—151no—
288C4⋊C4—151no—
289C4⋊C4—151no—
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⋊C4D3×D511yescharacteristic
299C22⋊C4—31no—
300C22⋊C4—31no—
301C22⋊C4—51no—
302C22⋊C4—51no—
303C22⋊C4—51no—
304C22⋊C4—151no—
305C22⋊C4—151no—
306C22⋊C4—151no—
307C42—51no—
308C42—151no—
309C42—151no—
310C42—151no—
311C42—151no—
312C3×C5#55211yescharacteristic, complemented, Hall
313C22×C3—101no—
314C22×C3—101no—
315C22×C3—101no—
316C22×C3C23×D511yescharacteristic
317C2×D3—21no—
318C2×D3—21no—
319C2×D3#71312yes—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—21no—
323C3×C4—101no—
324C3×C4—101no—
325C3×C4—101no—
326Dic3—21no—
327Dic3—21no—
328Dic3—101no—
329Dic3—101no—
330Dic3—101no—
331Dic3—101no—
332Dic3#71112yes—
333C2×C5—62no—
334C2×C5D3×#4111yescharacteristic
335C2×C5D3×#4111yescharacteristic
336C2×C5#101011yescharacteristic
337D5—41no—
338C23—31no—
339C23—51no—
340Q8—62no—
341D4—302no—
342C2×C4—31no—
343C2×C4—31no—
344C2×C4—31no—
345C2×C4—51no—
346C2×C4—51no—
347C2×C4—51no—
348C2×C4—62no—
349C2×C4—151no—
350C2×C4—151no—
351C2×C4—151no—
352C2×C4—151no—
353C2×C4—302no—
354C2×C4—302no—
355C2×C4—302no—
356C2×C4C2×D3×D511yescharacteristic
357C2×C4C2×D3×D511yescharacteristic
358C2×C4C2×D3×D511yescharacteristic
359C2×C3—201no—
360C2×C3C2×#71111yescharacteristic
361C2×C3C2×#71311yescharacteristic
362C2×C3#415011yescharacteristic
363D3—22no—
364C5#570811yescharacteristic, complemented, Sylow
365C22—32no—
366C22—61no—
367C22—61no—
368C22—101no—
369C22—101no—
370C22—101no—
371C22C22×D3×D511yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—32no—
376C4—61no—
377C4—61no—
378C4—101no—
379C4—101no—
380C4—101no—
381C4—301no—
382C4—301no—
383C4—301no—
384C4—301no—
385C3#6597611yescharacteristic, complemented, Sylow
386C2—62no—
387C2—201no—
388C2#9200111yescharacteristic
389C2D3×#71111yescharacteristic
390C2D3×#71311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C4⋊C4C22
prime radicalC2×#1201C22
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#552
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. #91779C2semidirect
2. C5×#896C2semidirect
3. C3×#4044C2semidirect
7. D3×C4⋊Dic5C2semidirect
8. #91421C2semidirect
9. #91400C2semidirect
10. #91398C2semidirect
11. #91394C2semidirect
12. #91362C2semidirect
13. #91346C2semidirect
14. #91343C2semidirect
15. Dic5×Dic6C2semidirect
59. #4044D3semidirect
90. #896D5semidirect
312. C3×C5#552semidirect
364. C5#5708semidirect
385. C3#65976semidirect

Maximal subgroups

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

subgroupindex
#917792
C5×#8962
C3×#40442
#914572
#914412
D3×C4⋊Dic52
#914212
#914002
#913982
#913942
#913622
#913462
#913432
Dic5×Dic62
#659763
#57085