Finite Group Databasebeta

← #11754730

Subgroups — #11754730

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#91824C211yesmaximal, characteristic
2C5×#935C211yesmaximal, characteristic
3C3×D4×Dic5C211yesmaximal, characteristic
4#91574C211yesmaximal, characteristic, complemented
5#91574C211yesmaximal, characteristic, complemented
6C2×#6668C211yesmaximal, characteristic, complemented
7#91532C211yesmaximal, characteristic, complemented
8#91531C211yesmaximal, characteristic, complemented
9#91530C211yesmaximal, characteristic, complemented
10#91529C211yesmaximal, characteristic, complemented
11#91528C211yesmaximal, characteristic, complemented
12#91378C211yesmaximal, characteristic, complemented
13#91346C211yesmaximal, characteristic, complemented
14#91339C211yesmaximal, characteristic, complemented
15#91323C211yesmaximal, characteristic, complemented
16#65984—31nomaximal, Hall
17C2×C3×C5×D4C2211yescharacteristic
18C22×Dic15C2211yescharacteristic
19C22×C5×Dic3C2211yescharacteristic
20C22×C3×Dic5C2211yescharacteristic
21C22×C3×Dic5C2211yescharacteristic
22C2×#1204C2211yescharacteristic
23#6719C2211yescharacteristic
24#6719C2211yescharacteristic
25#6719C2211yescharacteristic
26#6712C2211yescharacteristic
27#6712C2211yescharacteristic
28C5×#217C2211yescharacteristic
29C5×#217C2211yescharacteristic
30C5×#217C2211yescharacteristic
31C5×Dic3⋊C4C2211yescharacteristic
32C5×Dic3⋊C4C2211yescharacteristic
33C3×C22⋊Dic5C2211yescharacteristic
34C3×C22⋊Dic5C2211yescharacteristic
35C3×C4⋊Dic5C2211yescharacteristic
36C3×C4×Dic5C2211yescharacteristic
37Dic3⋊Dic5C2211yescharacteristic
38Dic3⋊Dic5C2211yescharacteristic
39Dic3⋊Dic5C2211yescharacteristic
40#6669C2211yescharacteristic
41#6669C2211yescharacteristic
42#6669C2211yescharacteristic
43#6668C2211yescharacteristic
44#6668C2211yescharacteristic
45#6668C2211yescharacteristic
46#6668C2211yescharacteristic
47#6668C2211yescharacteristic
48Dic3×Dic5C2211yescharacteristic
49Dic3×Dic5C2211yescharacteristic
50Dic3×Dic5C2211yescharacteristic
51Dic3×Dic5C2211yescharacteristic
52#5541—51nomaximal, Hall
53C5×#123—31no—
54#4081—31no—
55D4×Dic5D311yescharacteristic
56#4072—31no—
57C2×#683—31no—
58#4036—31no—
59#4035—31no—
60#4035—31no—
61#4033—31no—
62#4025—31no—
63#4025—31no—
64#4024—31no—
65#4024—31no—
66#4023—31no—
67#4023—31no—
68C23×C3×C5C2311yescharacteristic
69C23×C3×C5C2311yescharacteristic
70C3×C5×D4—22no—
71C2×C3×C4×C5C2311yescharacteristic
72C2×Dic15—22no—
73C2×Dic15C2311yescharacteristic
74C2×Dic15C2311yescharacteristic
75C2×Dic15C2311yescharacteristic
76C2×Dic15C2311yescharacteristic
77C2×C5×Dic3—22no—
78C2×C5×Dic3C2311yescharacteristic
79C2×C5×Dic3C2311yescharacteristic
80C2×C5×Dic3C2311yescharacteristic
81C2×C5×Dic3C2311yescharacteristic
82C2×C3×Dic5—22no—
83C2×C3×Dic5—22no—
84C2×C3×Dic5C2311yescharacteristic
85C2×C3×Dic5C2311yescharacteristic
86C2×C3×Dic5C2311yescharacteristic
87C2×C3×Dic5C2311yescharacteristic
88#1204—22no—
89C3×C4×D4—51no—
90#935—51no—
91#935D511yescharacteristic
92#926—51no—
93C2×C4⋊Dic3—51no—
94#924—51no—
95#924—51no—
96#889—51no—
97#889—51no—
98#879—51no—
99#879—51no—
100#877—51no—
101#877—51no—
102#870—51no—
103C4×Dic6—51no—
104C2×C5×D4C2×D311yescharacteristic
105C22×C4×C5—31no—
106C22×Dic5—31no—
107C22×Dic5C2×D311yescharacteristic
108C22×Dic5C2×D311yescharacteristic
109C2×Dic10—31no—
110C5×C4⋊C4—31no—
111C5×C4⋊C4—31no—
112C5×C22⋊C4—31no—
113C5×C22⋊C4—31no—
114C5×C22⋊C4—31no—
115C22⋊Dic5—31no—
116C22⋊Dic5—31no—
117C22⋊Dic5—31no—
118C22⋊Dic5C2×D311yescharacteristic
119C22⋊Dic5C2×D311yescharacteristic
120C4⋊Dic5—31no—
121C4⋊Dic5—31no—
122C4⋊Dic5—31no—
123C4⋊Dic5C2×D311yescharacteristic
124#683—31no—
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#683—31no—
134C4×Dic5—31no—
135C4×Dic5—31no—
136C4×Dic5—31no—
137C4×Dic5—31no—
138C4×Dic5C2×D311yescharacteristic
139#552—151noSylow
140C22×C3×C5—21no—
141C22×C3×C5—21no—
142C22×C3×C5—21no—
143C22×C3×C5—21no—
144C22×C3×C5—21no—
145C22×C3×C5#4112yes—
146C22×C3×C5C2411yescharacteristic
147C3×C4×C5—21no—
148Dic15—21no—
149Dic15—21no—
150Dic15—21no—
151Dic15—21no—
152C3×Dic5—21no—
153C3×Dic5—21no—
154C3×Dic5—21no—
155C3×Dic5#4112yes—
156C5×Dic3—21no—
157C5×Dic3—21no—
158C5×Dic3—21no—
159C5×Dic3—21no—
160C2×C3×D4C2×D511yescharacteristic
161C22×C3×C4—51no—
162C22×C3×C4—51no—
163C22×Dic3—51no—
164C22×Dic3C2×D511yescharacteristic
165C2×Dic6—51no—
166C3×C4⋊C4—51no—
167C3×C22⋊C4—51no—
168C3×C22⋊C4—51no—
169C3×C42—51no—
170#217—51no—
171#217—51no—
172#217—51no—
173#217C2×D511yescharacteristic
174#217C2×D511yescharacteristic
175#217C2×D511yescharacteristic
176C4⋊Dic3—51no—
177C4⋊Dic3—51no—
178C4⋊Dic3—51no—
179C4⋊Dic3—51no—
180C4⋊Dic3—51no—
181Dic3⋊C4—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×C5C22×D311yescharacteristic
196C23×C5C22×D311yescharacteristic
197C5×D4—22no—
198C2×C4×C5—31no—
199C2×C4×C5—31no—
200C2×C4×C5—31no—
201C2×C4×C5—31no—
202C2×C4×C5—62no—
203C2×C4×C5C22×D311yescharacteristic
204C2×Dic5—22no—
205C2×Dic5—22no—
206C2×Dic5—31no—
207C2×Dic5—31no—
208C2×Dic5—31no—
209C2×Dic5—31no—
210C2×Dic5—62no—
211C2×Dic5C22×D311yescharacteristic
212C2×Dic5C22×D311yescharacteristic
213C2×Dic5C22×D311yescharacteristic
214C2×Dic5C22×D311yescharacteristic
215Dic10—62no—
216#126—151no—
217#126—151no—
218#125—151no—
219#125—151no—
220#125—151no—
221#123—31no—
222#123—151no—
223C22⋊Q8—151no—
224C22⋊Q8—151no—
225C4×Q8—151no—
226C4×D4—51no—
227#117—151no—
228#117—151no—
229#117—151no—
230C2×C4⋊C4—151no—
231C2×C3×C5—22no—
232C2×C3×C5—41no—
233C2×C3×C5C2×#4111yescharacteristic
234C2×C3×C5C2×#4111yescharacteristic
235C2×C3×C52−1+411yescharacteristic
236C23×C3C22×D511yescharacteristic
237C23×C3C22×D511yescharacteristic
238C3×D4—22no—
239C2×C3×C4—51no—
240C2×C3×C4—51no—
241C2×C3×C4—51no—
242C2×C3×C4—51no—
243C2×C3×C4—102no—
244C2×C3×C4—102no—
245C2×C3×C4C22×D511yescharacteristic
246C2×Dic3—22no—
247C2×Dic3—51no—
248C2×Dic3—51no—
249C2×Dic3—51no—
250C2×Dic3—51no—
251C2×Dic3—102no—
252C2×Dic3C22×D511yescharacteristic
253C2×Dic3C22×D511yescharacteristic
254C2×Dic3C22×D511yescharacteristic
255C2×Dic3C22×D511yescharacteristic
256Dic6—102no—
257C22×C5—21no—
258C22×C5—21no—
259C22×C5—21no—
260C22×C5—21no—
261C22×C5—21no—
262C22×C5#23512yes—
263C22×C5C23×D311yescharacteristic
264C4×C5—21no—
265C4×C5—61no—
266C4×C5—61no—
267C4×C5—61no—
268C4×C5—61no—
269Dic5—21no—
270Dic5—21no—
271Dic5—21no—
272Dic5—61no—
273Dic5—61no—
274Dic5—61no—
275Dic5—61no—
276Dic5#23712yes—
277C2×Q8—151no—
278C2×D4D3×D511yescharacteristic
279C22×C4—31no—
280C22×C4—51no—
281C22×C4—51no—
282C22×C4—151no—
283C4⋊C4—31no—
284C4⋊C4—31no—
285C4⋊C4—51no—
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—
295C4⋊C4—151no—
296C4⋊C4—151no—
297C4⋊C4—151no—
298C4⋊C4—151no—
299C22⋊C4—31no—
300C22⋊C4—31no—
301C22⋊C4—31no—
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—21no—
314C22×C3—21no—
315C22×C3—21no—
316C22×C3—21no—
317C22×C3—21no—
318C22×C3#71112yes—
319C22×C3C23×D511yescharacteristic
320C3×C4—21no—
321C3×C4—52no—
322C3×C4—101no—
323C3×C4—101no—
324C3×C4—101no—
325Dic3—21no—
326Dic3—21no—
327Dic3—21no—
328Dic3—21no—
329Dic3—101no—
330Dic3—101no—
331Dic3—101no—
332Dic3—101no—
333C2×C5—22no—
334C2×C5—41no—
335C2×C5C2×#23511yescharacteristic
336C2×C5C2×#23711yescharacteristic
337C2×C5#101011yescharacteristic
338C23C2×D3×D511yescharacteristic
339C23C2×D3×D511yescharacteristic
340Q8—302no—
341D4—22no—
342C2×C4—31no—
343C2×C4—31no—
344C2×C4—31no—
345C2×C4—31no—
346C2×C4—51no—
347C2×C4—51no—
348C2×C4—51no—
349C2×C4—51no—
350C2×C4—62no—
351C2×C4—102no—
352C2×C4—102no—
353C2×C4—151no—
354C2×C4—151no—
355C2×C4—151no—
356C2×C4—151no—
357C2×C4—302no—
358C2×C4C2×D3×D511yescharacteristic
359C2×C3—22no—
360C2×C3—41no—
361C2×C3C2×#71111yescharacteristic
362C2×C3D5×#4111yescharacteristic
363C2×C3#415011yescharacteristic
364C5#554111yescharacteristic, complemented, Sylow
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22#678212yes—
371C22C22×D3×D511yescharacteristic
372C4—21no—
373C4—52no—
374C4—61no—
375C4—61no—
376C4—61no—
377C4—61no—
378C4—101no—
379C4—101no—
380C4—101no—
381C4—301no—
382C4—301no—
383C4—301no—
384C4—301no—
385C3#6598411yescharacteristic, complemented, Sylow
386C2—22no—
387C2—41no—
388C2#9202011yescharacteristic
389C2D5×#23711yescharacteristic
390C2C2×#678211yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
Fitting, prime radicalC2×C3×C5×D4C22
hypercenterC2×D4D3×D5
hypocenterC3×C5#552
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
4. #91574C2semidirect
5. #91574C2semidirect
6. C2×#6668C2semidirect
7. #91532C2semidirect
8. #91531C2semidirect
9. #91530C2semidirect
10. #91529C2semidirect
11. #91528C2semidirect
12. #91378C2semidirect
13. #91346C2semidirect
14. #91339C2semidirect
15. #91323C2semidirect
312. C3×C5#552semidirect
364. C5#5541semidirect
385. C3#65984semidirect

Maximal subgroups

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

subgroupindex
#918242
C5×#9352
C3×D4×Dic52
#915742
C2×#66682
#915322
#915312
#915302
#915292
#915282
#913782
#913462
#913392
#913232
#659843
#55415