Finite Group Databasebeta

← #11752989

Subgroups — #11752989

Order 960.

468 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#91766C211yesmaximal, characteristic, complemented
2C5×#884C211yesmaximal, characteristic
3C3×#4025C211yesmaximal, characteristic, complemented
4#67⋊Dic5C211yesmaximal, characteristic, complemented
5#67⋊Dic5C211yesmaximal, characteristic, complemented
6#91555C211yesmaximal, characteristic, complemented
7#91525C211yesmaximal, characteristic, complemented
8#91435C211yesmaximal, characteristic, complemented
9#91423C211yesmaximal, characteristic, complemented
10#91400C211yesmaximal, characteristic, complemented
11C4×D3×Dic5C211yesmaximal, characteristic, complemented
12#91372C211yesmaximal, characteristic, complemented
13#91352C211yesmaximal, characteristic, complemented
14#91346C211yesmaximal, characteristic, complemented
15#91325C211yesmaximal, characteristic, complemented
16#65934—31nomaximal, Hall
17C22×Dic15C2211yescharacteristic
18C2×C5×#67C2211yescharacteristic
19C2×C5×#67C2211yescharacteristic
20C2×C5×D12C2211yescharacteristic
21C2×C4×C5×D3C2211yescharacteristic
22C2×#1204C2211yescharacteristic
23C2×D3×Dic5C2211yescharacteristic
24C2×D3×Dic5C2211yescharacteristic
25C2×D3×Dic5C2211yescharacteristic
26C3×C5×C22⋊C4C2211yescharacteristic
27#6719C2211yescharacteristic
28#6712C2211yescharacteristic
29#6712C2211yescharacteristic
30C4×Dic15C2211yescharacteristic
31C4×Dic15C2211yescharacteristic
32C5×(C2×D3)⋊C4C2211yescharacteristic
33C5×Dic3⋊C4C2211yescharacteristic
34C3×C22⋊Dic5C2211yescharacteristic
35C3×C22⋊Dic5C2211yescharacteristic
36C3×C4⋊Dic5C2211yescharacteristic
37C3×#683C2211yescharacteristic
38C3×#683C2211yescharacteristic
39C3×C4×Dic5C2211yescharacteristic
40Dic3⋊Dic5C2211yescharacteristic
41Dic3⋊Dic5C2211yescharacteristic
42#6669C2211yescharacteristic
43#6668C2211yescharacteristic
44(C2×D3)⋊Dic5C2211yescharacteristic
45(C2×D3)⋊Dic5C2211yescharacteristic
46(C2×D3)⋊Dic5C2211yescharacteristic
47(C2×D3)⋊Dic5C2211yescharacteristic
48(C2×D3)⋊Dic5C2211yescharacteristic
49Dic3×Dic5C2211yescharacteristic
50Dic3×Dic5C2211yescharacteristic
51Dic3×Dic5C2211yescharacteristic
52#5706—51nomaximal, Hall
53C5×#121—31no—
54#4082—31no—
55#4081—31no—
56#4081—31no—
57D4×Dic5—31no—
58D4×Dic5—31no—
59D4×Dic5—31no—
60#4070—31no—
61C2×C4×Dic5—31no—
62#4036—31no—
63#4033—31no—
64#4025—31no—
65#4025D311yescharacteristic, complemented
66#4023—31no—
67#4023—31no—
68C23×C3×C5C2311yescharacteristic
69C22×C5×D3C2311yescharacteristic
70C22×C5×D3C2311yescharacteristic
71C2×C3×C4×C5C2311yescharacteristic
72C2×C3×C4×C5C2311yescharacteristic
73C2×Dic15—22no—
74C2×Dic15C2311yescharacteristic
75C2×Dic15C2311yescharacteristic
76C2×Dic15C2311yescharacteristic
77C2×Dic15C2311yescharacteristic
78C5×#67—22no—
79C5×#67—22no—
80C2×C5×Dic3C2311yescharacteristic
81C2×C5×Dic3C2311yescharacteristic
82C5×D12—22no—
83C4×C5×D3—22no—
84C2×C3×Dic5C2311yescharacteristic
85C2×C3×Dic5C2311yescharacteristic
86C2×C3×Dic5C2311yescharacteristic
87C2×C3×Dic5C2311yescharacteristic
88#1204—22no—
89D3×Dic5—22no—
90D3×Dic5—22no—
91D3×Dic5—22no—
92C3×#126—51no—
93#896—51no—
94#894—51no—
95#893—51no—
96#892—51no—
97#889—51no—
98#887—51no—
99#885—51no—
100#884D511yescharacteristic
101#883—51no—
102#67⋊C4—51no—
103#67⋊C4—51no—
104#877—51no—
105#876—51no—
106C42×D3—51no—
107C2×C5×D4—31no—
108C2×C5×D4—31no—
109C2×C5×D4—31no—
110C22×C4×C5—31no—
111C22×Dic5—31no—
112C22×Dic5—31no—
113C22×Dic5—31no—
114C22×Dic5—31no—
115C2×Dic10—31no—
116C5×C4⋊C4—31no—
117C5×C22⋊C4—31no—
118C5×C22⋊C4C2×D311yescharacteristic
119C22⋊Dic5—31no—
120C22⋊Dic5—31no—
121C22⋊Dic5—31no—
122C22⋊Dic5—31no—
123C22⋊Dic5—31no—
124C22⋊Dic5—31no—
125C22⋊Dic5C2×D311yescharacteristic
126C22⋊Dic5C2×D311yescharacteristic
127C4⋊Dic5—31no—
128C4⋊Dic5—31no—
129C4⋊Dic5C2×D311yescharacteristic
130#683—31no—
131#683—31no—
132#683—31no—
133#683—31no—
134#683C2×D311yescharacteristic
135#683C2×D311yescharacteristic
136C4×Dic5—31no—
137C4×Dic5—31no—
138C4×Dic5—31no—
139C4×Dic5—31no—
140C4×Dic5—31no—
141C4×Dic5C2×D311yescharacteristic
142#529—151noSylow
143C22×C3×C5—21no—
144C22×C3×C5—21no—
145C22×C3×C5—21no—
146C22×C3×C5C2411yescharacteristic
147C2×C5×D3—21no—
148C2×C5×D3—21no—
149C2×C5×D3—21no—
150C2×C5×D3—21no—
151C2×C5×D3—21no—
152C2×C5×D3#4112yes—
153C3×C4×C5—21no—
154C3×C4×C5—21no—
155Dic15—21no—
156Dic15—21no—
157Dic15—21no—
158Dic15#4112yes—
159C3×Dic5—21no—
160C3×Dic5—21no—
161C3×Dic5—21no—
162C3×Dic5—21no—
163C5×Dic3—21no—
164C5×Dic3#4112yes—
165C2×#67C2×D511yescharacteristic
166C2×#67C2×D511yescharacteristic
167C22×Dic3—51no—
168C2×D12C2×D511yescharacteristic
169C2×C4×D3—51no—
170C2×C4×D3—51no—
171C2×C4×D3—51no—
172C2×C4×D3C2×D511yescharacteristic
173C2×Dic6—51no—
174C3×C4⋊C4—51no—
175C3×C4⋊C4—51no—
176C3×C4⋊C4—51no—
177C3×C22⋊C4—51no—
178C3×C22⋊C4—51no—
179C3×C22⋊C4C2×D511yescharacteristic
180C3×C42—51no—
181#217—51no—
182(C2×D3)⋊C4—51no—
183(C2×D3)⋊C4—51no—
184(C2×D3)⋊C4—51no—
185(C2×D3)⋊C4—51no—
186(C2×D3)⋊C4—51no—
187(C2×D3)⋊C4C2×D511yescharacteristic
188C4⋊Dic3—51no—
189Dic3⋊C4—51no—
190Dic3⋊C4—51no—
191Dic3⋊C4—51no—
192Dic3⋊C4—51no—
193Dic3⋊C4—51no—
194Dic3⋊C4C2×D511yescharacteristic
195C4×Dic3—51no—
196C4×Dic3—51no—
197C4×Dic3—51no—
198C4×Dic3—51no—
199C4×Dic3—51no—
200C23×C5—31no—
201C23×C5—31no—
202C23×C5C22×D311yescharacteristic
203C5×D4—62no—
204C5×D4—62no—
205C5×D4—62no—
206C2×C4×C5—31no—
207C2×C4×C5—31no—
208C2×C4×C5—62no—
209C2×C4×C5C22×D311yescharacteristic
210C2×C4×C5C22×D311yescharacteristic
211C2×Dic5—31no—
212C2×Dic5—31no—
213C2×Dic5—31no—
214C2×Dic5—31no—
215C2×Dic5—62no—
216C2×Dic5—62no—
217C2×Dic5—62no—
218C2×Dic5—62no—
219C2×Dic5C22×D311yescharacteristic
220C2×Dic5C22×D311yescharacteristic
221C2×Dic5C22×D311yescharacteristic
222C2×Dic5C22×D311yescharacteristic
223Dic10—62no—
224#126—51no—
225#126—151no—
226#125—151no—
227#124—151no—
228#123—151no—
229#123—151no—
230C22⋊Q8—151no—
231#121—31no—
232C4×Q8—151no—
233C4×D4—151no—
234C4×D4—151no—
235C4×D4—151no—
236#117—151no—
237#117—151no—
238C2×C42—151no—
239C2×C3×C5—41no—
240C2×C3×C5C2×#4111yescharacteristic
241C2×C3×C5C2×#4111yescharacteristic
242C2×C3×C5C2×#4111yescharacteristic
243C5×D3—22no—
244C5×D3—41no—
245C23×C3C22×D511yescharacteristic
246C22×D3C22×D511yescharacteristic
247C22×D3C22×D511yescharacteristic
248C2×C3×C4—51no—
249C2×C3×C4—51no—
250C2×C3×C4—51no—
251C2×C3×C4—51no—
252C2×C3×C4C22×D511yescharacteristic
253C2×C3×C4C22×D511yescharacteristic
254#67—22no—
255#67—22no—
256C2×Dic3—51no—
257C2×Dic3—51no—
258C2×Dic3—51no—
259C2×Dic3—51no—
260C2×Dic3—102no—
261C2×Dic3C22×D511yescharacteristic
262C2×Dic3C22×D511yescharacteristic
263D12—22no—
264C4×D3—22no—
265C4×D3—102no—
266C4×D3—102no—
267C4×D3—102no—
268Dic6—102no—
269C22×C5—21no—
270C22×C5—21no—
271C22×C5—21no—
272C22×C5—32no—
273C22×C5—61no—
274C22×C5—61no—
275C22×C5—61no—
276C22×C5—61no—
277C22×C5—61no—
278C22×C5C23×D311yescharacteristic
279C4×C5—21no—
280C4×C5—21no—
281C4×C5—32no—
282C4×C5—61no—
283Dic5—21no—
284Dic5—21no—
285Dic5—21no—
286Dic5—21no—
287Dic5—32no—
288Dic5—61no—
289Dic5—61no—
290Dic5—61no—
291C2×Q8—151no—
292C2×D4—31no—
293C2×D4—31no—
294C2×D4—31no—
295C22×C4—31no—
296C22×C4—151no—
297C22×C4—151no—
298C22×C4—151no—
299C22×C4—151no—
300C4⋊C4—31no—
301C4⋊C4—51no—
302C4⋊C4—51no—
303C4⋊C4—51no—
304C4⋊C4—151no—
305C4⋊C4—151no—
306C4⋊C4—151no—
307C4⋊C4—151no—
308C4⋊C4—151no—
309C4⋊C4—151no—
310C22⋊C4—31no—
311C22⋊C4—51no—
312C22⋊C4—51no—
313C22⋊C4—151no—
314C22⋊C4—151no—
315C22⋊C4—151no—
316C22⋊C4—151no—
317C22⋊C4—151no—
318C22⋊C4—151no—
319C22⋊C4D3×D511yescharacteristic
320C42—51no—
321C42—151no—
322C42—151no—
323C42—151no—
324C42—151no—
325C42—151no—
326C3×C5#52911yescharacteristic, complemented, Hall
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3C23×D511yescharacteristic
331C2×D3—21no—
332C2×D3—21no—
333C2×D3—21no—
334C2×D3—21no—
335C2×D3—21no—
336C2×D3#71112yes—
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—101no—
340C3×C4—101no—
341C3×C4—101no—
342C3×C4—101no—
343Dic3—21no—
344Dic3—52no—
345Dic3—101no—
346Dic3—101no—
347Dic3—101no—
348Dic3#71112yes—
349C2×C5—41no—
350C2×C5—62no—
351C2×C5—121no—
352C2×C5D3×#4111yescharacteristic
353C2×C5D3×#4111yescharacteristic
354C2×C5D3×#4111yescharacteristic
355C23—31no—
356C23—31no—
357C23C2×D3×D511yescharacteristic
358Q8—302no—
359D4—62no—
360D4—62no—
361D4—62no—
362C2×C4—31no—
363C2×C4—31no—
364C2×C4—51no—
365C2×C4—51no—
366C2×C4—51no—
367C2×C4—51no—
368C2×C4—62no—
369C2×C4—151no—
370C2×C4—151no—
371C2×C4—151no—
372C2×C4—151no—
373C2×C4—302no—
374C2×C4—302no—
375C2×C4—302no—
376C2×C4—302no—
377C2×C4C2×D3×D511yescharacteristic
378C2×C4C2×D3×D511yescharacteristic
379C2×C3—41no—
380C2×C3C2×#71111yescharacteristic
381C2×C3C2×#71111yescharacteristic
382C2×C3D5×#4111yescharacteristic
383D3—22no—
384D3—41no—
385C5#570611yescharacteristic, complemented, Sylow
386C22—21no—
387C22—21no—
388C22—21no—
389C22—32no—
390C22—61no—
391C22—61no—
392C22—61no—
393C22—61no—
394C22—61no—
395C22C22×D3×D511yescharacteristic
396C4—21no—
397C4—21no—
398C4—32no—
399C4—61no—
400C4—101no—
401C4—101no—
402C4—101no—
403C4—101no—
404C4—152no—
405C4—301no—
406C4—301no—
407C4—301no—
408C3#6593411yescharacteristic, complemented, Sylow
409C2—41no—
410C2—62no—
411C2—121no—
412C2#9201611yescharacteristic
413C2D3×#71111yescharacteristic
414C2D3×#71111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C22⋊C4C22
prime radicalC5×#884C2
hypercenterC22⋊C4D3×D5
hypocenterC3×C5#529
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
3. C3×#4025C2semidirect
4. #67⋊Dic5C2semidirect
5. #67⋊Dic5C2semidirect
6. #91555C2semidirect
7. #91525C2semidirect
8. #91435C2semidirect
9. #91423C2semidirect
10. #91400C2semidirect
11. C4×D3×Dic5C2semidirect
12. #91372C2semidirect
13. #91352C2semidirect
14. #91346C2semidirect
15. #91325C2semidirect
65. #4025D3semidirect
326. C3×C5#529semidirect
385. C5#5706semidirect
408. C3#65934semidirect

Maximal subgroups

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

subgroupindex
#917662
C5×#8842
C3×#40252
#67⋊Dic52
#915552
#915252
#914352
#914232
#914002
C4×D3×Dic52
#913722
#913522
#913462
#913252
#659343
#57065