Finite Group Databasebeta

← #11752767

Subgroups — #11752767

Order 960.

496 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D60C211yesmaximal, characteristic, complemented
2C5×#872C211yesmaximal, characteristic, complemented
3C3×#4022C211yesmaximal, characteristic, complemented
4#91476C211yesmaximal, characteristic
5#91473C211yesmaximal, characteristic, complemented
6D3×#685C211yesmaximal, characteristic, complemented
7#91433C211yesmaximal, characteristic, complemented
8#91417C211yesmaximal, characteristic, complemented
9#91406C211yesmaximal, characteristic, complemented
10#91403C211yesmaximal, characteristic, complemented
11#91377C211yesmaximal, characteristic, complemented
12#91362C211yesmaximal, characteristic, complemented
13#91354C211yesmaximal, characteristic, complemented
14#91353C211yesmaximal, characteristic, complemented
15#91351C211yesmaximal, characteristic, complemented
16#65861—31nomaximal, Hall
17C22×D3×D5C2211yescharacteristic
18C2×D60C2211yescharacteristic
19C2×C4×D15C2211yescharacteristic
20C2×C4×D15C2211yescharacteristic, complemented
21C2×C4×C5×D3C2211yescharacteristic
22C2×#1204C2211yescharacteristic, complemented
23C2×#1203C2211yescharacteristic
24C2×#1202C2211yescharacteristic
25C2×#1200C2211yescharacteristic
26C2×D3×Dic5C2211yescharacteristic
27C3×C42×C5C2211yescharacteristic, complemented
28#6714C2211yescharacteristic
29#6714C2211yescharacteristic, complemented
30C4⋊Dic15C2211yescharacteristic, complemented
31C5×(C2×D3)⋊C4C2211yescharacteristic
32C5×(C2×D3)⋊C4C2211yescharacteristic
33C5×Dic3⋊C4C2211yescharacteristic, complemented
34C5×Dic3⋊C4C2211yescharacteristic, complemented
35C4×C5×Dic3C2211yescharacteristic, complemented
36C3×#685C2211yescharacteristic
37C3×#685C2211yescharacteristic
38C3×#685C2211yescharacteristic
39C3×#683C2211yescharacteristic, complemented
40C3×#683C2211yescharacteristic, complemented
41C3×#683C2211yescharacteristic, complemented
42#6669C2211yescharacteristic, complemented
43#6668C2211yescharacteristic, complemented
44#6667C2211yescharacteristic
45#6667C2211yescharacteristic
46#6667C2211yescharacteristic, complemented
47#6667C2211yescharacteristic, complemented
48(C2×D3)⋊Dic5C2211yescharacteristic
49#6665C2211yescharacteristic
50#6665C2211yescharacteristic
51Dic3×Dic5C2211yescharacteristic, complemented
52#5705—51nomaximal, Hall
53C5×#117—31no—
54#4075—31no—
55C2×#685—31no—
56#4044—31no—
57#4042—31no—
58#4040—31no—
59#4040—31no—
60#4028—31no—
61#4027—31no—
62D5×C22⋊C4—31no—
63#4024—31no—
64#4022D311yescharacteristic, complemented
65#4021—31no—
66C4×D20—31no—
67#4018—31no—
68C22×D15C2311yescharacteristic
69C22×D15C2311yescharacteristic
70C22×C5×D3C2311yescharacteristic
71C22×C3×D5C2311yescharacteristic
72C2×D3×D5—22no—
73C2×D3×D5—22no—
74C2×D3×D5—41no—
75C2×C3×C4×C5C2311yescharacteristic
76C2×C3×C4×C5C2311yescharacteristic
77C2×C3×C4×C5C2311yescharacteristic
78C2×Dic15C2311yescharacteristic
79C2×Dic15C2311yescharacteristic
80D60—22no—
81C4×D15—41no—
82C4×D15—41no—
83C2×C5×Dic3C2311yescharacteristic
84C2×C5×Dic3C2311yescharacteristic
85C2×C5×Dic3C2311yescharacteristic
86C4×C5×D3—22no—
87C2×C3×Dic5C2311yescharacteristic
88C2×C3×Dic5C2311yescharacteristic
89C2×C3×Dic5C2311yescharacteristic
90#1204—41no—
91#1203—22no—
92#1202—41no—
93#1200—22no—
94D3×Dic5—41no—
95C3×#126—51no—
96#897—51no—
97#896—51no—
98#894—51no—
99#894—51no—
100#893—51no—
101#892—51no—
102#885—51no—
103#883—51no—
104#882—51no—
105D3×C22⋊C4—51no—
106D3×C22⋊C4—51no—
107#879—51no—
108C4×D12—51no—
109#872D511yescharacteristic, complemented
110C23×D5—31no—
111C22×C4×C5—31no—
112C2×C22⋊D5—31no—
113C22×Dic5—31no—
114C2×D20—31no—
115C2×D20—31no—
116C2×C4×D5—31no—
117C2×C4×D5—31no—
118C2×C4×D5—31no—
119C2×Dic10—31no—
120C5×C4⋊C4—31no—
121C5×C4⋊C4—31no—
122C5×C22⋊C4—31no—
123C5×C22⋊C4—31no—
124C42×C5—31no—
125C42×C5C2×D311yescharacteristic, complemented
126C22⋊Dic5—31no—
127#685—31no—
128#685—31no—
129#685—31no—
130#685—31no—
131#685—31no—
132#685—31no—
133#685—31no—
134#685—31no—
135#685C2×D311yescharacteristic
136#685C2×D311yescharacteristic
137#685C2×D311yescharacteristic
138C4⋊Dic5—31no—
139#683—31no—
140#683—31no—
141#683C2×D311yescharacteristic, complemented
142#683C2×D311yescharacteristic, complemented
143#683C2×D311yescharacteristic, complemented
144C4×Dic5—31no—
145#551—151noSylow
146C22×C3×C5C2411yescharacteristic
147C2×D15—21no—
148C2×D15—21no—
149C2×D15—21no—
150C2×D15—21no—
151C2×D15—21no—
152C2×D15#4112yes—
153C2×C5×D3—21no—
154C2×C5×D3—21no—
155C2×C5×D3#4112yes—
156C2×C3×D5—21no—
157C2×C3×D5—21no—
158C2×C3×D5—21no—
159D3×D5—44no—
160C3×C4×C5—21no—
161C3×C4×C5—21no—
162C3×C4×C5—21no—
163Dic15—21no—
164Dic15—21no—
165C3×Dic5—21no—
166C3×Dic5—21no—
167C3×Dic5—21no—
168C5×Dic3—21no—
169C5×Dic3—21no—
170C5×Dic3—21no—
171C23×D3—51no—
172C2×#67—51no—
173C2×D12—51no—
174C2×D12—51no—
175C2×C4×D3—51no—
176C2×C4×D3—51no—
177C2×C4×D3—51no—
178C2×C4×D3—51no—
179C2×C4×D3C2×D511yescharacteristic
180C2×Dic6—51no—
181C3×C4⋊C4—51no—
182C3×C4⋊C4—51no—
183C3×C4⋊C4—51no—
184C3×C22⋊C4—51no—
185C3×C22⋊C4—51no—
186C3×C22⋊C4—51no—
187C3×C42C2×D511yescharacteristic, complemented
188#217—51no—
189#217—51no—
190(C2×D3)⋊C4—51no—
191(C2×D3)⋊C4—51no—
192(C2×D3)⋊C4—51no—
193(C2×D3)⋊C4—51no—
194(C2×D3)⋊C4—51no—
195(C2×D3)⋊C4—51no—
196(C2×D3)⋊C4—51no—
197(C2×D3)⋊C4C2×D511yescharacteristic
198(C2×D3)⋊C4C2×D511yescharacteristic
199C4⋊Dic3—51no—
200C4⋊Dic3—51no—
201Dic3⋊C4—51no—
202Dic3⋊C4C2×D511yescharacteristic, complemented
203Dic3⋊C4C2×D511yescharacteristic, complemented
204C4×Dic3—51no—
205C4×Dic3C2×D511yescharacteristic, complemented
206C23×C5—31no—
207C22×D5—31no—
208C22×D5—31no—
209C22×D5—62no—
210C22×D5—62no—
211C22×D5—121no—
212C22×D5C22×D311yescharacteristic
213C2×C4×C5—31no—
214C2×C4×C5—31no—
215C2×C4×C5—31no—
216C2×C4×C5—62no—
217C2×C4×C5C22×D311yescharacteristic
218C2×C4×C5C22×D311yescharacteristic
219C2×C4×C5C22×D311yescharacteristic
220C22⋊D5—62no—
221C2×Dic5—31no—
222C2×Dic5—31no—
223C2×Dic5—121no—
224C2×Dic5C22×D311yescharacteristic
225C2×Dic5C22×D311yescharacteristic
226C2×Dic5C22×D311yescharacteristic
227D20—62no—
228D20—121no—
229C4×D5—62no—
230C4×D5—121no—
231C4×D5—121no—
232Dic10—121no—
233#126—51no—
234#126—151no—
235#124—151no—
236#123—151no—
237#123—151no—
238#123—151no—
239C22⋊Q8—151no—
240C22⋊Q8—151no—
241#120—151no—
242C4×D4—151no—
243C4×D4—151no—
244#117—31no—
245#117—151no—
246C2×C22⋊C4—151no—
247C2×C22⋊C4—151no—
248C2×C3×C5C2×#4111yescharacteristic
249C2×C3×C5C2×#4111yescharacteristic
250C2×C3×C5H(5,𝔽2)11yescharacteristic
251D15—22no—
252D15—41no—
253C3×D5—41no—
254C5×D3—22no—
255C23×C3—51no—
256C22×D3—51no—
257C22×D3—51no—
258C22×D3—102no—
259C22×D3—102no—
260C22×D3—201no—
261C22×D3C22×D511yescharacteristic
262C2×C3×C4—51no—
263C2×C3×C4—51no—
264C2×C3×C4—51no—
265C2×C3×C4C22×D511yescharacteristic
266C2×C3×C4C22×D511yescharacteristic
267C2×C3×C4C22×D511yescharacteristic
268#67—201no—
269C2×Dic3—51no—
270C2×Dic3—51no—
271C2×Dic3C22×D511yescharacteristic
272C2×Dic3C22×D511yescharacteristic
273C2×Dic3C22×D511yescharacteristic
274D12—102no—
275D12—102no—
276C4×D3—22no—
277C4×D3—102no—
278C4×D3—201no—
279C4×D3—201no—
280C4×D3—201no—
281Dic6—201no—
282C22×C5—32no—
283C22×C5—61no—
284C22×C5—61no—
285C22×C5C23×D311yescharacteristic
286C2×D5—21no—
287C2×D5—21no—
288C2×D5—21no—
289C2×D5—32no—
290C2×D5—61no—
291C2×D5—61no—
292C2×D5—61no—
293C2×D5—61no—
294C2×D5—61no—
295C2×D5—124no—
296C4×C5—21no—
297C4×C5—21no—
298C4×C5—21no—
299C4×C5—61no—
300C4×C5—61no—
301C4×C5—61no—
302Dic5—21no—
303Dic5—21no—
304Dic5—21no—
305Dic5—61no—
306Dic5—61no—
307C24—151no—
308C2×Q8—151no—
309C2×D4—151no—
310C2×D4—151no—
311C2×D4—151no—
312C22×C4—31no—
313C22×C4—151no—
314C22×C4—151no—
315C22×C4—151no—
316C22×C4—151no—
317C4⋊C4—31no—
318C4⋊C4—31no—
319C4⋊C4—51no—
320C4⋊C4—51no—
321C4⋊C4—51no—
322C4⋊C4—151no—
323C4⋊C4—151no—
324C4⋊C4—151no—
325C22⋊C4—31no—
326C22⋊C4—31no—
327C22⋊C4—51no—
328C22⋊C4—51no—
329C22⋊C4—51no—
330C22⋊C4—151no—
331C22⋊C4—151no—
332C22⋊C4—151no—
333C22⋊C4—151no—
334C22⋊C4—151no—
335C22⋊C4—151no—
336C22⋊C4—151no—
337C22⋊C4—151no—
338C22⋊C4—151no—
339C42—31no—
340C42—151no—
341C42D3×D511yescharacteristic, complemented
342C3×C5#55111yescharacteristic, complemented, Hall
343C22×C3—101no—
344C22×C3—101no—
345C22×C3—101no—
346C22×C3C23×D511yescharacteristic
347C2×D3—21no—
348C2×D3—21no—
349C2×D3—52no—
350C2×D3—101no—
351C2×D3—101no—
352C2×D3—101no—
353C2×D3—101no—
354C2×D3—101no—
355C2×D3—204no—
356C2×D3#70912yes—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—101no—
361C3×C4—101no—
362C3×C4—101no—
363Dic3—21no—
364Dic3—21no—
365Dic3—21no—
366Dic3—101no—
367Dic3—101no—
368C2×C5—62no—
369C2×C5D3×#4111yescharacteristic
370C2×C5D3×#4111yescharacteristic
371C2×C5#100911yescharacteristic
372D5—41no—
373D5—62no—
374D5—121no—
375C23—31no—
376C23—51no—
377C23—151no—
378C23—151no—
379C23—302no—
380C23—302no—
381C23—601no—
382Q8—601no—
383D4—302no—
384D4—302no—
385D4—601no—
386C2×C4—31no—
387C2×C4—31no—
388C2×C4—31no—
389C2×C4—51no—
390C2×C4—51no—
391C2×C4—51no—
392C2×C4—62no—
393C2×C4—151no—
394C2×C4—151no—
395C2×C4—302no—
396C2×C4—601no—
397C2×C4—601no—
398C2×C4—601no—
399C2×C4C2×D3×D511yescharacteristic
400C2×C4C2×D3×D511yescharacteristic
401C2×C4C2×D3×D511yescharacteristic
402C2×C3—201no—
403C2×C3C2×#70911yescharacteristic
404C2×C3D5×#4111yescharacteristic
405C2×C3#414911yescharacteristic
406D3—22no—
407D3—102no—
408D3—201no—
409C5#570511yescharacteristic, complemented, Sylow
410C22—32no—
411C22—61no—
412C22—61no—
413C22—101no—
414C22—101no—
415C22—101no—
416C22—152no—
417C22—301no—
418C22—301no—
419C22—301no—
420C22—301no—
421C22—301no—
422C22—604no—
423C22C22×D3×D511yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—61no—
428C4—61no—
429C4—61no—
430C4—101no—
431C4—101no—
432C4—101no—
433C4—301no—
434C4—301no—
435C3#6586111yescharacteristic, complemented, Sylow
436C2—62no—
437C2—201no—
438C2—302no—
439C2—601no—
440C2D3×#70911yescharacteristic
441C2#9201611yescharacteristic
442C2#9201911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C42×C5C22
prime radical#91476C2
hypercenterC42D3×D5
hypocenterC3×C5#551
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C4×D60C2semidirect
2. C5×#872C2semidirect
3. C3×#4022C2semidirect
5. #91473C2semidirect
6. D3×#685C2semidirect
7. #91433C2semidirect
8. #91417C2semidirect
9. #91406C2semidirect
10. #91403C2semidirect
11. #91377C2semidirect
12. #91362C2semidirect
13. #91354C2semidirect
14. #91353C2semidirect
15. #91351C2semidirect
20. C2×C4×D15C22semidirect
22. C2×#1204C22semidirect
27. C3×C42×C5C22semidirect
29. #6714C22semidirect
30. C4⋊Dic15C22semidirect
33. C5×Dic3⋊C4C22semidirect
34. C5×Dic3⋊C4C22semidirect
35. C4×C5×Dic3C22semidirect
39. C3×#683C22semidirect
40. C3×#683C22semidirect
41. C3×#683C22semidirect
42. #6669C22semidirect
43. #6668C22semidirect
46. #6667C22semidirect
47. #6667C22semidirect
51. Dic3×Dic5C22semidirect
64. #4022D3semidirect
109. #872D5semidirect
125. C42×C5C2×D3semidirect
141. #683C2×D3semidirect
142. #683C2×D3semidirect
143. #683C2×D3semidirect
187. C3×C42C2×D5semidirect
202. Dic3⋊C4C2×D5semidirect
203. Dic3⋊C4C2×D5semidirect
205. C4×Dic3C2×D5semidirect
341. C42D3×D5semidirect
342. C3×C5#551semidirect
409. C5#5705semidirect
435. C3#65861semidirect

Maximal subgroups

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

subgroupindex
C4×D602
C5×#8722
C3×#40222
#914762
#914732
D3×#6852
#914332
#914172
#914062
#914032
#913772
#913622
#913542
#913532
#913512
#658613
#57055