Finite Group Databasebeta

← #11755256

Subgroups — #11755256

Order 960.

432 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#91833C211yesmaximal, characteristic, complemented
2C5×#947C211yesmaximal, characteristic, complemented
3C3×#4092C211yesmaximal, characteristic, complemented
4#91464C211yesmaximal, characteristic, complemented
5#91462C211yesmaximal, characteristic, complemented
6#91453C211yesmaximal, characteristic
7#91447C211yesmaximal, characteristic, complemented
8#91440C211yesmaximal, characteristic, complemented
9#91436C211yesmaximal, characteristic, complemented
10#91432C211yesmaximal, characteristic, complemented
11#91423C211yesmaximal, characteristic, complemented
12#91400C211yesmaximal, characteristic, complemented
13#91363C211yesmaximal, characteristic, complemented
14#91341C211yesmaximal, characteristic, complemented
15#91324C211yesmaximal, characteristic, complemented
16#66003—31nomaximal, Hall
17C2×C3×C5×Q8C2211yescharacteristic
18C2×Dic30C2211yescharacteristic
19C2×C5×D12C2211yescharacteristic
20C2×C3×C4×D5C2211yescharacteristic
21C2×#1204C2211yescharacteristic
22C2×#1201C2211yescharacteristic
23C2×#1201C2211yescharacteristic
24C2×D3×Dic5C2211yescharacteristic
25C2×D3×Dic5C2211yescharacteristic
26#6712C2211yescharacteristic
27#6712C2211yescharacteristic
28#6712C2211yescharacteristic
29#6712C2211yescharacteristic
30C4×Dic15C2211yescharacteristic
31C5×(C2×D3)⋊C4C2211yescharacteristic
32C5×(C2×D3)⋊C4C2211yescharacteristic
33C5×(C2×D3)⋊C4C2211yescharacteristic
34C5×(C2×D3)⋊C4C2211yescharacteristic
35C4×C5×Dic3C2211yescharacteristic
36C3×#685C2211yescharacteristic
37C3×#685C2211yescharacteristic
38C3×C4⋊Dic5C2211yescharacteristic
39C3×#683C2211yescharacteristic
40C3×#683C2211yescharacteristic
41Dic3⋊Dic5C2211yescharacteristic
42#6669C2211yescharacteristic
43#6668C2211yescharacteristic
44(C2×D3)⋊Dic5C2211yescharacteristic
45(C2×D3)⋊Dic5C2211yescharacteristic
46(C2×D3)⋊Dic5C2211yescharacteristic
47(C2×D3)⋊Dic5C2211yescharacteristic
48#6665C2211yescharacteristic
49#6665C2211yescharacteristic
50Dic3×Dic5C2211yescharacteristic
51Dic3×Dic5C2211yescharacteristic
52#5640—51nomaximal, Hall
53C5×#124—31no—
54#4092D311yescharacteristic, complemented
55#4090—31no—
56#4085—31no—
57#4081—31no—
58#4031—31no—
59#4031—31no—
60#4029—31no—
61#4027—31no—
62#4025—31no—
63#4024—31no—
64#4024—31no—
65#4023—31no—
66#4022—31no—
67C4×Dic10—31no—
68C22×C5×D3C2311yescharacteristic
69C22×C5×D3C2311yescharacteristic
70C22×C3×D5C2311yescharacteristic
71C3×C5×Q8—41no—
72C2×C3×C4×C5C2311yescharacteristic
73C2×C3×C4×C5C2311yescharacteristic
74C2×C3×C4×C5C2311yescharacteristic
75C2×Dic15C2311yescharacteristic
76C2×Dic15C2311yescharacteristic
77C2×Dic15C2311yescharacteristic
78C2×Dic15C2311yescharacteristic
79Dic30—41no—
80C2×C5×Dic3C2311yescharacteristic
81C2×C5×Dic3C2311yescharacteristic
82C5×D12—41no—
83C2×C3×Dic5C2311yescharacteristic
84C2×C3×Dic5C2311yescharacteristic
85C2×C3×Dic5C2311yescharacteristic
86C3×C4×D5—41no—
87#1204—22no—
88#1201—22no—
89#1201—41no—
90D3×Dic5—22no—
91D3×Dic5—41no—
92C3×C22⋊Q8—51no—
93#947D511yescharacteristic, complemented
94#944—51no—
95#929—51no—
96C4×#67—51no—
97#898—51no—
98#896—51no—
99#896—51no—
100#894—51no—
101#892—51no—
102#887—51no—
103#885—51no—
104#885—51no—
105#884—51no—
106#879—51no—
107C2×C5×Q8C2×D311yescharacteristic
108C2×C5×D4—31no—
109C2×C22⋊D5—31no—
110C2×C22⋊D5—31no—
111C22×Dic5—31no—
112C22×Dic5—31no—
113C2×C4×D5C2×D311yescharacteristic
114C2×Dic10—31no—
115C2×Dic10—31no—
116C5×C22⋊C4—31no—
117C5×C22⋊C4—31no—
118C5×C22⋊C4—31no—
119C5×C22⋊C4—31no—
120C42×C5—31no—
121C22⋊Dic5—31no—
122C22⋊Dic5—31no—
123C22⋊Dic5—31no—
124C22⋊Dic5—31no—
125#685—31no—
126#685—31no—
127#685C2×D311yescharacteristic
128#685C2×D311yescharacteristic
129C4⋊Dic5—31no—
130C4⋊Dic5C2×D311yescharacteristic
131#683—31no—
132#683—31no—
133#683—31no—
134#683—31no—
135#683—31no—
136#683—31no—
137#683C2×D311yescharacteristic
138#683C2×D311yescharacteristic
139C4×Dic5—31no—
140C4×Dic5—31no—
141C4×Dic5—31no—
142#542—151noSylow
143C22×C3×C5C2411yescharacteristic
144C2×C5×D3—21no—
145C2×C5×D3—21no—
146C2×C5×D3—21no—
147C2×C5×D3—21no—
148C2×C5×D3—21no—
149C2×C5×D3—21no—
150C2×C3×D5—21no—
151C2×C3×D5—21no—
152C2×C3×D5—21no—
153C3×C4×C5—21no—
154C3×C4×C5—21no—
155C3×C4×C5—21no—
156Dic15—21no—
157Dic15—21no—
158Dic15—21no—
159Dic15#4112yes—
160C3×Dic5—21no—
161C3×Dic5—21no—
162C3×Dic5—21no—
163C5×Dic3—21no—
164C5×Dic3—21no—
165C2×C3×Q8C2×D511yescharacteristic
166C22×C3×C4—51no—
167C2×#67—51no—
168C2×#67—51no—
169C2×D12C2×D511yescharacteristic
170C2×C4×D3—51no—
171C2×C4×D3—51no—
172C2×Dic6—51no—
173C2×Dic6—51no—
174C3×C4⋊C4—51no—
175C3×C4⋊C4—51no—
176C3×C4⋊C4—51no—
177C3×C22⋊C4—51no—
178C3×C22⋊C4—51no—
179#217—51no—
180#217—51no—
181(C2×D3)⋊C4—51no—
182(C2×D3)⋊C4—51no—
183(C2×D3)⋊C4—51no—
184(C2×D3)⋊C4—51no—
185(C2×D3)⋊C4C2×D511yescharacteristic
186(C2×D3)⋊C4C2×D511yescharacteristic
187(C2×D3)⋊C4C2×D511yescharacteristic
188(C2×D3)⋊C4C2×D511yescharacteristic
189C4⋊Dic3—51no—
190Dic3⋊C4—51no—
191Dic3⋊C4—51no—
192Dic3⋊C4—51no—
193Dic3⋊C4—51no—
194Dic3⋊C4—51no—
195Dic3⋊C4—51no—
196C4×Dic3—51no—
197C4×Dic3—51no—
198C4×Dic3—51no—
199C4×Dic3C2×D511yescharacteristic
200C23×C5—31no—
201C23×C5—31no—
202C22×D5C22×D311yescharacteristic
203C5×Q8—41no—
204C5×D4—121no—
205C2×C4×C5—31no—
206C2×C4×C5—31no—
207C2×C4×C5C22×D311yescharacteristic
208C2×C4×C5C22×D311yescharacteristic
209C2×C4×C5C22×D311yescharacteristic
210C22⋊D5—62no—
211C22⋊D5—121no—
212C2×Dic5—31no—
213C2×Dic5—31no—
214C2×Dic5—31no—
215C2×Dic5—31no—
216C2×Dic5—62no—
217C2×Dic5—121no—
218C2×Dic5C22×D311yescharacteristic
219C2×Dic5C22×D311yescharacteristic
220C2×Dic5C22×D311yescharacteristic
221C4×D5—41no—
222Dic10—62no—
223Dic10—121no—
224C4⋊Q8—151no—
225#126—151no—
226#126—151no—
227#124—31no—
228#124—151no—
229#124—151no—
230#123—151no—
231#123—151no—
232C22⋊Q8—51no—
233C22⋊Q8—151no—
234C22⋊Q8—151no—
235#121—151no—
236C4×Q8—151no—
237C4×D4—151no—
238#117—151no—
239C2×C3×C5C2×#4111yescharacteristic
240C2×C3×C5H(5,𝔽2)11yescharacteristic
241C2×C3×C52−1+411yescharacteristic
242C3×D5—41no—
243C5×D3—41no—
244C5×D3—41no—
245C23×C3—51no—
246C22×D3C22×D511yescharacteristic
247C22×D3C22×D511yescharacteristic
248C3×Q8—41no—
249C2×C3×C4—51no—
250C2×C3×C4—51no—
251C2×C3×C4—51no—
252C2×C3×C4—201no—
253C2×C3×C4C22×D511yescharacteristic
254C2×C3×C4C22×D511yescharacteristic
255C2×C3×C4C22×D511yescharacteristic
256#67—102no—
257#67—201no—
258C2×Dic3—51no—
259C2×Dic3—51no—
260C2×Dic3—51no—
261C2×Dic3—51no—
262C2×Dic3C22×D511yescharacteristic
263C2×Dic3C22×D511yescharacteristic
264D12—41no—
265C4×D3—102no—
266C4×D3—201no—
267Dic6—102no—
268Dic6—201no—
269C22×C5—61no—
270C22×C5—61no—
271C22×C5—61no—
272C22×C5—61no—
273C22×C5—61no—
274C22×C5—61no—
275C22×C5C23×D311yescharacteristic
276C2×D5—21no—
277C2×D5—21no—
278C2×D5—21no—
279C4×C5—21no—
280C4×C5—21no—
281C4×C5—21no—
282C4×C5—61no—
283C4×C5—61no—
284Dic5—21no—
285Dic5—21no—
286Dic5—21no—
287Dic5—32no—
288Dic5—61no—
289Dic5—61no—
290Dic5—61no—
291C2×Q8—151no—
292C2×Q8—151no—
293C2×Q8D3×D511yescharacteristic
294C2×D4—31no—
295C2×D4—151no—
296C2×D4—151no—
297C22×C4—51no—
298C22×C4—151no—
299C22×C4—151no—
300C4⋊C4—51no—
301C4⋊C4—51no—
302C4⋊C4—51no—
303C4⋊C4—151no—
304C4⋊C4—151no—
305C4⋊C4—151no—
306C4⋊C4—151no—
307C4⋊C4—151no—
308C4⋊C4—151no—
309C4⋊C4—151no—
310C22⋊C4—31no—
311C22⋊C4—31no—
312C22⋊C4—31no—
313C22⋊C4—31no—
314C22⋊C4—51no—
315C22⋊C4—51no—
316C22⋊C4—151no—
317C22⋊C4—151no—
318C22⋊C4—151no—
319C22⋊C4—151no—
320C22⋊C4—151no—
321C22⋊C4—151no—
322C42—31no—
323C42—151no—
324C42—151no—
325C42—151no—
326C3×C5#54211yescharacteristic, complemented, Hall
327C22×C3—101no—
328C22×C3—101no—
329C22×C3—101no—
330C22×C3C23×D511yescharacteristic
331C2×D3—21no—
332C2×D3—21no—
333C2×D3—21no—
334C2×D3—21no—
335C2×D3—21no—
336C2×D3—21no—
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—21no—
340C3×C4—101no—
341C3×C4—101no—
342C3×C4—101no—
343Dic3—21no—
344Dic3—21no—
345Dic3—52no—
346Dic3—101no—
347Dic3—101no—
348Dic3—101no—
349C2×C5—121no—
350C2×C5—121no—
351C2×C5#100411yescharacteristic
352C2×C5#100711yescharacteristic
353C2×C5D3×#4111yescharacteristic
354D5—41no—
355C23—31no—
356C23—31no—
357C23—51no—
358Q8—41no—
359Q8—302no—
360Q8—601no—
361D4—121no—
362D4—302no—
363D4—601no—
364C2×C4—31no—
365C2×C4—31no—
366C2×C4—51no—
367C2×C4—51no—
368C2×C4—51no—
369C2×C4—151no—
370C2×C4—151no—
371C2×C4—151no—
372C2×C4—151no—
373C2×C4—201no—
374C2×C4—302no—
375C2×C4—601no—
376C2×C4C2×D3×D511yescharacteristic
377C2×C4C2×D3×D511yescharacteristic
378C2×C4C2×D3×D511yescharacteristic
379C2×C3—201no—
380C2×C3#414411yescharacteristic
381C2×C3D5×#4111yescharacteristic
382C2×C3#415011yescharacteristic
383D3—41no—
384D3—41no—
385C5#564011yescharacteristic, complemented, Sylow
386C22—61no—
387C22—61no—
388C22—61no—
389C22—61no—
390C22—61no—
391C22—61no—
392C22—101no—
393C22—101no—
394C22—101no—
395C22C22×D3×D511yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—61no—
400C4—61no—
401C4—101no—
402C4—101no—
403C4—101no—
404C4—152no—
405C4—301no—
406C4—301no—
407C4—301no—
408C3#6600311yescharacteristic, complemented, Sylow
409C2—121no—
410C2—121no—
411C2—201no—
412C2#9203011yescharacteristic
413C2#9203411yescharacteristic
414C2#9204911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC2×C3×C5×Q8C22
prime radical#91453C2
hypercenterC2×Q8D3×D5
hypocenterC3×C5#542
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. #91833C2semidirect
2. C5×#947C2semidirect
3. C3×#4092C2semidirect
4. #91464C2semidirect
5. #91462C2semidirect
7. #91447C2semidirect
8. #91440C2semidirect
9. #91436C2semidirect
10. #91432C2semidirect
11. #91423C2semidirect
12. #91400C2semidirect
13. #91363C2semidirect
14. #91341C2semidirect
15. #91324C2semidirect
54. #4092D3semidirect
93. #947D5semidirect
326. C3×C5#542semidirect
385. C5#5640semidirect
408. C3#66003semidirect

Maximal subgroups

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

subgroupindex
#918332
C5×#9472
C3×#40922
#914642
#914622
#914532
#914472
#914402
#914362
#914322
#914232
#914002
#913632
#913412
#913242
#660033
#56405