Finite Group Databasebeta

← #11753722

Subgroups — #11753722

Order 960.

436 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#91783C211yesmaximal, characteristic, complemented
2C5×#889C211yesmaximal, characteristic, complemented
3C3×D5×C4⋊C4C211yesmaximal, characteristic, complemented
4#91450C211yesmaximal, characteristic
5#91444C211yesmaximal, characteristic, complemented
6C4×#1202C211yesmaximal, characteristic, complemented
7#91433C211yesmaximal, characteristic, complemented
8#91429C211yesmaximal, characteristic, complemented
9#91380C211yesmaximal, characteristic, complemented
10#91377C211yesmaximal, characteristic, complemented
11#91349C211yesmaximal, characteristic, complemented
12#91348C211yesmaximal, characteristic, complemented
13#91348C211yesmaximal, characteristic, complemented
14#91345C211yesmaximal, characteristic, complemented
15#91336C211yesmaximal, characteristic, complemented
16#66026—31nomaximal, Hall
17C2×D60C2211yescharacteristic
18C2×C4×D15C2211yescharacteristic
19C2×C3×C4×D5C2211yescharacteristic
20C2×C3×C4×D5C2211yescharacteristic
21C2×C3×C4×D5C2211yescharacteristic
22C2×#1204C2211yescharacteristic
23C2×#1202C2211yescharacteristic
24C2×#1202C2211yescharacteristic
25C2×#1200C2211yescharacteristic
26C3×C5×C4⋊C4C2211yescharacteristic
27#6714C2211yescharacteristic
28#6714C2211yescharacteristic
29#6714C2211yescharacteristic
30#6712C2211yescharacteristic
31C5×C4⋊Dic3C2211yescharacteristic
32C5×Dic3⋊C4C2211yescharacteristic
33C5×Dic3⋊C4C2211yescharacteristic
34C5×Dic3⋊C4C2211yescharacteristic
35C5×Dic3⋊C4C2211yescharacteristic
36C4×C5×Dic3C2211yescharacteristic
37C3×C4⋊Dic5C2211yescharacteristic
38C3×#683C2211yescharacteristic
39C3×#683C2211yescharacteristic
40Dic3⋊Dic5C2211yescharacteristic
41#6669C2211yescharacteristic
42#6669C2211yescharacteristic
43#6668C2211yescharacteristic
44#6667C2211yescharacteristic
45#6667C2211yescharacteristic
46#6667C2211yescharacteristic
47#6667C2211yescharacteristic
48#6667C2211yescharacteristic
49#6665C2211yescharacteristic
50#6665C2211yescharacteristic
51Dic3×Dic5C2211yescharacteristic
52#5515—51nomaximal, Hall
53C5×#125—31no—
54#4044—31no—
55#4043—31no—
56#4042—31no—
57#4042—31no—
58#4041—31no—
59#4040—31no—
60#4040—31no—
61#4040—31no—
62#4040—31no—
63#4039—31no—
64D5×C4⋊C4D311yescharacteristic, complemented
65#4035—31no—
66#4022—31no—
67C4×D20—31no—
68C22×D15C2311yescharacteristic
69C22×D15C2311yescharacteristic
70C22×C3×D5C2311yescharacteristic
71C2×C3×C4×C5C2311yescharacteristic
72C2×C3×C4×C5C2311yescharacteristic
73C2×C3×C4×C5C2311yescharacteristic
74C2×Dic15C2311yescharacteristic
75C2×Dic15C2311yescharacteristic
76D60—41no—
77C4×D15—41no—
78C2×C5×Dic3C2311yescharacteristic
79C2×C5×Dic3C2311yescharacteristic
80C2×C5×Dic3C2311yescharacteristic
81C2×C5×Dic3C2311yescharacteristic
82C2×C3×Dic5C2311yescharacteristic
83C2×C3×Dic5C2311yescharacteristic
84C2×C3×Dic5C2311yescharacteristic
85C3×C4×D5—22no—
86C3×C4×D5—41no—
87C3×C4×D5—41no—
88#1204—41no—
89#1202—22no—
90#1202—22no—
91#1200—41no—
92C2×C3×C4⋊C4—51no—
93#930—51no—
94#929—51no—
95#929—51no—
96C4×#67—51no—
97C4×#67—51no—
98#924—51no—
99#898—51no—
100#898—51no—
101#896—51no—
102#896—51no—
103#894—51no—
104#894—51no—
105#889—51no—
106#889D511yescharacteristic, complemented
107C2×D20—31no—
108C2×D20—31no—
109C2×D20—31no—
110C2×C4×D5—31no—
111C2×C4×D5—31no—
112C2×C4×D5C2×D311yescharacteristic
113C2×C4×D5C2×D311yescharacteristic
114C2×C4×D5C2×D311yescharacteristic
115C2×Dic10—31no—
116C5×C4⋊C4—31no—
117C5×C4⋊C4—31no—
118C5×C4⋊C4—31no—
119C5×C4⋊C4—31no—
120C5×C4⋊C4—31no—
121C5×C4⋊C4C2×D311yescharacteristic
122C42×C5—31no—
123#685—31no—
124#685—31no—
125#685—31no—
126#685—31no—
127#685—31no—
128#685—31no—
129#685—31no—
130#685—31no—
131#685—31no—
132#685—31no—
133C4⋊Dic5—31no—
134C4⋊Dic5C2×D311yescharacteristic
135#683—31no—
136#683—31no—
137#683—31no—
138#683—31no—
139#683C2×D311yescharacteristic
140#683C2×D311yescharacteristic
141C4×Dic5—31no—
142#539—151noSylow
143C22×C3×C5C2411yescharacteristic
144C2×D15—21no—
145C2×D15—21no—
146C2×D15—21no—
147C2×D15—21no—
148C2×D15—21no—
149C2×D15—21no—
150C2×C3×D5—21no—
151C2×C3×D5—21no—
152C2×C3×D5#4112yes—
153C3×C4×C5—21no—
154C3×C4×C5—21no—
155C3×C4×C5—21no—
156Dic15—21no—
157Dic15—21no—
158C3×Dic5—21no—
159C3×Dic5—21no—
160C3×Dic5—21no—
161C5×Dic3—21no—
162C5×Dic3—21no—
163C5×Dic3—21no—
164C5×Dic3—21no—
165C22×C3×C4—51no—
166C22×C3×C4—51no—
167C22×C3×C4—51no—
168C2×#67—51no—
169C2×#67—51no—
170C2×D12—51no—
171C2×C4×D3—51no—
172C2×C4×D3—51no—
173C2×Dic6—51no—
174C3×C4⋊C4—51no—
175C3×C4⋊C4—51no—
176C3×C4⋊C4—51no—
177C3×C4⋊C4C2×D511yescharacteristic
178#217—51no—
179#217—51no—
180(C2×D3)⋊C4—51no—
181(C2×D3)⋊C4—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)⋊C4—51no—
188C4⋊Dic3—51no—
189C4⋊Dic3C2×D511yescharacteristic
190Dic3⋊C4—51no—
191Dic3⋊C4—51no—
192Dic3⋊C4—51no—
193Dic3⋊C4—51no—
194Dic3⋊C4C2×D511yescharacteristic
195Dic3⋊C4C2×D511yescharacteristic
196Dic3⋊C4C2×D511yescharacteristic
197Dic3⋊C4C2×D511yescharacteristic
198C4×Dic3—51no—
199C4×Dic3C2×D511yescharacteristic
200C22×D5—31no—
201C22×D5—31no—
202C22×D5C22×D311yescharacteristic
203C2×C4×C5—31no—
204C2×C4×C5—31no—
205C2×C4×C5—31no—
206C2×C4×C5—31no—
207C2×C4×C5C22×D311yescharacteristic
208C2×C4×C5C22×D311yescharacteristic
209C2×C4×C5C22×D311yescharacteristic
210C2×Dic5—31no—
211C2×Dic5—31no—
212C2×Dic5C22×D311yescharacteristic
213C2×Dic5C22×D311yescharacteristic
214C2×Dic5C22×D311yescharacteristic
215D20—62no—
216D20—62no—
217D20—121no—
218C4×D5—22no—
219C4×D5—41no—
220C4×D5—41no—
221C4×D5—121no—
222C4×D5—121no—
223Dic10—121no—
224#126—151no—
225#126—151no—
226#125—31no—
227#125—151no—
228#123—151no—
229#123—151no—
230#123—151no—
231#123—151no—
232C22⋊Q8—151no—
233C22⋊Q8—151no—
234C22⋊Q8—151no—
235#121—151no—
236C4×D4—151no—
237C4×D4—151no—
238C2×C4⋊C4—51no—
239C2×C3×C5C2×#4111yescharacteristic
240C2×C3×C5H(5,𝔽2)11yescharacteristic
241C2×C3×C52−1+411yescharacteristic
242D15—41no—
243D15—41no—
244C3×D5—22no—
245C23×C3—51no—
246C22×D3—51no—
247C22×D3—51no—
248C2×C3×C4—51no—
249C2×C3×C4—51no—
250C2×C3×C4—51no—
251C2×C3×C4—102no—
252C2×C3×C4—201no—
253C2×C3×C4—201no—
254C2×C3×C4C22×D511yescharacteristic
255C2×C3×C4C22×D511yescharacteristic
256C2×C3×C4C22×D511yescharacteristic
257#67—102no—
258#67—102no—
259C2×Dic3—51no—
260C2×Dic3—51no—
261C2×Dic3C22×D511yescharacteristic
262C2×Dic3C22×D511yescharacteristic
263C2×Dic3C22×D511yescharacteristic
264C2×Dic3C22×D511yescharacteristic
265D12—201no—
266C4×D3—201no—
267C4×D3—201no—
268Dic6—201no—
269C22×C5C23×D311yescharacteristic
270C2×D5—21no—
271C2×D5—21no—
272C2×D5—61no—
273C2×D5—61no—
274C2×D5—61no—
275C2×D5—61no—
276C2×D5—61no—
277C2×D5—61no—
278C2×D5#23512yes—
279C4×C5—21no—
280C4×C5—21no—
281C4×C5—21no—
282C4×C5—61no—
283C4×C5—61no—
284C4×C5—61no—
285C4×C5—61no—
286Dic5—21no—
287Dic5—21no—
288Dic5—21no—
289Dic5—61no—
290Dic5—61no—
291C2×Q8—151no—
292C2×D4—151no—
293C2×D4—151no—
294C2×D4—151no—
295C22×C4—51no—
296C22×C4—51no—
297C22×C4—51no—
298C22×C4—151no—
299C22×C4—151no—
300C4⋊C4—31no—
301C4⋊C4—31no—
302C4⋊C4—31no—
303C4⋊C4—31no—
304C4⋊C4—31no—
305C4⋊C4—51no—
306C4⋊C4—51no—
307C4⋊C4—51no—
308C4⋊C4—151no—
309C4⋊C4—151no—
310C4⋊C4—151no—
311C4⋊C4—151no—
312C4⋊C4—151no—
313C4⋊C4D3×D511yescharacteristic
314C22⋊C4—151no—
315C22⋊C4—151no—
316C22⋊C4—151no—
317C22⋊C4—151no—
318C22⋊C4—151no—
319C22⋊C4—151no—
320C22⋊C4—151no—
321C22⋊C4—151no—
322C22⋊C4—151no—
323C22⋊C4—151no—
324C42—31no—
325C42—151no—
326C3×C5#53911yescharacteristic, complemented, Hall
327C22×C3—52no—
328C22×C3—101no—
329C22×C3—101no—
330C22×C3C23×D511yescharacteristic
331C2×D3—101no—
332C2×D3—101no—
333C2×D3—101no—
334C2×D3—101no—
335C2×D3—101no—
336C2×D3—101no—
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—21no—
340C3×C4—101no—
341C3×C4—101no—
342C3×C4—101no—
343Dic3—21no—
344Dic3—21no—
345Dic3—21no—
346Dic3—21no—
347Dic3—101no—
348Dic3—101no—
349C2×C5C2×#23511yescharacteristic
350C2×C5#100411yescharacteristic
351C2×C5#100711yescharacteristic
352D5—22no—
353D5—121no—
354D5—121no—
355C23—51no—
356C23—151no—
357C23—151no—
358Q8—601no—
359D4—302no—
360D4—302no—
361D4—601no—
362C2×C4—31no—
363C2×C4—31no—
364C2×C4—31no—
365C2×C4—31no—
366C2×C4—51no—
367C2×C4—51no—
368C2×C4—51no—
369C2×C4—102no—
370C2×C4—151no—
371C2×C4—151no—
372C2×C4—201no—
373C2×C4—201no—
374C2×C4—601no—
375C2×C4—601no—
376C2×C4C2×D3×D511yescharacteristic
377C2×C4C2×D3×D511yescharacteristic
378C2×C4C2×D3×D511yescharacteristic
379C2×C3—102no—
380C2×C3#414711yescharacteristic
381C2×C3D5×#4111yescharacteristic
382C2×C3#414911yescharacteristic
383D3—201no—
384D3—201no—
385C5#551511yescharacteristic, complemented, Sylow
386C22—52no—
387C22—101no—
388C22—101no—
389C22—301no—
390C22—301no—
391C22—301no—
392C22—301no—
393C22—301no—
394C22—301no—
395C22C22×D3×D511yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—61no—
400C4—61no—
401C4—61no—
402C4—61no—
403C4—101no—
404C4—101no—
405C4—101no—
406C4—301no—
407C4—301no—
408C3#6602611yescharacteristic, complemented, Sylow
409C2—102no—
410C2—601no—
411C2—601no—
412C2D5×#23511yescharacteristic
413C2#9202611yescharacteristic
414C2#9202911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C4⋊C4C22
prime radical#91450C2
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#539
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. #91783C2semidirect
2. C5×#889C2semidirect
3. C3×D5×C4⋊C4C2semidirect
5. #91444C2semidirect
6. C4×#1202C2semidirect
7. #91433C2semidirect
8. #91429C2semidirect
9. #91380C2semidirect
10. #91377C2semidirect
11. #91349C2semidirect
12. #91348C2semidirect
13. #91348C2semidirect
14. #91345C2semidirect
15. #91336C2semidirect
64. D5×C4⋊C4D3semidirect
106. #889D5semidirect
326. C3×C5#539semidirect
385. C5#5515semidirect
408. C3#66026semidirect

Maximal subgroups

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

subgroupindex
#917832
C5×#8892
C3×D5×C4⋊C42
#914502
#914442
C4×#12022
#914332
#914292
#913802
#913772
#913492
#913482
#913452
#913362
#660263
#55155