Finite Group Databasebeta

← #11753820

Subgroups — #11753820

Order 960.

440 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#91784C211yesmaximal, characteristic, complemented
2C5×#889C211yesmaximal, characteristic, complemented
3C3×#4042C211yesmaximal, characteristic, complemented
4#91459C211yesmaximal, characteristic, complemented
5#91459C211yesmaximal, characteristic, complemented
6#91450C211yesmaximal, characteristic, complemented
7#91433C211yesmaximal, characteristic, complemented
8#91433C211yesmaximal, characteristic, complemented
9#91419C211yesmaximal, characteristic, complemented
10#91411C211yesmaximal, characteristic, complemented
11#91377C211yesmaximal, characteristic, complemented
12#91374C211yesmaximal, characteristic, complemented
13#91354C211yesmaximal, characteristic, complemented
14#91353C211yesmaximal, characteristic, complemented
15#91348C211yesmaximal, characteristic, complemented
16#66034—31nomaximal, Hall
17C2×D60C2211yescharacteristic
18C2×D60C2211yescharacteristic
19C2×D60C2211yescharacteristic
20C2×C4×D15C2211yescharacteristic
21C2×C3×C4×D5C2211yescharacteristic
22C2×C3×Dic10C2211yescharacteristic
23C2×#1204C2211yescharacteristic
24C2×#1202C2211yescharacteristic
25C2×#1202C2211yescharacteristic
26C2×#1202C2211yescharacteristic
27C2×#1200C2211yescharacteristic
28C2×#1200C2211yescharacteristic
29C3×C5×C4⋊C4C2211yescharacteristic
30#6714C2211yescharacteristic
31#6714C2211yescharacteristic
32C5×C4⋊Dic3C2211yescharacteristic
33C5×Dic3⋊C4C2211yescharacteristic
34C5×Dic3⋊C4C2211yescharacteristic
35C5×Dic3⋊C4C2211yescharacteristic
36C5×Dic3⋊C4C2211yescharacteristic
37C4×C5×Dic3C2211yescharacteristic
38C3×#685C2211yescharacteristic
39C3×#685C2211yescharacteristic
40C3×#683C2211yescharacteristic
41C3×#683C2211yescharacteristic
42#6669C2211yescharacteristic
43#6668C2211yescharacteristic
44#6667C2211yescharacteristic
45#6667C2211yescharacteristic
46#6667C2211yescharacteristic
47#6667C2211yescharacteristic
48#6667C2211yescharacteristic
49#6667C2211yescharacteristic
50#6667C2211yescharacteristic
51#6665C2211yescharacteristic
52#5647—51nomaximal, Hall
53C5×#125—31no—
54#4042—31no—
55#4042—31no—
56#4042—31no—
57#4042D311yescharacteristic, complemented
58#4041—31no—
59#4041—31no—
60#4041—31no—
61#4041—31no—
62#4040—31no—
63#4040—31no—
64#4040—31no—
65#4040—31no—
66#4021—31no—
67#4021—31no—
68C22×D15C2311yescharacteristic
69C22×D15C2311yescharacteristic
70C22×D15C2311yescharacteristic
71C22×C3×D5C2311yescharacteristic
72C2×C3×C4×C5C2311yescharacteristic
73C2×C3×C4×C5C2311yescharacteristic
74C2×C3×C4×C5C2311yescharacteristic
75C2×Dic15C2311yescharacteristic
76D60—41no—
77D60—41no—
78D60—41no—
79C4×D15—41no—
80C2×C5×Dic3C2311yescharacteristic
81C2×C5×Dic3C2311yescharacteristic
82C2×C5×Dic3C2311yescharacteristic
83C2×C5×Dic3C2311yescharacteristic
84C2×C3×Dic5C2311yescharacteristic
85C2×C3×Dic5C2311yescharacteristic
86C2×C3×Dic5C2311yescharacteristic
87C3×C4×D5—41no—
88C3×Dic10—41no—
89#1204—41no—
90#1202—41no—
91#1202—41no—
92#1202—41no—
93#1200—41no—
94#1200—41no—
95C3×C22⋊Q8—51no—
96#947—51no—
97#946—51no—
98#930—51no—
99#929—51no—
100#897—51no—
101#896—51no—
102#895—51no—
103#894—51no—
104#894—51no—
105#889D511yescharacteristic, complemented
106#885—51no—
107#884—51no—
108#884—51no—
109#883—51no—
110C2×D20—31no—
111C2×D20—31no—
112C2×D20—31no—
113C2×D20—31no—
114C2×D20—31no—
115C2×D20—31no—
116C2×C4×D5—31no—
117C2×C4×D5—31no—
118C2×C4×D5—31no—
119C2×C4×D5C2×D311yescharacteristic
120C2×Dic10—31no—
121C2×Dic10C2×D311yescharacteristic
122C5×C4⋊C4—31no—
123C5×C4⋊C4—31no—
124C5×C4⋊C4—31no—
125C5×C4⋊C4—31no—
126C5×C4⋊C4—31no—
127C5×C4⋊C4C2×D311yescharacteristic
128C42×C5—31no—
129#685—31no—
130#685—31no—
131#685—31no—
132#685—31no—
133#685—31no—
134#685—31no—
135#685—31no—
136#685—31no—
137#685—31no—
138#685—31no—
139#685C2×D311yescharacteristic
140#685C2×D311yescharacteristic
141#683—31no—
142#683—31no—
143#683C2×D311yescharacteristic
144#683C2×D311yescharacteristic
145#562—151noSylow
146C22×C3×C5C2411yescharacteristic
147C2×D15—21no—
148C2×D15—21no—
149C2×D15—21no—
150C2×D15—21no—
151C2×D15—21no—
152C2×D15—21no—
153C2×D15—21no—
154C2×D15—21no—
155C2×D15—21no—
156C2×C3×D5—21no—
157C2×C3×D5—21no—
158C2×C3×D5—21no—
159C3×C4×C5—21no—
160C3×C4×C5—21no—
161C3×C4×C5—21no—
162Dic15—21no—
163C3×Dic5—21no—
164C3×Dic5—21no—
165C3×Dic5—21no—
166C5×Dic3—21no—
167C5×Dic3—21no—
168C5×Dic3—21no—
169C5×Dic3—21no—
170C2×C3×Q8—51no—
171C22×C3×C4—51no—
172C2×#67—51no—
173C2×#67—51no—
174C2×#67—51no—
175C2×D12—51no—
176C2×D12—51no—
177C2×D12—51no—
178C2×C4×D3—51no—
179C2×C4×D3—51no—
180C2×C4×D3—51no—
181C2×Dic6—51no—
182C3×C4⋊C4—51no—
183C3×C4⋊C4—51no—
184C3×C4⋊C4C2×D511yescharacteristic
185C3×C22⋊C4—51no—
186C3×C22⋊C4—51no—
187#217—51no—
188(C2×D3)⋊C4—51no—
189(C2×D3)⋊C4—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—
197C4⋊Dic3—51no—
198C4⋊Dic3C2×D511yescharacteristic
199Dic3⋊C4—51no—
200Dic3⋊C4C2×D511yescharacteristic
201Dic3⋊C4C2×D511yescharacteristic
202Dic3⋊C4C2×D511yescharacteristic
203Dic3⋊C4C2×D511yescharacteristic
204C4×Dic3C2×D511yescharacteristic
205C22×D5—31no—
206C22×D5—31no—
207C22×D5—31no—
208C22×D5C22×D311yescharacteristic
209C2×C4×C5—31no—
210C2×C4×C5—31no—
211C2×C4×C5—31no—
212C2×C4×C5—31no—
213C2×C4×C5C22×D311yescharacteristic
214C2×C4×C5C22×D311yescharacteristic
215C2×C4×C5C22×D311yescharacteristic
216C2×Dic5—31no—
217C2×Dic5C22×D311yescharacteristic
218C2×Dic5C22×D311yescharacteristic
219C2×Dic5C22×D311yescharacteristic
220D20—121no—
221D20—121no—
222D20—121no—
223D20—121no—
224D20—121no—
225D20—121no—
226C4×D5—41no—
227C4×D5—121no—
228C4×D5—121no—
229C4×D5—121no—
230Dic10—41no—
231Dic10—121no—
232#125—31no—
233#124—151no—
234#124—151no—
235#123—151no—
236#123—151no—
237#123—151no—
238#123—151no—
239C22⋊Q8—51no—
240C22⋊Q8—151no—
241C22⋊Q8—151no—
242C22⋊Q8—151no—
243#121—151no—
244#121—151no—
245#121—151no—
246#121—151no—
247C2×C3×C5H(5,𝔽2)11yescharacteristic
248C2×C3×C5H(5,𝔽2)11yescharacteristic
249C2×C3×C52−1+411yescharacteristic
250D15—41no—
251D15—41no—
252D15—41no—
253C3×D5—41no—
254C23×C3—51no—
255C22×D3—51no—
256C22×D3—51no—
257C22×D3—51no—
258C3×Q8—201no—
259C2×C3×C4—51no—
260C2×C3×C4—51no—
261C2×C3×C4—51no—
262C2×C3×C4—201no—
263C2×C3×C4C22×D511yescharacteristic
264C2×C3×C4C22×D511yescharacteristic
265C2×C3×C4C22×D511yescharacteristic
266#67—201no—
267#67—201no—
268#67—201no—
269C2×Dic3—51no—
270C2×Dic3C22×D511yescharacteristic
271C2×Dic3C22×D511yescharacteristic
272C2×Dic3C22×D511yescharacteristic
273C2×Dic3C22×D511yescharacteristic
274D12—201no—
275D12—201no—
276D12—201no—
277C4×D3—201no—
278C4×D3—201no—
279C4×D3—201no—
280Dic6—201no—
281C22×C5C23×D311yescharacteristic
282C2×D5—21no—
283C2×D5—21no—
284C2×D5—21no—
285C2×D5—61no—
286C2×D5—61no—
287C2×D5—61no—
288C2×D5—61no—
289C2×D5—61no—
290C2×D5—61no—
291C2×D5—61no—
292C2×D5—61no—
293C2×D5—61no—
294C4×C5—21no—
295C4×C5—21no—
296C4×C5—21no—
297C4×C5—61no—
298C4×C5—61no—
299C4×C5—61no—
300C4×C5—61no—
301Dic5—21no—
302Dic5—21no—
303Dic5—21no—
304Dic5—61no—
305C2×Q8—51no—
306C2×Q8—151no—
307C2×D4—151no—
308C2×D4—151no—
309C2×D4—151no—
310C2×D4—151no—
311C2×D4—151no—
312C2×D4—151no—
313C22×C4—51no—
314C22×C4—151no—
315C22×C4—151no—
316C22×C4—151no—
317C4⋊C4—31no—
318C4⋊C4—31no—
319C4⋊C4—31no—
320C4⋊C4—31no—
321C4⋊C4—31no—
322C4⋊C4—51no—
323C4⋊C4—51no—
324C4⋊C4—151no—
325C4⋊C4—151no—
326C4⋊C4D3×D511yescharacteristic
327C22⋊C4—51no—
328C22⋊C4—51no—
329C22⋊C4—151no—
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—
340C3×C5#56211yescharacteristic, complemented, Hall
341C22×C3—101no—
342C22×C3—101no—
343C22×C3—101no—
344C22×C3C23×D511yescharacteristic
345C2×D3—101no—
346C2×D3—101no—
347C2×D3—101no—
348C2×D3—101no—
349C2×D3—101no—
350C2×D3—101no—
351C2×D3—101no—
352C2×D3—101no—
353C2×D3—101no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—101no—
358C3×C4—101no—
359C3×C4—101no—
360Dic3—21no—
361Dic3—21no—
362Dic3—21no—
363Dic3—21no—
364Dic3—101no—
365C2×C5#100411yescharacteristic
366C2×C5#100711yescharacteristic
367C2×C5#100911yescharacteristic
368D5—41no—
369D5—121no—
370D5—121no—
371D5—121no—
372C23—51no—
373C23—151no—
374C23—151no—
375C23—151no—
376Q8—201no—
377Q8—601no—
378D4—601no—
379D4—601no—
380D4—601no—
381D4—601no—
382D4—601no—
383D4—601no—
384C2×C4—31no—
385C2×C4—31no—
386C2×C4—31no—
387C2×C4—31no—
388C2×C4—51no—
389C2×C4—51no—
390C2×C4—51no—
391C2×C4—151no—
392C2×C4—201no—
393C2×C4—601no—
394C2×C4—601no—
395C2×C4—601no—
396C2×C4C2×D3×D511yescharacteristic
397C2×C4C2×D3×D511yescharacteristic
398C2×C4C2×D3×D511yescharacteristic
399C2×C3—201no—
400C2×C3#414711yescharacteristic
401C2×C3#414911yescharacteristic
402C2×C3#414911yescharacteristic
403D3—201no—
404D3—201no—
405D3—201no—
406C5#564711yescharacteristic, complemented, Sylow
407C22—101no—
408C22—101no—
409C22—101no—
410C22—301no—
411C22—301no—
412C22—301no—
413C22—301no—
414C22—301no—
415C22—301no—
416C22—301no—
417C22—301no—
418C22—301no—
419C22C22×D3×D511yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—61no—
424C4—61no—
425C4—61no—
426C4—61no—
427C4—101no—
428C4—101no—
429C4—101no—
430C4—301no—
431C3#6603411yescharacteristic, complemented, Sylow
432C2—201no—
433C2—601no—
434C2—601no—
435C2—601no—
436C2#9201911yescharacteristic
437C2#9202611yescharacteristic
438C2#9202911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C4⋊C4C22
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#562
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. #91784C2semidirect
2. C5×#889C2semidirect
3. C3×#4042C2semidirect
4. #91459C2semidirect
5. #91459C2semidirect
6. #91450C2semidirect
7. #91433C2semidirect
8. #91433C2semidirect
9. #91419C2semidirect
10. #91411C2semidirect
11. #91377C2semidirect
12. #91374C2semidirect
13. #91354C2semidirect
14. #91353C2semidirect
15. #91348C2semidirect
57. #4042D3semidirect
105. #889D5semidirect
340. C3×C5#562semidirect
406. C5#5647semidirect
431. C3#66034semidirect

Maximal subgroups

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

subgroupindex
#917842
C5×#8892
C3×#40422
#914592
#914502
#914332
#914192
#914112
#913772
#913742
#913542
#913532
#913482
#660343
#56475