Finite Group Databasebeta

← #11753934

Subgroups — #11753934

Order 960.

500 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#91784C211yesmaximal, characteristic, complemented
2C5×#898C211yesmaximal, characteristic, complemented
3C3×#4044C211yesmaximal, characteristic, complemented
4#91476C211yesmaximal, characteristic, complemented
5#91476C211yesmaximal, characteristic, complemented
6#91473C211yesmaximal, characteristic, complemented
7#91459C211yesmaximal, characteristic, complemented
8#91438C211yesmaximal, characteristic, complemented
9#91428C211yesmaximal, characteristic, complemented
10#91420C211yesmaximal, characteristic, complemented
11#91418C211yesmaximal, characteristic, complemented
12#91377C211yesmaximal, characteristic, complemented
13#91356C211yesmaximal, characteristic, complemented
14#91353C211yesmaximal, characteristic, complemented
15#91350C211yesmaximal, characteristic, complemented
16#66038—31nomaximal, Hall
17C22×D3×D5C2211yescharacteristic
18C2×D60C2211yescharacteristic
19C2×D60C2211yescharacteristic
20C2×D60C2211yescharacteristic, complemented
21C2×C4×D15C2211yescharacteristic
22C2×#1204C2211yescharacteristic, complemented
23C2×#1203C2211yescharacteristic
24C2×#1203C2211yescharacteristic
25C2×#1202C2211yescharacteristic
26C2×#1202C2211yescharacteristic
27C2×#1200C2211yescharacteristic
28C2×#1200C2211yescharacteristic, complemented
29C2×#1200C2211yescharacteristic, complemented
30C3×C5×C4⋊C4C2211yescharacteristic, complemented
31#6714C2211yescharacteristic, complemented
32#6714C2211yescharacteristic, complemented
33C5×(C2×D3)⋊C4C2211yescharacteristic
34C5×(C2×D3)⋊C4C2211yescharacteristic
35C5×(C2×D3)⋊C4C2211yescharacteristic
36C5×C4⋊Dic3C2211yescharacteristic, complemented
37C5×Dic3⋊C4C2211yescharacteristic, complemented
38C4×C5×Dic3C2211yescharacteristic, complemented
39C3×#685C2211yescharacteristic
40C3×#685C2211yescharacteristic
41C3×#685C2211yescharacteristic
42C3×C4⋊Dic5C2211yescharacteristic, complemented
43C3×#683C2211yescharacteristic, complemented
44C3×C4×Dic5C2211yescharacteristic, complemented
45#6669C2211yescharacteristic, complemented
46#6667C2211yescharacteristic
47#6667C2211yescharacteristic
48#6667C2211yescharacteristic, complemented
49#6667C2211yescharacteristic, complemented
50(C2×D3)⋊Dic5C2211yescharacteristic
51#6665C2211yescharacteristic
52#5704—51nomaximal, Hall
53C5×#126—31no—
54#4044D311yescharacteristic, complemented
55#4042—31no—
56#4041—31no—
57#4041—31no—
58#4040—31no—
59#4039—31no—
60#4031—31no—
61#4030—31no—
62#4029—31no—
63#4028—31no—
64#4028—31no—
65D5×C22⋊C4—31no—
66#4021—31no—
67C4×D20—31no—
68C22×D15C2311yescharacteristic
69C22×D15C2311yescharacteristic
70C22×D15C2311yescharacteristic
71C22×C5×D3C2311yescharacteristic
72C22×C3×D5C2311yescharacteristic
73C2×D3×D5—22no—
74C2×D3×D5—41no—
75C2×D3×D5—41no—
76C2×C3×C4×C5C2311yescharacteristic
77C2×C3×C4×C5C2311yescharacteristic
78C2×C3×C4×C5C2311yescharacteristic
79C2×Dic15C2311yescharacteristic
80D60—22no—
81D60—22no—
82D60—41no—
83C4×D15—41no—
84C2×C5×Dic3C2311yescharacteristic
85C2×C5×Dic3C2311yescharacteristic
86C2×C5×Dic3C2311yescharacteristic
87C2×C3×Dic5C2311yescharacteristic
88C2×C3×Dic5C2311yescharacteristic
89C2×C3×Dic5C2311yescharacteristic
90#1204—41no—
91#1203—41no—
92#1203—41no—
93#1202—41no—
94#1202—41no—
95#1200—41no—
96#1200—41no—
97#1200—41no—
98C3×#126—51no—
99#898D511yescharacteristic, complemented
100#896—51no—
101#895—51no—
102#895—51no—
103#894—51no—
104#893—51no—
105#885—51no—
106#884—51no—
107#883—51no—
108#882—51no—
109#882—51no—
110D3×C22⋊C4—51no—
111#875—51no—
112C4×D12—51no—
113C23×D5—31no—
114C2×C22⋊D5—31no—
115C2×C22⋊D5—31no—
116C2×D20—31no—
117C2×D20—31no—
118C2×D20—31no—
119C2×D20—31no—
120C2×D20—31no—
121C2×C4×D5—31no—
122C2×C4×D5—31no—
123C2×C4×D5—31no—
124C2×C4×D5—31no—
125C2×Dic10—31no—
126C5×C4⋊C4—31no—
127C5×C4⋊C4—31no—
128C5×C4⋊C4C2×D311yescharacteristic, complemented
129C5×C22⋊C4—31no—
130C5×C22⋊C4—31no—
131C5×C22⋊C4—31no—
132C42×C5—31no—
133C22⋊Dic5—31no—
134#685—31no—
135#685—31no—
136#685—31no—
137#685—31no—
138#685—31no—
139#685—31no—
140#685—31no—
141#685C2×D311yescharacteristic
142#685C2×D311yescharacteristic
143#685C2×D311yescharacteristic
144C4⋊Dic5C2×D311yescharacteristic, complemented
145#683—31no—
146#683C2×D311yescharacteristic, complemented
147C4×Dic5C2×D311yescharacteristic, complemented
148#538—151noSylow
149C22×C3×C5C2411yescharacteristic
150C2×D15—21no—
151C2×D15—21no—
152C2×D15—21no—
153C2×D15—21no—
154C2×D15—21no—
155C2×D15—21no—
156C2×D15—21no—
157C2×D15—21no—
158C2×D15#4112yes—
159C2×C5×D3—21no—
160C2×C5×D3—21no—
161C2×C5×D3—21no—
162C2×C3×D5—21no—
163C2×C3×D5—21no—
164C2×C3×D5—21no—
165D3×D5—44no—
166C3×C4×C5—21no—
167C3×C4×C5—21no—
168C3×C4×C5—21no—
169Dic15—21no—
170C3×Dic5—21no—
171C3×Dic5—21no—
172C3×Dic5—21no—
173C5×Dic3—21no—
174C5×Dic3—21no—
175C5×Dic3—21no—
176C23×D3—51no—
177C2×#67—51no—
178C2×#67—51no—
179C2×D12—51no—
180C2×D12—51no—
181C2×D12—51no—
182C2×D12—51no—
183C2×D12—51no—
184C2×C4×D3—51no—
185C2×C4×D3—51no—
186C2×C4×D3—51no—
187C2×C4×D3—51no—
188C2×Dic6—51no—
189C3×C4⋊C4—51no—
190C3×C4⋊C4—51no—
191C3×C4⋊C4C2×D511yescharacteristic, complemented
192C3×C22⋊C4—51no—
193C3×C22⋊C4—51no—
194C3×C22⋊C4—51no—
195C3×C42—51no—
196#217—51no—
197(C2×D3)⋊C4—51no—
198(C2×D3)⋊C4—51no—
199(C2×D3)⋊C4—51no—
200(C2×D3)⋊C4—51no—
201(C2×D3)⋊C4—51no—
202(C2×D3)⋊C4—51no—
203(C2×D3)⋊C4—51no—
204(C2×D3)⋊C4C2×D511yescharacteristic
205(C2×D3)⋊C4C2×D511yescharacteristic
206(C2×D3)⋊C4C2×D511yescharacteristic
207C4⋊Dic3C2×D511yescharacteristic, complemented
208Dic3⋊C4—51no—
209Dic3⋊C4C2×D511yescharacteristic, complemented
210C4×Dic3C2×D511yescharacteristic, complemented
211C23×C5—31no—
212C22×D5—31no—
213C22×D5—31no—
214C22×D5—31no—
215C22×D5—62no—
216C22×D5—121no—
217C22×D5—121no—
218C22×D5C22×D311yescharacteristic
219C2×C4×C5—31no—
220C2×C4×C5—31no—
221C2×C4×C5—31no—
222C2×C4×C5C22×D311yescharacteristic
223C2×C4×C5C22×D311yescharacteristic
224C2×C4×C5C22×D311yescharacteristic
225C22⋊D5—121no—
226C22⋊D5—121no—
227C2×Dic5—31no—
228C2×Dic5C22×D311yescharacteristic
229C2×Dic5C22×D311yescharacteristic
230C2×Dic5C22×D311yescharacteristic
231D20—62no—
232D20—62no—
233D20—121no—
234D20—121no—
235D20—121no—
236C4×D5—121no—
237C4×D5—121no—
238C4×D5—121no—
239C4×D5—121no—
240Dic10—121no—
241#126—31no—
242#126—51no—
243#124—151no—
244#124—151no—
245#123—151no—
246#123—151no—
247C22⋊Q8—151no—
248#121—151no—
249#121—151no—
250#121—151no—
251#120—151no—
252#120—151no—
253C4×D4—151no—
254C4×D4—151no—
255C2×C22⋊C4—151no—
256C2×C3×C5C2×#4111yescharacteristic
257C2×C3×C5H(5,𝔽2)11yescharacteristic
258C2×C3×C5H(5,𝔽2)11yescharacteristic
259D15—22no—
260D15—41no—
261D15—41no—
262C3×D5—41no—
263C5×D3—41no—
264C23×C3—51no—
265C22×D3—51no—
266C22×D3—51no—
267C22×D3—51no—
268C22×D3—102no—
269C22×D3—201no—
270C22×D3—201no—
271C22×D3C22×D511yescharacteristic
272C2×C3×C4—51no—
273C2×C3×C4—51no—
274C2×C3×C4—51no—
275C2×C3×C4C22×D511yescharacteristic
276C2×C3×C4C22×D511yescharacteristic
277C2×C3×C4C22×D511yescharacteristic
278#67—201no—
279#67—201no—
280C2×Dic3—51no—
281C2×Dic3C22×D511yescharacteristic
282C2×Dic3C22×D511yescharacteristic
283C2×Dic3C22×D511yescharacteristic
284D12—102no—
285D12—102no—
286D12—201no—
287D12—201no—
288D12—201no—
289C4×D3—201no—
290C4×D3—201no—
291C4×D3—201no—
292C4×D3—201no—
293Dic6—201no—
294C22×C5—61no—
295C22×C5—61no—
296C22×C5—61no—
297C22×C5C23×D311yescharacteristic
298C2×D5—21no—
299C2×D5—21no—
300C2×D5—21no—
301C2×D5—32no—
302C2×D5—61no—
303C2×D5—61no—
304C2×D5—61no—
305C2×D5—61no—
306C2×D5—61no—
307C2×D5—61no—
308C2×D5—61no—
309C2×D5—61no—
310C2×D5—124no—
311C4×C5—21no—
312C4×C5—21no—
313C4×C5—21no—
314C4×C5—61no—
315C4×C5—61no—
316C4×C5—61no—
317Dic5—21no—
318Dic5—21no—
319Dic5—21no—
320Dic5—61no—
321C24—151no—
322C2×Q8—151no—
323C2×D4—151no—
324C2×D4—151no—
325C2×D4—151no—
326C2×D4—151no—
327C2×D4—151no—
328C2×D4—151no—
329C2×D4—151no—
330C22×C4—151no—
331C22×C4—151no—
332C22×C4—151no—
333C22×C4—151no—
334C4⋊C4—31no—
335C4⋊C4—31no—
336C4⋊C4—51no—
337C4⋊C4—51no—
338C4⋊C4—151no—
339C4⋊C4D3×D511yescharacteristic, complemented
340C22⋊C4—31no—
341C22⋊C4—31no—
342C22⋊C4—31no—
343C22⋊C4—51no—
344C22⋊C4—51no—
345C22⋊C4—51no—
346C22⋊C4—151no—
347C22⋊C4—151no—
348C22⋊C4—151no—
349C22⋊C4—151no—
350C22⋊C4—151no—
351C22⋊C4—151no—
352C22⋊C4—151no—
353C22⋊C4—151no—
354C42—31no—
355C42—51no—
356C3×C5#53811yescharacteristic, complemented, Hall
357C22×C3—101no—
358C22×C3—101no—
359C22×C3—101no—
360C22×C3C23×D511yescharacteristic
361C2×D3—21no—
362C2×D3—21no—
363C2×D3—21no—
364C2×D3—52no—
365C2×D3—101no—
366C2×D3—101no—
367C2×D3—101no—
368C2×D3—101no—
369C2×D3—101no—
370C2×D3—101no—
371C2×D3—101no—
372C2×D3—101no—
373C2×D3—204no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—101no—
378C3×C4—101no—
379C3×C4—101no—
380Dic3—21no—
381Dic3—21no—
382Dic3—21no—
383Dic3—101no—
384C2×C5—121no—
385C2×C5D3×#4111yescharacteristic
386C2×C5#100911yescharacteristic
387C2×C5#100911yescharacteristic
388D5—41no—
389D5—62no—
390D5—121no—
391D5—121no—
392C23—31no—
393C23—51no—
394C23—151no—
395C23—151no—
396C23—151no—
397C23—302no—
398C23—601no—
399C23—601no—
400Q8—601no—
401D4—302no—
402D4—302no—
403D4—601no—
404D4—601no—
405D4—601no—
406D4—601no—
407D4—601no—
408C2×C4—31no—
409C2×C4—31no—
410C2×C4—31no—
411C2×C4—51no—
412C2×C4—51no—
413C2×C4—51no—
414C2×C4—151no—
415C2×C4—601no—
416C2×C4—601no—
417C2×C4—601no—
418C2×C4—601no—
419C2×C4C2×D3×D511yescharacteristic
420C2×C4C2×D3×D511yescharacteristic
421C2×C4C2×D3×D511yescharacteristic
422C2×C3—201no—
423C2×C3D5×#4111yescharacteristic
424C2×C3#414911yescharacteristic
425C2×C3#414911yescharacteristic
426D3—41no—
427D3—102no—
428D3—201no—
429D3—201no—
430C5#570411yescharacteristic, complemented, Sylow
431C22—61no—
432C22—61no—
433C22—61no—
434C22—101no—
435C22—101no—
436C22—101no—
437C22—152no—
438C22—301no—
439C22—301no—
440C22—301no—
441C22—301no—
442C22—301no—
443C22—301no—
444C22—301no—
445C22—301no—
446C22—604no—
447C22C22×D3×D511yescharacteristic
448C4—21no—
449C4—21no—
450C4—21no—
451C4—61no—
452C4—61no—
453C4—61no—
454C4—101no—
455C4—101no—
456C4—101no—
457C4—301no—
458C3#6603811yescharacteristic, complemented, Sylow
459C2—121no—
460C2—201no—
461C2—302no—
462C2—601no—
463C2—601no—
464C2#9201911yescharacteristic
465C2#9202411yescharacteristic
466C2#9203511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C4⋊C4C22
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#538
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×#898C2semidirect
3. C3×#4044C2semidirect
4. #91476C2semidirect
5. #91476C2semidirect
6. #91473C2semidirect
7. #91459C2semidirect
8. #91438C2semidirect
9. #91428C2semidirect
10. #91420C2semidirect
11. #91418C2semidirect
12. #91377C2semidirect
13. #91356C2semidirect
14. #91353C2semidirect
15. #91350C2semidirect
20. C2×D60C22semidirect
22. C2×#1204C22semidirect
28. C2×#1200C22semidirect
29. C2×#1200C22semidirect
30. C3×C5×C4⋊C4C22semidirect
31. #6714C22semidirect
32. #6714C22semidirect
36. C5×C4⋊Dic3C22semidirect
37. C5×Dic3⋊C4C22semidirect
38. C4×C5×Dic3C22semidirect
42. C3×C4⋊Dic5C22semidirect
43. C3×#683C22semidirect
44. C3×C4×Dic5C22semidirect
45. #6669C22semidirect
48. #6667C22semidirect
49. #6667C22semidirect
54. #4044D3semidirect
99. #898D5semidirect
128. C5×C4⋊C4C2×D3semidirect
144. C4⋊Dic5C2×D3semidirect
146. #683C2×D3semidirect
147. C4×Dic5C2×D3semidirect
191. C3×C4⋊C4C2×D5semidirect
207. C4⋊Dic3C2×D5semidirect
209. Dic3⋊C4C2×D5semidirect
210. C4×Dic3C2×D5semidirect
339. C4⋊C4D3×D5semidirect
356. C3×C5#538semidirect
430. C5#5704semidirect
458. C3#66038semidirect

Maximal subgroups

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

subgroupindex
#917842
C5×#8982
C3×#40442
#914762
#914732
#914592
#914382
#914282
#914202
#914182
#913772
#913562
#913532
#913502
#660383
#57045