Finite Group Databasebeta

← #11753153

Subgroups — #11753153

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
1C22⋊C4×D15C211yesmaximal, characteristic, complemented
2C5×#883C211yesmaximal, characteristic, complemented
3C3×#4031C211yesmaximal, characteristic, complemented
4#91573C211yesmaximal, characteristic, complemented
5#91572C211yesmaximal, characteristic, complemented
6#91549C211yesmaximal, characteristic, complemented
7#91530C211yesmaximal, characteristic, complemented
8#91461C211yesmaximal, characteristic, complemented
9#91454C211yesmaximal, characteristic, complemented
10C4×#1203C211yesmaximal, characteristic, complemented
11#91413C211yesmaximal, characteristic, complemented
12#91396C211yesmaximal, characteristic, complemented
13#91390C211yesmaximal, characteristic, complemented
14#91387C211yesmaximal, characteristic, complemented
15#91326C211yesmaximal, characteristic, complemented
16#65991—31nomaximal, Hall
17C23×D15C2211yescharacteristic
18C2×C4×D15C2211yescharacteristic
19C2×C4×D15C2211yescharacteristic
20C2×C5×#67C2211yescharacteristic
21C2×C4×C5×D3C2211yescharacteristic, complemented
22C2×C3×C22⋊D5C2211yescharacteristic
23C2×C3×Dic10C2211yescharacteristic, complemented
24C2×#1203C2211yescharacteristic
25C2×#1203C2211yescharacteristic
26C2×#1202C2211yescharacteristic
27C2×#1202C2211yescharacteristic
28C2×#1201C2211yescharacteristic, complemented
29C2×D5×Dic3C2211yescharacteristic, complemented
30C3×C5×C22⋊C4C2211yescharacteristic
31#6719C2211yescharacteristic
32#6714C2211yescharacteristic
33#6714C2211yescharacteristic
34C5×#217C2211yescharacteristic
35C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
36C5×C4⋊Dic3C2211yescharacteristic, complemented
37C5×Dic3⋊C4C2211yescharacteristic, complemented
38C3×C22⋊Dic5C2211yescharacteristic
39C3×#685C2211yescharacteristic, complemented
40C3×#685C2211yescharacteristic, complemented
41C3×C4×Dic5C2211yescharacteristic, complemented
42Dic3⋊Dic5C2211yescharacteristic, complemented
43Dic3⋊Dic5C2211yescharacteristic, complemented
44#6669C2211yescharacteristic, complemented
45#6668C2211yescharacteristic, complemented
46#6667C2211yescharacteristic
47#6667C2211yescharacteristic
48#6667C2211yescharacteristic
49#6667C2211yescharacteristic
50(C2×D3)⋊Dic5C2211yescharacteristic, complemented
51Dic3×Dic5C2211yescharacteristic, complemented
52#5678—51nomaximal, Hall
53C5×#123—31no—
54#4084—31no—
55#4083—31no—
56#4076—31no—
57C4×C22⋊D5—31no—
58#4044—31no—
59#4043—31no—
60#4040—31no—
61#4039—31no—
62#4031—31no—
63#4031D311yescharacteristic, complemented
64#4030—31no—
65#4028—31no—
66D5×C22⋊C4—31no—
67#4025—31no—
68C23×C3×C5C2311yescharacteristic
69C22×D15—22no—
70C22×D15—41no—
71C22×D15—41no—
72C22×D15C2311yescharacteristic
73C22×D15C2311yescharacteristic
74C22×C5×D3C2311yescharacteristic
75C22×C3×D5C2311yescharacteristic
76C2×C3×C4×C5C2311yescharacteristic
77C2×C3×C4×C5C2311yescharacteristic
78C2×Dic15C2311yescharacteristic
79C2×Dic15C2311yescharacteristic
80C4×D15—41no—
81C4×D15—41no—
82C5×#67—41no—
83C2×C5×Dic3C2311yescharacteristic
84C2×C5×Dic3C2311yescharacteristic
85C2×C5×Dic3C2311yescharacteristic
86C4×C5×D3—41no—
87C3×C22⋊D5—41no—
88C2×C3×Dic5C2311yescharacteristic
89C2×C3×Dic5C2311yescharacteristic
90C2×C3×Dic5C2311yescharacteristic
91C3×Dic10—41no—
92#1203—22no—
93#1203—41no—
94#1202—22no—
95#1202—41no—
96#1201—41no—
97D5×Dic3—41no—
98C3×#124—51no—
99#947—51no—
100#946—51no—
101#939—51no—
102#937—51no—
103#886—51no—
104#884—51no—
105#884—51no—
106#883D511yescharacteristic, complemented
107#882—51no—
108#67⋊C4—51no—
109D3×C22⋊C4—51no—
110#879—51no—
111#876—51no—
112C4×D12—51no—
113C23×D5—31no—
114C2×C5×D4—31no—
115C22×C4×C5—31no—
116C2×C22⋊D5—31no—
117C2×C22⋊D5—31no—
118C2×C22⋊D5—31no—
119C2×C22⋊D5C2×D311yescharacteristic
120C2×D20—31no—
121C2×D20—31no—
122C2×C4×D5—31no—
123C2×C4×D5—31no—
124C2×C4×D5—31no—
125C2×Dic10C2×D311yescharacteristic, complemented
126C5×C4⋊C4—31no—
127C5×C4⋊C4—31no—
128C5×C22⋊C4—31no—
129C5×C22⋊C4—31no—
130C5×C22⋊C4C2×D311yescharacteristic
131C22⋊Dic5—31no—
132C22⋊Dic5—31no—
133C22⋊Dic5C2×D311yescharacteristic
134#685—31no—
135#685—31no—
136#685—31no—
137#685—31no—
138#685—31no—
139#685—31no—
140#685C2×D311yescharacteristic, complemented
141#685C2×D311yescharacteristic, complemented
142C4⋊Dic5—31no—
143C4⋊Dic5—31no—
144#683—31no—
145#683—31no—
146C4×Dic5—31no—
147C4×Dic5C2×D311yescharacteristic, complemented
148#538—151noSylow
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5—21no—
152C22×C3×C5C2411yescharacteristic
153C2×D15—21no—
154C2×D15—21no—
155C2×D15—21no—
156C2×D15—21no—
157C2×D15—21no—
158C2×D15—44no—
159C2×D15#4112yes—
160C2×C5×D3—21no—
161C2×C5×D3—21no—
162C2×C5×D3—21no—
163C2×C3×D5—21no—
164C2×C3×D5—21no—
165C2×C3×D5—21no—
166C3×C4×C5—21no—
167C3×C4×C5—21no—
168Dic15—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×C3×Q8—51no—
178C2×C3×D4—51no—
179C2×#67—51no—
180C2×#67—51no—
181C2×#67—51no—
182C2×#67C2×D511yescharacteristic
183C22×Dic3—51no—
184C2×D12—51no—
185C2×D12—51no—
186C2×C4×D3—51no—
187C2×C4×D3—51no—
188C2×C4×D3C2×D511yescharacteristic, complemented
189C3×C22⋊C4—51no—
190C3×C22⋊C4—51no—
191C3×C22⋊C4—51no—
192C3×C22⋊C4C2×D511yescharacteristic
193C3×C42—51no—
194#217—51no—
195#217C2×D511yescharacteristic
196(C2×D3)⋊C4—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)⋊C4C2×D511yescharacteristic, complemented
204C4⋊Dic3—51no—
205C4⋊Dic3C2×D511yescharacteristic, complemented
206Dic3⋊C4—51no—
207Dic3⋊C4—51no—
208Dic3⋊C4—51no—
209Dic3⋊C4C2×D511yescharacteristic, complemented
210C4×Dic3—51no—
211C23×C5—31no—
212C23×C5C22×D311yescharacteristic
213C22×D5—31no—
214C22×D5—31no—
215C22×D5—62no—
216C22×D5—121no—
217C22×D5—121no—
218C22×D5C22×D311yescharacteristic
219C5×D4—121no—
220C2×C4×C5—31no—
221C2×C4×C5—31no—
222C2×C4×C5—31no—
223C2×C4×C5—121no—
224C2×C4×C5C22×D311yescharacteristic
225C2×C4×C5C22×D311yescharacteristic
226C22⋊D5—41no—
227C22⋊D5—62no—
228C22⋊D5—121no—
229C22⋊D5—121no—
230C2×Dic5—31no—
231C2×Dic5—31no—
232C2×Dic5C22×D311yescharacteristic
233C2×Dic5C22×D311yescharacteristic
234C2×Dic5C22×D311yescharacteristic
235D20—62no—
236D20—121no—
237C4×D5—121no—
238C4×D5—121no—
239C4×D5—121no—
240Dic10—41no—
241#126—151no—
242#126—151no—
243#124—51no—
244#124—151no—
245#123—31no—
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×C5—41no—
257C2×C3×C5C2×#4111yescharacteristic
258C2×C3×C5H(5,𝔽2)11yescharacteristic
259C2×C3×C5H(5,𝔽2)11yescharacteristic
260D15—22no—
261D15—41no—
262C3×D5—41no—
263C5×D3—41no—
264C23×C3—51no—
265C23×C3C22×D511yescharacteristic
266C22×D3—51no—
267C22×D3—51no—
268C22×D3—102no—
269C22×D3—201no—
270C22×D3—201no—
271C22×D3C22×D511yescharacteristic
272C3×Q8—201no—
273C3×D4—201no—
274C2×C3×C4—51no—
275C2×C3×C4—51no—
276C2×C3×C4—51no—
277C2×C3×C4C22×D511yescharacteristic
278C2×C3×C4C22×D511yescharacteristic
279#67—41no—
280#67—102no—
281#67—201no—
282#67—201no—
283C2×Dic3—51no—
284C2×Dic3—51no—
285C2×Dic3—201no—
286C2×Dic3C22×D511yescharacteristic
287C2×Dic3C22×D511yescharacteristic
288C2×Dic3C22×D511yescharacteristic
289D12—102no—
290D12—201no—
291C4×D3—41no—
292C4×D3—201no—
293C4×D3—201no—
294C22×C5—21no—
295C22×C5—21no—
296C22×C5—21no—
297C22×C5—61no—
298C22×C5—61no—
299C22×C5—61no—
300C22×C5C23×D311yescharacteristic
301C2×D5—21no—
302C2×D5—21no—
303C2×D5—21no—
304C2×D5—32no—
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—61no—
314C4×C5—61no—
315C4×C5—61no—
316Dic5—21no—
317Dic5—21no—
318Dic5—21no—
319Dic5—61no—
320Dic5—61no—
321C24—151no—
322C2×Q8—51no—
323C2×D4—31no—
324C2×D4—51no—
325C2×D4—151no—
326C2×D4—151no—
327C2×D4—151no—
328C2×D4—151no—
329C2×D4—151no—
330C22×C4—31no—
331C22×C4—151no—
332C22×C4—151no—
333C22×C4—151no—
334C4⋊C4—31no—
335C4⋊C4—31no—
336C4⋊C4—151no—
337C4⋊C4—151no—
338C4⋊C4—151no—
339C4⋊C4—151no—
340C22⋊C4—31no—
341C22⋊C4—31no—
342C22⋊C4—51no—
343C22⋊C4—51no—
344C22⋊C4—51no—
345C22⋊C4—151no—
346C22⋊C4—151no—
347C22⋊C4—151no—
348C22⋊C4—151no—
349C22⋊C4—151no—
350C22⋊C4—151no—
351C22⋊C4—151no—
352C22⋊C4—151no—
353C22⋊C4D3×D511yescharacteristic
354C42—51no—
355C42—151no—
356C3×C5#53811yescharacteristic, complemented, Hall
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—101no—
361C22×C3—101no—
362C22×C3—101no—
363C22×C3C23×D511yescharacteristic
364C2×D3—21no—
365C2×D3—21no—
366C2×D3—21no—
367C2×D3—52no—
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—101no—
377C3×C4—101no—
378C3×C4—101no—
379Dic3—21no—
380Dic3—21no—
381Dic3—21no—
382Dic3—101no—
383Dic3—101no—
384C2×C5—41no—
385C2×C5—121no—
386C2×C5#100411yescharacteristic
387C2×C5D3×#4111yescharacteristic
388C2×C5#100911yescharacteristic
389D5—41no—
390D5—62no—
391D5—121no—
392C23—31no—
393C23—51no—
394C23—151no—
395C23—151no—
396C23—302no—
397C23—601no—
398C23—601no—
399C23C2×D3×D511yescharacteristic
400Q8—201no—
401D4—121no—
402D4—201no—
403D4—302no—
404D4—302no—
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—121no—
415C2×C4—151no—
416C2×C4—151no—
417C2×C4—601no—
418C2×C4—601no—
419C2×C4—601no—
420C2×C4C2×D3×D511yescharacteristic
421C2×C4C2×D3×D511yescharacteristic
422C2×C3—41no—
423C2×C3—201no—
424C2×C3#414411yescharacteristic
425C2×C3D5×#4111yescharacteristic
426C2×C3#414911yescharacteristic
427D3—41no—
428D3—102no—
429D3—201no—
430C5#567811yescharacteristic, complemented, Sylow
431C22—21no—
432C22—21no—
433C22—21no—
434C22—61no—
435C22—61no—
436C22—61no—
437C22—101no—
438C22—101no—
439C22—101no—
440C22—152no—
441C22—301no—
442C22—301no—
443C22—301no—
444C22—301no—
445C22—301no—
446C22—604no—
447C22C22×D3×D511yescharacteristic
448C4—21no—
449C4—21no—
450C4—61no—
451C4—61no—
452C4—61no—
453C4—101no—
454C4—101no—
455C4—101no—
456C4—301no—
457C4—301no—
458C3#6599111yescharacteristic, complemented, Sylow
459C2—41no—
460C2—121no—
461C2—201no—
462C2—302no—
463C2—601no—
464C2#9201611yescharacteristic
465C2#9202611yescharacteristic
466C2#9202711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C22⋊C4C22
hypercenterC22⋊C4D3×D5
hypocenterC3×C5#538
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22⋊C4×D15C2semidirect
2. C5×#883C2semidirect
3. C3×#4031C2semidirect
4. #91573C2semidirect
5. #91572C2semidirect
6. #91549C2semidirect
7. #91530C2semidirect
8. #91461C2semidirect
9. #91454C2semidirect
10. C4×#1203C2semidirect
11. #91413C2semidirect
12. #91396C2semidirect
13. #91390C2semidirect
14. #91387C2semidirect
15. #91326C2semidirect
21. C2×C4×C5×D3C22semidirect
23. C2×C3×Dic10C22semidirect
28. C2×#1201C22semidirect
29. C2×D5×Dic3C22semidirect
35. C5×(C2×D3)⋊C4C22semidirect
36. C5×C4⋊Dic3C22semidirect
37. C5×Dic3⋊C4C22semidirect
39. C3×#685C22semidirect
40. C3×#685C22semidirect
41. C3×C4×Dic5C22semidirect
42. Dic3⋊Dic5C22semidirect
43. Dic3⋊Dic5C22semidirect
44. #6669C22semidirect
45. #6668C22semidirect
50. (C2×D3)⋊Dic5C22semidirect
51. Dic3×Dic5C22semidirect
63. #4031D3semidirect
106. #883D5semidirect
125. C2×Dic10C2×D3semidirect
140. #685C2×D3semidirect
141. #685C2×D3semidirect
147. C4×Dic5C2×D3semidirect
188. C2×C4×D3C2×D5semidirect
203. (C2×D3)⋊C4C2×D5semidirect
205. C4⋊Dic3C2×D5semidirect
209. Dic3⋊C4C2×D5semidirect
356. C3×C5#538semidirect
430. C5#5678semidirect
458. C3#65991semidirect

Maximal subgroups

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

subgroupindex
C22⋊C4×D152
C5×#8832
C3×#40312
#915732
#915722
#915492
#915302
#914612
#914542
C4×#12032
#914132
#913962
#913902
#913872
#913262
#659913
#56785