Finite Group Databasebeta

← #11757059

Subgroups — #11757059

Order 960.

1620 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#92101C211yesmaximal, characteristic, complemented
2C5×#1009C211yesmaximal, characteristic, complemented
3C3×D5×#41C211yesmaximal, characteristic, complemented
4#92034C212yesmaximal, complemented
5#92030C212yesmaximal, complemented
6#92025C216yesmaximal, complemented
7D3×#711C216yesmaximal, complemented
8#92018C213yesmaximal, complemented
9D5×#235C213yesmaximal, complemented
10C2×#6772C213yesmaximal, complemented
11#92001C213yesmaximal, complemented
12#66285—31nomaximal, Hall
13C3×C5×#41C2211yescharacteristic, complemented
14Q8×D15C2212yescomplemented
15#6819C2216yescomplemented
16#6817C2213yescomplemented
17C2×Dic30C2213yescomplemented
18C5×#239C2212yescomplemented
19C5×D3×D4C2216yescomplemented
20C5×#235C2213yescomplemented
21C2×C5×D12C2213yescomplemented
22C3×#713C2211yescharacteristic, complemented
23C3×Q8×D5C2211yescharacteristic, complemented
24C3×#711C2213yescomplemented
25C3×D4×D5C2213yescomplemented
26C3×#709C2213yescomplemented
27C2×C3×C4×D5C2213yescomplemented
28D3×C22⋊D5C22112yescomplemented
29D5×#67C2216yescomplemented
30C2×#1201C2216yescomplemented
31#6782C2216yescomplemented
32C2×D3×Dic5C2216yescomplemented
33#6780C22112yescomplemented
34#6777C2216yescomplemented
35D5×D12C2213yescomplemented
36C4×D3×D5C2216yescomplemented
37#6773C2211yescharacteristic, complemented
38#6772C2216yescomplemented
39#6772C2213yescomplemented
40#6772C2216yescomplemented
41#6772C2216yescomplemented
42#6771C2216yescomplemented
43#6768C2216yescomplemented
44D3×Dic10C2216yescomplemented
45#6765C2216yescomplemented
46D5×Dic6C2213yescomplemented
47#5964—51nomaximal, Hall
48C5×H(5,𝔽2)—31no—
49#4150—31no—
50#4150—32no—
51#4150—33no—
52D5×#41—32no—
53D5×#41—33no—
54D5×#41D311yescharacteristic, complemented
55#4144—36no—
56#4144—33no—
57C2×#711—36no—
58C2×#711—33no—
59C22×C5×D3C2316yes—
60C22×C3×D5C2313yes—
61C2×D3×D5C2316yes—
62C3×C5×Q8C2311yescharacteristic
63C3×C5×D4C2313yes—
64C2×C3×C4×C5C2313yes—
65#1220C2316yes—
66C2×Dic15C2316yes—
67D60C2311yescharacteristic
68C4×D15C2316yes—
69Dic30C2313yes—
70Dic30C2316yes—
71C5×#67C2316yes—
72C5×D12C2316yes—
73C5×D12C2313yes—
74C4×C5×D3C2316yes—
75C5×Dic6C2311yescharacteristic
76C3×C22⋊D5C2316yes—
77C2×C3×Dic5C2313yes—
78C3×D20C2313yes—
79C3×C4×D5C2313yes—
80C3×C4×D5C2313yes—
81C3×C4×D5C2311yescharacteristic
82C3×C4×D5C2313yes—
83C3×Dic10C2313yes—
84#1204C2316yes—
85#1203C2316yes—
86#1202C2312yes—
87#1201C23112yes—
88#1201C2316yes—
89#1200C2312yes—
90D3×Dic5C23112yes—
91D3×Dic5C2316yes—
92D5×Dic3C2316yes—
93C2×C3×#41—51no—
94#1010—51no—
95#1010—53no—
96#1009—53no—
97#1009D511yescharacteristic, complemented
98D3×#41—52no—
99D3×#41—56no—
100#1007—52no—
101#1004—56no—
102C2×#235—53no—
103C2×#235—53no—
104C5×#41—32no—
105C5×#41—33no—
106C5×#41C2×D311yescharacteristic, complemented
107C2×C5×D4—36no—
108C2×C5×D4—33no—
109C2×C22⋊D5—36no—
110C2×C22⋊D5—312no—
111C22×Dic5—36no—
112#713—31no—
113#713C2×D311yescharacteristic, complemented
114Q8×D5—32no—
115Q8×D5—33no—
116Q8×D5C2×D311yescharacteristic, complemented
117#711—36no—
118#711—312no—
119#711—36no—
120#711—36no—
121#711—33no—
122#711—36no—
123#711—36no—
124#711—36no—
125#711C2×D313yescomplemented
126D4×D5—36no—
127D4×D5—36no—
128D4×D5—33no—
129D4×D5C2×D313yescomplemented
130#709—33no—
131#709—36no—
132#709—36no—
133#709C2×D313yescomplemented
134C2×C4×D5—36no—
135C2×C4×D5C2×D313yescomplemented
136C2×Dic10—33no—
137C2×Dic10—36no—
138#585—151noSylow
139C22×C3×C5C2413yes—
140C2×D15C2412yes—
141C2×C5×D3—46no—
142C2×C5×D3C2416yes—
143C2×C3×D5—43no—
144C2×C3×D5C2413yes—
145C2×C3×D5C2411yescharacteristic
146D3×D5—46no—
147C3×C4×C5C2413yes—
148C3×C4×C5C2411yescharacteristic
149Dic15C2416yes—
150C3×Dic5C2411yescharacteristic
151C3×Dic5C2413yes—
152C5×Dic3C2412yes—
153C3×#41—51no—
154C3×#41—53no—
155C3×#41—53no—
156C3×#41C2×D511yescharacteristic, complemented
157C2×C3×Q8—51no—
158C2×C3×D4—53no—
159C22×C3×C4—53no—
160C2×#67—56no—
161C2×#67—56no—
162#239—56no—
163#239C2×D512yescomplemented
164D3×Q8—52no—
165D3×Q8—56no—
166#237—56no—
167#237—512no—
168#237—56no—
169D3×D4—512no—
170D3×D4—56no—
171D3×D4C2×D516yescomplemented
172#235—53no—
173#235—56no—
174#235—53no—
175#235—56no—
176#235—56no—
177#235—56no—
178#235—56no—
179#235—51no—
180#235C2×D513yescomplemented
181C2×D12—53no—
182C2×D12C2×D513yescomplemented
183C2×C4×D3—56no—
184C2×C4×D3—56no—
185C2×Dic6—53no—
186C2×Dic6—53no—
187C23×C5—36no—
188C22×D5—36no—
189C22×D5C22×D313yes—
190C5×Q8—31no—
191C5×Q8C22×D311yescharacteristic
192C5×D4—36no—
193C5×D4—33no—
194C5×D4—36no—
195C5×D4C22×D313yes—
196C2×C4×C5—36no—
197C2×C4×C5C22×D313yes—
198C22⋊D5—36no—
199C22⋊D5—312no—
200C22⋊D5—36no—
201C22⋊D5—36no—
202C22⋊D5C22×D316yes—
203C2×Dic5—36no—
204C2×Dic5—312no—
205C2×Dic5—36no—
206C2×Dic5C22×D313yes—
207D20—32no—
208D20—31no—
209D20C22×D313yes—
210C4×D5—36no—
211C4×D5—36no—
212C4×D5—32no—
213C4×D5C22×D313yes—
214C4×D5C22×D311yescharacteristic
215C4×D5C22×D313yes—
216C4×D5C22×D313yes—
217Dic10—33no—
218Dic10—36no—
219Dic10—36no—
220Dic10C22×D313yes—
2212−1+4—152no—
2222−1+4—153no—
2232−1+4—151no—
224H(5,𝔽2)—31no—
225H(5,𝔽2)—156no—
226H(5,𝔽2)—153no—
227C2×#41—51no—
228C2×#41—153no—
229C2×#41—153no—
230C2×#41—156no—
231C2×#41—152no—
232C2×C3×C5—23no—
233C2×C3×C5C2511yescharacteristic
234D15—22no—
235C3×D5—23no—
236C3×D5—21no—
237C5×D3—26no—
238C23×C3—53no—
239C22×D3—56no—
240C22×D3C22×D516yes—
241C3×Q8—53no—
242C3×Q8C22×D511yescharacteristic
243C3×D4—56no—
244C3×D4—53no—
245C3×D4C22×D513yes—
246C2×C3×C4—53no—
247C2×C3×C4—53no—
248C2×C3×C4—53no—
249C2×C3×C4—51no—
250C2×C3×C4—53no—
251C2×C3×C4C22×D513yes—
252#67—56no—
253#67—56no—
254#67—512no—
255#67—52no—
256#67C22×D516yes—
257C2×Dic3—56no—
258C2×Dic3—56no—
259D12—56no—
260D12—51no—
261D12C22×D513yes—
262D12C22×D516yes—
263C4×D3—56no—
264C4×D3—512no—
265C4×D3—56no—
266C4×D3—52no—
267C4×D3C22×D516yes—
268Dic6—53no—
269Dic6—56no—
270Dic6—56no—
271Dic6C22×D511yescharacteristic
272C22×C5—36no—
273C22×C5—126no—
274C22×C5C23×D313yes—
275C2×D5—32no—
276C2×D5—43no—
277C2×D5—126no—
278C2×D5C23×D313yes—
279C2×D5C23×D311yescharacteristic
280C4×C5—32no—
281C4×C5C23×D311yescharacteristic
282C4×C5C23×D313yes—
283Dic5—36no—
284Dic5C23×D313yes—
285Dic5C23×D311yescharacteristic
286#41—32no—
287#41—33no—
288#41—51no—
289#41—53no—
290#41—53no—
291#41—156no—
292#41—156no—
293#41—156no—
294#41—153no—
295#41—156no—
296#41—156no—
297#41—156no—
298#41—151no—
299#41—1512no—
300#41—156no—
301#41—156no—
302#41—153no—
303#41D3×D511yescharacteristic, complemented
304C2×Q8—51no—
305C2×Q8—156no—
306C2×Q8—153no—
307C2×Q8—152no—
308C2×Q8—153no—
309C2×D4—36no—
310C2×D4—33no—
311C2×D4—53no—
312C2×D4—153no—
313C2×D4—156no—
314C2×D4—156no—
315C2×D4—1512no—
316C2×D4—156no—
317C22×C4—53no—
318C22×C4—156no—
319C22×C4—156no—
320C3×C5#58511yescharacteristic, complemented, Hall
321C22×C3—53no—
322C22×C3—51no—
323C22×C3—203no—
324C22×C3C23×D513yes—
325C2×D3—46no—
326C2×D3—52no—
327C2×D3—206no—
328C2×D3C23×D516yes—
329C3×C4—53no—
330C3×C4—51no—
331C3×C4C23×D511yescharacteristic
332C3×C4C23×D513yes—
333Dic3—56no—
334Dic3C23×D512yes—
335C2×C5—23no—
336C2×C5—66no—
337C2×C5C24×D311yescharacteristic
338D5—21no—
339D5—23no—
340D5—62no—
341C23—36no—
342C23—53no—
343C23—156no—
344Q8—31no—
345Q8—53no—
346Q8—156no—
347Q8—156no—
348Q8—153no—
349Q8C2×D3×D511yescharacteristic
350D4—36no—
351D4—36no—
352D4—33no—
353D4—56no—
354D4—53no—
355D4—152no—
356D4—156no—
357D4—156no—
358D4—1512no—
359D4—156no—
360D4—151no—
361D4C2×D3×D513yes—
362C2×C4—36no—
363C2×C4—53no—
364C2×C4—51no—
365C2×C4—53no—
366C2×C4—53no—
367C2×C4—53no—
368C2×C4—152no—
369C2×C4—156no—
370C2×C4—156no—
371C2×C4—1512no—
372C2×C4—156no—
373C2×C4—156no—
374C2×C4C2×D3×D513yes—
375C2×C3—23no—
376C2×C3—103no—
377C2×C3—101no—
378C2×C3C24×D511yescharacteristic
379D3—26no—
380D3—102no—
381C5#596411yescharacteristic, complemented, Sylow
382C22—36no—
383C22—51no—
384C22—53no—
385C22—126no—
386C22—152no—
387C22—203no—
388C22—606no—
389C22C22×D3×D513yes—
390C4—32no—
391C4—51no—
392C4—53no—
393C4—156no—
394C4C22×D3×D513yes—
395C4C22×D3×D511yescharacteristic
396C3#6628511yescharacteristic, complemented, Sylow
397C2—23no—
398C2—66no—
399C2—101no—
400C2—103no—
401C2—302no—
402C2C23×D3×D511yescharacteristic
subgroupG/H
center, FrattiniC2C23×D3×D5
commutator, socle, cosocleC2×C3×C5C25
FittingC3×C5×#41C22
hypercenter#41D3×D5
hypocenterC3×C5#585
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ #41

Complements

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

NH ≅ G/Ntype
1. #92101C2semidirect
2. C5×#1009C2semidirect
3. C3×D5×#41C2semidirect
4. #92034C2semidirect
5. #92030C2semidirect
6. #92025C2semidirect
7. D3×#711C2semidirect
8. #92018C2semidirect
9. D5×#235C2semidirect
10. C2×#6772C2semidirect
11. #92001C2semidirect
13. C3×C5×#41C22semidirect
14. Q8×D15C22semidirect
15. #6819C22semidirect
16. #6817C22semidirect
17. C2×Dic30C22semidirect
18. C5×#239C22semidirect
19. C5×D3×D4C22semidirect
20. C5×#235C22semidirect
21. C2×C5×D12C22semidirect
22. C3×#713C22semidirect
23. C3×Q8×D5C22semidirect
24. C3×#711C22semidirect
25. C3×D4×D5C22semidirect
26. C3×#709C22semidirect
27. C2×C3×C4×D5C22semidirect
28. D3×C22⋊D5C22semidirect
29. D5×#67C22semidirect
30. C2×#1201C22semidirect
31. #6782C22semidirect
32. C2×D3×Dic5C22semidirect
33. #6780C22semidirect
34. #6777C22semidirect
35. D5×D12C22semidirect
36. C4×D3×D5C22semidirect
37. #6773C22semidirect
38. #6772C22semidirect
39. #6772C22semidirect
40. #6772C22semidirect
41. #6772C22semidirect
42. #6771C22semidirect
43. #6768C22semidirect
44. D3×Dic10C22semidirect
45. #6765C22semidirect
46. D5×Dic6C22semidirect
54. D5×#41D3semidirect
97. #1009D5semidirect
106. C5×#41C2×D3semidirect
113. #713C2×D3semidirect
116. Q8×D5C2×D3semidirect
125. #711C2×D3semidirect
129. D4×D5C2×D3semidirect
133. #709C2×D3semidirect
135. C2×C4×D5C2×D3semidirect
156. C3×#41C2×D5semidirect
163. #239C2×D5semidirect
171. D3×D4C2×D5semidirect
180. #235C2×D5semidirect
182. C2×D12C2×D5semidirect
303. #41D3×D5semidirect
320. C3×C5#585semidirect
381. C5#5964semidirect
396. C3#66285semidirect

Maximal subgroups

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

subgroupindex
#921012
C5×#10092
C3×D5×#412
#920342
#920302
#920252
D3×#7112
#920182
D5×#2352
C2×#67722
#920012
#662853
#59645