Finite Group Databasebeta

← #11757062

Subgroups — #11757062

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#41×D15C211yesmaximal, characteristic, complemented
2C5×#1010C211yesmaximal, characteristic, complemented
3C3×#4149C211yesmaximal, characteristic, complemented
4D3×#713C212yesmaximal, complemented
5#92028C212yesmaximal, complemented
6#92026C216yesmaximal, complemented
7D5×#237C216yesmaximal, complemented
8#92017C213yesmaximal, complemented
9#92016C213yesmaximal, complemented
10#92000C213yesmaximal, complemented
11C2×#6766C213yesmaximal, complemented
12#66287—31nomaximal, Hall
13C3×C5×#41C2211yescharacteristic, complemented
14#6821C2211yescharacteristic, complemented
15Q8×D15C2211yescharacteristic, complemented
16#6819C2213yescomplemented
17D4×D15C2213yescomplemented
18#6817C2213yescomplemented
19C2×C4×D15C2213yescomplemented
20C5×D3×Q8C2212yescomplemented
21C5×#237C2216yescomplemented
22C5×#235C2213yescomplemented
23C2×C5×Dic6C2213yescomplemented
24C3×#713C2212yescomplemented
25C3×D4×D5C2216yescomplemented
26C3×#709C2213yescomplemented
27C2×C3×D20C2213yescomplemented
28#6790C2216yescomplemented
29D5×#67C22112yescomplemented
30C2×#1202C2216yescomplemented
31#6780C2216yescomplemented
32#6779C22112yescomplemented
33C2×D5×Dic3C2216yescomplemented
34#6777C2213yescomplemented
35D3×D20C2216yescomplemented
36C4×D3×D5C2216yescomplemented
37#6773C2216yescomplemented
38#6771C2216yescomplemented
39D15⋊Q8C2213yescomplemented
40#6768C2211yescharacteristic, complemented
41#6766C2213yescomplemented
42#6766C2216yescomplemented
43#6766C2216yescomplemented
44#6766C2216yescomplemented
45#6765C2216yescomplemented
46D5×Dic6C2216yescomplemented
47#5966—51nomaximal, Hall
48C5×2−1+4—31no—
49#4149—36no—
50#4149—33no—
51#4149D311yescharacteristic, complemented
52D5×#41—31no—
53D5×#41—36no—
54D5×#41—33no—
55#4147—32no—
56#4147—33no—
57C2×#713—32no—
58C2×#713—33no—
59C22×D15C2313yes—
60C22×C3×D5C2316yes—
61C2×D3×D5C2316yes—
62C3×C5×Q8C2311yescharacteristic
63C3×C5×D4C2313yes—
64C2×C3×C4×C5C2313yes—
65#1220C2316yes—
66C2×Dic15C2313yes—
67D60C2313yes—
68C4×D15C2311yescharacteristic
69C4×D15C2313yes—
70C4×D15C2313yes—
71C4×D15C2313yes—
72Dic30C2313yes—
73C5×#67C2316yes—
74C2×C5×Dic3C2316yes—
75C5×D12C2311yescharacteristic
76C4×C5×D3C2316yes—
77C5×Dic6C2316yes—
78C5×Dic6C2313yes—
79C3×C22⋊D5C2316yes—
80C3×D20C2316yes—
81C3×D20C2313yes—
82C3×C4×D5C2316yes—
83C3×Dic10C2311yescharacteristic
84#1204C2316yes—
85#1203C2312yes—
86#1202C2316yes—
87#1202C23112yes—
88#1201C2316yes—
89#1200C2316yes—
90D3×Dic5C2312yes—
91D5×Dic3C23112yes—
92D5×Dic3C2316yes—
93C3×H(5,𝔽2)—51no—
94#1010—52no—
95#1010—53no—
96#1010D511yescharacteristic, complemented
97D3×#41—51no—
98D3×#41—52no—
99D3×#41—53no—
100#1004—56no—
101#1004—53no—
102C2×#237—56no—
103C2×#237—53no—
104C5×#41—36no—
105C5×#41—33no—
106C5×#41C2×D311yescharacteristic, complemented
107C2×C5×Q8—32no—
108C2×C5×Q8—33no—
109#713—31no—
110#713—36no—
111#713—33no—
112#713—36no—
113#713—36no—
114#713—36no—
115#713C2×D312yescomplemented
116Q8×D5—31no—
117Q8×D5—36no—
118Q8×D5—33no—
119#711—33no—
120#711—36no—
121#711—31no—
122D4×D5—312no—
123D4×D5—33no—
124D4×D5—36no—
125D4×D5—33no—
126D4×D5C2×D316yescomplemented
127#709—33no—
128#709—312no—
129#709—36no—
130#709—36no—
131#709C2×D313yescomplemented
132C2×D20—36no—
133C2×D20—36no—
134C2×D20C2×D313yescomplemented
135C2×C4×D5—36no—
136C2×C4×D5—33no—
137C2×C4×D5—36no—
138#585—151noSylow
139C22×C3×C5C2413yes—
140C2×D15—43no—
141C2×D15C2413yes—
142C2×D15C2411yescharacteristic
143C2×C5×D3C2412yes—
144C2×C3×D5—46no—
145C2×C3×D5C2416yes—
146D3×D5—46no—
147C3×C4×C5C2411yescharacteristic
148C3×C4×C5C2413yes—
149Dic15C2411yescharacteristic
150Dic15C2413yes—
151C3×Dic5C2412yes—
152C5×Dic3C2416yes—
153C3×#41—52no—
154C3×#41—53no—
155C3×#41C2×D511yescharacteristic, complemented
156C2×C3×D4—56no—
157C2×C3×D4—53no—
158C2×#67—512no—
159C2×#67—56no—
160C22×Dic3—56no—
161#239—51no—
162#239—51no—
163D3×Q8—51no—
164D3×Q8—53no—
165D3×Q8C2×D512yescomplemented
166#237—53no—
167#237—56no—
168#237—512no—
169#237—56no—
170#237—56no—
171#237—53no—
172#237—56no—
173#237—56no—
174#237C2×D516yescomplemented
175D3×D4—53no—
176D3×D4—56no—
177D3×D4—53no—
178D3×D4—56no—
179#235—53no—
180#235—56no—
181#235—56no—
182#235C2×D513yescomplemented
183C2×C4×D3—53no—
184C2×C4×D3—56no—
185C2×Dic6—56no—
186C2×Dic6C2×D513yescomplemented
187C22×D5—33no—
188C22×D5—36no—
189C22×D5C22×D316yes—
190C5×Q8—36no—
191C5×Q8—33no—
192C5×Q8C22×D311yescharacteristic
193C5×D4—36no—
194C5×D4—31no—
195C5×D4C22×D313yes—
196C2×C4×C5—36no—
197C2×C4×C5—36no—
198C2×C4×C5C22×D313yes—
199C22⋊D5—36no—
200C22⋊D5—36no—
201C22⋊D5—32no—
202C22⋊D5C22×D316yes—
203C2×Dic5—33no—
204C2×Dic5—32no—
205D20—36no—
206D20—312no—
207D20—33no—
208D20C22×D316yes—
209D20C22×D313yes—
210C4×D5—36no—
211C4×D5—312no—
212C4×D5—33no—
213C4×D5—31no—
214C4×D5—33no—
215C4×D5—33no—
216C4×D5—36no—
217C4×D5C22×D316yes—
218Dic10—33no—
219Dic10—36no—
220Dic10C22×D311yescharacteristic
2212−1+4—31no—
2222−1+4—152no—
2232−1+4—153no—
224H(5,𝔽2)—51no—
225H(5,𝔽2)—156no—
226H(5,𝔽2)—153no—
227C2×#41—153no—
228C2×#41—156no—
229C2×#41—152no—
230C2×#41—153no—
231C2×#41—151no—
232C2×C3×C5—23no—
233C2×C3×C5C2511yescharacteristic
234D15—23no—
235D15—21no—
236C3×D5—26no—
237C5×D3—22no—
238C23×C3—56no—
239C22×D3—53no—
240C22×D3—56no—
241C3×Q8—51no—
242C3×Q8C22×D511yescharacteristic
243C3×D4—56no—
244C3×D4—56no—
245C3×D4—53no—
246C3×D4C22×D513yes—
247C2×C3×C4—56no—
248C2×C3×C4C22×D513yes—
249#67—56no—
250#67—56no—
251#67—56no—
252#67—512no—
253#67C22×D516yes—
254C2×Dic3—53no—
255C2×Dic3—512no—
256C2×Dic3—56no—
257C2×Dic3C22×D516yes—
258D12—52no—
259D12—53no—
260D12C22×D511yescharacteristic
261C4×D3—52no—
262C4×D3—53no—
263C4×D3—51no—
264C4×D3—53no—
265C4×D3—53no—
266C4×D3—56no—
267C4×D3C22×D516yes—
268Dic6—53no—
269Dic6—56no—
270Dic6C22×D516yes—
271Dic6C22×D513yes—
272C22×C5—32no—
273C22×C5C23×D313yes—
274C2×D5—33no—
275C2×D5—31no—
276C2×D5—46no—
277C2×D5—126no—
278C2×D5—123no—
279C2×D5C23×D316yes—
280C4×C5—36no—
281C4×C5C23×D313yes—
282C4×C5C23×D311yescharacteristic
283Dic5—33no—
284Dic5—31no—
285Dic5C23×D312yes—
286#41—36no—
287#41—33no—
288#41—52no—
289#41—53no—
290#41—156no—
291#41—1512no—
292#41—156no—
293#41—156no—
294#41—156no—
295#41—151no—
296#41—153no—
297#41—156no—
298#41—156no—
299#41—156no—
300#41—151no—
301#41—153no—
302#41—153no—
303#41D3×D511yescharacteristic, complemented
304C2×Q8—32no—
305C2×Q8—33no—
306C2×Q8—156no—
307C2×Q8—153no—
308C2×Q8—151no—
309C2×D4—56no—
310C2×D4—53no—
311C2×D4—156no—
312C2×D4—156no—
313C2×D4—156no—
314C2×D4—153no—
315C2×D4—1512no—
316C2×D4—153no—
317C22×C4—156no—
318C22×C4—156no—
319C22×C4—153no—
320C3×C5#58511yescharacteristic, complemented, Hall
321C22×C3—56no—
322C22×C3—206no—
323C22×C3C23×D513yes—
324C2×D3—53no—
325C2×D3—51no—
326C2×D3—206no—
327C2×D3—203no—
328C2×D3C23×D512yes—
329C3×C4—52no—
330C3×C4C23×D513yes—
331C3×C4C23×D511yescharacteristic
332Dic3—53no—
333Dic3—51no—
334Dic3C23×D516yes—
335C2×C5—23no—
336C2×C5—62no—
337C2×C5C24×D311yescharacteristic
338D5—26no—
339D5—63no—
340D5—61no—
341C23—56no—
342C23—156no—
343C23—153no—
344Q8—36no—
345Q8—33no—
346Q8—51no—
347Q8—156no—
348Q8—153no—
349Q8C2×D3×D511yescharacteristic
350D4—36no—
351D4—31no—
352D4—56no—
353D4—56no—
354D4—53no—
355D4—1512no—
356D4—156no—
357D4—152no—
358D4—156no—
359D4—156no—
360D4—153no—
361D4C2×D3×D513yes—
362C2×C4—36no—
363C2×C4—36no—
364C2×C4—56no—
365C2×C4—156no—
366C2×C4—156no—
367C2×C4—1512no—
368C2×C4—152no—
369C2×C4—153no—
370C2×C4—153no—
371C2×C4—151no—
372C2×C4—153no—
373C2×C4—153no—
374C2×C4C2×D3×D513yes—
375C2×C3—23no—
376C2×C3—106no—
377C2×C3C24×D511yescharacteristic
378D3—22no—
379D3—103no—
380D3—101no—
381C5#596611yescharacteristic, complemented, Sylow
382C22—32no—
383C22—56no—
384C22—153no—
385C22—151no—
386C22—206no—
387C22—603no—
388C22—606no—
389C22C22×D3×D513yes—
390C4—36no—
391C4—52no—
392C4—151no—
393C4—153no—
394C4C22×D3×D513yes—
395C4C22×D3×D511yescharacteristic
396C3#6628711yescharacteristic, complemented, Sylow
397C2—23no—
398C2—62no—
399C2—106no—
400C2—301no—
401C2—303no—
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. #41×D15C2semidirect
2. C5×#1010C2semidirect
3. C3×#4149C2semidirect
4. D3×#713C2semidirect
5. #92028C2semidirect
6. #92026C2semidirect
7. D5×#237C2semidirect
8. #92017C2semidirect
9. #92016C2semidirect
10. #92000C2semidirect
11. C2×#6766C2semidirect
13. C3×C5×#41C22semidirect
14. #6821C22semidirect
15. Q8×D15C22semidirect
16. #6819C22semidirect
17. D4×D15C22semidirect
18. #6817C22semidirect
19. C2×C4×D15C22semidirect
20. C5×D3×Q8C22semidirect
21. C5×#237C22semidirect
22. C5×#235C22semidirect
23. C2×C5×Dic6C22semidirect
24. C3×#713C22semidirect
25. C3×D4×D5C22semidirect
26. C3×#709C22semidirect
27. C2×C3×D20C22semidirect
28. #6790C22semidirect
29. D5×#67C22semidirect
30. C2×#1202C22semidirect
31. #6780C22semidirect
32. #6779C22semidirect
33. C2×D5×Dic3C22semidirect
34. #6777C22semidirect
35. D3×D20C22semidirect
36. C4×D3×D5C22semidirect
37. #6773C22semidirect
38. #6771C22semidirect
39. D15⋊Q8C22semidirect
40. #6768C22semidirect
41. #6766C22semidirect
42. #6766C22semidirect
43. #6766C22semidirect
44. #6766C22semidirect
45. #6765C22semidirect
46. D5×Dic6C22semidirect
51. #4149D3semidirect
96. #1010D5semidirect
106. C5×#41C2×D3semidirect
115. #713C2×D3semidirect
126. D4×D5C2×D3semidirect
131. #709C2×D3semidirect
134. C2×D20C2×D3semidirect
155. C3×#41C2×D5semidirect
165. D3×Q8C2×D5semidirect
174. #237C2×D5semidirect
182. #235C2×D5semidirect
186. C2×Dic6C2×D5semidirect
303. #41D3×D5semidirect
320. C3×C5#585semidirect
381. C5#5966semidirect
396. C3#66287semidirect

Maximal subgroups

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

subgroupindex
#41×D152
C5×#10102
C3×#41492
D3×#7132
#920282
#920262
D5×#2372
#920172
#920162
#920002
C2×#67662
#662873
#59665