Finite Group Databasebeta

← #11757064

Subgroups — #11757064

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×#1009C211yesmaximal, characteristic, complemented
3C3×#4150C211yesmaximal, characteristic, complemented
4D5×#239C212yesmaximal, complemented
5#92030C212yesmaximal, complemented
6#92027C216yesmaximal, complemented
7D3×#711C216yesmaximal, complemented
8#92018C213yesmaximal, complemented
9#92016C213yesmaximal, complemented
10#92004C213yesmaximal, complemented
11C2×#6768C213yesmaximal, complemented
12#66285—31nomaximal, Hall
13C3×C5×#41C2211yescharacteristic, complemented
14#6821C2211yescharacteristic, complemented
15Q8×D15C2211yescharacteristic, complemented
16#6819C2213yescomplemented
17D4×D15C2213yescomplemented
18#6817C2213yescomplemented
19C2×C4×D15C2213yescomplemented
20C5×#239C2212yescomplemented
21C5×D3×D4C2216yescomplemented
22C5×#235C2213yescomplemented
23C2×C5×D12C2213yescomplemented
24C3×Q8×D5C2212yescomplemented
25C3×#711C2216yescomplemented
26C3×#709C2213yescomplemented
27C2×C3×Dic10C2213yescomplemented
28#6790C2216yescomplemented
29D3×C22⋊D5C22112yescomplemented
30C2×#1203C2216yescomplemented
31#6782C22112yescomplemented
32C2×D3×Dic5C2216yescomplemented
33#6780C2216yescomplemented
34#6777C2213yescomplemented
35D5×D12C2216yescomplemented
36C4×D3×D5C2216yescomplemented
37#6772C2216yescomplemented
38#6771C2216yescomplemented
39D15⋊Q8C2213yescomplemented
40#6769C2216yescomplemented
41#6768C2213yescomplemented
42#6768C2216yescomplemented
43#6768C2216yescomplemented
44#6768C2216yescomplemented
45D3×Dic10C2216yescomplemented
46#6766C2211yescharacteristic, complemented
47#5968—51nomaximal, Hall
48C5×H(5,𝔽2)—31no—
49#4150—32no—
50#4150—33no—
51#4150D311yescharacteristic, complemented
52D5×#41—31no—
53D5×#41—32no—
54D5×#41—33no—
55#4144—36no—
56#4144—33no—
57C2×#711—36no—
58C2×#711—33no—
59C22×D15C2313yes—
60C22×C5×D3C2316yes—
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—
74C5×D12C2313yes—
75C5×D12C2316yes—
76C4×C5×D3C2316yes—
77C5×Dic6C2311yescharacteristic
78C3×C22⋊D5C2316yes—
79C2×C3×Dic5C2316yes—
80C3×D20C2311yescharacteristic
81C3×C4×D5C2316yes—
82C3×Dic10C2316yes—
83C3×Dic10C2313yes—
84#1204C2316yes—
85#1203C2316yes—
86#1203C23112yes—
87#1202C2312yes—
88#1201C2316yes—
89#1200C2316yes—
90D3×Dic5C23112yes—
91D3×Dic5C2316yes—
92D5×Dic3C2312yes—
93C3×2−1+4—51no—
94#1009—56no—
95#1009—53no—
96#1009D511yescharacteristic, complemented
97D3×#41—51no—
98D3×#41—56no—
99D3×#41—53no—
100#1007—52no—
101#1007—53no—
102C2×#239—52no—
103C2×#239—53no—
104C5×#41—32no—
105C5×#41—33no—
106C5×#41C2×D311yescharacteristic, complemented
107C2×C5×D4—36no—
108C2×C5×D4—33no—
109C2×C22⋊D5—312no—
110C2×C22⋊D5—36no—
111C22×Dic5—36no—
112#713—31no—
113#713—31no—
114Q8×D5—31no—
115Q8×D5—33no—
116Q8×D5C2×D312yescomplemented
117#711—33no—
118#711—36no—
119#711—312no—
120#711—36no—
121#711—36no—
122#711—33no—
123#711—36no—
124#711—36no—
125#711C2×D316yescomplemented
126D4×D5—33no—
127D4×D5—36no—
128D4×D5—33no—
129D4×D5—36no—
130#709—33no—
131#709—36no—
132#709—36no—
133#709C2×D313yescomplemented
134C2×C4×D5—33no—
135C2×C4×D5—36no—
136C2×Dic10—36no—
137C2×Dic10C2×D313yescomplemented
138#585—151noSylow
139C22×C3×C5C2413yes—
140C2×D15—43no—
141C2×D15C2413yes—
142C2×D15C2411yescharacteristic
143C2×C5×D3—46no—
144C2×C5×D3C2416yes—
145C2×C3×D5C2412yes—
146D3×D5—46no—
147C3×C4×C5C2411yescharacteristic
148C3×C4×C5C2413yes—
149Dic15C2411yescharacteristic
150Dic15C2413yes—
151C3×Dic5C2416yes—
152C5×Dic3C2412yes—
153C3×#41—56no—
154C3×#41—53no—
155C3×#41C2×D511yescharacteristic, complemented
156C2×C3×Q8—52no—
157C2×C3×Q8—53no—
158#239—51no—
159#239—56no—
160#239—53no—
161#239—56no—
162#239—56no—
163#239—56no—
164#239C2×D512yescomplemented
165D3×Q8—51no—
166D3×Q8—56no—
167D3×Q8—53no—
168#237—53no—
169#237—56no—
170#237—51no—
171D3×D4—512no—
172D3×D4—53no—
173D3×D4—56no—
174D3×D4—53no—
175D3×D4C2×D516yescomplemented
176#235—53no—
177#235—512no—
178#235—56no—
179#235—56no—
180#235C2×D513yescomplemented
181C2×D12—56no—
182C2×D12—56no—
183C2×D12C2×D513yescomplemented
184C2×C4×D3—56no—
185C2×C4×D3—53no—
186C2×C4×D3—56no—
187C23×C5—36no—
188C22×D5—33no—
189C22×D5—36no—
190C5×Q8—31no—
191C5×Q8C22×D311yescharacteristic
192C5×D4—36no—
193C5×D4—36no—
194C5×D4—33no—
195C5×D4C22×D313yes—
196C2×C4×C5—36no—
197C2×C4×C5C22×D313yes—
198C22⋊D5—36no—
199C22⋊D5—36no—
200C22⋊D5—36no—
201C22⋊D5—312no—
202C22⋊D5C22×D316yes—
203C2×Dic5—33no—
204C2×Dic5—312no—
205C2×Dic5—36no—
206C2×Dic5C22×D316yes—
207D20—32no—
208D20—33no—
209D20C22×D311yescharacteristic
210C4×D5—32no—
211C4×D5—33no—
212C4×D5—31no—
213C4×D5—33no—
214C4×D5—33no—
215C4×D5—36no—
216C4×D5C22×D316yes—
217Dic10—33no—
218Dic10—36no—
219Dic10C22×D316yes—
220Dic10C22×D313yes—
2212−1+4—51no—
2222−1+4—152no—
2232−1+4—153no—
224H(5,𝔽2)—31no—
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—22no—
237C5×D3—26no—
238C22×D3—53no—
239C22×D3—56no—
240C22×D3C22×D516yes—
241C3×Q8—56no—
242C3×Q8—53no—
243C3×Q8C22×D511yescharacteristic
244C3×D4—56no—
245C3×D4—51no—
246C3×D4C22×D513yes—
247C2×C3×C4—56no—
248C2×C3×C4—56no—
249C2×C3×C4C22×D513yes—
250#67—56no—
251#67—56no—
252#67—52no—
253#67C22×D516yes—
254C2×Dic3—53no—
255C2×Dic3—52no—
256D12—56no—
257D12—512no—
258D12—53no—
259D12C22×D516yes—
260D12C22×D513yes—
261C4×D3—56no—
262C4×D3—512no—
263C4×D3—53no—
264C4×D3—51no—
265C4×D3—53no—
266C4×D3—53no—
267C4×D3—56no—
268C4×D3C22×D516yes—
269Dic6—53no—
270Dic6—56no—
271Dic6C22×D511yescharacteristic
272C22×C5—36no—
273C22×C5—126no—
274C22×C5C23×D313yes—
275C2×D5—33no—
276C2×D5—31no—
277C2×D5—126no—
278C2×D5—123no—
279C2×D5C23×D312yes—
280C4×C5—32no—
281C4×C5C23×D313yes—
282C4×C5C23×D311yescharacteristic
283Dic5—33no—
284Dic5—31no—
285Dic5C23×D316yes—
286#41—32no—
287#41—33no—
288#41—56no—
289#41—53no—
290#41—156no—
291#41—156no—
292#41—1512no—
293#41—156no—
294#41—156no—
295#41—153no—
296#41—156no—
297#41—156no—
298#41—156no—
299#41—151no—
300#41—151no—
301#41—153no—
302#41—153no—
303#41D3×D511yescharacteristic, complemented
304C2×Q8—52no—
305C2×Q8—53no—
306C2×Q8—156no—
307C2×Q8—153no—
308C2×Q8—151no—
309C2×D4—36no—
310C2×D4—33no—
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—52no—
322C22×C3C23×D513yes—
323C2×D3—46no—
324C2×D3—53no—
325C2×D3—51no—
326C2×D3—206no—
327C2×D3—203no—
328C2×D3C23×D516yes—
329C3×C4—56no—
330C3×C4C23×D513yes—
331C3×C4C23×D511yescharacteristic
332Dic3—53no—
333Dic3—51no—
334Dic3C23×D512yes—
335C2×C5—23no—
336C2×C5—66no—
337C2×C5C24×D311yescharacteristic
338D5—22no—
339D5—63no—
340D5—61no—
341C23—36no—
342C23—156no—
343C23—153no—
344Q8—31no—
345Q8—56no—
346Q8—53no—
347Q8—156no—
348Q8—153no—
349Q8C2×D3×D511yescharacteristic
350D4—36no—
351D4—36no—
352D4—33no—
353D4—56no—
354D4—51no—
355D4—152no—
356D4—1512no—
357D4—156no—
358D4—156no—
359D4—156no—
360D4—153no—
361D4C2×D3×D513yes—
362C2×C4—36no—
363C2×C4—56no—
364C2×C4—56no—
365C2×C4—156no—
366C2×C4—152no—
367C2×C4—156no—
368C2×C4—1512no—
369C2×C4—153no—
370C2×C4—153no—
371C2×C4—151no—
372C2×C4—153no—
373C2×C4—153no—
374C2×C4C2×D3×D513yes—
375C2×C3—23no—
376C2×C3—102no—
377C2×C3C24×D511yescharacteristic
378D3—26no—
379D3—103no—
380D3—101no—
381C5#596811yescharacteristic, complemented, Sylow
382C22—36no—
383C22—52no—
384C22—126no—
385C22—153no—
386C22—151no—
387C22—603no—
388C22—606no—
389C22C22×D3×D513yes—
390C4—32no—
391C4—56no—
392C4—151no—
393C4—153no—
394C4C22×D3×D513yes—
395C4C22×D3×D511yescharacteristic
396C3#6628511yescharacteristic, complemented, Sylow
397C2—23no—
398C2—66no—
399C2—102no—
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×#1009C2semidirect
3. C3×#4150C2semidirect
4. D5×#239C2semidirect
5. #92030C2semidirect
6. #92027C2semidirect
7. D3×#711C2semidirect
8. #92018C2semidirect
9. #92016C2semidirect
10. #92004C2semidirect
11. C2×#6768C2semidirect
13. C3×C5×#41C22semidirect
14. #6821C22semidirect
15. Q8×D15C22semidirect
16. #6819C22semidirect
17. D4×D15C22semidirect
18. #6817C22semidirect
19. C2×C4×D15C22semidirect
20. C5×#239C22semidirect
21. C5×D3×D4C22semidirect
22. C5×#235C22semidirect
23. C2×C5×D12C22semidirect
24. C3×Q8×D5C22semidirect
25. C3×#711C22semidirect
26. C3×#709C22semidirect
27. C2×C3×Dic10C22semidirect
28. #6790C22semidirect
29. D3×C22⋊D5C22semidirect
30. C2×#1203C22semidirect
31. #6782C22semidirect
32. C2×D3×Dic5C22semidirect
33. #6780C22semidirect
34. #6777C22semidirect
35. D5×D12C22semidirect
36. C4×D3×D5C22semidirect
37. #6772C22semidirect
38. #6771C22semidirect
39. D15⋊Q8C22semidirect
40. #6769C22semidirect
41. #6768C22semidirect
42. #6768C22semidirect
43. #6768C22semidirect
44. #6768C22semidirect
45. D3×Dic10C22semidirect
46. #6766C22semidirect
51. #4150D3semidirect
96. #1009D5semidirect
106. C5×#41C2×D3semidirect
116. Q8×D5C2×D3semidirect
125. #711C2×D3semidirect
133. #709C2×D3semidirect
137. C2×Dic10C2×D3semidirect
155. C3×#41C2×D5semidirect
164. #239C2×D5semidirect
175. D3×D4C2×D5semidirect
180. #235C2×D5semidirect
183. C2×D12C2×D5semidirect
303. #41D3×D5semidirect
320. C3×C5#585semidirect
381. C5#5968semidirect
396. C3#66285semidirect

Maximal subgroups

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

subgroupindex
#41×D152
C5×#10092
C3×#41502
D5×#2392
#920302
#920272
D3×#7112
#920182
#920162
#920042
C2×#67682
#662853
#59685