Finite Group Databasebeta

← #10618660

Subgroups — #10618660

Order 640.

1492 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4147C211yesmaximal, characteristic, complemented
2C22×Q8×D5C211yesmaximal, characteristic, complemented
3C5×D4×Q8C211yesmaximal, characteristic, complemented
4#66151C211yesmaximal, characteristic, complemented
5Q8×C22⋊D5C211yesmaximal, characteristic, complemented
6#66061C213yesmaximal, complemented
7#66058C213yesmaximal, complemented
8#65967C213yesmaximal, complemented
9#65966C213yesmaximal, complemented
10#65962C213yesmaximal, complemented
11#65961C213yesmaximal, complemented
12#65910C211yesmaximal, characteristic, complemented
13#65906C211yesmaximal, characteristic, complemented
14#65886C213yesmaximal, complemented
15#65881C213yesmaximal, complemented
16C22×C5×Q8C2211yescharacteristic
17C22×C5×Q8C2211yescharacteristic, complemented
18#4147—28no—
19C2×#713C2213yes—
20C2×#713C2211yescharacteristic, complemented
21C2×Q8×D5—28no—
22C2×Q8×D5C2213yes—
23C2×Q8×D5C2213yes—
24C2×Q8×D5C2211yescharacteristic
25C2×Q8×D5C2211yescharacteristic
26C2×Q8×D5C2213yescomplemented
27C2×#709C2213yes—
28C2×#709C2213yescomplemented
29C22×C4×D5C2213yes—
30C22×Dic10C2213yes—
31C5×C4⋊Q8C2213yescomplemented
32C5×C22⋊Q8C2213yes—
33C5×C22⋊Q8C2213yescomplemented
34C4×C5×Q8C2211yescharacteristic, complemented
35C4×C5×D4C2213yes—
36#4093C2213yescomplemented
37#4092C2213yes—
38#4092C2213yescomplemented
39Q8×Dic5C2211yescharacteristic, complemented
40#4090C2213yescomplemented
41#4085C2213yes—
42#4083C2211yescharacteristic
43#4076C2213yes—
44C4×C22⋊D5C2213yes—
45C4×C22⋊D5C2213yes—
46#4070C2213yescomplemented
47#4043C2213yescomplemented
48#4042C2213yes—
49#4042C2216yescomplemented
50#4042C2216yescomplemented
51#4041C2213yes—
52#4040C2213yes—
53#4040C2216yes—
54#4039C2216yes—
55#4038C2213yes—
56#4034C2216yescomplemented
57#4033C2213yescomplemented
58#4031C2216yescomplemented
59#4030C2213yes—
60#4029C2213yes—
61#4028C2213yes—
62#4027C2216yes—
63#4024C2213yes—
64#4021C2213yescomplemented
65C4×D20C2213yes—
66#4018C2213yes—
67C4×Dic10C2213yescomplemented
68#3486—51nomaximal, Sylow
69C23×D5C2311yescharacteristic
70C2×C5×Q8—24no—
71C2×C5×Q8—24no—
72C2×C5×Q8C2313yes—
73C2×C5×Q8C2313yes—
74C2×C5×Q8C2311yescharacteristic
75C2×C5×D4C2311yescharacteristic
76C22×C4×C5C2313yes—
77C22×C4×C5C2313yes—
78C2×C22⋊D5C2311yescharacteristic
79C2×C22⋊D5C2313yes—
80C2×C22⋊D5C2313yes—
81C2×C22⋊D5C2311yescharacteristic
82C22×Dic5C2313yes—
83#713—24no—
84#713—212no—
85Q8×D5—24no—
86Q8×D5—212no—
87Q8×D5—212no—
88Q8×D5—212no—
89Q8×D5D418yescomplemented
90#709—212no—
91#709—212no—
92C2×D20C2313yes—
93C2×D20C2313yes—
94C2×D20C2313yes—
95C2×C4×D5—212no—
96C2×C4×D5C2313yes—
97C2×C4×D5C2313yes—
98C2×C4×D5C2313yes—
99C2×C4×D5C2313yes—
100C2×C4×D5C2316yes—
101C2×C4×D5C2313yes—
102C2×Dic10—212no—
103C2×Dic10C2313yes—
104C2×Dic10C2316yes—
105C2×Dic10C2313yes—
106C2×Dic10C2313yes—
107C5×C4⋊C4C2313yes—
108C5×C4⋊C4C2313yes—
109C5×C4⋊C4C2316yes—
110C5×C22⋊C4C2313yes—
111C5×C22⋊C4C2313yes—
112C42×C5C2313yes—
113C22⋊Dic5C2311yescharacteristic
114C22⋊Dic5C2313yes—
115#685C2311yescharacteristic
116#685C2313yes—
117#685C2311yescharacteristic
118#685C2313yes—
119#685C2316yes—
120#685C2313yes—
121#685C2313yes—
122#685C2316yes—
123C4⋊Dic5C2313yes—
124C4⋊Dic5C2313yes—
125#683C2313yes—
126#683C2313yes—
127#683C2313yes—
128#683C2316yes—
129#683C2313yes—
130C4×Dic5C2316yes—
131C4×Dic5C2313yes—
132C2×2−1+4—51no—
133C23×Q8—51no—
134D4×Q8—51no—
135D4×Q8—53no—
136D4×Q8—53no—
137D4×Q8D511yescharacteristic, complemented
138#548—51no—
139#548—53no—
140#548—51no—
141#548—53no—
142#536—53no—
143#536—53no—
144#525—53no—
145#525—53no—
146#519—51no—
147C23×C5C2411yescharacteristic
148C23×C5C2411yescharacteristic
149C22×D5—22no—
150C22×D5—22no—
151C22×D5—22no—
152C22×D5C2413yes—
153C22×D5C2411yescharacteristic
154C22×D5C2411yescharacteristic
155C5×Q8—26no—
156C5×Q8—26no—
157C5×Q8C2×D414yes—
158C5×D4—22no—
159C2×C4×C5—26no—
160C2×C4×C5—26no—
161C2×C4×C5C2413yes—
162C2×C4×C5C2411yescharacteristic
163C2×C4×C5C2413yes—
164C2×C4×C5C2413yes—
165C2×C4×C5C2413yes—
166C22⋊D5—26no—
167C22⋊D5—22no—
168C22⋊D5—22no—
169C22⋊D5—26no—
170C2×Dic5—26no—
171C2×Dic5C2411yescharacteristic
172C2×Dic5C2413yes—
173C2×Dic5C2411yescharacteristic
174C2×Dic5C2413yes—
175C2×Dic5C2413yes—
176D20—26no—
177D20—26no—
178D20—26no—
179C4×D5—26no—
180C4×D5—26no—
181C4×D5—26no—
182C4×D5—26no—
183C4×D5—212no—
184C4×D5C2×D4112yes—
185Dic10—26no—
186Dic10—212no—
187Dic10—26no—
188Dic10C2×D4112yes—
1892−1+4—108no—
190C2×#41—53no—
191C2×#41—51no—
192C2×#41—53no—
193C2×#41—53no—
194C22×Q8—51no—
195C22×Q8—53no—
196C22×Q8—53no—
197C22×Q8—51no—
198C22×Q8—53no—
199C22×Q8—53no—
200C22×Q8—108no—
201C22×Q8C2×D511yescharacteristic
202C22×Q8C2×D511yescharacteristic, complemented
203C23×C4—53no—
204C4⋊Q8—53no—
205C4⋊Q8—56no—
206C4⋊Q8C2×D513yescomplemented
207#124—53no—
208#124—56no—
209#124—53no—
210#123—56no—
211#123—53no—
212#123—53no—
213C22⋊Q8—53no—
214C22⋊Q8—53no—
215C22⋊Q8—53no—
216C22⋊Q8—53no—
217C22⋊Q8—56no—
218C22⋊Q8—56no—
219C22⋊Q8—53no—
220C22⋊Q8—53no—
221C22⋊Q8C2×D513yes—
222C22⋊Q8C2×D513yescomplemented
223#121—53no—
224#121—53no—
225#121—53no—
226#121—53no—
227#120—51no—
228#120—53no—
229C4×Q8—51no—
230C4×Q8—53no—
231C4×Q8—53no—
232C4×Q8C2×D511yescharacteristic, complemented
233C4×D4—53no—
234C4×D4—53no—
235C4×D4—56no—
236C4×D4—56no—
237C4×D4—53no—
238C4×D4C2×D513yes—
239#117—53no—
240#117—53no—
241C22×C5—21no—
242C22×C5—21no—
243C22×C5—21no—
244C22×C5—21no—
245C22×C5—21no—
246C22×C52−1+412yescomplemented
247C22×C5C2511yescharacteristic
248C2×D5—28no—
249C2×D5—21no—
250C2×D5—21no—
251C2×D5—21no—
252C2×D5—21no—
253C2×D5—23no—
254C2×D5—23no—
255C2×D5—23no—
256C2×D5C22×D412yes—
257C2×D52−1+412yescomplemented
258C4×C5—23no—
259C4×C5—23no—
260C4×C5—23no—
261C4×C5—21no—
262C4×C5C22×D416yes—
263Dic5—23no—
264Dic5—21no—
265Dic5—23no—
266Dic5—21no—
267Dic5C22×D416yes—
268C24—51no—
269#41—1012no—
270#41—1012no—
271#41—1012no—
272#41—104no—
273C2×Q8—24no—
274C2×Q8—24no—
275C2×Q8—58no—
276C2×Q8—53no—
277C2×Q8—56no—
278C2×Q8—53no—
279C2×Q8—53no—
280C2×Q8—1012no—
281C2×Q8—1012no—
282C2×Q8—1012no—
283C2×Q8—1012no—
284C2×Q8—104no—
285C2×Q8C22×D513yes—
286C2×Q8C22×D513yes—
287C2×Q8C22×D511yescharacteristic
288C2×D4—51no—
289C2×D4—53no—
290C2×D4—51no—
291C2×D4—53no—
292C2×D4—53no—
293C2×D4—53no—
294C2×D4—53no—
295C2×D4C22×D511yescharacteristic
296C22×C4—53no—
297C22×C4—53no—
298C22×C4—53no—
299C22×C4—53no—
300C22×C4—56no—
301C22×C4—53no—
302C22×C4—53no—
303C22×C4—1012no—
304C22×C4C22×D513yes—
305C22×C4C22×D513yes—
306C4⋊C4—53no—
307C4⋊C4—53no—
308C4⋊C4—53no—
309C4⋊C4—53no—
310C4⋊C4—56no—
311C4⋊C4—53no—
312C4⋊C4—53no—
313C4⋊C4C22×D513yes—
314C4⋊C4C22×D516yes—
315C4⋊C4C22×D513yes—
316C22⋊C4—51no—
317C22⋊C4—53no—
318C22⋊C4—53no—
319C22⋊C4—51no—
320C22⋊C4—53no—
321C22⋊C4—51no—
322C22⋊C4—53no—
323C22⋊C4—56no—
324C22⋊C4—56no—
325C22⋊C4—53no—
326C22⋊C4C22×D513yes—
327C22⋊C4C22×D513yes—
328C42—56no—
329C42—53no—
330C42C22×D513yes—
331C2×C5—22no—
332C2×C5—41no—
333C2×C5C23×D411yescharacteristic
334C2×C5C2×2−1+411yescharacteristic
335C2×C5C2×2−1+411yescharacteristic
336D5—22no—
337D5—22no—
338D5—43no—
339C23—51no—
340C23—51no—
341C23—53no—
342C23—102no—
343C23—102no—
344C23—102no—
345C23C23×D511yescharacteristic
346C23C23×D511yescharacteristic
347Q8—26no—
348Q8—26no—
349Q8—512no—
350Q8—1012no—
351Q8—106no—
352Q8—106no—
353Q8D4×D514yes—
354D4—22no—
355D4—106no—
356D4—106no—
357D4—106no—
358D4—102no—
359D4—102no—
360D4—106no—
361D4—106no—
362C2×C4—26no—
363C2×C4—26no—
364C2×C4—53no—
365C2×C4—512no—
366C2×C4—53no—
367C2×C4—51no—
368C2×C4—53no—
369C2×C4—51no—
370C2×C4—106no—
371C2×C4—1012no—
372C2×C4—106no—
373C2×C4—106no—
374C2×C4—106no—
375C2×C4—106no—
376C2×C4C23×D513yes—
377C2×C4C23×D511yescharacteristic
378C2×C4C23×D513yes—
379C2×C4C23×D513yes—
380C2×C4C23×D513yes—
381C5#348611yescharacteristic, complemented, Sylow
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—52no—
388C22—52no—
389C22—108no—
390C22—101no—
391C22—101no—
392C22—101no—
393C22—101no—
394C22—103no—
395C22—103no—
396C22—103no—
397C22#414712yescomplemented
398C22C24×D511yescharacteristic
399C4—23no—
400C4—23no—
401C4—21no—
402C4—23no—
403C4—56no—
404C4—101no—
405C4—103no—
406C4—103no—
407C4—101no—
408C4C2×D4×D516yes—
409C2—22no—
410C2—41no—
411C2—102no—
412C2—102no—
413C2—203no—
414C2C22×D4×D511yescharacteristic
415C2C2×#414711yescharacteristic
416C2D5×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×D5
commutator, socle, cosocleC22×C5C25
FittingC5×D4×Q8C2
hypercenterD4×Q8D5
hypocenterC5#3486
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#4147C2semidirect
2. C22×Q8×D5C2semidirect
3. C5×D4×Q8C2semidirect
4. #66151C2semidirect
5. Q8×C22⋊D5C2semidirect
6. #66061C2semidirect
7. #66058C2semidirect
8. #65967C2semidirect
9. #65966C2semidirect
10. #65962C2semidirect
11. #65961C2semidirect
12. #65910C2semidirect
13. #65906C2semidirect
14. #65886C2semidirect
15. #65881C2semidirect
17. C22×C5×Q8C22semidirect
20. C2×#713C22semidirect
26. C2×Q8×D5C22semidirect
28. C2×#709C22semidirect
31. C5×C4⋊Q8C22semidirect
33. C5×C22⋊Q8C22semidirect
34. C4×C5×Q8C22semidirect
36. #4093C22semidirect
38. #4092C22semidirect
39. Q8×Dic5C22semidirect
40. #4090C22semidirect
46. #4070C22semidirect
47. #4043C22semidirect
49. #4042C22semidirect
50. #4042C22semidirect
56. #4034C22semidirect
57. #4033C22semidirect
58. #4031C22semidirect
64. #4021C22semidirect
67. C4×Dic10C22semidirect
89. Q8×D5D4semidirect
137. D4×Q8D5semidirect
202. C22×Q8C2×D5semidirect
206. C4⋊Q8C2×D5semidirect
222. C22⋊Q8C2×D5semidirect
232. C4×Q8C2×D5semidirect
246. C22×C52−1+4semidirect
257. C2×D52−1+4semidirect
381. C5#3486semidirect
397. C22#4147semidirect

Maximal subgroups

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

subgroupindex
C2×#41472
C22×Q8×D52
C5×D4×Q82
#661512
Q8×C22⋊D52
#660612
#660582
#659672
#659662
#659622
#659612
#659102
#659062
#658862
#658812
#34865