Finite Group Databasebeta

← #10611600

Subgroups — #10611600

Order 640.

488 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#65882C211yesmaximal, characteristic, complemented
2C4×D4×D5C211yesmaximal, characteristic, complemented
3C5×#442C211yesmaximal, characteristic, complemented
4#65445C211yesmaximal, characteristic, complemented
5#65439C211yesmaximal, characteristic, complemented
6#65303C211yesmaximal, characteristic, complemented
7#65303C211yesmaximal, characteristic, complemented
8#65159C211yesmaximal, characteristic, complemented
9#65152C211yesmaximal, characteristic, complemented
10#65075C211yesmaximal, characteristic, complemented
11#65066C211yesmaximal, characteristic, complemented
12#65062C211yesmaximal, characteristic, complemented
13#65050C211yesmaximal, characteristic, complemented
14#65000C211yesmaximal, characteristic, complemented
15#64994C211yesmaximal, characteristic, complemented
16C2×D4×D5C2211yescharacteristic
17C2×#709—21no—
18C22×C4×D5—21no—
19C2×C5×D8C2211yescharacteristic
20C4×C5×D4C2211yescharacteristic
21C4×C5×D4C2211yescharacteristic, complemented
22#4086C2211yescharacteristic, complemented
23#4084C2211yescharacteristic
24D4×Dic5C2211yescharacteristic
25C2×#686C2211yescharacteristic
26C2×#686C2211yescharacteristic
27C4×C22⋊D5—21no—
28C4×C22⋊D5—21no—
29C2×D40C2211yescharacteristic
30#4041C2211yescharacteristic
31#4039C2211yescharacteristic
32D5×C4⋊C4C2211yescharacteristic
33#4034C2211yescharacteristic, complemented
34#4031—21no—
35#4030—21no—
36#4027—21no—
37D5×C22⋊C4—21no—
38C4×D20C2211yescharacteristic
39C4×D20C2211yescharacteristic, complemented
40C42×D5C2211yescharacteristic
41C5×#106C2211yescharacteristic, complemented
42C5×#102C2211yescharacteristic
43C5×#102C2211yescharacteristic, complemented
44C5×#97C2211yescharacteristic, complemented
45#3964C2211yescharacteristic
46#3964C2211yescharacteristic, complemented
47#3953C2211yescharacteristic
48#3953C2211yescharacteristic, complemented
49#3952C2211yescharacteristic
50#3952C2211yescharacteristic
51#3949C2211yescharacteristic, complemented
52#3946C2211yescharacteristic, complemented
53#3946C2211yescharacteristic, complemented
54#3941C2211yescharacteristic
55#3941C2211yescharacteristic, complemented
56#3940C2211yescharacteristic, complemented
57#3940C2211yescharacteristic, complemented
58#3935C2211yescharacteristic, complemented
59#3109—51nomaximal, Sylow
60C23×D5—21no—
61C2×C5×D4C2311yescharacteristic
62C2×C5×D4C2311yescharacteristic
63C22×C4×C5—21no—
64C22×C4×C5—21no—
65C2×C22⋊D5—21no—
66C2×C22⋊D5—21no—
67C2×C22⋊D5—21no—
68C2×C22⋊D5—21no—
69C22×Dic5—21no—
70D4×D5—22no—
71D4×D5—22no—
72#709—44no—
73C2×D20—21no—
74C2×D20C2311yescharacteristic
75C2×D20C2311yescharacteristic
76C2×C4×D5—21no—
77C2×C4×D5—21no—
78C2×C4×D5—21no—
79C2×C4×D5—21no—
80C2×C4×D5—44no—
81C2×C4×D5D411yescharacteristic
82C2×C4×D5D411yescharacteristic
83C2×C4×D5C2311yescharacteristic
84C2×Dic10—21no—
85C5×D8—22no—
86C2×C5×C8C2311yescharacteristic
87C2×C5×C8C2311yescharacteristic
88C5×C4⋊C4C2311yescharacteristic
89C5×C4⋊C4C2311yescharacteristic
90C5×C22⋊C4—21no—
91C5×C22⋊C4—21no—
92C42×C5C2311yescharacteristic
93C22⋊Dic5—21no—
94C22⋊Dic5—21no—
95#686—22no—
96#686—22no—
97#685—21no—
98#685—21no—
99#685—21no—
100#685—21no—
101C4⋊Dic5C2311yescharacteristic
102C4⋊Dic5C2311yescharacteristic
103#683—21no—
104#683—21no—
105C4×Dic5D411yescharacteristic
106C4×Dic5D411yescharacteristic
107C4×Dic5C2311yescharacteristic
108C2×#168C2311yescharacteristic
109C2×#168C2311yescharacteristic
110D40—22no—
111#532—51no—
112C2×C4×D4—51no—
113#481—51no—
114#481—51no—
115#476—51no—
116#476—51no—
117#459—51no—
118#459—51no—
119#447—51no—
120#447—51no—
121#442—51no—
122#442—51no—
123#442—51no—
124#442D511yescharacteristic, complemented
125#432—51no—
126C23×C5—21no—
127C23×C5—21no—
128C22×D5—24no—
129C22×D5—21no—
130C22×D5—21no—
131C22×D5—42no—
132C22×D5—42no—
133C22×D5C2×D411yescharacteristic
134C5×D4—21no—
135C5×D4—21no—
136C5×D4—21no—
137C5×D4#4112yescomplemented
138C2×C4×C5—21no—
139C2×C4×C5—21no—
140C2×C4×C5—42no—
141C2×C4×C5—42no—
142C2×C4×C5C2×D411yescharacteristic
143C2×C4×C5C2×D411yescharacteristic
144C2×C4×C5C2411yescharacteristic
145C22⋊D5—24no—
146C22⋊D5—42no—
147C22⋊D5—42no—
148C22⋊D5—42no—
149C2×Dic5—21no—
150C2×Dic5—21no—
151C2×Dic5—42no—
152C2×Dic5C2×D411yescharacteristic
153C2×Dic5C2×D411yescharacteristic
154C2×Dic5C2×D411yescharacteristic
155D20—21no—
156D20—21no—
157D20—21no—
158D20—42no—
159D20#4112yescomplemented
160C4×D5—22no—
161C4×D5—21no—
162C4×D5—21no—
163C4×D5—22no—
164C4×D5—42no—
165C4×D5—42no—
166C4×D5—42no—
167C4×D5—42no—
168Dic10—42no—
169C5×C8—21no—
170C5×C8—21no—
171#168—21no—
172#168—21no—
173C2×#41—101no—
174C22×D4—51no—
175C23×C4—101no—
176C2×D8—51no—
177C2×D8—51no—
178C2×D8—51no—
179C2×D8C2×D511yescharacteristic
180C4⋊Q8—51no—
181#127—51no—
182#124—101no—
183#121—51no—
184#121—51no—
185#121—101no—
186C4×D4—51no—
187C4×D4—51no—
188C4×D4—51no—
189C4×D4—51no—
190C4×D4—101no—
191C4×D4—101no—
192C4×D4—101no—
193C4×D4C2×D511yescharacteristic
194C4×D4C2×D511yescharacteristic, complemented
195C2×C4⋊C4—51no—
196C2×C22⋊C4—101no—
197C2×C42—51no—
198#106—51no—
199#106—51no—
200#106—51no—
201#106C2×D511yescharacteristic, complemented
202C4⋊C8—51no—
203C4⋊C8—51no—
204#102—51no—
205#102—51no—
206#102—51no—
207#102—51no—
208#102—51no—
209#102—51no—
210#102C2×D511yescharacteristic
211#102C2×D511yescharacteristic, complemented
212C22⋊C8—51no—
213C22⋊C8—51no—
214#97—51no—
215#97C2×D511yescharacteristic, complemented
216C22×C5—22no—
217C22×C5—41no—
218C22×C5—41no—
219C22×C5—41no—
220C22×C5—41no—
221C22×C5—41no—
222C22×C5C22×D411yescharacteristic
223C2×D5—21no—
224C2×D5—21no—
225C2×D5—22no—
226C2×D5—48no—
227C2×D5—41no—
228C2×D5—41no—
229C2×D5—41no—
230C2×D5—41no—
231C2×D5—41no—
232C2×D5AGL(1,ℤ/8)12yes—
233C4×C5—21no—
234C4×C5—21no—
235C4×C5—41no—
236C4×C5—41no—
237C4×C5C2×#4111yescharacteristic
238C4×C5C2×#4111yescharacteristic
239Dic5—21no—
240Dic5—21no—
241Dic5—41no—
242Dic5—41no—
243Dic5AGL(1,ℤ/8)12yes—
244C24—101no—
245#41—204no—
246C2×Q8—101no—
247C2×D4—51no—
248C2×D4—51no—
249C2×D4—101no—
250C2×D4—101no—
251C2×D4—101no—
252C2×D4—101no—
253C2×D4—102no—
254C2×D4—102no—
255C2×D4—101no—
256C2×D4C22×D511yescharacteristic
257C2×D4C22×D511yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—51no—
261C22×C4—51no—
262C22×C4—51no—
263C22×C4—101no—
264C22×C4—101no—
265C22×C4—101no—
266C22×C4—101no—
267C22×C4—101no—
268C22×C4—204no—
269D8—22no—
270D8—102no—
271D8—102no—
272D8—102no—
273C2×C8—51no—
274C2×C8—51no—
275C2×C8C22×D511yescharacteristic
276C2×C8C22×D511yescharacteristic
277C4⋊C4—51no—
278C4⋊C4—51no—
279C4⋊C4—101no—
280C4⋊C4—101no—
281C4⋊C4C22×D511yescharacteristic
282C4⋊C4C22×D511yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—101no—
286C22⋊C4—101no—
287C22⋊C4—101no—
288C22⋊C4—101no—
289C22⋊C4—101no—
290C22⋊C4—101no—
291C42—51no—
292C42—51no—
293C42—51no—
294C42C22×D511yescharacteristic
295C2×C5—42no—
296C2×C5—81no—
297C2×C5#52511yescharacteristic
298C2×C5C2×AGL(1,ℤ/8)11yescharacteristic
299C2×C5C2×AGL(1,ℤ/8)11yescharacteristic
300D5—22no—
301D5—42no—
302D5—81no—
303C23—21no—
304C23—21no—
305C23—51no—
306C23—104no—
307C23—101no—
308C23—101no—
309C23—202no—
310C23—202no—
311Q8—202no—
312D4—21no—
313D4—21no—
314D4—21no—
315D4—52no—
316D4—104no—
317D4—101no—
318D4—101no—
319D4—101no—
320D4—202no—
321D4—202no—
322D4—202no—
323D4—202no—
324D4#70912yescomplemented
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—51no—
330C2×C4—51no—
331C2×C4—51no—
332C2×C4—102no—
333C2×C4—102no—
334C2×C4—101no—
335C2×C4—101no—
336C2×C4—101no—
337C2×C4—101no—
338C2×C4—202no—
339C2×C4—202no—
340C2×C4—202no—
341C2×C4—202no—
342C2×C4—202no—
343C2×C4D4×D511yescharacteristic
344C2×C4D4×D511yescharacteristic
345C2×C4C23×D511yescharacteristic
346C8—21no—
347C8—21no—
348C8—101no—
349C8—101no—
350C5#310911yescharacteristic, complemented, Sylow
351C22—22no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—52no—
358C22—101no—
359C22—101no—
360C22—102no—
361C22—208no—
362C22—201no—
363C22—201no—
364C22—201no—
365C22—201no—
366C22—201no—
367C22C2×D4×D511yescharacteristic
368C4—21no—
369C4—21no—
370C4—41no—
371C4—41no—
372C4—52no—
373C4—101no—
374C4—101no—
375C4—201no—
376C4—201no—
377C4C2×#70911yescharacteristic
378C4D5×#4111yescharacteristic
379C2—42no—
380C2—81no—
381C2—102no—
382C2—202no—
383C2—401no—
384C2#6588111yescharacteristic
385C2D5×AGL(1,ℤ/8)11yescharacteristic
386C2D5×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#442C2
socleC22×C5C22×D4
hypercenter#442D5
hypocenterC5#3109
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #65882C2semidirect
2. C4×D4×D5C2semidirect
3. C5×#442C2semidirect
4. #65445C2semidirect
5. #65439C2semidirect
6. #65303C2semidirect
7. #65303C2semidirect
8. #65159C2semidirect
9. #65152C2semidirect
10. #65075C2semidirect
11. #65066C2semidirect
12. #65062C2semidirect
13. #65050C2semidirect
14. #65000C2semidirect
15. #64994C2semidirect
21. C4×C5×D4C22semidirect
22. #4086C22semidirect
33. #4034C22semidirect
39. C4×D20C22semidirect
41. C5×#106C22semidirect
43. C5×#102C22semidirect
44. C5×#97C22semidirect
46. #3964C22semidirect
48. #3953C22semidirect
51. #3949C22semidirect
52. #3946C22semidirect
53. #3946C22semidirect
55. #3941C22semidirect
56. #3940C22semidirect
57. #3940C22semidirect
58. #3935C22semidirect
124. #442D5semidirect
137. C5×D4#41semidirect
159. D20#41semidirect
194. C4×D4C2×D5semidirect
201. #106C2×D5semidirect
211. #102C2×D5semidirect
215. #97C2×D5semidirect
324. D4#709semidirect
350. C5#3109semidirect

Maximal subgroups

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

subgroupindex
#658822
C4×D4×D52
C5×#4422
#654452
#654392
#653032
#651592
#651522
#650752
#650662
#650622
#650502
#650002
#649942
#31095