Finite Group Databasebeta

← #10613069

Subgroups — #10613069

Order 640.

386 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#65950C211yesmaximal, characteristic, complemented
2#65841C211yesmaximal, characteristic, complemented
3C5×#481C211yesmaximal, characteristic, complemented
4#65328C211yesmaximal, characteristic, complemented
5#65253C211yesmaximal, characteristic, complemented
6#65159C211yesmaximal, characteristic, complemented
7#65155C211yesmaximal, characteristic, complemented
8#65150C211yesmaximal, characteristic, complemented
9#65144C211yesmaximal, characteristic, complemented
10#65071C211yesmaximal, characteristic, complemented
11#65066C211yesmaximal, characteristic, complemented
12#65048C211yesmaximal, characteristic, complemented
13#65045C211yesmaximal, characteristic, complemented
14#65026C211yesmaximal, characteristic, complemented
15#65018C211yesmaximal, characteristic, complemented
16C2×#709—21no—
17C5×#121C2211yescharacteristic
18C2×C5×C4⋊C4C2211yescharacteristic
19#4085—21no—
20#4084C2211yescharacteristic
21#4082—21no—
22D4×Dic5C2211yescharacteristic
23C2×#686C2211yescharacteristic
24#4076C2211yescharacteristic
25#4075—21no—
26C4×C22⋊D5C2211yescharacteristic
27#4072C2211yescharacteristic
28C2×#681C2211yescharacteristic
29C2×#676C2211yescharacteristic
30#4042—21no—
31#4041C2211yescharacteristic
32#4040—21no—
33#4039C2211yescharacteristic
34#4038C2211yescharacteristic
35D5×C4⋊C4C2211yescharacteristic
36#4034C2211yescharacteristic
37#4034C2211yescharacteristic
38#4031—21no—
39#4023—21no—
40C5×#106C2211yescharacteristic
41C5×#106C2211yescharacteristic
42C5×#102C2211yescharacteristic
43C5×#102C2211yescharacteristic
44C5×C22⋊C8C2211yescharacteristic
45#3964C2211yescharacteristic
46#3953C2211yescharacteristic
47#3953C2211yescharacteristic
48#3952C2211yescharacteristic
49#3950C2211yescharacteristic
50#3949C2211yescharacteristic
51#3946C2211yescharacteristic
52C8×Dic5C2211yescharacteristic
53#3941C2211yescharacteristic
54#3940C2211yescharacteristic
55#3940C2211yescharacteristic
56#3940C2211yescharacteristic
57#3939C2211yescharacteristic
58#3939C2211yescharacteristic
59#3354—51nomaximal, Sylow
60C2×C5×D4—21no—
61C2×C5×D4C2311yescharacteristic
62C22×C4×C5—21no—
63C22×C4×C5C2311yescharacteristic
64C2×C22⋊D5—21no—
65C2×C22⋊D5—21no—
66C2×C22⋊D5D411yescharacteristic
67C22×Dic5—21no—
68#709—44no—
69C2×D20—21no—
70C2×D20C2311yescharacteristic
71C2×C4×D5—21no—
72C2×C4×D5—21no—
73C2×C4×D5C2311yescharacteristic
74C2×Dic10—21no—
75C2×Dic10—21no—
76C2×C5×C8C2311yescharacteristic
77C2×C5×C8C2311yescharacteristic
78C5×C4⋊C4—21no—
79C5×C4⋊C4C2311yescharacteristic
80C5×C4⋊C4C2311yescharacteristic
81C5×C4⋊C4C2311yescharacteristic
82C5×C22⋊C4—21no—
83C22⋊Dic5—21no—
84C22⋊Dic5—21no—
85C22⋊Dic5—21no—
86C22⋊Dic5D411yescharacteristic
87#686—22no—
88#685—21no—
89#685—21no—
90#685—21no—
91#685—21no—
92#685D411yescharacteristic
93C4⋊Dic5C2311yescharacteristic
94C4⋊Dic5C2311yescharacteristic
95C4⋊Dic5C2311yescharacteristic
96#683—21no—
97#683—21no—
98#683—21no—
99#683D411yescharacteristic
100C4×Dic5—21no—
101C4×Dic5—21no—
102C4×Dic5C2311yescharacteristic
103#681—22no—
104C2×#168C2311yescharacteristic
105C2×#168C2311yescharacteristic
106#676—22no—
107#555—51no—
108#547—51no—
109#498—51no—
110#482—51no—
111#482—51no—
112#481—51no—
113#481D511yescharacteristic, complemented
114#476—51no—
115#474—51no—
116#469—51no—
117#469—51no—
118C4×D8—51no—
119#436—51no—
120#428—51no—
121#428—51no—
122C23×C5—21no—
123C23×C5C2×D411yescharacteristic
124C22×D5—21no—
125C22×D5C2×D411yescharacteristic
126C5×D4—21no—
127C5×D4—21no—
128C5×D4—81no—
129C2×C4×C5—21no—
130C2×C4×C5—21no—
131C2×C4×C5—21no—
132C2×C4×C5—21no—
133C2×C4×C5—21no—
134C2×C4×C5—42no—
135C2×C4×C5C2×D411yescharacteristic
136C2×C4×C5C2411yescharacteristic
137C22⋊D5—22no—
138C22⋊D5—42no—
139C22⋊D5—81no—
140C2×Dic5—21no—
141C2×Dic5—21no—
142C2×Dic5—21no—
143C2×Dic5—42no—
144C2×Dic5C2×D411yescharacteristic
145C2×Dic5C2×D411yescharacteristic
146C2×Dic5C2×D411yescharacteristic
147D20—21no—
148D20—21no—
149D20—42no—
150C4×D5—21no—
151C4×D5—21no—
152C4×D5—42no—
153C4×D5—42no—
154Dic10—42no—
155Dic10—81no—
156C5×C8—21no—
157C5×C8—21no—
158#168—21no—
159#168#4112yescomplemented
160C2×#41—101no—
161C2×D8—51no—
162C2×M16—51no—
163C2×M16—51no—
164C4⋊Q8—51no—
165C4⋊Q8—51no—
166#124—101no—
167#124—101no—
168#123—101no—
169#123—101no—
170C22⋊Q8—101no—
171#121—51no—
172#121—51no—
173#121—51no—
174#121—101no—
175#121C2×D511yescharacteristic
176C4×D4—51no—
177C4×D4—51no—
178C4×D4—51no—
179#117—51no—
180#117—51no—
181#117—101no—
182C2×C4⋊C4—51no—
183C2×C4⋊C4C2×D511yescharacteristic
184#107—51no—
185#107—51no—
186#107—51no—
187#106—51no—
188#106—51no—
189#106—51no—
190#106—51no—
191#106C2×D511yescharacteristic
192#106C2×D511yescharacteristic
193C4⋊C8—51no—
194#102—51no—
195#102—51no—
196#102—51no—
197#102—51no—
198#102C2×D511yescharacteristic
199#102C2×D511yescharacteristic
200C22⋊C8—51no—
201C22⋊C8C2×D511yescharacteristic
202C4×C8—51no—
203C22×C5—21no—
204C22×C5—21no—
205C22×C5—21no—
206C22×C5—41no—
207C22×C5—41no—
208C22×C5—41no—
209C22×C5C22×D411yescharacteristic
210C2×D5—21no—
211C2×D5—21no—
212C2×D5—21no—
213C2×D5—41no—
214C2×D5—41no—
215C2×D5—41no—
216C4×C5—21no—
217C4×C5—41no—
218C4×C5—41no—
219C4×C5—41no—
220C4×C5C2×#4111yescharacteristic
221C4×C52−1+411yescharacteristic
222Dic5—21no—
223Dic5—21no—
224Dic5—41no—
225Dic5—41no—
226Dic5—41no—
227Dic5AGL(1,ℤ/8)12yes—
228#41—204no—
229C2×Q8—101no—
230C2×Q8—101no—
231C2×D4—21no—
232C2×D4—51no—
233C2×D4—51no—
234C2×D4—101no—
235C2×D4—101no—
236C2×D4—101no—
237C2×D4C22×D511yescharacteristic
238C22×C4—21no—
239C22×C4—51no—
240C22×C4—101no—
241C22×C4—101no—
242C22×C4—101no—
243C22×C4C22×D511yescharacteristic
244D8—102no—
245M16—102no—
246M16—102no—
247C2×C8—51no—
248C2×C8—51no—
249C2×C8C22×D511yescharacteristic
250C2×C8C22×D511yescharacteristic
251C4⋊C4—21no—
252C4⋊C4—51no—
253C4⋊C4—51no—
254C4⋊C4—51no—
255C4⋊C4—51no—
256C4⋊C4—101no—
257C4⋊C4—101no—
258C4⋊C4—101no—
259C4⋊C4C22×D511yescharacteristic
260C4⋊C4C22×D511yescharacteristic
261C4⋊C4C22×D511yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—51no—
264C22⋊C4—51no—
265C22⋊C4—101no—
266C22⋊C4—101no—
267C22⋊C4—101no—
268C22⋊C4—101no—
269C22⋊C4—101no—
270C22⋊C4—101no—
271C22⋊C4—101no—
272C42—51no—
273C42—101no—
274C42—101no—
275C2×C5—41no—
276C2×C5—81no—
277C2×C5#54711yescharacteristic
278C2×C5C2×AGL(1,ℤ/8)11yescharacteristic
279C2×C5#57711yescharacteristic
280D5—41no—
281D5—81no—
282C23—21no—
283C23—51no—
284C23—101no—
285C23D4×D511yescharacteristic
286Q8—202no—
287Q8—401no—
288D4—21no—
289D4—21no—
290D4—81no—
291D4—102no—
292D4—101no—
293D4—101no—
294D4—202no—
295D4—202no—
296D4—401no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—42no—
303C2×C4—51no—
304C2×C4—51no—
305C2×C4—51no—
306C2×C4—101no—
307C2×C4—101no—
308C2×C4—101no—
309C2×C4—101no—
310C2×C4—101no—
311C2×C4—202no—
312C2×C4—202no—
313C2×C4—202no—
314C2×C4D4×D511yescharacteristic
315C2×C4C23×D511yescharacteristic
316C8—21no—
317C8—21no—
318C8—52no—
319C8—101no—
320C5#335411yescharacteristic, complemented, Sylow
321C22—21no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—101no—
328C22—101no—
329C22—101no—
330C22—201no—
331C22—201no—
332C22—201no—
333C22C2×D4×D511yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—52no—
339C4—101no—
340C4—101no—
341C4—201no—
342C4—201no—
343C4—201no—
344C4D5×#4111yescharacteristic
345C4#415011yescharacteristic
346C2—41no—
347C2—81no—
348C2—201no—
349C2—401no—
350C2#6598911yescharacteristic
351C2#6609611yescharacteristic
352C2D5×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#481C2
socleC22×C5C22×D4
hypercenter#481D5
hypocenterC5#3354
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #65950C2semidirect
2. #65841C2semidirect
3. C5×#481C2semidirect
4. #65328C2semidirect
5. #65253C2semidirect
6. #65159C2semidirect
7. #65155C2semidirect
8. #65150C2semidirect
9. #65144C2semidirect
10. #65071C2semidirect
11. #65066C2semidirect
12. #65048C2semidirect
13. #65045C2semidirect
14. #65026C2semidirect
15. #65018C2semidirect
113. #481D5semidirect
159. #168#41semidirect
320. C5#3354semidirect

Maximal subgroups

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

subgroupindex
#659502
#658412
C5×#4812
#653282
#652532
#651592
#651552
#651502
#651442
#650712
#650662
#650482
#650452
#650262
#650182
#33545