Finite Group Databasebeta

← #10611615

Subgroups — #10611615

Order 640.

388 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#65892C211yesmaximal, characteristic, complemented
2#65885C211yesmaximal, characteristic, complemented
3C5×#442C211yesmaximal, characteristic, complemented
4#65448C211yesmaximal, characteristic, complemented
5#65446C211yesmaximal, characteristic, complemented
6#65298C211yesmaximal, characteristic, complemented
7#65297C211yesmaximal, characteristic, complemented
8#65150C211yesmaximal, characteristic, complemented
9D5×#106C211yesmaximal, characteristic, complemented
10#65073C211yesmaximal, characteristic, complemented
11#65066C211yesmaximal, characteristic, complemented
12#65066C211yesmaximal, characteristic, complemented
13#65063C211yesmaximal, characteristic, complemented
14#64995C211yesmaximal, characteristic, complemented
15#64991C211yesmaximal, characteristic, complemented
16C2×#709—21no—
17C2×C5×D8C2211yescharacteristic
18C4×C5×D4C2211yescharacteristic
19C4×C5×D4C2211yescharacteristic
20#4084C2211yescharacteristic
21#4084C2211yescharacteristic
22#4084C2211yescharacteristic
23#4084C2211yescharacteristic
24#4075—21no—
25C4×C22⋊D5—21no—
26#4070—21no—
27C2×#676C2211yescharacteristic
28C2×C8×D5C2211yescharacteristic
29#4038C2211yescharacteristic
30D5×C4⋊C4C2211yescharacteristic
31D5×C4⋊C4C2211yescharacteristic
32D5×C4⋊C4C2211yescharacteristic
33#4030—21no—
34#4029—21no—
35#4029—21no—
36#4025—21no—
37C4×D20C2211yescharacteristic
38#4016C2211yescharacteristic
39#4015C2211yescharacteristic
40C5×#106C2211yescharacteristic
41C5×#102C2211yescharacteristic
42C5×#102C2211yescharacteristic
43C5×#97C2211yescharacteristic
44#3964C2211yescharacteristic
45#3964C2211yescharacteristic
46#3964C2211yescharacteristic
47#3964C2211yescharacteristic
48#3952C2211yescharacteristic
49#3952C2211yescharacteristic
50#3950C2211yescharacteristic
51#3950C2211yescharacteristic
52#3949C2211yescharacteristic
53#3949C2211yescharacteristic
54#3940C2211yescharacteristic
55#3940C2211yescharacteristic
56#3940C2211yescharacteristic
57#3939C2211yescharacteristic
58C4⋊#168C2211yescharacteristic
59#3345—51nomaximal, Sylow
60C2×C5×D4C2311yescharacteristic
61C2×C5×D4C2311yescharacteristic
62C22×C4×C5—21no—
63C22×C4×C5—21no—
64C2×C22⋊D5—21no—
65C2×C22⋊D5—21no—
66C2×C22⋊D5—21no—
67C2×C22⋊D5—21no—
68#709—44no—
69C2×D20D411yescharacteristic
70C2×C4×D5—21no—
71C2×C4×D5—21no—
72C2×C4×D5—21no—
73C2×C4×D5C2311yescharacteristic
74C2×C4×D5C2311yescharacteristic
75C2×Dic10—21no—
76C5×D8—22no—
77C2×C5×C8C2311yescharacteristic
78C2×C5×C8C2311yescharacteristic
79C5×C4⋊C4C2311yescharacteristic
80C5×C4⋊C4C2311yescharacteristic
81C5×C22⋊C4—21no—
82C5×C22⋊C4—21no—
83C42×C5C2311yescharacteristic
84C22⋊Dic5—21no—
85C22⋊Dic5—21no—
86C22⋊Dic5—21no—
87C22⋊Dic5—21no—
88#685—21no—
89#685D411yescharacteristic
90#685D411yescharacteristic
91C4⋊Dic5—21no—
92C4⋊Dic5D411yescharacteristic
93C4⋊Dic5C2311yescharacteristic
94C4⋊Dic5C2311yescharacteristic
95C4⋊Dic5C2311yescharacteristic
96C4⋊Dic5C2311yescharacteristic
97#683—21no—
98#683—21no—
99#683—21no—
100#683—21no—
101#683—21no—
102C4×Dic5—21no—
103C2×#168C2311yescharacteristic
104C2×#168C2311yescharacteristic
105#676—22no—
106C8×D5—22no—
107#553—51no—
108#547—51no—
109#501—51no—
110#482—51no—
111#481—51no—
112#481—51no—
113#480—51no—
114#478—51no—
115#476—51no—
116#469—51no—
117#466—51no—
118#442D511yescharacteristic, complemented
119#435—51no—
120#428—51no—
121C2×#106—51no—
122C23×C5—21no—
123C23×C5—21no—
124C22×D5C2×D411yescharacteristic
125C22×D5C2×D411yescharacteristic
126C5×D4—21no—
127C5×D4—21no—
128C5×D4—21no—
129C5×D4—21no—
130C2×C4×C5—21no—
131C2×C4×C5—21no—
132C2×C4×C5—42no—
133C2×C4×C5—81no—
134C2×C4×C5C2×D411yescharacteristic
135C2×C4×C5C2×D411yescharacteristic
136C2×C4×C5C2411yescharacteristic
137C22⋊D5—42no—
138C22⋊D5—42no—
139C22⋊D5—42no—
140C22⋊D5—81no—
141C2×Dic5—21no—
142C2×Dic5—21no—
143C2×Dic5—21no—
144C2×Dic5—21no—
145C2×Dic5C2×D411yescharacteristic
146C2×Dic5C2×D411yescharacteristic
147D20—22no—
148C4×D5—21no—
149C4×D5—21no—
150C4×D5—21no—
151C4×D5—21no—
152C4×D5—42no—
153C4×D5—42no—
154C4×D5—81no—
155Dic10—42no—
156C5×C8—21no—
157C5×C8#4112yescomplemented
158#168—21no—
159#168—21no—
160C2×#41—101no—
161C2×D8C2×D511yescharacteristic
162C2×M16—51no—
163C22×C8—51no—
164C4⋊Q8—51no—
165#126—101no—
166#125—51no—
167#123—101no—
168#123—101no—
169#123—101no—
170C22⋊Q8—101no—
171#121—51no—
172#121—51no—
173#121—51no—
174#121—51no—
175#121—101no—
176C4×D4—51no—
177C4×D4—101no—
178C4×D4C2×D511yescharacteristic
179C4×D4C2×D511yescharacteristic
180#117—51no—
181C2×C4⋊C4—51no—
182C2×C4⋊C4—51no—
183C2×C4⋊C4—51no—
184#107—51no—
185#107—51no—
186#107—51no—
187#106—51no—
188#106—51no—
189#106—51no—
190#106—51no—
191#106—51no—
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⋊C8—51no—
202#97C2×D511yescharacteristic
203C22×C5—41no—
204C22×C5—41no—
205C22×C5—41no—
206C22×C5—41no—
207C22×C5—41no—
208C22×C5—41no—
209C22×C5C22×D411yescharacteristic
210C2×D5—21no—
211C2×D5—21no—
212C2×D5—21no—
213C2×D5—21no—
214C2×D5—21no—
215C2×D5AGL(1,ℤ/8)12yes—
216C4×C5—21no—
217C4×C5—21no—
218C4×C5—41no—
219C4×C5—41no—
220C4×C5C2×#4111yescharacteristic
221C4×C52−1+411yescharacteristic
222Dic5—21no—
223Dic5—21no—
224Dic5—41no—
225Dic5—41no—
226Dic5—41no—
227Dic5—41no—
228#41—204no—
229C2×Q8—101no—
230C2×D4—51no—
231C2×D4—101no—
232C2×D4—101no—
233C2×D4—101no—
234C2×D4—101no—
235C2×D4C22×D511yescharacteristic
236C2×D4C22×D511yescharacteristic
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—51no—
240C22×C4—51no—
241C22×C4—101no—
242C22×C4—101no—
243C22×C4—101no—
244D8—22no—
245M16—102no—
246C2×C8—51no—
247C2×C8—51no—
248C2×C8—102no—
249C2×C8C22×D511yescharacteristic
250C2×C8C22×D511yescharacteristic
251C4⋊C4—51no—
252C4⋊C4—51no—
253C4⋊C4—51no—
254C4⋊C4—51no—
255C4⋊C4—51no—
256C4⋊C4—101no—
257C4⋊C4—101no—
258C4⋊C4—101no—
259C4⋊C4—101no—
260C4⋊C4—101no—
261C4⋊C4—101no—
262C4⋊C4C22×D511yescharacteristic
263C4⋊C4C22×D511yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—51no—
267C22⋊C4—51no—
268C22⋊C4—101no—
269C22⋊C4—101no—
270C22⋊C4—101no—
271C22⋊C4—101no—
272C22⋊C4—101no—
273C42—101no—
274C42C22×D511yescharacteristic
275C2×C5—81no—
276C2×C5—81no—
277C2×C5#54711yescharacteristic
278C2×C5C2×AGL(1,ℤ/8)11yescharacteristic
279C2×C5#57711yescharacteristic
280D5—22no—
281D5—41no—
282C23—21no—
283C23—21no—
284C23—51no—
285C23—51no—
286Q8—202no—
287D4—21no—
288D4—21no—
289D4—21no—
290D4—21no—
291D4—102no—
292D4—202no—
293D4—202no—
294D4—202no—
295D4—401no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—42no—
299C2×C4—51no—
300C2×C4—51no—
301C2×C4—81no—
302C2×C4—101no—
303C2×C4—101no—
304C2×C4—101no—
305C2×C4—101no—
306C2×C4—101no—
307C2×C4—101no—
308C2×C4—101no—
309C2×C4—101no—
310C2×C4—202no—
311C2×C4—202no—
312C2×C4—401no—
313C2×C4D4×D511yescharacteristic
314C2×C4D4×D511yescharacteristic
315C2×C4C23×D511yescharacteristic
316C8—21no—
317C8—101no—
318C8—101no—
319C8#70912yescomplemented
320C5#334511yescharacteristic, complemented, Sylow
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—52no—
328C22—101no—
329C22—101no—
330C22—101no—
331C22—101no—
332C22—101no—
333C22C2×D4×D511yescharacteristic
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—101no—
339C4—101no—
340C4—201no—
341C4—201no—
342C4—201no—
343C4—201no—
344C4C2×#70911yescharacteristic
345C4#415011yescharacteristic
346C2—81no—
347C2—81no—
348C2—102no—
349C2—201no—
350C2#6588511yescharacteristic
351C2D5×AGL(1,ℤ/8)11yescharacteristic
352C2#6610911yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#442C2
socleC22×C5C22×D4
hypercenter#442D5
hypocenterC5#3345
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. #65892C2semidirect
2. #65885C2semidirect
3. C5×#442C2semidirect
4. #65448C2semidirect
5. #65446C2semidirect
6. #65298C2semidirect
7. #65297C2semidirect
8. #65150C2semidirect
9. D5×#106C2semidirect
10. #65073C2semidirect
11. #65066C2semidirect
12. #65066C2semidirect
13. #65063C2semidirect
14. #64995C2semidirect
15. #64991C2semidirect
118. #442D5semidirect
157. C5×C8#41semidirect
319. C8#709semidirect
320. C5#3345semidirect

Maximal subgroups

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

subgroupindex
#658922
#658852
C5×#4422
#654482
#654462
#652982
#652972
#651502
D5×#1062
#650732
#650662
#650632
#649952
#649912
#33455