Finite Group Databasebeta

← #10611539

Subgroups — #10611539

Order 640.

348 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#65915C211yesmaximal, characteristic, complemented
2#65897C211yesmaximal, characteristic
3C5×#440C211yesmaximal, characteristic, complemented
4#65463C211yesmaximal, characteristic, complemented
5#65460C211yesmaximal, characteristic, complemented
6#65309C211yesmaximal, characteristic, complemented
7#65298C211yesmaximal, characteristic, complemented
8#65170C211yesmaximal, characteristic, complemented
9#65169C211yesmaximal, characteristic, complemented
10#65104C211yesmaximal, characteristic, complemented
11#65103C211yesmaximal, characteristic, complemented
12#65073C211yesmaximal, characteristic, complemented
13#65066C211yesmaximal, characteristic, complemented
14#64995C211yesmaximal, characteristic, complemented
15#64991C211yesmaximal, characteristic, complemented
16C2×C5×SD16C2211yescharacteristic
17C4×C5×Q8C2211yescharacteristic
18C4×C5×D4C2211yescharacteristic
19#4092C2211yescharacteristic
20#4092C2211yescharacteristic
21#4084C2211yescharacteristic
22#4084C2211yescharacteristic
23#4076—21no—
24#4072—21no—
25C2×#676C2211yescharacteristic
26C2×C8×D5C2211yescharacteristic
27#4040—21no—
28#4038C2211yescharacteristic
29#4038C2211yescharacteristic
30#4038C2211yescharacteristic
31D5×C4⋊C4C2211yescharacteristic
32#4035—21no—
33#4031—21no—
34#4031—21no—
35#4022—21no—
36C4×D20C2211yescharacteristic
37#4018—21no—
38#4016C2211yescharacteristic
39#4015C2211yescharacteristic
40C5×#107C2211yescharacteristic
41C5×#103C2211yescharacteristic
42C5×#102C2211yescharacteristic
43C5×#97C2211yescharacteristic
44#3967C2211yescharacteristic
45#3967C2211yescharacteristic
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#3348—51nomaximal, Sylow
60C2×C5×Q8C2311yescharacteristic
61C2×C5×D4C2311yescharacteristic
62C22×C4×C5—21no—
63C2×C22⋊D5—21no—
64C2×C22⋊D5—21no—
65C2×D20D411yescharacteristic
66C2×C4×D5—21no—
67C2×C4×D5C2311yescharacteristic
68C2×C4×D5C2311yescharacteristic
69C2×Dic10—21no—
70C5×SD16—22no—
71C2×C5×C8C2311yescharacteristic
72C2×C5×C8C2311yescharacteristic
73C5×C4⋊C4—21no—
74C5×C4⋊C4C2311yescharacteristic
75C5×C4⋊C4C2311yescharacteristic
76C5×C22⋊C4—21no—
77C42×C5—21no—
78C42×C5C2311yescharacteristic
79C22⋊Dic5—21no—
80C22⋊Dic5—21no—
81#685—21no—
82#685—21no—
83#685—21no—
84#685—21no—
85#685—21no—
86#685D411yescharacteristic
87#685D411yescharacteristic
88C4⋊Dic5—21no—
89C4⋊Dic5D411yescharacteristic
90C4⋊Dic5C2311yescharacteristic
91C4⋊Dic5C2311yescharacteristic
92C4⋊Dic5C2311yescharacteristic
93C4⋊Dic5C2311yescharacteristic
94#683—21no—
95#683—21no—
96#683—21no—
97#683—21no—
98#683—21no—
99C4×Dic5—21no—
100C4×Dic5—21no—
101C4×Dic5—21no—
102C2×#168C2311yescharacteristic
103C2×#168C2311yescharacteristic
104#676—22no—
105C8×D5—22no—
106#555—51no—
107#552—51no—
108#501—51no—
109#485—51no—
110#485—51no—
111#482—51no—
112#481—51no—
113#478—51no—
114#475—51no—
115#468—51no—
116#465—51no—
117#440D511yescharacteristic, complemented
118#435—51no—
119#428—51no—
120#427—51no—
121C23×C5—21no—
122C22×D5C2×D411yescharacteristic
123C22×D5C2×D411yescharacteristic
124C5×Q8—21no—
125C5×Q8—21no—
126C5×D4—21no—
127C5×D4—21no—
128C2×C4×C5—21no—
129C2×C4×C5—21no—
130C2×C4×C5—21no—
131C2×C4×C5—42no—
132C2×C4×C5C2×D411yescharacteristic
133C2×C4×C5C2×D411yescharacteristic
134C2×C4×C5C2411yescharacteristic
135C22⋊D5—81no—
136C22⋊D5—81no—
137C2×Dic5—21no—
138C2×Dic5—21no—
139C2×Dic5—21no—
140C2×Dic5—21no—
141C2×Dic5C2×D411yescharacteristic
142C2×Dic5C2×D411yescharacteristic
143D20—41no—
144C4×D5—21no—
145C4×D5—21no—
146C4×D5—21no—
147C4×D5—21no—
148C4×D5—42no—
149Dic10—81no—
150C5×C8—21no—
151C5×C8#4112yes—
152#168—21no—
153#168—21no—
154C2×SD16C2×D511yescharacteristic
155C2×M16—51no—
156C22×C8—51no—
157C4⋊Q8—51no—
158#126—101no—
159#125—51no—
160#125—101no—
161#124—101no—
162#124—101no—
163#123—101no—
164C22⋊Q8—51no—
165C22⋊Q8—51no—
166#121—51no—
167#121—51no—
168#121—101no—
169C4×Q8C2×D511yescharacteristic
170C4×D4—51no—
171C4×D4C2×D511yescharacteristic
172#117—51no—
173#117—51no—
174#117—51no—
175#117—101no—
176#117—101no—
177C2×C4⋊C4—51no—
178#107—51no—
179#107—51no—
180#107—51no—
181#107C2×D511yescharacteristic
182#106—51no—
183#106—51no—
184#106—51no—
185#106—51no—
186#106—51no—
187C4⋊C8—51no—
188#103—51no—
189#103—51no—
190#103C2×D511yescharacteristic
191#102—51no—
192#102—51no—
193#102C2×D511yescharacteristic
194C22⋊C8—51no—
195C22⋊C8—51no—
196#97C2×D511yescharacteristic
197C22×C5—41no—
198C22×C5—41no—
199C22×C5—41no—
200C22×C5C22×D411yescharacteristic
201C2×D5—21no—
202C2×D5—21no—
203C2×D5—21no—
204C2×D5—21no—
205C2×D5—21no—
206C2×D5—21no—
207C4×C5—21no—
208C4×C5—21no—
209C4×C5—41no—
210C4×C5—41no—
211C4×C5—41no—
212C4×C5C2×#4111yescharacteristic
213C4×C52−1+411yescharacteristic
214Dic5—21no—
215Dic5—21no—
216Dic5—41no—
217Dic5—41no—
218Dic5—41no—
219Dic5—41no—
220C2×Q8—101no—
221C2×Q8C22×D511yescharacteristic
222C2×D4—51no—
223C2×D4—101no—
224C2×D4—101no—
225C2×D4C22×D511yescharacteristic
226C22×C4—21no—
227C22×C4—51no—
228C22×C4—51no—
229C22×C4—101no—
230SD16—22no—
231M16—102no—
232C2×C8—51no—
233C2×C8—51no—
234C2×C8—102no—
235C2×C8C22×D511yescharacteristic
236C2×C8C22×D511yescharacteristic
237C4⋊C4—21no—
238C4⋊C4—51no—
239C4⋊C4—51no—
240C4⋊C4—51no—
241C4⋊C4—51no—
242C4⋊C4—51no—
243C4⋊C4—101no—
244C4⋊C4—101no—
245C4⋊C4—101no—
246C4⋊C4—101no—
247C4⋊C4—101no—
248C4⋊C4—101no—
249C4⋊C4C22×D511yescharacteristic
250C4⋊C4C22×D511yescharacteristic
251C22⋊C4—21no—
252C22⋊C4—51no—
253C22⋊C4—51no—
254C22⋊C4—101no—
255C22⋊C4—101no—
256C22⋊C4—101no—
257C22⋊C4—101no—
258C22⋊C4—101no—
259C22⋊C4—101no—
260C22⋊C4—101no—
261C42—21no—
262C42—101no—
263C42—101no—
264C42—101no—
265C42C22×D511yescharacteristic
266C2×C5—81no—
267C2×C5#54711yescharacteristic
268C2×C5#57511yescharacteristic
269C2×C5#57711yescharacteristic
270D5—41no—
271D5—41no—
272C23—21no—
273C23—51no—
274C23—51no—
275Q8—21no—
276Q8—21no—
277Q8—401no—
278D4—21no—
279D4—21no—
280D4—201no—
281D4—401no—
282D4—401no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—42no—
287C2×C4—51no—
288C2×C4—51no—
289C2×C4—101no—
290C2×C4—101no—
291C2×C4—101no—
292C2×C4—101no—
293C2×C4—101no—
294C2×C4—101no—
295C2×C4—101no—
296C2×C4—101no—
297C2×C4—202no—
298C2×C4D4×D511yescharacteristic
299C2×C4D4×D511yescharacteristic
300C2×C4C23×D511yescharacteristic
301C8—21no—
302C8—101no—
303C8—101no—
304C8#70912yes—
305C5#334811yescharacteristic, complemented, Sylow
306C22—41no—
307C22—41no—
308C22—41no—
309C22—101no—
310C22—101no—
311C22—101no—
312C22—101no—
313C22—101no—
314C22—101no—
315C22C2×D4×D511yescharacteristic
316C4—21no—
317C4—21no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—101no—
322C4—101no—
323C4—201no—
324C4—201no—
325C4—201no—
326C4—201no—
327C4C2×#70911yescharacteristic
328C4#415011yescharacteristic
329C2—81no—
330C2—201no—
331C2—201no—
332C2#6588511yescharacteristic
333C2#6610711yescharacteristic
334C2#6611211yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#440C2
socleC22×C5C22×D4
prime radical#65897C2
hypercenter#440D5
hypocenterC5#3348
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #65915C2semidirect
3. C5×#440C2semidirect
4. #65463C2semidirect
5. #65460C2semidirect
6. #65309C2semidirect
7. #65298C2semidirect
8. #65170C2semidirect
9. #65169C2semidirect
10. #65104C2semidirect
11. #65103C2semidirect
12. #65073C2semidirect
13. #65066C2semidirect
14. #64995C2semidirect
15. #64991C2semidirect
117. #440D5semidirect
305. C5#3348semidirect

Maximal subgroups

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

subgroupindex
#659152
#658972
C5×#4402
#654632
#654602
#653092
#652982
#651702
#651692
#651042
#651032
#650732
#650662
#649952
#649912
#33485