Finite Group Databasebeta

← #10613091

Subgroups — #10613091

Order 640.

332 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#65953C211yesmaximal, characteristic
2#65853C211yesmaximal, characteristic, complemented
3C5×#482C211yesmaximal, characteristic, complemented
4#65322C211yesmaximal, characteristic, complemented
5#65292C211yesmaximal, characteristic, complemented
6#65179C211yesmaximal, characteristic, complemented
7#65165C211yesmaximal, characteristic, complemented
8#65160C211yesmaximal, characteristic, complemented
9#65147C211yesmaximal, characteristic, complemented
10#65053C211yesmaximal, characteristic, complemented
11#65052C211yesmaximal, characteristic, complemented
12#65050C211yesmaximal, characteristic, complemented
13#65049C211yesmaximal, characteristic, complemented
14#65024C211yesmaximal, characteristic, complemented
15#65009C211yesmaximal, characteristic, complemented
16C5×#121C2211yescharacteristic
17C5×#117C2211yescharacteristic
18#4086C2211yescharacteristic
19#4085—21no—
20#4084—21no—
21D4×Dic5C2211yescharacteristic
22#4076C2211yescharacteristic
23#4072C2211yescharacteristic
24C2×C4⋊Dic5C2211yescharacteristic
25#4039C2211yescharacteristic
26#4036C2211yescharacteristic
27#4036C2211yescharacteristic
28#4036C2211yescharacteristic
29#4034C2211yescharacteristic
30#4034C2211yescharacteristic
31#4032—21no—
32#4029—21no—
33#4024—21no—
34#4024—21no—
35#4016—21no—
36#4015—21no—
37C5×#107C2211yescharacteristic
38C5×#106C2211yescharacteristic
39C5×#102C2211yescharacteristic
40C5×#102C2211yescharacteristic
41C5×C22⋊C8C2211yescharacteristic
42#3964C2211yescharacteristic
43#3964C2211yescharacteristic
44C22⋊#168C2211yescharacteristic
45#3953C2211yescharacteristic
46#3953C2211yescharacteristic
47#3949C2211yescharacteristic
48#3949C2211yescharacteristic
49#3947C2211yescharacteristic
50#3946C2211yescharacteristic
51#3946C2211yescharacteristic
52C8×Dic5C2211yescharacteristic
53#3941C2211yescharacteristic
54#3941C2211yescharacteristic
55#3940C2211yescharacteristic
56#3939C2211yescharacteristic
57#3939C2211yescharacteristic
58#3939C2211yescharacteristic
59#3241—51nomaximal, Sylow
60C2×C5×D4—21no—
61C2×C5×D4C2311yescharacteristic
62C22×C4×C5C2311yescharacteristic
63C2×C22⋊D5—21no—
64C2×C22⋊D5—21no—
65C2×C22⋊D5—21no—
66C22×Dic5—21no—
67C22×Dic5—21no—
68C2×D20C2311yescharacteristic
69C2×C4×D5—21no—
70C2×Dic10—21no—
71C2×Dic10—21no—
72C2×C5×C8C2311yescharacteristic
73C2×C5×C8C2311yescharacteristic
74C5×C4⋊C4C2311yescharacteristic
75C5×C4⋊C4C2311yescharacteristic
76C5×C4⋊C4C2311yescharacteristic
77C5×C22⋊C4—21no—
78C5×C22⋊C4—21no—
79C42×C5—21no—
80C22⋊Dic5—21no—
81C22⋊Dic5D411yescharacteristic
82C22⋊Dic5D411yescharacteristic
83#685—21no—
84#685—21no—
85C4⋊Dic5—21no—
86C4⋊Dic5—21no—
87C4⋊Dic5—21no—
88C4⋊Dic5—21no—
89C4⋊Dic5D411yescharacteristic
90C4⋊Dic5D411yescharacteristic
91C4⋊Dic5C2311yescharacteristic
92C4⋊Dic5C2311yescharacteristic
93C4⋊Dic5C2311yescharacteristic
94#683—21no—
95#683—21no—
96#683—21no—
97#683—21no—
98#683—21no—
99C4×Dic5C2311yescharacteristic
100C4×Dic5C2311yescharacteristic
101C2×#168C2311yescharacteristic
102C2×#168C2311yescharacteristic
103#544—51no—
104#540—51no—
105#501—51no—
106#499—51no—
107#490—51no—
108#486—51no—
109#482—51no—
110#482D511yescharacteristic, complemented
111#481—51no—
112#480—51no—
113#478—51no—
114#478—51no—
115#476—51no—
116#474—51no—
117#433—51no—
118C23×C5—21no—
119C23×C5C2×D411yescharacteristic
120C22×D5—21no—
121C5×D4—21no—
122C5×D4—21no—
123C5×D4—81no—
124C2×C4×C5—21no—
125C2×C4×C5—21no—
126C2×C4×C5—21no—
127C2×C4×C5—21no—
128C2×C4×C5—21no—
129C2×C4×C5C2×D411yescharacteristic
130C2×C4×C5C2411yescharacteristic
131C22⋊D5—81no—
132C22⋊D5—81no—
133C22⋊D5—81no—
134C2×Dic5—21no—
135C2×Dic5—21no—
136C2×Dic5—21no—
137C2×Dic5—81no—
138C2×Dic5—81no—
139C2×Dic5C2×D411yescharacteristic
140C2×Dic5C2×D411yescharacteristic
141C2×Dic5C2×D411yescharacteristic
142C2×Dic5C2×D411yescharacteristic
143D20—21no—
144D20—21no—
145C4×D5—81no—
146Dic10—81no—
147Dic10—81no—
148C5×C8—21no—
149C5×C8—21no—
150#168—21no—
151#168—21no—
152C4⋊Q8—51no—
153C4⋊Q8—51no—
154C4⋊Q8—101no—
155#127—51no—
156#125—51no—
157#125—51no—
158#125—51no—
159#125—101no—
160#123—101no—
161#123—101no—
162C22⋊Q8—101no—
163C22⋊Q8—101no—
164#121—51no—
165#121—101no—
166#121—101no—
167#121C2×D511yescharacteristic
168C4×D4—51no—
169C4×D4—51no—
170#117—51no—
171#117C2×D511yescharacteristic
172C2×C4⋊C4—51no—
173#107—51no—
174#107—51no—
175#107—51no—
176#107C2×D511yescharacteristic
177#106—51no—
178#106—51no—
179#106—51no—
180#106C2×D511yescharacteristic
181C4⋊C8—51no—
182C4⋊C8—51no—
183#102—51no—
184#102—51no—
185#102—51no—
186#102—51no—
187#102—51no—
188#102—51no—
189#102C2×D511yescharacteristic
190#102C2×D511yescharacteristic
191C22⋊C8—51no—
192C22⋊C8C2×D511yescharacteristic
193#97—51no—
194C4×C8—51no—
195C22×C5—21no—
196C22×C5—21no—
197C22×C5—21no—
198C22×C5—41no—
199C22×C5—41no—
200C22×C5—41no—
201C22×C5C22×D411yescharacteristic
202C2×D5—41no—
203C2×D5—41no—
204C2×D5—41no—
205C4×C5—21no—
206C4×C5—41no—
207C4×C5—41no—
208C4×C5—41no—
209C4×C52−1+411yescharacteristic
210C4×C52−1+411yescharacteristic
211Dic5—21no—
212Dic5—21no—
213Dic5—21no—
214Dic5—21no—
215Dic5—41no—
216Dic5—41no—
217Dic5—41no—
218C2×Q8—101no—
219C2×Q8—101no—
220C2×D4—21no—
221C2×D4—51no—
222C2×D4—101no—
223C2×D4—101no—
224C2×D4—101no—
225C2×D4C22×D511yescharacteristic
226C22×C4—101no—
227C22×C4—101no—
228C22×C4—101no—
229C22×C4C22×D511yescharacteristic
230C2×C8—51no—
231C2×C8—51no—
232C2×C8C22×D511yescharacteristic
233C2×C8C22×D511yescharacteristic
234C4⋊C4—51no—
235C4⋊C4—51no—
236C4⋊C4—51no—
237C4⋊C4—51no—
238C4⋊C4—51no—
239C4⋊C4—101no—
240C4⋊C4—101no—
241C4⋊C4—101no—
242C4⋊C4—101no—
243C4⋊C4—101no—
244C4⋊C4—101no—
245C4⋊C4—101no—
246C4⋊C4—101no—
247C4⋊C4—101no—
248C4⋊C4C22×D511yescharacteristic
249C4⋊C4C22×D511yescharacteristic
250C4⋊C4C22×D511yescharacteristic
251C22⋊C4—21no—
252C22⋊C4—21no—
253C22⋊C4—51no—
254C22⋊C4—51no—
255C22⋊C4—101no—
256C22⋊C4—101no—
257C22⋊C4—101no—
258C42—21no—
259C42—51no—
260C42—51no—
261C2×C5—41no—
262C2×C5—81no—
263C2×C5#53611yescharacteristic
264C2×C5#57611yescharacteristic
265C2×C5#57711yescharacteristic
266D5—81no—
267C23—21no—
268C23—101no—
269C23D4×D511yescharacteristic
270Q8—401no—
271Q8—401no—
272D4—21no—
273D4—21no—
274D4—81no—
275D4—101no—
276D4—101no—
277D4—401no—
278D4—401no—
279D4—401no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—51no—
286C2×C4—51no—
287C2×C4—51no—
288C2×C4—51no—
289C2×C4—101no—
290C2×C4—101no—
291C2×C4—101no—
292C2×C4—401no—
293C2×C4—401no—
294C2×C4—401no—
295C2×C4D4×D511yescharacteristic
296C2×C4C23×D511yescharacteristic
297C8—21no—
298C8—21no—
299C8—101no—
300C8—101no—
301C5#324111yescharacteristic, complemented, Sylow
302C22—21no—
303C22—21no—
304C22—21no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—201no—
309C22—201no—
310C22—201no—
311C22C2×D4×D511yescharacteristic
312C4—21no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—101no—
317C4—101no—
318C4—101no—
319C4—101no—
320C4—201no—
321C4—201no—
322C4—201no—
323C4#415011yescharacteristic
324C4#415011yescharacteristic
325C2—41no—
326C2—81no—
327C2—401no—
328C2#6598211yescharacteristic
329C2#6610411yescharacteristic
330C2#6610811yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#482C2
socleC22×C5C22×D4
prime radical#65953C2
hypercenter#482D5
hypocenterC5#3241
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #65853C2semidirect
3. C5×#482C2semidirect
4. #65322C2semidirect
5. #65292C2semidirect
6. #65179C2semidirect
7. #65165C2semidirect
8. #65160C2semidirect
9. #65147C2semidirect
10. #65053C2semidirect
11. #65052C2semidirect
12. #65050C2semidirect
13. #65049C2semidirect
14. #65024C2semidirect
15. #65009C2semidirect
110. #482D5semidirect
301. C5#3241semidirect

Maximal subgroups

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

subgroupindex
#659532
#658532
C5×#4822
#653222
#652922
#651792
#651652
#651602
#651472
#650532
#650522
#650502
#650492
#650242
#650092
#32415