Finite Group Databasebeta

← #10613235

Subgroups — #10613235

Order 640.

308 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#65959C211yesmaximal, characteristic
2#65853C211yesmaximal, characteristic
3C5×#485C211yesmaximal, characteristic
4#65332C211yesmaximal, characteristic
5#65285C211yesmaximal, characteristic
6#65167C211yesmaximal, characteristic, complemented
7#65166C211yesmaximal, characteristic, complemented
8#65145C211yesmaximal, characteristic, complemented
9#65143C211yesmaximal, characteristic, complemented
10#65086C211yesmaximal, characteristic, complemented
11#65085C211yesmaximal, characteristic, complemented
12#65083C211yesmaximal, characteristic, complemented
13#65081C211yesmaximal, characteristic, complemented
14#65011C211yesmaximal, characteristic
15#65009C211yesmaximal, characteristic
16C5×C22⋊Q8C2211yescharacteristic
17C5×#117C2211yescharacteristic
18Q8×Dic5C2211yescharacteristic
19#4090C2211yescharacteristic
20#4072C2211yescharacteristic
21C2×C4⋊Dic5C2211yescharacteristic
22#4070C2211yescharacteristic
23#4036—21no—
24#4036C2211yescharacteristic
25#4036C2211yescharacteristic
26#4036C2211yescharacteristic
27#4035—21no—
28#4034C2211yescharacteristic
29#4034C2211yescharacteristic
30#4033C2211yescharacteristic
31#4025—21no—
32#4025—21no—
33#4024—21no—
34#4024—21no—
35#4016—21no—
36#4015—21no—
37C5×#107C2211yescharacteristic
38C5×#106C2211yescharacteristic
39C5×#103C2211yescharacteristic
40C5×#103C2211yescharacteristic
41C5×C22⋊C8C2211yescharacteristic
42#3967C2211yescharacteristic
43#3967C2211yescharacteristic
44C22⋊#168C2211yescharacteristic
45#3950C2211yescharacteristic
46#3950C2211yescharacteristic
47#3948C2211yescharacteristic
48#3948C2211yescharacteristic
49#3947C2211yescharacteristic
50#3946C2211yescharacteristic
51#3946C2211yescharacteristic
52C8×Dic5C2211yescharacteristic
53#3942C2211yescharacteristic
54#3942C2211yescharacteristic
55#3940C2211yescharacteristic
56#3940C2211yescharacteristic
57#3940C2211yescharacteristic
58#3939C2211yescharacteristic
59#3242—51nomaximal, Sylow
60C2×C5×Q8C2311yescharacteristic
61C22×C4×C5C2311yescharacteristic
62C22×Dic5—21no—
63C2×Dic10—21no—
64C2×Dic10—21no—
65C2×Dic10C2311yescharacteristic
66C2×C5×C8C2311yescharacteristic
67C2×C5×C8C2311yescharacteristic
68C5×C4⋊C4—21no—
69C5×C4⋊C4C2311yescharacteristic
70C5×C4⋊C4C2311yescharacteristic
71C5×C4⋊C4C2311yescharacteristic
72C5×C22⋊C4—21no—
73C5×C22⋊C4—21no—
74C42×C5—21no—
75C22⋊Dic5—21no—
76C22⋊Dic5D411yescharacteristic
77C22⋊Dic5D411yescharacteristic
78C4⋊Dic5—21no—
79C4⋊Dic5—21no—
80C4⋊Dic5—21no—
81C4⋊Dic5—21no—
82C4⋊Dic5—21no—
83C4⋊Dic5D411yescharacteristic
84C4⋊Dic5D411yescharacteristic
85C4⋊Dic5C2311yescharacteristic
86C4⋊Dic5C2311yescharacteristic
87C4⋊Dic5C2311yescharacteristic
88#683—21no—
89#683—21no—
90#683—21no—
91#683—21no—
92#683—21no—
93#683—21no—
94#683—21no—
95#683—21no—
96#683—21no—
97C4×Dic5—21no—
98C4×Dic5—21no—
99C4×Dic5C2311yescharacteristic
100C4×Dic5C2311yescharacteristic
101C2×#168C2311yescharacteristic
102C2×#168C2311yescharacteristic
103#544—51no—
104#541—51no—
105#501—51no—
106#499—51no—
107#491—51no—
108#487—51no—
109#485—51no—
110#485D511yescharacteristic
111#484—51no—
112#483—51no—
113#479—51no—
114#479—51no—
115#477—51no—
116#475—51no—
117#433—51no—
118C23×C5C2×D411yescharacteristic
119C5×Q8—21no—
120C5×Q8—21no—
121C2×C4×C5—21no—
122C2×C4×C5—21no—
123C2×C4×C5—21no—
124C2×C4×C5—21no—
125C2×C4×C5—21no—
126C2×C4×C5—21no—
127C2×C4×C5C2×D411yescharacteristic
128C2×C4×C5C2411yescharacteristic
129C2×Dic5—21no—
130C2×Dic5—21no—
131C2×Dic5—21no—
132C2×Dic5—21no—
133C2×Dic5—81no—
134C2×Dic5C2×D411yescharacteristic
135C2×Dic5C2×D411yescharacteristic
136C2×Dic5C2×D411yescharacteristic
137C2×Dic5C2×D411yescharacteristic
138Dic10—21no—
139Dic10—21no—
140Dic10—81no—
141Dic10—81no—
142C5×C8—21no—
143C5×C8—21no—
144#168—21no—
145#168—21no—
146C4⋊Q8—51no—
147C4⋊Q8—51no—
148C4⋊Q8—51no—
149C4⋊Q8—101no—
150#126—101no—
151#126—101no—
152#125—51no—
153#125—51no—
154#125—51no—
155#125—101no—
156#125—101no—
157#125—101no—
158C22⋊Q8—51no—
159C22⋊Q8—101no—
160C22⋊Q8—101no—
161C22⋊Q8C2×D511yescharacteristic
162C4×Q8—51no—
163C4×Q8—51no—
164#117—51no—
165#117C2×D511yescharacteristic
166C2×C4⋊C4—51no—
167#107—51no—
168#107—51no—
169#107—51no—
170#107C2×D511yescharacteristic
171#106—51no—
172#106—51no—
173#106—51no—
174#106C2×D511yescharacteristic
175C4⋊C8—51no—
176C4⋊C8—51no—
177#103—51no—
178#103—51no—
179#103—51no—
180#103—51no—
181#103—51no—
182#103—51no—
183#103C2×D511yescharacteristic
184#103C2×D511yescharacteristic
185C22⋊C8—51no—
186C22⋊C8C2×D511yescharacteristic
187#97—51no—
188C4×C8—51no—
189C22×C5—21no—
190C22×C5—21no—
191C22×C5—21no—
192C22×C5C22×D411yescharacteristic
193C4×C5—21no—
194C4×C5—41no—
195C4×C5—41no—
196C4×C5—41no—
197C4×C5—41no—
198C4×C52−1+411yescharacteristic
199C4×C52−1+411yescharacteristic
200Dic5—21no—
201Dic5—21no—
202Dic5—21no—
203Dic5—21no—
204Dic5—41no—
205Dic5—41no—
206Dic5—41no—
207Dic5—41no—
208C2×Q8—51no—
209C2×Q8—101no—
210C2×Q8—101no—
211C2×Q8C22×D511yescharacteristic
212C22×C4—101no—
213C22×C4C22×D511yescharacteristic
214C2×C8—51no—
215C2×C8—51no—
216C2×C8C22×D511yescharacteristic
217C2×C8C22×D511yescharacteristic
218C4⋊C4—21no—
219C4⋊C4—51no—
220C4⋊C4—51no—
221C4⋊C4—51no—
222C4⋊C4—51no—
223C4⋊C4—51no—
224C4⋊C4—101no—
225C4⋊C4—101no—
226C4⋊C4—101no—
227C4⋊C4—101no—
228C4⋊C4—101no—
229C4⋊C4—101no—
230C4⋊C4—101no—
231C4⋊C4—101no—
232C4⋊C4—101no—
233C4⋊C4—101no—
234C4⋊C4—101no—
235C4⋊C4—101no—
236C4⋊C4—101no—
237C4⋊C4—101no—
238C4⋊C4C22×D511yescharacteristic
239C4⋊C4C22×D511yescharacteristic
240C4⋊C4C22×D511yescharacteristic
241C22⋊C4—21no—
242C22⋊C4—21no—
243C22⋊C4—51no—
244C22⋊C4—51no—
245C22⋊C4—101no—
246C42—21no—
247C42—51no—
248C42—51no—
249C42—101no—
250C42—101no—
251C2×C5—41no—
252C2×C5#53611yescharacteristic
253C2×C5#57711yescharacteristic
254C2×C5#57811yescharacteristic
255C23D4×D511yescharacteristic
256Q8—21no—
257Q8—21no—
258Q8—101no—
259Q8—101no—
260Q8—401no—
261Q8—401no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—51no—
269C2×C4—51no—
270C2×C4—51no—
271C2×C4—51no—
272C2×C4—101no—
273C2×C4—101no—
274C2×C4—101no—
275C2×C4—101no—
276C2×C4—401no—
277C2×C4D4×D511yescharacteristic
278C2×C4C23×D511yescharacteristic
279C8—21no—
280C8—21no—
281C8—101no—
282C8—101no—
283C5#324211yescharacteristic, complemented, Sylow
284C22—21no—
285C22—21no—
286C22—21no—
287C22C2×D4×D511yescharacteristic
288C4—21no—
289C4—41no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—101no—
294C4—101no—
295C4—101no—
296C4—101no—
297C4—201no—
298C4—201no—
299C4—201no—
300C4—201no—
301C4#415011yescharacteristic
302C4#415011yescharacteristic
303C2—41no—
304C2#6598211yescharacteristic
305C2#6610511yescharacteristic
306C2#6611211yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#485C2
socleC22×C5C22×D4
prime radicalC23×C5C2×D4
hypercenter#485D5
hypocenterC5#3242
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
6. #65167C2semidirect
7. #65166C2semidirect
8. #65145C2semidirect
9. #65143C2semidirect
10. #65086C2semidirect
11. #65085C2semidirect
12. #65083C2semidirect
13. #65081C2semidirect
283. C5#3242semidirect

Maximal subgroups

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

subgroupindex
#659592
#658532
C5×#4852
#653322
#652852
#651672
#651662
#651452
#651432
#650862
#650852
#650832
#650812
#650112
#650092
#32425