Finite Group Databasebeta

← #10612969

Subgroups — #10612969

Order 640.

324 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#125C211yesmaximal, characteristic
2#65912C211yesmaximal, characteristic
3C5×#479C211yesmaximal, characteristic, complemented
4#65352C211yesmaximal, characteristic, complemented
5#65311C211yesmaximal, characteristic, complemented
6#65173C211yesmaximal, characteristic
7#65165C211yesmaximal, characteristic, complemented
8#65151C211yesmaximal, characteristic
9#65145C211yesmaximal, characteristic, complemented
10#65124C211yesmaximal, characteristic
11#65118C211yesmaximal, characteristic, complemented
12#65098C211yesmaximal, characteristic
13#65094C211yesmaximal, characteristic
14#65086C211yesmaximal, characteristic, complemented
15#65086C211yesmaximal, characteristic, complemented
16C5×#125C2211yescharacteristic
17C4×C5×Q8C2211yescharacteristic
18#4092C2211yescharacteristic
19#4090C2211yescharacteristic
20#4043C2211yescharacteristic
21#4042—21no—
22D5×C4⋊C4—21no—
23D5×C4⋊C4—21no—
24D5×C4⋊C4C2211yescharacteristic
25D5×C4⋊C4C2211yescharacteristic
26#4036C2211yescharacteristic
27#4036C2211yescharacteristic
28#4035—21no—
29#4035—21no—
30#4035—21no—
31#4034C2211yescharacteristic
32#4018—21no—
33C42×D5C2211yescharacteristic
34#4016C2211yescharacteristic
35C4×Dic10—21no—
36C4×Dic10C2211yescharacteristic
37C5×#107C2211yescharacteristic
38C5×#106C2211yescharacteristic
39C5×C4⋊C8C2211yescharacteristic
40C5×#103C2211yescharacteristic
41C5×#103C2211yescharacteristic
42#3967C2211yescharacteristic
43#3967C2211yescharacteristic
44#3952C2211yescharacteristic
45#3952C2211yescharacteristic
46#3950C2211yescharacteristic
47#3949C2211yescharacteristic
48#3948C2211yescharacteristic
49#3948C2211yescharacteristic
50#3947C2211yescharacteristic
51#3947C2211yescharacteristic
52#3942C2211yescharacteristic
53#3942C2211yescharacteristic
54#3940C2211yescharacteristic
55#3940C2211yescharacteristic
56#3939C2211yescharacteristic
57#3939C2211yescharacteristic
58C4⋊#168C2211yescharacteristic
59#3236—51nomaximal, Sylow
60C2×C5×Q8C2311yescharacteristic
61C2×C4×D5—21no—
62C2×C4×D5—21no—
63C2×C4×D5D411yescharacteristic
64C2×C4×D5D411yescharacteristic
65C2×C4×D5C2311yescharacteristic
66C2×Dic10—21no—
67C2×Dic10C2311yescharacteristic
68C2×C5×C8C2311yescharacteristic
69C2×C5×C8C2311yescharacteristic
70C5×C4⋊C4—21no—
71C5×C4⋊C4—21no—
72C5×C4⋊C4—21no—
73C5×C4⋊C4C2311yescharacteristic
74C5×C4⋊C4C2311yescharacteristic
75C5×C4⋊C4C2311yescharacteristic
76C42×C5—21no—
77C42×C5C2311yescharacteristic
78#685—21no—
79#685—21no—
80C4⋊Dic5—21no—
81C4⋊Dic5—21no—
82C4⋊Dic5—21no—
83C4⋊Dic5C2311yescharacteristic
84C4⋊Dic5C2311yescharacteristic
85C4⋊Dic5C2311yescharacteristic
86#683—21no—
87#683—21no—
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×Dic5D411yescharacteristic
99C4×Dic5D411yescharacteristic
100C4×Dic5C2311yescharacteristic
101C2×#168C2311yescharacteristic
102C2×#168C2311yescharacteristic
103#533—51no—
104C2×#125—51no—
105#501—51no—
106#501—51no—
107#491—51no—
108#491—51no—
109#484—51no—
110#484—51no—
111#483—51no—
112#483—51no—
113#479—51no—
114#479—51no—
115#479—51no—
116#479D511yescharacteristic, complemented
117#432—51no—
118C22×D5C2×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×C5C2×D411yescharacteristic
126C2×C4×C5C2×D411yescharacteristic
127C2×C4×C5C2411yescharacteristic
128C2×Dic5—21no—
129C2×Dic5—21no—
130C2×Dic5—21no—
131C2×Dic5—21no—
132C2×Dic5C2×D411yescharacteristic
133C2×Dic5C2×D411yescharacteristic
134C2×Dic5C2×D411yescharacteristic
135C4×D5—22no—
136C4×D5—21no—
137C4×D5—21no—
138C4×D5—41no—
139C4×D5—42no—
140C4×D5—42no—
141Dic10—21no—
142Dic10—21no—
143Dic10—42no—
144C5×C8—21no—
145C5×C8—21no—
146#168—21no—
147#168—21no—
148C4⋊Q8—51no—
149C4⋊Q8—51no—
150#125—51no—
151#125—51no—
152#125—51no—
153#125—101no—
154#125—101no—
155#125—101no—
156#125C2×D511yescharacteristic
157C22⋊Q8—51no—
158C22⋊Q8—51no—
159C22⋊Q8—101no—
160C4×Q8—51no—
161C4×Q8—101no—
162C4×Q8C2×D511yescharacteristic
163#117—101no—
164C2×C4⋊C4—51no—
165C2×C4⋊C4—51no—
166C2×C4⋊C4—101no—
167C2×C4⋊C4—101no—
168C2×C42—51no—
169#107—51no—
170#107—51no—
171#107—51no—
172#107C2×D511yescharacteristic
173#106—51no—
174#106—51no—
175#106—51no—
176#106C2×D511yescharacteristic
177C4⋊C8—51no—
178C4⋊C8C2×D511yescharacteristic
179#103—51no—
180#103—51no—
181#103—51no—
182#103—51no—
183#103—51no—
184#103—51no—
185#103C2×D511yescharacteristic
186#103C2×D511yescharacteristic
187C22⋊C8—51no—
188C22⋊C8—51no—
189#97—51no—
190#97—51no—
191C22×C5C22×D411yescharacteristic
192C2×D5—21no—
193C2×D5—21no—
194C2×D5#13712yes—
195C4×C5—21no—
196C4×C5—21no—
197C4×C5—41no—
198C4×C5—41no—
199C4×C5—41no—
200C4×C5—41no—
201C4×C52−1+411yescharacteristic
202C4×C52−1+411yescharacteristic
203Dic5—21no—
204Dic5—21no—
205Dic5—21no—
206Dic5—41no—
207Dic5—41no—
208Dic5—41no—
209Dic5—41no—
210C2×Q8—51no—
211C2×Q8—101no—
212C2×Q8C22×D511yescharacteristic
213C22×C4—51no—
214C22×C4—51no—
215C22×C4—51no—
216C22×C4—101no—
217C22×C4—101no—
218C2×C8—51no—
219C2×C8—51no—
220C2×C8C22×D511yescharacteristic
221C2×C8C22×D511yescharacteristic
222C4⋊C4—21no—
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—51no—
226C4⋊C4—51no—
227C4⋊C4—51no—
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⋊C4—101no—
239C4⋊C4—101no—
240C4⋊C4—101no—
241C4⋊C4—101no—
242C4⋊C4C22×D511yescharacteristic
243C4⋊C4C22×D511yescharacteristic
244C4⋊C4C22×D511yescharacteristic
245C22⋊C4—101no—
246C22⋊C4—101no—
247C42—21no—
248C42—51no—
249C42—51no—
250C42—51no—
251C42—101no—
252C42C22×D511yescharacteristic
253C2×C5#53611yescharacteristic
254C2×C5C2×#13711yescharacteristic
255C2×C5#57511yescharacteristic
256D5—22no—
257C23—51no—
258Q8—21no—
259Q8—21no—
260Q8—101no—
261Q8—101no—
262Q8—202no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—51no—
268C2×C4—51no—
269C2×C4—51no—
270C2×C4—102no—
271C2×C4—101no—
272C2×C4—101no—
273C2×C4—101no—
274C2×C4—101no—
275C2×C4—101no—
276C2×C4—101no—
277C2×C4—201no—
278C2×C4—202no—
279C2×C4—202no—
280C2×C4D4×D511yescharacteristic
281C2×C4D4×D511yescharacteristic
282C2×C4C23×D511yescharacteristic
283C8—21no—
284C8—21no—
285C8—101no—
286C8—101no—
287C5#323611yescharacteristic, complemented, Sylow
288C22—52no—
289C22—101no—
290C22—101no—
291C22C2×D4×D511yescharacteristic
292C4—21no—
293C4—21no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—41no—
298C4—101no—
299C4—101no—
300C4—101no—
301C4—201no—
302C4—201no—
303C4—201no—
304C4—201no—
305C4#414711yescharacteristic
306C4#415011yescharacteristic
307C2—102no—
308C2#6596211yescharacteristic
309C2#6610211yescharacteristic
310C2D5×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#479C2
socleC22×C5C22×D4
prime radicalC22×D5C2×D4
hypercenter#479D5
hypocenterC5#3236
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
3. C5×#479C2semidirect
4. #65352C2semidirect
5. #65311C2semidirect
7. #65165C2semidirect
9. #65145C2semidirect
11. #65118C2semidirect
14. #65086C2semidirect
15. #65086C2semidirect
116. #479D5semidirect
287. C5#3236semidirect

Maximal subgroups

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

subgroupindex
D5×#1252
#659122
C5×#4792
#653522
#653112
#651732
#651652
#651512
#651452
#651242
#651182
#650982
#650942
#650862
#32365