Finite Group Databasebeta

← #10611985

Subgroups — #10611985

Order 640.

382 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#66158C211yesmaximal, characteristic
2#65976C211yesmaximal, characteristic, complemented
3C5×#452C211yesmaximal, characteristic, complemented
4#65521C211yesmaximal, characteristic, complemented
5#65477C211yesmaximal, characteristic, complemented
6#65471C211yesmaximal, characteristic, complemented
7#65462C211yesmaximal, characteristic, complemented
8#65453C211yesmaximal, characteristic, complemented
9#65341C211yesmaximal, characteristic, complemented
10#65103C211yesmaximal, characteristic, complemented
11#65086C211yesmaximal, characteristic, complemented
12#65061C211yesmaximal, characteristic, complemented
13#65055C211yesmaximal, characteristic, complemented
14#65017C211yesmaximal, characteristic, complemented
15#65011C211yesmaximal, characteristic, complemented
16C2×C5×#41C2211yescharacteristic
17C2×#711C2211yescharacteristic
18C2×C5×Q16C2211yescharacteristic
19C2×C5×SD16C2211yescharacteristic
20C5×C22⋊Q8C2211yescharacteristic
21#4092C2211yescharacteristic
22#4092C2211yescharacteristic
23Q8×Dic5C2211yescharacteristic
24#4090C2211yescharacteristic
25C2×#689C2211yescharacteristic
26#4085—21no—
27#4081—21no—
28D4×Dic5C2211yescharacteristic
29#4075—21no—
30C4×C22⋊D5C2211yescharacteristic
31C2×C4⋊Dic5C2211yescharacteristic
32#4070C2211yescharacteristic
33C2×#683—21no—
34C2×#681C2211yescharacteristic
35C2×C8×D5C2211yescharacteristic
36#4044—21no—
37#4038C2211yescharacteristic
38#4036—21no—
39#4036C2211yescharacteristic
40#4032—21no—
41#4023—21no—
42C5×#103C2211yescharacteristic
43C5×#102C2211yescharacteristic
44C5×C22⋊C8C2211yescharacteristic
45#3967C2211yescharacteristic
46#3967C2211yescharacteristic
47#3967C2211yescharacteristic
48#3964C2211yescharacteristic
49#3964C2211yescharacteristic
50#3952C2211yescharacteristic
51#3950C2211yescharacteristic
52#3950C2211yescharacteristic
53#3948C2211yescharacteristic
54#3948C2211yescharacteristic
55#3947C2211yescharacteristic
56#3946C2211yescharacteristic
57#3942C2211yescharacteristic
58#3940C2211yescharacteristic
59#3315—51nomaximal, Sylow
60C5×#41—22no—
61C5×#41—41no—
62C2×C5×Q8C2311yescharacteristic
63C2×C5×Q8C2311yescharacteristic
64C2×C5×D4—21no—
65C2×C5×D4C2311yescharacteristic
66C22×C4×C5—21no—
67C22×C4×C5C2311yescharacteristic
68C2×C22⋊D5—21no—
69C2×C22⋊D5D411yescharacteristic
70C22×Dic5—21no—
71C22×Dic5—21no—
72C22×Dic5—21no—
73#711—22no—
74#711—41no—
75C2×C4×D5C2311yescharacteristic
76C2×Dic10C2311yescharacteristic
77C5×Q16—41no—
78C5×SD16—22no—
79C2×C5×C8C2311yescharacteristic
80C2×C5×C8C2311yescharacteristic
81C5×C4⋊C4—21no—
82C5×C4⋊C4C2311yescharacteristic
83C5×C22⋊C4—21no—
84C22⋊Dic5—21no—
85C22⋊Dic5—21no—
86C22⋊Dic5D411yescharacteristic
87#689—41no—
88#685—21no—
89#685—21no—
90#685—21no—
91#685D411yescharacteristic
92C4⋊Dic5—21no—
93C4⋊Dic5—21no—
94C4⋊Dic5—21no—
95C4⋊Dic5C2311yescharacteristic
96C4⋊Dic5C2311yescharacteristic
97C4⋊Dic5C2311yescharacteristic
98#683—21no—
99#683—21no—
100#683—21no—
101#683—21no—
102#683—21no—
103#683—21no—
104#683D411yescharacteristic
105C4×Dic5—21no—
106C4×Dic5—21no—
107C4×Dic5C2311yescharacteristic
108#681—41no—
109C2×#168C2311yescharacteristic
110C2×#168C2311yescharacteristic
111C8×D5—41no—
112#552—51no—
113#547—51no—
114#491—51no—
115#485—51no—
116#484—51no—
117#478—51no—
118#470—51no—
119#467—51no—
120#462—51no—
121#452—51no—
122#452D511yescharacteristic, complemented
123#440—51no—
124#435—51no—
125#417—51no—
126#416—51no—
127C23×C5—21no—
128C23×C5C2×D411yescharacteristic
129C22×D5C2×D411yescharacteristic
130C5×Q8—21no—
131C5×Q8—21no—
132C5×Q8—21no—
133C5×Q8—21no—
134C5×D4—21no—
135C5×D4—42no—
136C5×D4#4112yes—
137C2×C4×C5—21no—
138C2×C4×C5—21no—
139C2×C4×C5—21no—
140C2×C4×C5—21no—
141C2×C4×C5—21no—
142C2×C4×C5—42no—
143C2×C4×C5C2×D411yescharacteristic
144C2×C4×C5C2411yescharacteristic
145C22⋊D5—41no—
146C22⋊D5—42no—
147C2×Dic5—21no—
148C2×Dic5—21no—
149C2×Dic5—21no—
150C2×Dic5—21no—
151C2×Dic5—42no—
152C2×Dic5—42no—
153C2×Dic5—42no—
154C2×Dic5C2×D411yescharacteristic
155C2×Dic5C2×D411yescharacteristic
156C2×Dic5C2×D411yescharacteristic
157C4×D5—21no—
158C4×D5—21no—
159Dic10—21no—
160Dic10—21no—
161C5×C8—21no—
162C5×C8—21no—
163#168—21no—
164#168—21no—
165C2×#41—51no—
166C2×#41C2×D511yescharacteristic
167C2×Q16—51no—
168C2×Q16C2×D511yescharacteristic
169C2×SD16C2×D511yescharacteristic
170C2×M16—51no—
171C22×C8—51no—
172C4⋊Q8—51no—
173#126—101no—
174#125—51no—
175#125—101no—
176#123—101no—
177#123—101no—
178#123—101no—
179C22⋊Q8—51no—
180C22⋊Q8—51no—
181C22⋊Q8—51no—
182C22⋊Q8C2×D511yescharacteristic
183#121—101no—
184C4×Q8—51no—
185C4×D4—51no—
186C4×D4—51no—
187#117—51no—
188#117—101no—
189C2×C4⋊C4—51no—
190C2×C4⋊C4—101no—
191#107—51no—
192#107—51no—
193#106—51no—
194C4⋊C8—51no—
195#103—51no—
196#103—51no—
197#103—51no—
198#103—51no—
199#103—51no—
200#103—51no—
201#103C2×D511yescharacteristic
202#102—51no—
203#102—51no—
204#102C2×D511yescharacteristic
205C22⋊C8—51no—
206C22⋊C8C2×D511yescharacteristic
207#97—51no—
208C22×C5—22no—
209C22×C5—21no—
210C22×C5—21no—
211C22×C5—21no—
212C22×C5—41no—
213C22×C5—41no—
214C22×C5C22×D411yescharacteristic
215C2×D5—21no—
216C2×D5—21no—
217C2×D5—21no—
218C4×C5—21no—
219C4×C5—41no—
220C4×C5—41no—
221C4×C5—41no—
222C4×C5C2×#4111yescharacteristic
223C4×C5H(5,𝔽2)11yescharacteristic
224Dic5—21no—
225Dic5—21no—
226Dic5—21no—
227Dic5—41no—
228Dic5—41no—
229Dic5—41no—
230Dic5—41no—
231#41—22no—
232#41—41no—
233#41—102no—
234#41—201no—
235C2×Q8—51no—
236C2×Q8C22×D511yescharacteristic
237C2×Q8C22×D511yescharacteristic
238C2×D4—21no—
239C2×D4—51no—
240C2×D4—101no—
241C2×D4C22×D511yescharacteristic
242C22×C4—21no—
243C22×C4—51no—
244C22×C4—101no—
245C22×C4—101no—
246C22×C4—101no—
247C22×C4C22×D511yescharacteristic
248Q16—41no—
249Q16—201no—
250SD16—22no—
251M16—201no—
252C2×C8—51no—
253C2×C8—51no—
254C2×C8—201no—
255C2×C8C22×D511yescharacteristic
256C2×C8C22×D511yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—51no—
259C4⋊C4—51no—
260C4⋊C4—51no—
261C4⋊C4—51no—
262C4⋊C4—101no—
263C4⋊C4—101no—
264C4⋊C4—101no—
265C4⋊C4—101no—
266C4⋊C4—101no—
267C4⋊C4—101no—
268C4⋊C4—101no—
269C4⋊C4—101no—
270C4⋊C4—101no—
271C4⋊C4C22×D511yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—51no—
274C22⋊C4—51no—
275C22⋊C4—101no—
276C22⋊C4—101no—
277C22⋊C4—101no—
278C22⋊C4—101no—
279C22⋊C4—101no—
280C42—51no—
281C42—101no—
282C42—101no—
283C2×C5—41no—
284C2×C5—42no—
285C2×C5#54611yescharacteristic
286C2×C5#57511yescharacteristic
287C2×C5#57811yescharacteristic
288D5—41no—
289C23—21no—
290C23—51no—
291C23D4×D511yescharacteristic
292Q8—21no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—101no—
297Q8—101no—
298D4—21no—
299D4—42no—
300D4—201no—
301D4—202no—
302D4#71112yes—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—51no—
310C2×C4—51no—
311C2×C4—51no—
312C2×C4—101no—
313C2×C4—101no—
314C2×C4—101no—
315C2×C4—101no—
316C2×C4—101no—
317C2×C4—101no—
318C2×C4—202no—
319C2×C4—202no—
320C2×C4—202no—
321C2×C4D4×D511yescharacteristic
322C2×C4C23×D511yescharacteristic
323C8—21no—
324C8—21no—
325C8—101no—
326C8—101no—
327C5#331511yescharacteristic, complemented, Sylow
328C22—21no—
329C22—21no—
330C22—21no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—101no—
335C22—101no—
336C22—101no—
337C22C2×D4×D511yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—101no—
343C4—101no—
344C4—101no—
345C4—201no—
346C4—201no—
347C4—201no—
348C4—201no—
349C4C2×#71111yescharacteristic
350C4#414411yescharacteristic
351C2—41no—
352C2—42no—
353C2—201no—
354C2#6592511yescharacteristic
355C2#6610511yescharacteristic
356C2#6611111yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#452C2
socleC22×C5C22×D4
prime radical#66158C2
hypercenter#452D5
hypocenterC5#3315
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
2. #65976C2semidirect
3. C5×#452C2semidirect
4. #65521C2semidirect
5. #65477C2semidirect
6. #65471C2semidirect
7. #65462C2semidirect
8. #65453C2semidirect
9. #65341C2semidirect
10. #65103C2semidirect
11. #65086C2semidirect
12. #65061C2semidirect
13. #65055C2semidirect
14. #65017C2semidirect
15. #65011C2semidirect
122. #452D5semidirect
327. C5#3315semidirect

Maximal subgroups

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

subgroupindex
#661582
#659762
C5×#4522
#655212
#654772
#654712
#654622
#654532
#653412
#651032
#650862
#650612
#650552
#650172
#650112
#33155