Finite Group Databasebeta

← #10613207

Subgroups — #10613207

Order 640.

356 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#65969C211yesmaximal, characteristic
2#65845C211yesmaximal, characteristic
3C5×#484C211yesmaximal, characteristic, complemented
4#65340C211yesmaximal, characteristic, complemented
5C2×#3939C211yesmaximal, characteristic, complemented
6#65173C211yesmaximal, characteristic, complemented
7D5×#107C211yesmaximal, characteristic, complemented
8#65164C211yesmaximal, characteristic, complemented
9#65163C211yesmaximal, characteristic, complemented
10#65102C211yesmaximal, characteristic, complemented
11#65098C211yesmaximal, characteristic, complemented
12#65083C211yesmaximal, characteristic, complemented
13#65079C211yesmaximal, characteristic, complemented
14#65014C211yesmaximal, characteristic
15#65011C211yesmaximal, characteristic, complemented
16C5×C22⋊Q8C2211yescharacteristic
17C2×C5×C4⋊C4C2211yescharacteristic
18#4092C2211yescharacteristic
19Q8×Dic5C2211yescharacteristic
20C2×#689C2211yescharacteristic
21C4×C22⋊D5—21no—
22C4×C22⋊D5C2211yescharacteristic
23C2×C4⋊Dic5C2211yescharacteristic
24#4070—21no—
25#4070C2211yescharacteristic
26C22×#168C2211yescharacteristic
27C2×C8×D5C2211yescharacteristic
28#4043—21no—
29#4043C2211yescharacteristic
30#4042—21no—
31D5×C4⋊C4C2211yescharacteristic
32D5×C4⋊C4C2211yescharacteristic
33#4035—21no—
34#4035—21no—
35#4034C2211yescharacteristic
36#4034C2211yescharacteristic
37#4033C2211yescharacteristic
38#4027—21no—
39#4024—21no—
40C5×#107C2211yescharacteristic
41C5×#107C2211yescharacteristic
42C5×#103C2211yescharacteristic
43C5×#103C2211yescharacteristic
44C5×C22⋊C8C2211yescharacteristic
45#3967C2211yescharacteristic
46#3952C2211yescharacteristic
47#3950C2211yescharacteristic
48#3950C2211yescharacteristic
49#3948C2211yescharacteristic
50#3948C2211yescharacteristic
51#3946C2211yescharacteristic
52C8×Dic5C2211yescharacteristic
53#3942C2211yescharacteristic
54#3939C2211yescharacteristic
55#3939C2211yescharacteristic
56#3939C2211yescharacteristic
57#3939C2211yescharacteristic
58#3939C2211yescharacteristic
59#3338—51nomaximal, Sylow
60C2×C5×Q8C2311yescharacteristic
61C22×C4×C5—21no—
62C22×C4×C5C2311yescharacteristic
63C2×C22⋊D5D411yescharacteristic
64C22×Dic5—21no—
65C2×C4×D5—21no—
66C2×C4×D5—21no—
67C2×C4×D5C2311yescharacteristic
68C2×Dic10—21no—
69C2×Dic10—21no—
70C2×Dic10C2311yescharacteristic
71C2×C5×C8C2311yescharacteristic
72C2×C5×C8C2311yescharacteristic
73C5×C4⋊C4—21no—
74C5×C4⋊C4—21no—
75C5×C4⋊C4C2311yescharacteristic
76C5×C4⋊C4C2311yescharacteristic
77C5×C4⋊C4C2311yescharacteristic
78C5×C22⋊C4—21no—
79C22⋊Dic5—21no—
80C22⋊Dic5D411yescharacteristic
81#689—22no—
82#685—21no—
83#685—21no—
84#685D411yescharacteristic
85C4⋊Dic5—21no—
86C4⋊Dic5—21no—
87C4⋊Dic5—21no—
88C4⋊Dic5C2311yescharacteristic
89C4⋊Dic5C2311yescharacteristic
90C4⋊Dic5C2311yescharacteristic
91#683—21no—
92#683—21no—
93#683—21no—
94#683—21no—
95#683—21no—
96#683—21no—
97#683—21no—
98#683D411yescharacteristic
99C4×Dic5—21no—
100C4×Dic5—21no—
101C4×Dic5C2311yescharacteristic
102C2×#168—22no—
103C2×#168C2311yescharacteristic
104C2×#168C2311yescharacteristic
105C8×D5—22no—
106#554—51no—
107#554—51no—
108#500—51no—
109#484—51no—
110#484—51no—
111#484—51no—
112#484D511yescharacteristic, complemented
113#477—51no—
114#477—51no—
115#467—51no—
116#467—51no—
117C4×Q16—51no—
118C8×D4—51no—
119C2×#107—51no—
120C2×#107—51no—
121C23×C5C2×D411yescharacteristic
122C22×D5C2×D411yescharacteristic
123C5×Q8—21no—
124C5×Q8—21no—
125C2×C4×C5—21no—
126C2×C4×C5—21no—
127C2×C4×C5—21no—
128C2×C4×C5—21no—
129C2×C4×C5—21no—
130C2×C4×C5—21no—
131C2×C4×C5—81no—
132C2×C4×C5C2×D411yescharacteristic
133C2×C4×C5C2411yescharacteristic
134C22⋊D5Q1614yescomplemented
135C2×Dic5—21no—
136C2×Dic5—21no—
137C2×Dic5—21no—
138C2×Dic5—21no—
139C2×Dic5—81no—
140C2×Dic5C2×D411yescharacteristic
141C2×Dic5C2×D411yescharacteristic
142C2×Dic5C2×D411yescharacteristic
143C4×D5—21no—
144C4×D5—21no—
145C4×D5—81no—
146C4×D5—81no—
147Dic10—21no—
148Dic10—21no—
149Dic10—81no—
150Dic10—81no—
151C5×C8—21no—
152C5×C8—21no—
153#168—21no—
154#168#4112yes—
155C2×Q16—51no—
156C22×C8—51no—
157C22×C8—51no—
158C4⋊Q8—51no—
159C4⋊Q8—51no—
160#125—101no—
161#125—101no—
162C22⋊Q8—51no—
163C22⋊Q8—51no—
164C22⋊Q8—51no—
165C22⋊Q8—101no—
166C22⋊Q8—101no—
167C22⋊Q8—101no—
168C22⋊Q8—101no—
169C22⋊Q8C2×D511yescharacteristic
170C4×Q8—51no—
171C4×Q8—51no—
172C4×D4—51no—
173C4×D4—101no—
174C4×D4—101no—
175C2×C4⋊C4—51no—
176C2×C4⋊C4—51no—
177C2×C4⋊C4—51no—
178C2×C4⋊C4C2×D511yescharacteristic
179#107—51no—
180#107—51no—
181#107—51no—
182#107—51no—
183#107—51no—
184#107—51no—
185#107—51no—
186#107C2×D511yescharacteristic
187#107C2×D511yescharacteristic
188C4⋊C8—51no—
189#103—51no—
190#103—51no—
191#103—51no—
192#103—51no—
193#103C2×D511yescharacteristic
194#103C2×D511yescharacteristic
195C22⋊C8—51no—
196C22⋊C8C2×D511yescharacteristic
197C4×C8—51no—
198C22×C5—21no—
199C22×C5—21no—
200C22×C5C2×Q1612yes—
201C22×C5C22×D411yescharacteristic
202C2×D5—21no—
203C2×D5—21no—
204C2×D5C2×Q1612yes—
205C4×C5—21no—
206C4×C5—41no—
207C4×C5—41no—
208C4×C5—41no—
209C4×C5—41no—
210C4×C5C2×#4111yescharacteristic
211C4×C52−1+411yescharacteristic
212Dic5—21no—
213Dic5—21no—
214Dic5—41no—
215Dic5—41no—
216Dic5—41no—
217Dic5—41no—
218Dic5C2×Q1612yes—
219C2×Q8—51no—
220C2×Q8—101no—
221C2×Q8—101no—
222C2×Q8C22×D511yescharacteristic
223C2×D4—51no—
224C22×C4—21no—
225C22×C4—51no—
226C22×C4—101no—
227C22×C4—101no—
228C22×C4—101no—
229C22×C4C22×D511yescharacteristic
230Q16—102no—
231C2×C8—51no—
232C2×C8—51no—
233C2×C8—102no—
234C2×C8—102no—
235C2×C8C22×D511yescharacteristic
236C2×C8C22×D511yescharacteristic
237C4⋊C4—21no—
238C4⋊C4—21no—
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⋊C4—101no—
250C4⋊C4—101no—
251C4⋊C4—101no—
252C4⋊C4—101no—
253C4⋊C4C22×D511yescharacteristic
254C4⋊C4C22×D511yescharacteristic
255C4⋊C4C22×D511yescharacteristic
256C22⋊C4—21no—
257C22⋊C4—51no—
258C22⋊C4—51no—
259C22⋊C4—101no—
260C22⋊C4—101no—
261C22⋊C4—101no—
262C42—51no—
263C42—101no—
264C42—101no—
265C2×C5—22no—
266C2×C5#54711yescharacteristic
267C2×C5C22×Q1611yescharacteristic
268C2×C5#57611yescharacteristic
269D5—22no—
270C23—51no—
271C23D4×D511yescharacteristic
272Q8—21no—
273Q8—21no—
274Q8—101no—
275Q8—101no—
276Q8—401no—
277Q8—401no—
278D4—54no—
279C2×C4—21no—
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—81no—
289C2×C4—101no—
290C2×C4—101no—
291C2×C4—101no—
292C2×C4—101no—
293C2×C4—101no—
294C2×C4—101no—
295C2×C4—401no—
296C2×C4—401no—
297C2×C4—401no—
298C2×C4D4×D511yescharacteristic
299C2×C4C23×D511yescharacteristic
300C8—21no—
301C8—21no—
302C8—52no—
303C8—101no—
304C5#333811yescharacteristic, complemented, Sylow
305C22—21no—
306C22—21no—
307C22—52no—
308C22—101no—
309C22—101no—
310C22D5×Q1612yes—
311C22C2×D4×D511yescharacteristic
312C4—21no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—52no—
318C4—101no—
319C4—101no—
320C4—201no—
321C4—201no—
322C4—201no—
323C4—201no—
324C4D5×#4111yescharacteristic
325C4#415011yescharacteristic
326C2—22no—
327C2—102no—
328C2#6598911yescharacteristic
329C2C2×D5×Q1611yescharacteristic
330C2#6610811yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#484C2
socleC22×C5C22×D4
prime radicalC2×C22⋊D5D4
hypercenter#484D5
hypocenterC5#3338
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. C5×#484C2semidirect
4. #65340C2semidirect
5. C2×#3939C2semidirect
6. #65173C2semidirect
7. D5×#107C2semidirect
8. #65164C2semidirect
9. #65163C2semidirect
10. #65102C2semidirect
11. #65098C2semidirect
12. #65083C2semidirect
13. #65079C2semidirect
15. #65011C2semidirect
112. #484D5semidirect
134. C22⋊D5Q16semidirect
304. C5#3338semidirect

Maximal subgroups

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

subgroupindex
#659692
#658452
C5×#4842
#653402
C2×#39392
#651732
D5×#1072
#651642
#651632
#651022
#650982
#650832
#650792
#650142
#650112
#33385