Finite Group Databasebeta

← #10612972

Subgroups — #10612972

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#66023C211yesmaximal, characteristic
2#65917C211yesmaximal, characteristic
3C5×#479C211yesmaximal, characteristic, complemented
4#65352C211yesmaximal, characteristic, complemented
5#65309C211yesmaximal, characteristic, complemented
6#65177C211yesmaximal, characteristic
7#65167C211yesmaximal, characteristic, complemented
8#65151C211yesmaximal, characteristic
9#65145C211yesmaximal, characteristic, complemented
10#65139C211yesmaximal, characteristic, complemented
11#65129C211yesmaximal, characteristic
12#65103C211yesmaximal, characteristic
13#65098C211yesmaximal, characteristic
14#65086C211yesmaximal, characteristic, complemented
15#65081C211yesmaximal, characteristic, complemented
16C5×#125C2211yescharacteristic
17C4×C5×Q8C2211yescharacteristic
18#4092C2211yescharacteristic
19#4090C2211yescharacteristic
20#4044—21no—
21#4043—21no—
22#4043C2211yescharacteristic
23#4042—21no—
24#4038C2211yescharacteristic
25D5×C4⋊C4C2211yescharacteristic
26#4036C2211yescharacteristic
27#4036C2211yescharacteristic
28#4035—21no—
29#4035—21no—
30#4034—21no—
31#4034C2211yescharacteristic
32#4022—21no—
33#4018C2211yescharacteristic
34#4016—21no—
35#4015C2211yescharacteristic
36C4×Dic10C2211yescharacteristic
37C5×#107C2211yescharacteristic
38C5×#106C2211yescharacteristic
39C5×C4⋊C8C2211yescharacteristic
40C5×#103C2211yescharacteristic
41C5×#103C2211yescharacteristic
42#3967C2211yescharacteristic
43#3967C2211yescharacteristic
44#3952C2211yescharacteristic
45#3952C2211yescharacteristic
46#3950C2211yescharacteristic
47#3950C2211yescharacteristic
48#3948C2211yescharacteristic
49#3948C2211yescharacteristic
50#3947C2211yescharacteristic
51C8×Dic5C2211yescharacteristic
52#3942C2211yescharacteristic
53#3942C2211yescharacteristic
54#3940C2211yescharacteristic
55#3940C2211yescharacteristic
56#3940C2211yescharacteristic
57#3939C2211yescharacteristic
58C4⋊#168C2211yescharacteristic
59#3242—51nomaximal, Sylow
60C2×C5×Q8C2311yescharacteristic
61C2×C4×D5—21no—
62C2×C4×D5C2311yescharacteristic
63C2×Dic10—21no—
64C2×Dic10—21no—
65C2×Dic10C2311yescharacteristic
66C2×C5×C8C2311yescharacteristic
67C2×C5×C8C2311yescharacteristic
68C5×C4⋊C4—21no—
69C5×C4⋊C4—21no—
70C5×C4⋊C4—21no—
71C5×C4⋊C4C2311yescharacteristic
72C5×C4⋊C4C2311yescharacteristic
73C5×C4⋊C4C2311yescharacteristic
74C42×C5—21no—
75C42×C5C2311yescharacteristic
76#685—21no—
77#685—21no—
78#685—21no—
79#685D411yescharacteristic
80#685D411yescharacteristic
81C4⋊Dic5—21no—
82C4⋊Dic5—21no—
83C4⋊Dic5—21no—
84C4⋊Dic5—21no—
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#683D411yescharacteristic
97#683D411yescharacteristic
98C4×Dic5—21no—
99C4×Dic5—21no—
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#485—51no—
111#484—51no—
112#483—51no—
113#479—51no—
114#479D511yescharacteristic, complemented
115#477—51no—
116#475—51no—
117#433—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—21no—
136C4×D5—21no—
137C4×D5—81no—
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—101no—
155#125—101no—
156#125—101no—
157#125C2×D511yescharacteristic
158C22⋊Q8—51no—
159C22⋊Q8—51no—
160C22⋊Q8—101no—
161C22⋊Q8—101no—
162C4×Q8—51no—
163C4×Q8C2×D511yescharacteristic
164#117—51no—
165#117—51no—
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⋊C8C2×D511yescharacteristic
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⋊C8—51no—
187#97—51no—
188C4×C8—51no—
189C22×C5C22×D411yescharacteristic
190C2×D5—21no—
191C2×D5—21no—
192C2×D5—21no—
193C4×C5—21no—
194C4×C5—21no—
195C4×C5—41no—
196C4×C5—41no—
197C4×C5—41no—
198C4×C5—41no—
199C4×C52−1+411yescharacteristic
200C4×C52−1+411yescharacteristic
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—51no—
213C22×C4—101no—
214C2×C8—51no—
215C2×C8—51no—
216C2×C8C22×D511yescharacteristic
217C2×C8C22×D511yescharacteristic
218C4⋊C4—21no—
219C4⋊C4—21no—
220C4⋊C4—21no—
221C4⋊C4—51no—
222C4⋊C4—51no—
223C4⋊C4—51no—
224C4⋊C4—51no—
225C4⋊C4—51no—
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—51no—
242C22⋊C4—51no—
243C22⋊C4—101no—
244C22⋊C4—101no—
245C22⋊C4—101no—
246C42—21no—
247C42—51no—
248C42—101no—
249C42—101no—
250C42C22×D511yescharacteristic
251C2×C5#53611yescharacteristic
252C2×C5#57711yescharacteristic
253C2×C5#57811yescharacteristic
254D5—41no—
255C23—51no—
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—51no—
267C2×C4—51no—
268C2×C4—51no—
269C2×C4—101no—
270C2×C4—101no—
271C2×C4—101no—
272C2×C4—101no—
273C2×C4—101no—
274C2×C4—101no—
275C2×C4—401no—
276C2×C4D4×D511yescharacteristic
277C2×C4D4×D511yescharacteristic
278C2×C4C23×D511yescharacteristic
279C8—21no—
280C8—21no—
281C8—101no—
282C8—101no—
283C5#324211yescharacteristic, complemented, Sylow
284C22—101no—
285C22—101no—
286C22—101no—
287C22C2×D4×D511yescharacteristic
288C4—21no—
289C4—21no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—41no—
294C4—101no—
295C4—101no—
296C4—101no—
297C4—201no—
298C4—201no—
299C4—201no—
300C4—201no—
301C4#414711yescharacteristic
302C4#415011yescharacteristic
303C2—201no—
304C2#6596211yescharacteristic
305C2#6610511yescharacteristic
306C2#6611211yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#479C2
socleC22×C5C22×D4
prime radicalC22×D5C2×D4
hypercenter#479D5
hypocenterC5#3242
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. #65309C2semidirect
7. #65167C2semidirect
9. #65145C2semidirect
10. #65139C2semidirect
14. #65086C2semidirect
15. #65081C2semidirect
114. #479D5semidirect
283. C5#3242semidirect

Maximal subgroups

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

subgroupindex
#660232
#659172
C5×#4792
#653522
#653092
#651772
#651672
#651512
#651452
#651392
#651292
#651032
#650982
#650862
#650812
#32425