Finite Group Databasebeta

← #10611580

Subgroups — #10611580

Order 640.

372 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#65917C211yesmaximal, characteristic, complemented
2#65908C211yesmaximal, characteristic
3C5×#441C211yesmaximal, characteristic, complemented
4#65476C211yesmaximal, characteristic
5#65471C211yesmaximal, characteristic, complemented
6C4×#689C211yesmaximal, characteristic, complemented
7C4×#688C211yesmaximal, characteristic, complemented
8#65160C211yesmaximal, characteristic, complemented
9#65151C211yesmaximal, characteristic, complemented
10#65107C211yesmaximal, characteristic, complemented
11#65099C211yesmaximal, characteristic
12#65098C211yesmaximal, characteristic, complemented
13#65085C211yesmaximal, characteristic, complemented
14#64999C211yesmaximal, characteristic, complemented
15#64998C211yesmaximal, characteristic, complemented
16C2×#713C2211yescharacteristic
17C2×C5×Q16C2211yescharacteristic
18C4×C5×Q8C2211yescharacteristic
19C4×C5×Q8C2211yescharacteristic
20#4092C2211yescharacteristic
21Q8×Dic5C2211yescharacteristic
22#4090C2211yescharacteristic
23C2×#689C2211yescharacteristic
24C2×#688C2211yescharacteristic
25C2×#677C2211yescharacteristic
26#4044—21no—
27#4043C2211yescharacteristic
28#4039—21no—
29#4039C2211yescharacteristic
30D5×C4⋊C4—21no—
31D5×C4⋊C4C2211yescharacteristic
32#4036C2211yescharacteristic
33#4035—21no—
34#4022—21no—
35C4×D20—21no—
36C4×D20C2211yescharacteristic
37#4018—21no—
38#4018C2211yescharacteristic
39#4016—21no—
40C4×Dic10C2211yescharacteristic
41C5×#106C2211yescharacteristic
42C5×#103C2211yescharacteristic
43C5×#103C2211yescharacteristic
44C5×#97C2211yescharacteristic
45#3967C2211yescharacteristic
46#3967C2211yescharacteristic
47#3953C2211yescharacteristic
48#3952C2211yescharacteristic
49#3952C2211yescharacteristic
50#3950C2211yescharacteristic
51#3948C2211yescharacteristic
52#3946C2211yescharacteristic
53#3946C2211yescharacteristic
54#3942C2211yescharacteristic
55#3941C2211yescharacteristic
56#3940C2211yescharacteristic
57#3939C2211yescharacteristic
58C4×#168C2211yescharacteristic
59#3120—51nomaximal, Sylow
60C2×C5×Q8C2311yescharacteristic
61C2×C5×Q8C2311yescharacteristic
62#713—22no—
63#713—22no—
64C2×D20—21no—
65C2×D20C2311yescharacteristic
66C2×C4×D5—21no—
67C2×C4×D5—21no—
68C2×C4×D5—21no—
69C2×C4×D5—21no—
70C2×C4×D5C2311yescharacteristic
71C2×Dic10C2311yescharacteristic
72C5×Q16—22no—
73C2×C5×C8C2311yescharacteristic
74C2×C5×C8C2311yescharacteristic
75C5×C4⋊C4—21no—
76C5×C4⋊C4—21no—
77C5×C4⋊C4C2311yescharacteristic
78C5×C4⋊C4C2311yescharacteristic
79C42×C5—21no—
80C42×C5—21no—
81C42×C5C2311yescharacteristic
82#689—22no—
83#688—22no—
84#685—21no—
85#685—21no—
86#685—21no—
87#685—21no—
88#685D411yescharacteristic
89#685D411yescharacteristic
90C4⋊Dic5—21no—
91C4⋊Dic5—21no—
92C4⋊Dic5—21no—
93C4⋊Dic5C2311yescharacteristic
94C4⋊Dic5C2311yescharacteristic
95#683—21no—
96#683—21no—
97#683—21no—
98#683—21no—
99#683—21no—
100#683—21no—
101#683D411yescharacteristic
102#683D411yescharacteristic
103C4×Dic5—21no—
104C4×Dic5—21no—
105C4×Dic5C2311yescharacteristic
106C2×#168C2311yescharacteristic
107C2×#168C2311yescharacteristic
108#677—22no—
109#541—51no—
110#520—51no—
111#484—51no—
112#483—51no—
113#479—51no—
114#478—51no—
115#462—51no—
116#461—51no—
117#452—51no—
118#452—51no—
119#441D511yescharacteristic, complemented
120#440—51no—
121C4×Q16—51no—
122C4×SD16—51no—
123#433—51no—
124C22×D5—21no—
125C22×D5C2×D411yescharacteristic
126C5×Q8—21no—
127C5×Q8—21no—
128C5×Q8—21no—
129C5×Q8#4112yes—
130C2×C4×C5—21no—
131C2×C4×C5—21no—
132C2×C4×C5—21no—
133C2×C4×C5—21no—
134C2×C4×C5C2×D411yescharacteristic
135C2×C4×C5C2×D411yescharacteristic
136C2×C4×C5C2411yescharacteristic
137C2×Dic5—21no—
138C2×Dic5—21no—
139C2×Dic5—21no—
140C2×Dic5C2×D411yescharacteristic
141C2×Dic5C2×D411yescharacteristic
142C2×Dic5C2×D411yescharacteristic
143D20—24no—
144D20—21no—
145D20#4112yes—
146C4×D5—24no—
147C4×D5—21no—
148C4×D5—21no—
149C4×D5—81no—
150C4×D5—81no—
151C4×D5—81no—
152Dic10—21no—
153Dic10—21no—
154C5×C8—21no—
155C5×C8—21no—
156#168—21no—
157#168—21no—
158C2×#41—51no—
159C2×Q16—51no—
160C2×Q16C2×D511yescharacteristic
161C2×SD16—51no—
162C2×SD16—51no—
163C4⋊Q8—51no—
164#126—101no—
165#126—101no—
166#125—51no—
167#125—101no—
168#125—101no—
169C22⋊Q8—51no—
170C22⋊Q8—51no—
171C4×Q8—51no—
172C4×Q8—51no—
173C4×Q8C2×D511yescharacteristic
174C4×Q8C2×D511yescharacteristic
175C4×D4—51no—
176C4×D4—51no—
177C4×D4—101no—
178C4×D4—101no—
179#117—51no—
180#117—101no—
181C2×C4⋊C4—51no—
182C2×C4⋊C4—101no—
183#107—51no—
184#107—51no—
185#106—51no—
186#106C2×D511yescharacteristic
187C4⋊C8—51no—
188C4⋊C8—51no—
189#103—51no—
190#103—51no—
191#103—51no—
192#103—51no—
193#103C2×D511yescharacteristic
194#103C2×D511yescharacteristic
195#102—51no—
196#102—51no—
197C22⋊C8—51no—
198C22⋊C8—51no—
199#97C2×D511yescharacteristic
200C4×C8—51no—
201C22×C5C22×D411yescharacteristic
202C2×D5—21no—
203C2×D5—22no—
204C2×D5—21no—
205C2×D5—21no—
206C2×D5—41no—
207C2×D5—41no—
208C4×C5—22no—
209C4×C5—21no—
210C4×C5—21no—
211C4×C5—41no—
212C4×C5—41no—
213C4×C5—41no—
214C4×C5C2×#4111yescharacteristic
215C4×C5C2×#4111yescharacteristic
216Dic5—21no—
217Dic5—21no—
218Dic5—21no—
219Dic5—41no—
220Dic5—41no—
221Dic5—41no—
222#41—102no—
223#41—102no—
224C2×Q8—51no—
225C2×Q8C22×D511yescharacteristic
226C2×Q8C22×D511yescharacteristic
227C2×D4—51no—
228C2×D4—101no—
229C22×C4—51no—
230C22×C4—101no—
231C22×C4—101no—
232C22×C4—101no—
233C22×C4—101no—
234Q16—22no—
235Q16—102no—
236SD16—102no—
237SD16—102no—
238C2×C8—51no—
239C2×C8—51no—
240C2×C8C22×D511yescharacteristic
241C2×C8C22×D511yescharacteristic
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—51no—
245C4⋊C4—51no—
246C4⋊C4—51no—
247C4⋊C4—51no—
248C4⋊C4—101no—
249C4⋊C4—101no—
250C4⋊C4—101no—
251C4⋊C4—101no—
252C4⋊C4—101no—
253C4⋊C4—101no—
254C4⋊C4—101no—
255C4⋊C4—101no—
256C4⋊C4—101no—
257C4⋊C4C22×D511yescharacteristic
258C4⋊C4C22×D511yescharacteristic
259C22⋊C4—51no—
260C22⋊C4—51no—
261C22⋊C4—101no—
262C22⋊C4—101no—
263C22⋊C4—101no—
264C22⋊C4—101no—
265C42—21no—
266C42—21no—
267C42—51no—
268C42—101no—
269C42—101no—
270C42C22×D511yescharacteristic
271C2×C5#52511yescharacteristic
272C2×C5#57711yescharacteristic
273C2×C5#57811yescharacteristic
274D5—41no—
275D5—42no—
276C23—51no—
277C23—101no—
278Q8—21no—
279Q8—21no—
280Q8—21no—
281Q8—101no—
282Q8—101no—
283Q8#70912yes—
284D4—52no—
285D4—104no—
286D4—101no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—51no—
292C2×C4—51no—
293C2×C4—51no—
294C2×C4—104no—
295C2×C4—101no—
296C2×C4—101no—
297C2×C4—101no—
298C2×C4—101no—
299C2×C4—101no—
300C2×C4—401no—
301C2×C4—401no—
302C2×C4—401no—
303C2×C4D4×D511yescharacteristic
304C2×C4D4×D511yescharacteristic
305C2×C4C23×D511yescharacteristic
306C8—21no—
307C8—21no—
308C8—101no—
309C8—101no—
310C5#312011yescharacteristic, complemented, Sylow
311C22—101no—
312C22—101no—
313C22—102no—
314C22—101no—
315C22—201no—
316C22—201no—
317C22C2×D4×D511yescharacteristic
318C4—21no—
319C4—21no—
320C4—22no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—101no—
325C4—101no—
326C4—101no—
327C4—201no—
328C4—201no—
329C4—201no—
330C4C2×#70911yescharacteristic
331C4D5×#4111yescharacteristic
332C2—201no—
333C2—202no—
334C2#6588111yescharacteristic
335C2#6611211yescharacteristic
336C2#6611311yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#441C2
socleC22×C5C22×D4
prime radicalC2×#713C22
hypercenter#441D5
hypocenterC5#3120
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
1. #65917C2semidirect
3. C5×#441C2semidirect
5. #65471C2semidirect
6. C4×#689C2semidirect
7. C4×#688C2semidirect
8. #65160C2semidirect
9. #65151C2semidirect
10. #65107C2semidirect
12. #65098C2semidirect
13. #65085C2semidirect
14. #64999C2semidirect
15. #64998C2semidirect
119. #441D5semidirect
310. C5#3120semidirect

Maximal subgroups

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

subgroupindex
#659172
#659082
C5×#4412
#654762
#654712
C4×#6892
C4×#6882
#651602
#651512
#651072
#650992
#650982
#650852
#649992
#649982
#31205