Finite Group Databasebeta

← #10613106

Subgroups — #10613106

Order 640.

418 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#65941C211yesmaximal, characteristic
2#65857C211yesmaximal, characteristic, complemented
3C5×#482C211yesmaximal, characteristic, complemented
4#65322C211yesmaximal, characteristic, complemented
5#65292C211yesmaximal, characteristic, complemented
6#65171C211yesmaximal, characteristic, complemented
7#65170C211yesmaximal, characteristic, complemented
8#65155C211yesmaximal, characteristic, complemented
9#65149C211yesmaximal, characteristic, complemented
10#65068C211yesmaximal, characteristic, complemented
11#65066C211yesmaximal, characteristic, complemented
12#65059C211yesmaximal, characteristic, complemented
13D5×#102C211yesmaximal, characteristic, complemented
14#65024C211yesmaximal, characteristic, complemented
15#65016C211yesmaximal, characteristic, complemented
16C2×D4×D5C2211yescharacteristic
17C2×#709C2211yescharacteristic
18C5×#121C2211yescharacteristic
19C5×#117C2211yescharacteristic, complemented
20#4086—21no—
21#4084C2211yescharacteristic
22#4083—21no—
23#4076C2211yescharacteristic
24C2×C4⋊Dic5C2211yescharacteristic, complemented
25C2×#676C2211yescharacteristic
26C2×C8×D5C2211yescharacteristic
27#4041C2211yescharacteristic
28#4038C2211yescharacteristic
29#4038C2211yescharacteristic
30#4038C2211yescharacteristic, complemented
31D5×C4⋊C4C2211yescharacteristic
32D5×C4⋊C4C2211yescharacteristic, complemented
33#4031—21no—
34#4028—21no—
35#4027—21no—
36#4027—21no—
37C4×D20—21no—
38C4×Dic10—21no—
39C5×#107C2211yescharacteristic, complemented
40C5×#106C2211yescharacteristic, complemented
41C5×#102C2211yescharacteristic
42C5×#102C2211yescharacteristic
43C5×C22⋊C8C2211yescharacteristic, complemented
44#3964C2211yescharacteristic
45#3964C2211yescharacteristic
46C22⋊#168C2211yescharacteristic, complemented
47#3953C2211yescharacteristic
48#3953C2211yescharacteristic
49#3952C2211yescharacteristic, complemented
50#3952C2211yescharacteristic, complemented
51#3949C2211yescharacteristic, complemented
52#3949C2211yescharacteristic, complemented
53#3941C2211yescharacteristic
54#3941C2211yescharacteristic
55#3940C2211yescharacteristic, complemented
56#3939C2211yescharacteristic, complemented
57#3939C2211yescharacteristic, complemented
58#3939C2211yescharacteristic, complemented
59#3096—51nomaximal, Sylow
60C23×D5—21no—
61C2×C5×D4—21no—
62C2×C5×D4C2311yescharacteristic
63C22×C4×C5C2311yescharacteristic
64C2×C22⋊D5—21no—
65C2×C22⋊D5—21no—
66C2×C22⋊D5—21no—
67C2×C22⋊D5D411yescharacteristic
68C2×C22⋊D5D411yescharacteristic
69C22×Dic5—21no—
70D4×D5—22no—
71D4×D5—22no—
72#709—22no—
73#709—22no—
74C2×D20—21no—
75C2×D20D411yescharacteristic
76C2×D20C2311yescharacteristic
77C2×C4×D5—21no—
78C2×C4×D5—21no—
79C2×C4×D5C2311yescharacteristic
80C2×C4×D5C2311yescharacteristic
81C2×Dic10D411yescharacteristic
82C2×C5×C8C2311yescharacteristic
83C2×C5×C8C2311yescharacteristic
84C5×C4⋊C4C2311yescharacteristic
85C5×C4⋊C4C2311yescharacteristic
86C5×C4⋊C4C2311yescharacteristic
87C5×C22⋊C4—21no—
88C5×C22⋊C4—21no—
89C42×C5—21no—
90C22⋊Dic5—21no—
91#685—21no—
92#685—21no—
93#685—21no—
94#685—21no—
95#685—21no—
96C4⋊Dic5—21no—
97C4⋊Dic5C2311yescharacteristic
98C4⋊Dic5C2311yescharacteristic
99C4⋊Dic5C2311yescharacteristic
100#683—21no—
101#683—21no—
102C4×Dic5—21no—
103C4×Dic5—21no—
104C4×Dic5—21no—
105C2×#168C2311yescharacteristic
106C2×#168C2311yescharacteristic
107#676—22no—
108C8×D5—22no—
109#535—51no—
110#520—51no—
111#482—51no—
112#482—51no—
113#482—51no—
114#482D511yescharacteristic, complemented
115#481—51no—
116#481—51no—
117#480—51no—
118#480—51no—
119#428—51no—
120#427—51no—
121#418—51no—
122C2×#102—51no—
123#408—51no—
124C23×C5—21no—
125C23×C5C2×D411yescharacteristic
126C22×D5—21no—
127C22×D5—42no—
128C22×D5—81no—
129C22×D5—81no—
130C22×D5C2×D411yescharacteristic
131C22×D5C2×D411yescharacteristic
132C5×D4—21no—
133C5×D4—21no—
134C5×D4—81no—
135C2×C4×C5—21no—
136C2×C4×C5—21no—
137C2×C4×C5—21no—
138C2×C4×C5—21no—
139C2×C4×C5—21no—
140C2×C4×C5C2×D411yescharacteristic
141C2×C4×C5C2411yescharacteristic
142C22⋊D5—22no—
143C22⋊D5—22no—
144C22⋊D5—42no—
145C22⋊D5—81no—
146C22⋊D5—81no—
147C2×Dic5—21no—
148C2×Dic5—21no—
149C2×Dic5—21no—
150C2×Dic5—81no—
151C2×Dic5C2×D411yescharacteristic
152C2×Dic5C2×D411yescharacteristic
153D20—22no—
154D20—21no—
155D20—21no—
156D20—81no—
157C4×D5—21no—
158C4×D5—21no—
159C4×D5—81no—
160C4×D5—81no—
161C4×D5#4112yes—
162C4×D5#4112yes—
163Dic10—22no—
164C5×C8—21no—
165C5×C8—21no—
166#168—21no—
167#168—21no—
168C2×#41—51no—
169C22×D4—51no—
170C2×M16—51no—
171C22×C8—51no—
172#127—101no—
173#124—101no—
174#121—51no—
175#121—51no—
176#121—51no—
177#121C2×D511yescharacteristic
178#120—101no—
179#120—101no—
180C4×Q8—101no—
181C4×D4—101no—
182C4×D4—101no—
183C4×D4—101no—
184#117—51no—
185#117—51no—
186#117—51no—
187#117C2×D511yescharacteristic, complemented
188C2×C4⋊C4—51no—
189C2×C4⋊C4—51no—
190C2×C4⋊C4—51no—
191#107—51no—
192#107—51no—
193#107—51no—
194#107C2×D511yescharacteristic, complemented
195#106—51no—
196#106—51no—
197#106—51no—
198#106C2×D511yescharacteristic, complemented
199#102—51no—
200#102—51no—
201#102—51no—
202#102—51no—
203#102—51no—
204#102—51no—
205#102C2×D511yescharacteristic
206#102C2×D511yescharacteristic
207C22⋊C8—51no—
208C22⋊C8—51no—
209C22⋊C8—51no—
210C22⋊C8C2×D511yescharacteristic, complemented
211C22×C5—21no—
212C22×C5—21no—
213C22×C5—21no—
214C22×C5—41no—
215C22×C5—41no—
216C22×C5—41no—
217C22×C5C22×D411yescharacteristic
218C2×D5—21no—
219C2×D5—21no—
220C2×D5—21no—
221C2×D5—21no—
222C2×D5—21no—
223C2×D5—41no—
224C2×D5—41no—
225C2×D5—41no—
226C2×D5—84no—
227C2×D5#12312yes—
228C4×C5—21no—
229C4×C5—41no—
230C4×C5—41no—
231C4×C5—41no—
232C4×C5C2×#4111yescharacteristic
233C4×C5C2×#4111yescharacteristic
234Dic5—21no—
235Dic5—41no—
236Dic5—41no—
237Dic5—41no—
238Dic5#12312yes—
239C24—101no—
240#41—102no—
241#41—102no—
242C2×Q8—51no—
243C2×D4—21no—
244C2×D4—51no—
245C2×D4—51no—
246C2×D4—51no—
247C2×D4—51no—
248C2×D4—101no—
249C2×D4—102no—
250C2×D4—102no—
251C2×D4—101no—
252C2×D4—101no—
253C2×D4—101no—
254C2×D4C22×D511yescharacteristic
255C22×C4—51no—
256C22×C4—51no—
257C22×C4—101no—
258C22×C4—101no—
259C22×C4—101no—
260C22×C4C22×D511yescharacteristic
261M16—102no—
262C2×C8—51no—
263C2×C8—51no—
264C2×C8—102no—
265C2×C8C22×D511yescharacteristic
266C2×C8C22×D511yescharacteristic
267C4⋊C4—51no—
268C4⋊C4—51no—
269C4⋊C4—51no—
270C4⋊C4—101no—
271C4⋊C4—101no—
272C4⋊C4—101no—
273C4⋊C4C22×D511yescharacteristic
274C4⋊C4C22×D511yescharacteristic
275C4⋊C4C22×D511yescharacteristic
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—101no—
279C22⋊C4—101no—
280C22⋊C4—101no—
281C22⋊C4—101no—
282C22⋊C4—101no—
283C22⋊C4—101no—
284C42—21no—
285C42—101no—
286C42—101no—
287C42—101no—
288C2×C5—41no—
289C2×C5—81no—
290C2×C5C2×#12311yescharacteristic
291C2×C5#57611yescharacteristic
292C2×C5#57711yescharacteristic
293D5—22no—
294D5—41no—
295D5—81no—
296C23—21no—
297C23—51no—
298C23—51no—
299C23—101no—
300C23—202no—
301C23—401no—
302C23—401no—
303C23D4×D511yescharacteristic
304Q8—102no—
305D4—21no—
306D4—21no—
307D4—81no—
308D4—102no—
309D4—102no—
310D4—102no—
311D4—101no—
312D4—101no—
313D4—202no—
314D4—401no—
315D4—401no—
316D4—401no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—51no—
323C2×C4—52no—
324C2×C4—52no—
325C2×C4—51no—
326C2×C4—101no—
327C2×C4—101no—
328C2×C4—101no—
329C2×C4—101no—
330C2×C4—101no—
331C2×C4—401no—
332C2×C4—401no—
333C2×C4—401no—
334C2×C4D4×D511yescharacteristic
335C2×C4C23×D511yescharacteristic
336C8—21no—
337C8—21no—
338C8—101no—
339C8—101no—
340C5#309611yescharacteristic, complemented, Sylow
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—52no—
348C22—101no—
349C22—101no—
350C22—101no—
351C22—101no—
352C22—101no—
353C22—201no—
354C22—201no—
355C22—201no—
356C22—404no—
357C22C2×D4×D511yescharacteristic
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—52no—
363C4—101no—
364C4—201no—
365C4—201no—
366C4—201no—
367C4D5×#4111yescharacteristic
368C4D5×#4111yescharacteristic
369C2—41no—
370C2—81no—
371C2—102no—
372C2—201no—
373C2—401no—
374C2D5×#12311yescharacteristic
375C2#6610411yescharacteristic
376C2#6610811yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#482C2
socleC22×C5C22×D4
prime radical#65941C2
hypercenter#482D5
hypocenterC5#3096
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #65857C2semidirect
3. C5×#482C2semidirect
4. #65322C2semidirect
5. #65292C2semidirect
6. #65171C2semidirect
7. #65170C2semidirect
8. #65155C2semidirect
9. #65149C2semidirect
10. #65068C2semidirect
11. #65066C2semidirect
12. #65059C2semidirect
13. D5×#102C2semidirect
14. #65024C2semidirect
15. #65016C2semidirect
19. C5×#117C22semidirect
24. C2×C4⋊Dic5C22semidirect
30. #4038C22semidirect
32. D5×C4⋊C4C22semidirect
39. C5×#107C22semidirect
40. C5×#106C22semidirect
43. C5×C22⋊C8C22semidirect
46. C22⋊#168C22semidirect
49. #3952C22semidirect
50. #3952C22semidirect
51. #3949C22semidirect
52. #3949C22semidirect
55. #3940C22semidirect
56. #3939C22semidirect
57. #3939C22semidirect
58. #3939C22semidirect
114. #482D5semidirect
187. #117C2×D5semidirect
194. #107C2×D5semidirect
198. #106C2×D5semidirect
210. C22⋊C8C2×D5semidirect
340. C5#3096semidirect

Maximal subgroups

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

subgroupindex
#659412
#658572
C5×#4822
#653222
#652922
#651712
#651702
#651552
#651492
#650682
#650662
#650592
D5×#1022
#650242
#650162
#30965