Finite Group Databasebeta

← #10612464

Subgroups — #10612464

Order 640.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#65950C211yesmaximal, characteristic, complemented
2#65946C211yesmaximal, characteristic, complemented
3C5×#466C211yesmaximal, characteristic, complemented
4#65445C211yesmaximal, characteristic, complemented
5#65442C211yesmaximal, characteristic, complemented
6#65402C211yesmaximal, characteristic, complemented
7#65400C211yesmaximal, characteristic, complemented
8#65326C211yesmaximal, characteristic, complemented
9#65324C211yesmaximal, characteristic, complemented
10#65179C211yesmaximal, characteristic, complemented
11#65177C211yesmaximal, characteristic, complemented
12#65074C211yesmaximal, characteristic, complemented
13#65069C211yesmaximal, characteristic, complemented
14#65059C211yesmaximal, characteristic, complemented
15#65054C211yesmaximal, characteristic, complemented
16C2×D4×D5C2211yescharacteristic
17C2×#709C2211yescharacteristic
18C2×C5×D8C2211yescharacteristic
19C22×C5×C8C2211yescharacteristic, complemented
20C5×#121C2211yescharacteristic
21C5×#121C2211yescharacteristic, complemented
22#4085—21no—
23#4084—21no—
24#4084C2211yescharacteristic
25#4083—21no—
26#4082—21no—
27#4082C2211yescharacteristic
28D4×Dic5C2211yescharacteristic, complemented
29C2×#687C2211yescharacteristic, complemented
30C2×#686C2211yescharacteristic
31C4×C22⋊D5C2211yescharacteristic
32#4072C2211yescharacteristic, complemented
33C2×#676C2211yescharacteristic
34#4043C2211yescharacteristic
35#4039C2211yescharacteristic
36#4038C2211yescharacteristic
37#4034C2211yescharacteristic, complemented
38#4031—21no—
39#4029—21no—
40D5×C22⋊C4—21no—
41#4023—21no—
42C5×#107C2211yescharacteristic, complemented
43C5×#102C2211yescharacteristic
44C5×#102C2211yescharacteristic, complemented
45#3964C2211yescharacteristic
46#3964C2211yescharacteristic
47C22⋊#168C2211yescharacteristic, complemented
48#3953C2211yescharacteristic
49#3953C2211yescharacteristic
50#3952C2211yescharacteristic
51#3948C2211yescharacteristic, complemented
52#3948C2211yescharacteristic, complemented
53#3947C2211yescharacteristic, complemented
54#3946C2211yescharacteristic, complemented
55#3942C2211yescharacteristic, complemented
56#3941C2211yescharacteristic
57#3940C2211yescharacteristic, complemented
58#3939C2211yescharacteristic, complemented
59#3319—51nomaximal, Sylow
60C23×D5—21no—
61C2×C5×D4—21no—
62C2×C5×D4—21no—
63C2×C5×D4C2311yescharacteristic
64C2×C5×D4C2311yescharacteristic
65C22×C4×C5C2311yescharacteristic
66C2×C22⋊D5—21no—
67C2×C22⋊D5—21no—
68C2×C22⋊D5—21no—
69C2×C22⋊D5D411yescharacteristic
70C22×Dic5—21no—
71D4×D5—22no—
72D4×D5—41no—
73#709—22no—
74#709—41no—
75C2×D20C2311yescharacteristic
76C2×C4×D5—21no—
77C2×C4×D5—21no—
78C2×C4×D5C2311yescharacteristic
79C2×Dic10—21no—
80C2×Dic10C2311yescharacteristic
81C5×D8—41no—
82C2×C5×C8—41no—
83C2×C5×C8C2311yescharacteristic
84C2×C5×C8C2311yescharacteristic
85C5×C4⋊C4C2311yescharacteristic
86C5×C4⋊C4C2311yescharacteristic
87C5×C22⋊C4—21no—
88C5×C22⋊C4—21no—
89C22⋊Dic5—21no—
90C22⋊Dic5—21no—
91C22⋊Dic5—21no—
92C22⋊Dic5—21no—
93C22⋊Dic5—21no—
94C22⋊Dic5D411yescharacteristic
95#687—41no—
96#686—22no—
97#685—21no—
98#685—21no—
99#685—21no—
100#685D411yescharacteristic
101C4⋊Dic5—21no—
102C4⋊Dic5C2311yescharacteristic
103C4⋊Dic5C2311yescharacteristic
104#683—21no—
105#683D411yescharacteristic
106C4×Dic5—21no—
107C4×Dic5—21no—
108C4×Dic5C2311yescharacteristic
109C2×#168C2311yescharacteristic
110C2×#168C2311yescharacteristic
111#676—41no—
112#555—51no—
113#546—51no—
114#489—51no—
115#485—51no—
116#482—51no—
117#474—51no—
118#468—51no—
119#466D511yescharacteristic, complemented
120#463—51no—
121#449—51no—
122#447—51no—
123#442—51no—
124#435—51no—
125#418—51no—
126#416—51no—
127C23×C5—21no—
128C23×C5—21no—
129C23×C5C2×D411yescharacteristic
130C22×D5—21no—
131C22×D5—42no—
132C22×D5—42no—
133C22×D5—81no—
134C22×D5C2×D411yescharacteristic
135C5×D4—21no—
136C5×D4—21no—
137C5×D4—21no—
138C5×D4—21no—
139C5×D4—81no—
140C5×D4—81no—
141C2×C4×C5—21no—
142C2×C4×C5—21no—
143C2×C4×C5—21no—
144C2×C4×C5—21no—
145C2×C4×C5C2×D411yescharacteristic
146C2×C4×C5C2411yescharacteristic
147C22⋊D5—41no—
148C22⋊D5—42no—
149C22⋊D5—42no—
150C22⋊D5—81no—
151C2×Dic5—21no—
152C2×Dic5—21no—
153C2×Dic5—21no—
154C2×Dic5—42no—
155C2×Dic5C2×D411yescharacteristic
156C2×Dic5C2×D411yescharacteristic
157C2×Dic5C2×D411yescharacteristic
158D20—21no—
159D20#4112yes—
160C4×D5—21no—
161C4×D5—21no—
162C4×D5—42no—
163C4×D5—81no—
164Dic10—21no—
165Dic10—21no—
166Dic10—81no—
167C5×C8—21no—
168C5×C8—21no—
169#168—21no—
170#168—21no—
171C2×#41—51no—
172C22×D4—51no—
173C2×SD16—51no—
174C2×D8—51no—
175C2×D8C2×D511yescharacteristic
176C2×M16—51no—
177C22×C8C2×D511yescharacteristic, complemented
178C4⋊Q8—51no—
179#124—51no—
180#124—101no—
181#124—101no—
182#123—101no—
183C22⋊Q8—51no—
184#121—51no—
185#121—101no—
186#121—101no—
187#121C2×D511yescharacteristic
188#121C2×D511yescharacteristic, complemented
189#120—101no—
190C4×D4—51no—
191C4×D4—51no—
192C4×D4—51no—
193#117—51no—
194#117—51no—
195#117—101no—
196C2×C22⋊C4—101no—
197#107—51no—
198#107C2×D511yescharacteristic, complemented
199#106—51no—
200C4⋊C8—51no—
201#103—51no—
202#103—51no—
203#103—51no—
204#102—51no—
205#102—51no—
206#102—51no—
207#102—51no—
208#102—51no—
209#102C2×D511yescharacteristic
210#102C2×D511yescharacteristic, complemented
211C22⋊C8—51no—
212C22⋊C8—51no—
213#97—51no—
214C22×C5—21no—
215C22×C5—21no—
216C22×C5—21no—
217C22×C5—41no—
218C22×C5—41no—
219C22×C5—41no—
220C22×C5—41no—
221C22×C5—41no—
222C22×C5—41no—
223C22×C5C22×D411yescharacteristic
224C2×D5—21no—
225C2×D5—22no—
226C2×D5—21no—
227C2×D5—21no—
228C2×D5—41no—
229C2×D5—41no—
230C2×D5—84no—
231C4×C5—21no—
232C4×C5—41no—
233C4×C5—41no—
234C4×C5C2×#4111yescharacteristic
235C4×C5H(5,𝔽2)11yescharacteristic
236Dic5—21no—
237Dic5—21no—
238Dic5—21no—
239Dic5—41no—
240Dic5—41no—
241Dic5—41no—
242C24—101no—
243#41—102no—
244#41—201no—
245C2×Q8—51no—
246C2×Q8—101no—
247C2×D4—21no—
248C2×D4—21no—
249C2×D4—51no—
250C2×D4—51no—
251C2×D4—101no—
252C2×D4—102no—
253C2×D4—101no—
254C2×D4—101no—
255C2×D4—201no—
256C2×D4C22×D511yescharacteristic
257C2×D4C22×D511yescharacteristic
258C22×C4—51no—
259C22×C4—101no—
260C22×C4—101no—
261C22×C4—101no—
262C22×C4C22×D511yescharacteristic
263SD16—201no—
264D8—41no—
265D8—102no—
266M16—201no—
267C2×C8—41no—
268C2×C8—51no—
269C2×C8—51no—
270C2×C8C22×D511yescharacteristic
271C2×C8C22×D511yescharacteristic
272C4⋊C4—51no—
273C4⋊C4—51no—
274C4⋊C4—51no—
275C4⋊C4—101no—
276C4⋊C4—101no—
277C4⋊C4C22×D511yescharacteristic
278C4⋊C4C22×D511yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—51no—
282C22⋊C4—51no—
283C22⋊C4—101no—
284C22⋊C4—101no—
285C22⋊C4—101no—
286C22⋊C4—101no—
287C22⋊C4—101no—
288C22⋊C4—101no—
289C22⋊C4—101no—
290C22⋊C4—101no—
291C42—51no—
292C42—101no—
293C42—101no—
294C2×C5—41no—
295C2×C5—81no—
296C2×C5—81no—
297C2×C5#54611yescharacteristic
298C2×C5#57511yescharacteristic
299C2×C5#57611yescharacteristic
300D5—41no—
301D5—42no—
302C23—21no—
303C23—21no—
304C23—51no—
305C23—101no—
306C23—202no—
307C23—202no—
308C23—401no—
309C23D4×D511yescharacteristic
310Q8—101no—
311Q8—101no—
312Q8—401no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—52no—
318D4—81no—
319D4—81no—
320D4—101no—
321D4—201no—
322D4—202no—
323D4—202no—
324D4—401no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—51no—
330C2×C4—51no—
331C2×C4—51no—
332C2×C4—101no—
333C2×C4—101no—
334C2×C4—101no—
335C2×C4—101no—
336C2×C4—101no—
337C2×C4—202no—
338C2×C4—202no—
339C2×C4—401no—
340C2×C4D4×D511yescharacteristic
341C2×C4C23×D511yescharacteristic
342C8—21no—
343C8—21no—
344C8—101no—
345C8—101no—
346C5#331911yescharacteristic, complemented, Sylow
347C22—21no—
348C22—21no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—101no—
357C22—101no—
358C22—101no—
359C22—102no—
360C22—201no—
361C22—201no—
362C22—404no—
363C22C2×D4×D511yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—101no—
368C4—101no—
369C4—101no—
370C4—201no—
371C4—201no—
372C4—201no—
373C4#414411yescharacteristic
374C4D5×#4111yescharacteristic
375C2—41no—
376C2—81no—
377C2—81no—
378C2—201no—
379C2—202no—
380C2#6594411yescharacteristic
381C2#6609111yescharacteristic
382C2#6610211yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#466C2
socleC22×C5C22×D4
hypercenter#466D5
hypocenterC5#3319
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #65950C2semidirect
2. #65946C2semidirect
3. C5×#466C2semidirect
4. #65445C2semidirect
5. #65442C2semidirect
6. #65402C2semidirect
7. #65400C2semidirect
8. #65326C2semidirect
9. #65324C2semidirect
10. #65179C2semidirect
11. #65177C2semidirect
12. #65074C2semidirect
13. #65069C2semidirect
14. #65059C2semidirect
15. #65054C2semidirect
19. C22×C5×C8C22semidirect
21. C5×#121C22semidirect
28. D4×Dic5C22semidirect
29. C2×#687C22semidirect
32. #4072C22semidirect
37. #4034C22semidirect
42. C5×#107C22semidirect
44. C5×#102C22semidirect
47. C22⋊#168C22semidirect
51. #3948C22semidirect
52. #3948C22semidirect
53. #3947C22semidirect
54. #3946C22semidirect
55. #3942C22semidirect
57. #3940C22semidirect
58. #3939C22semidirect
119. #466D5semidirect
177. C22×C8C2×D5semidirect
188. #121C2×D5semidirect
198. #107C2×D5semidirect
210. #102C2×D5semidirect
346. C5#3319semidirect

Maximal subgroups

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

subgroupindex
#659502
#659462
C5×#4662
#654452
#654422
#654022
#654002
#653262
#653242
#651792
#651772
#650742
#650692
#650592
#650542
#33195