Finite Group Databasebeta

← #10613059

Subgroups — #10613059

Order 640.

398 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#65942C211yesmaximal, characteristic
2#65838C211yesmaximal, characteristic, complemented
3C5×#481C211yesmaximal, characteristic, complemented
4#65324C211yesmaximal, characteristic, complemented
5#65260C211yesmaximal, characteristic, complemented
6#65156C211yesmaximal, characteristic, complemented
7#65151C211yesmaximal, characteristic, complemented
8#65150C211yesmaximal, characteristic, complemented
9D5×#106C211yesmaximal, characteristic, complemented
10#65073C211yesmaximal, characteristic, complemented
11#65066C211yesmaximal, characteristic, complemented
12#65061C211yesmaximal, characteristic, complemented
13#65060C211yesmaximal, characteristic, complemented
14#65016C211yesmaximal, characteristic, complemented
15#65012C211yesmaximal, characteristic, complemented
16C2×#711C2211yescharacteristic
17C2×#709C2211yescharacteristic
18C5×#121C2211yescharacteristic
19C2×C5×C4⋊C4C2211yescharacteristic
20#4085—21no—
21#4084—21no—
22#4084C2211yescharacteristic
23C4×C22⋊D5—21no—
24C4×C22⋊D5—21no—
25#4072C2211yescharacteristic
26#4070C2211yescharacteristic
27C2×#676C2211yescharacteristic
28C2×C8×D5C2211yescharacteristic
29#4043C2211yescharacteristic
30#4039—21no—
31#4038C2211yescharacteristic
32#4038C2211yescharacteristic
33D5×C4⋊C4C2211yescharacteristic
34D5×C4⋊C4C2211yescharacteristic
35D5×C4⋊C4C2211yescharacteristic
36#4033—21no—
37#4030—21no—
38#4024—21no—
39C5×#106C2211yescharacteristic
40C5×#106C2211yescharacteristic
41C5×#102C2211yescharacteristic
42C5×#102C2211yescharacteristic
43C5×C22⋊C8C2211yescharacteristic
44#3964C2211yescharacteristic
45#3964C2211yescharacteristic
46C22⋊#168C2211yescharacteristic
47#3952C2211yescharacteristic
48#3952C2211yescharacteristic
49#3950C2211yescharacteristic
50#3949C2211yescharacteristic
51#3948C2211yescharacteristic
52#3948C2211yescharacteristic
53#3942C2211yescharacteristic
54#3942C2211yescharacteristic
55#3940C2211yescharacteristic
56#3940C2211yescharacteristic
57#3940C2211yescharacteristic
58#3939C2211yescharacteristic
59#3099—51nomaximal, Sylow
60C2×C5×D4—21no—
61C2×C5×D4C2311yescharacteristic
62C22×C4×C5—21no—
63C22×C4×C5C2311yescharacteristic
64C2×C22⋊D5—21no—
65C2×C22⋊D5—21no—
66C2×C22⋊D5D411yescharacteristic
67C2×C22⋊D5D411yescharacteristic
68C22×Dic5—21no—
69#711—22no—
70#711—22no—
71#709—22no—
72#709—22no—
73C2×D20D411yescharacteristic
74C2×C4×D5—21no—
75C2×C4×D5—21no—
76C2×C4×D5—21no—
77C2×C4×D5C2311yescharacteristic
78C2×C4×D5C2311yescharacteristic
79C2×Dic10D411yescharacteristic
80C2×Dic10C2311yescharacteristic
81C2×C5×C8C2311yescharacteristic
82C2×C5×C8C2311yescharacteristic
83C5×C4⋊C4—21no—
84C5×C4⋊C4C2311yescharacteristic
85C5×C4⋊C4C2311yescharacteristic
86C5×C4⋊C4C2311yescharacteristic
87C5×C22⋊C4—21no—
88C22⋊Dic5—21no—
89C22⋊Dic5—21no—
90C22⋊Dic5—21no—
91#685—21no—
92#685—21no—
93#685—21no—
94C4⋊Dic5—21no—
95C4⋊Dic5C2311yescharacteristic
96C4⋊Dic5C2311yescharacteristic
97C4⋊Dic5C2311yescharacteristic
98#683—21no—
99#683—21no—
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#537—51no—
110#520—51no—
111#485—51no—
112#485—51no—
113#483—51no—
114#483—51no—
115#482—51no—
116#482—51no—
117#481—51no—
118#481D511yescharacteristic, complemented
119#428—51no—
120C2×#106—51no—
121#417—51no—
122#416—51no—
123#408—51no—
124C23×C5—21no—
125C23×C5C2×D411yescharacteristic
126C22×D5C2×D411yescharacteristic
127C22×D5C2×D411yescharacteristic
128C5×D4—21no—
129C5×D4—21no—
130C5×D4—81no—
131C2×C4×C5—21no—
132C2×C4×C5—21no—
133C2×C4×C5—21no—
134C2×C4×C5—21no—
135C2×C4×C5—21no—
136C2×C4×C5—81no—
137C2×C4×C5C2×D411yescharacteristic
138C2×C4×C5C2411yescharacteristic
139C22⋊D5—22no—
140C22⋊D5—22no—
141C22⋊D5—42no—
142C22⋊D5—81no—
143C2×Dic5—21no—
144C2×Dic5—21no—
145C2×Dic5—21no—
146C2×Dic5—21no—
147C2×Dic5—42no—
148C2×Dic5C2×D411yescharacteristic
149C2×Dic5C2×D411yescharacteristic
150D20—22no—
151C4×D5—21no—
152C4×D5—21no—
153C4×D5—81no—
154C4×D5—81no—
155C4×D5—81no—
156C4×D5#4112yes—
157C4×D5#4112yes—
158Dic10—22no—
159Dic10—21no—
160Dic10—21no—
161C5×C8—21no—
162C5×C8—21no—
163#168—21no—
164#168—21no—
165C2×#41—51no—
166C2×#41—51no—
167C2×M16—51no—
168C22×C8—51no—
169C22⋊Q8—51no—
170C22⋊Q8—51no—
171C22⋊Q8—101no—
172#121—51no—
173#121—101no—
174#121—101no—
175#121—101no—
176#121C2×D511yescharacteristic
177C4×Q8—101no—
178C4×D4—101no—
179C4×D4—101no—
180C4×D4—101no—
181#117—51no—
182#117—51no—
183#117—51no—
184C2×C4⋊C4—51no—
185C2×C4⋊C4—51no—
186C2×C4⋊C4—51no—
187C2×C4⋊C4C2×D511yescharacteristic
188#107—51no—
189#107—51no—
190#106—51no—
191#106—51no—
192#106—51no—
193#106—51no—
194#106C2×D511yescharacteristic
195#106C2×D511yescharacteristic
196#103—51no—
197#103—51no—
198#103—51no—
199#103—51no—
200#102—51no—
201#102—51no—
202#102C2×D511yescharacteristic
203#102C2×D511yescharacteristic
204C22⋊C8—51no—
205C22⋊C8—51no—
206C22⋊C8—51no—
207C22⋊C8C2×D511yescharacteristic
208C22×C5—21no—
209C22×C5—21no—
210C22×C5—21no—
211C22×C5—41no—
212C22×C5—41no—
213C22×C5—41no—
214C22×C5C22×D411yescharacteristic
215C2×D5—21no—
216C2×D5—21no—
217C2×D5—21no—
218C2×D5—21no—
219C2×D5—21no—
220C2×D5#12312yes—
221C4×C5—21no—
222C4×C5—41no—
223C4×C5—41no—
224C4×C5—41no—
225C4×C5C2×#4111yescharacteristic
226C4×C5C2×#4111yescharacteristic
227Dic5—21no—
228Dic5—41no—
229Dic5—41no—
230Dic5—41no—
231Dic5—41no—
232Dic5#12312yes—
233#41—102no—
234#41—102no—
235#41—102no—
236#41—102no—
237C2×Q8—51no—
238C2×Q8—51no—
239C2×D4—21no—
240C2×D4—51no—
241C2×D4—51no—
242C2×D4—51no—
243C2×D4—101no—
244C2×D4—101no—
245C2×D4C22×D511yescharacteristic
246C22×C4—21no—
247C22×C4—51no—
248C22×C4—51no—
249C22×C4—101no—
250C22×C4—101no—
251C22×C4—101no—
252C22×C4—101no—
253C22×C4C22×D511yescharacteristic
254M16—102no—
255C2×C8—51no—
256C2×C8—51no—
257C2×C8—102no—
258C2×C8C22×D511yescharacteristic
259C2×C8C22×D511yescharacteristic
260C4⋊C4—21no—
261C4⋊C4—51no—
262C4⋊C4—51no—
263C4⋊C4—51no—
264C4⋊C4—101no—
265C4⋊C4—101no—
266C4⋊C4—101no—
267C4⋊C4—101no—
268C4⋊C4—101no—
269C4⋊C4C22×D511yescharacteristic
270C4⋊C4C22×D511yescharacteristic
271C4⋊C4C22×D511yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—101no—
274C22⋊C4—101no—
275C22⋊C4—101no—
276C22⋊C4—101no—
277C22⋊C4—101no—
278C22⋊C4—101no—
279C42—101no—
280C42—101no—
281C42—101no—
282C2×C5—41no—
283C2×C5—81no—
284C2×C5C2×#12311yescharacteristic
285C2×C5#57711yescharacteristic
286C2×C5#57711yescharacteristic
287D5—22no—
288D5—41no—
289C23—21no—
290C23—51no—
291C23—51no—
292C23D4×D511yescharacteristic
293Q8—102no—
294Q8—101no—
295Q8—101no—
296D4—21no—
297D4—21no—
298D4—81no—
299D4—102no—
300D4—102no—
301D4—102no—
302D4—202no—
303D4—401no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—51no—
310C2×C4—52no—
311C2×C4—52no—
312C2×C4—51no—
313C2×C4—81no—
314C2×C4—101no—
315C2×C4—101no—
316C2×C4—101no—
317C2×C4—101no—
318C2×C4—101no—
319C2×C4—101no—
320C2×C4—202no—
321C2×C4—401no—
322C2×C4—401no—
323C2×C4—401no—
324C2×C4D4×D511yescharacteristic
325C2×C4C23×D511yescharacteristic
326C8—21no—
327C8—21no—
328C8—101no—
329C8—101no—
330C5#309911yescharacteristic, complemented, Sylow
331C22—21no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—52no—
338C22—101no—
339C22—101no—
340C22—101no—
341C22—101no—
342C22—101no—
343C22C2×D4×D511yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—52no—
349C4—101no—
350C4—201no—
351C4—201no—
352C4—201no—
353C4—201no—
354C4D5×#4111yescharacteristic
355C4D5×#4111yescharacteristic
356C2—41no—
357C2—81no—
358C2—102no—
359C2—201no—
360C2D5×#12311yescharacteristic
361C2#6609611yescharacteristic
362C2#6610911yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#481C2
socleC22×C5C22×D4
prime radical#65942C2
hypercenter#481D5
hypocenterC5#3099
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. #65838C2semidirect
3. C5×#481C2semidirect
4. #65324C2semidirect
5. #65260C2semidirect
6. #65156C2semidirect
7. #65151C2semidirect
8. #65150C2semidirect
9. D5×#106C2semidirect
10. #65073C2semidirect
11. #65066C2semidirect
12. #65061C2semidirect
13. #65060C2semidirect
14. #65016C2semidirect
15. #65012C2semidirect
118. #481D5semidirect
330. C5#3099semidirect

Maximal subgroups

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

subgroupindex
#659422
#658382
C5×#4812
#653242
#652602
#651562
#651512
#651502
D5×#1062
#650732
#650662
#650612
#650602
#650162
#650122
#30995