Finite Group Databasebeta

← #10606031

Subgroups — #10606031

Order 640.

440 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#383C211yesmaximal, characteristic, complemented
2C4×#685C211yesmaximal, characteristic
3#65222C211yesmaximal, characteristic, complemented
4#64957C211yesmaximal, characteristic
5#64957C211yesmaximal, characteristic
6#64956C211yesmaximal, characteristic
7#64953C211yesmaximal, characteristic
8#64953C211yesmaximal, characteristic
9D5×#95C211yesmaximal, characteristic
10C5⋊#401C211yesmaximal, characteristic, complemented
11#64949C211yesmaximal, characteristic, complemented
12#64949C211yesmaximal, characteristic, complemented
13#64948C211yesmaximal, characteristic, complemented
14#64943C211yesmaximal, characteristic, complemented
15#64941C211yesmaximal, characteristic, complemented
16C22×C4×D5C2211yescharacteristic
17C22×C4×D5C2211yescharacteristic
18C22×C4×D5C2211yescharacteristic
19C2×C42×C5C2211yescharacteristic
20C2×#685C2211yescharacteristic
21C2×#685C2211yescharacteristic
22C2×#685C2211yescharacteristic
23C2×#685C2211yescharacteristic
24C2×C4⋊Dic5C2211yescharacteristic
25C2×C4⋊Dic5C2211yescharacteristic
26C2×#683C2211yescharacteristic
27C2×#683C2211yescharacteristic
28C2×#683C2211yescharacteristic
29C2×#683C2211yescharacteristic
30C2×C4×Dic5C2211yescharacteristic
31C5×#95C2211yescharacteristic
32C5×#95C2211yescharacteristic
33C5×#95C2211yescharacteristic
34C5×#95C2211yescharacteristic
35C5×#95C2211yescharacteristic
36C5×#95C2211yescharacteristic
37#3963C2211yescharacteristic
38#3963C2211yescharacteristic
39#3963C2211yescharacteristic
40#3963C2211yescharacteristic
41#3963C2211yescharacteristic
42#3963C2211yescharacteristic
43#3963C2211yescharacteristic
44#3963C2211yescharacteristic
45#3963C2211yescharacteristic
46#3963C2211yescharacteristic
47#3963C2211yescharacteristic
48#3963C2211yescharacteristic
49#3963C2211yescharacteristic
50#3963C2211yescharacteristic
51#2493—51nomaximal, Sylow
52C23×D5C2311yescharacteristic
53C22×C4×C5C2311yescharacteristic
54C22×C4×C5C2311yescharacteristic
55C22×C4×C5C2311yescharacteristic
56C22×C4×C5C2311yescharacteristic
57C22×C4×C5C2311yescharacteristic
58C22×C4×C5C2311yescharacteristic
59C22×C4×C5C2311yescharacteristic
60C22×Dic5C2311yescharacteristic
61C22×Dic5C2311yescharacteristic
62C22×Dic5C2311yescharacteristic
63C22×Dic5C2311yescharacteristic
64C22×Dic5C2311yescharacteristic
65C22×Dic5C2311yescharacteristic
66C22×Dic5C2311yescharacteristic
67C2×C4×D5—22no—
68C2×C4×D5—22no—
69C2×C4×D5—22no—
70C2×C4×D5—22no—
71C2×C4×D5—22no—
72C2×C4×D5—22no—
73C2×C4×D5—22no—
74C2×C4×D5—41no—
75C2×C4×D5—41no—
76C42×C5—22no—
77#685—22no—
78#685—22no—
79#685—22no—
80#685—22no—
81C4⋊Dic5—22no—
82C4⋊Dic5—41no—
83#683—22no—
84#683—22no—
85#683—41no—
86#683—41no—
87C4×Dic5—41no—
88#401—51no—
89#400—51no—
90#400—51no—
91#400—51no—
92#387—51no—
93#387—51no—
94#387—51no—
95#385—51no—
96#385—51no—
97#383D511yescharacteristic, complemented
98#381—51no—
99#381—51no—
100#380—51no—
101C4×C22⋊C4—51no—
102C2×#95—51no—
103C23×C5C2411yescharacteristic
104C22×D5—21no—
105C22×D5—21no—
106C22×D5—21no—
107C22×D5—21no—
108C22×D5#4112yes—
109C22×D5#4112yes—
110C22×D5#4112yes—
111C2×C4×C5—21no—
112C2×C4×C5—21no—
113C2×C4×C5—21no—
114C2×C4×C5—21no—
115C2×C4×C5—21no—
116C2×C4×C5—21no—
117C2×C4×C5—21no—
118C2×C4×C5—21no—
119C2×C4×C5—21no—
120C2×C4×C5—21no—
121C2×C4×C5—21no—
122C2×C4×C5—21no—
123C2×C4×C5—21no—
124C2×C4×C5—21no—
125C2×C4×C5—21no—
126C2×C4×C5—21no—
127C2×C4×C5—21no—
128C2×C4×C5—21no—
129C2×C4×C5—21no—
130C2×C4×C5—21no—
131C2×C4×C5#4112yes—
132C2×Dic5—21no—
133C2×Dic5—21no—
134C2×Dic5—21no—
135C2×Dic5—21no—
136C2×Dic5—21no—
137C2×Dic5—21no—
138C2×Dic5—21no—
139C2×Dic5—21no—
140C2×Dic5—21no—
141C2×Dic5—21no—
142C2×Dic5—21no—
143C2×Dic5—21no—
144C2×Dic5—21no—
145C2×Dic5—21no—
146C2×Dic5—21no—
147C2×Dic5—21no—
148C2×Dic5—21no—
149C2×Dic5—21no—
150C2×Dic5—21no—
151C2×Dic5—21no—
152C2×Dic5#4112yes—
153C4×D5—44no—
154C4×D5—44no—
155C4×D5—44no—
156C23×C4—51no—
157C23×C4—51no—
158C23×C4—51no—
159C2×C4⋊C4—51no—
160C2×C4⋊C4—51no—
161C2×C4⋊C4—51no—
162C2×C4⋊C4—51no—
163C2×C4⋊C4—51no—
164C2×C4⋊C4—51no—
165C2×C22⋊C4—51no—
166C2×C22⋊C4—51no—
167C2×C22⋊C4—51no—
168C2×C22⋊C4—51no—
169C2×C42—51no—
170C2×C42C2×D511yescharacteristic
171#95—51no—
172#95—51no—
173#95—51no—
174#95—51no—
175#95—51no—
176#95—51no—
177#95—51no—
178#95—51no—
179#95—51no—
180#95—51no—
181#95—51no—
182#95—51no—
183#95—51no—
184#95—51no—
185#95C2×D511yescharacteristic
186#95C2×D511yescharacteristic
187#95C2×D511yescharacteristic
188#95C2×D511yescharacteristic
189#95C2×D511yescharacteristic
190#95C2×D511yescharacteristic
191C22×C5C2×#4111yescharacteristic
192C22×C5C2×#4111yescharacteristic
193C22×C5C2×#4111yescharacteristic
194C22×C5C2×#4111yescharacteristic
195C22×C5C2×#4111yescharacteristic
196C22×C5H(5,𝔽2)11yescharacteristic
197C22×C52−1+411yescharacteristic
198C2×D5—22no—
199C2×D5—22no—
200C2×D5—22no—
201C2×D5—22no—
202C2×D5—22no—
203C2×D5—22no—
204C2×D5#12614yes—
205C4×C5—22no—
206C4×C5—41no—
207C4×C5—41no—
208C4×C5—41no—
209C4×C5—41no—
210C4×C5—41no—
211C4×C5—41no—
212Dic5—22no—
213Dic5—41no—
214Dic5—41no—
215Dic5—41no—
216Dic5—41no—
217Dic5—41no—
218Dic5—41no—
219C24—51no—
220C22×C4—51no—
221C22×C4—51no—
222C22×C4—51no—
223C22×C4—51no—
224C22×C4—51no—
225C22×C4—51no—
226C22×C4—51no—
227C22×C4—102no—
228C22×C4—102no—
229C22×C4—102no—
230C22×C4—102no—
231C22×C4—102no—
232C22×C4—102no—
233C22×C4—102no—
234C22×C4—201no—
235C22×C4—201no—
236C22×C4C22×D511yescharacteristic
237C22×C4C22×D511yescharacteristic
238C22×C4C22×D511yescharacteristic
239C22×C4C22×D511yescharacteristic
240C22×C4C22×D511yescharacteristic
241C22×C4C22×D511yescharacteristic
242C22×C4C22×D511yescharacteristic
243C4⋊C4—102no—
244C4⋊C4—102no—
245C4⋊C4—102no—
246C4⋊C4—201no—
247C4⋊C4—201no—
248C4⋊C4—201no—
249C22⋊C4—102no—
250C22⋊C4—102no—
251C22⋊C4—102no—
252C22⋊C4—102no—
253C42—22no—
254C42—201no—
255C2×C5C2×#12611yescharacteristic
256C2×C5#52911yescharacteristic
257C2×C5#53911yescharacteristic
258C2×C5#55111yescharacteristic
259C2×C5#55111yescharacteristic
260C2×C5#55211yescharacteristic
261C2×C5#55211yescharacteristic
262D5—24no—
263C23—52no—
264C23—52no—
265C23—52no—
266C23—101no—
267C23—101no—
268C23—101no—
269C23—101no—
270C23C23×D511yescharacteristic
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—52no—
292C2×C4—101no—
293C2×C4—101no—
294C2×C4—101no—
295C2×C4—101no—
296C2×C4—101no—
297C2×C4—101no—
298C2×C4—101no—
299C2×C4—101no—
300C2×C4—101no—
301C2×C4—101no—
302C2×C4—101no—
303C2×C4—101no—
304C2×C4—101no—
305C2×C4—101no—
306C2×C4—101no—
307C2×C4—101no—
308C2×C4—101no—
309C2×C4—101no—
310C2×C4—101no—
311C2×C4—101no—
312C2×C4—204no—
313C2×C4—204no—
314C2×C4—204no—
315C2×C4#70912yes—
316C5#249311yescharacteristic, complemented, Sylow
317C22—54no—
318C22—102no—
319C22—102no—
320C22—102no—
321C22—102no—
322C22—102no—
323C22—102no—
324C22C2×#70911yescharacteristic
325C22D5×#4111yescharacteristic
326C22D5×#4111yescharacteristic
327C22D5×#4111yescharacteristic
328C22D5×#4111yescharacteristic
329C22#414911yescharacteristic
330C22#415011yescharacteristic
331C4—22no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—102no—
339C4—201no—
340C4—201no—
341C4—201no—
342C4—201no—
343C4—201no—
344C4—201no—
345C2—104no—
346C2#6586111yescharacteristic
347C2#6586211yescharacteristic
348C2#6586311yescharacteristic
349C2D5×#12611yescharacteristic
350C2#6603911yescharacteristic
351C2#6604111yescharacteristic
352C2#6604211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#383C2
prime radicalC23×D5C23
hypercenter#383D5
hypocenterC5#2493
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #383

Complements

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

NH ≅ G/Ntype
1. C5×#383C2semidirect
3. #65222C2semidirect
10. C5⋊#401C2semidirect
11. #64949C2semidirect
12. #64949C2semidirect
13. #64948C2semidirect
14. #64943C2semidirect
15. #64941C2semidirect
97. #383D5semidirect
316. C5#2493semidirect

Maximal subgroups

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

subgroupindex
C5×#3832
C4×#6852
#652222
#649572
#649562
#649532
D5×#952
C5⋊#4012
#649492
#649482
#649432
#649412
#24935