Finite Group Databasebeta

← #10608014

Subgroups — #10608014

Order 640.

358 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#389C211yesmaximal, characteristic, complemented
2#65283C211yesmaximal, characteristic
3#65283C211yesmaximal, characteristic
4#65282C211yesmaximal, characteristic
5#65281C211yesmaximal, characteristic
6#65275C211yesmaximal, characteristic, complemented
7#65272C211yesmaximal, characteristic, complemented
8#65271C211yesmaximal, characteristic, complemented
9#65269C211yesmaximal, characteristic, complemented
10#65229C211yesmaximal, characteristic
11#65222C211yesmaximal, characteristic, complemented
12#64964C211yesmaximal, characteristic
13#64964C211yesmaximal, characteristic
14#64946C211yesmaximal, characteristic, complemented
15#64946C211yesmaximal, characteristic, complemented
16C2×C5×C4⋊C4C2211yescharacteristic
17C2×C5×C4⋊C4C2211yescharacteristic
18C2×C5×C4⋊C4C2211yescharacteristic
19C2×C5×C4⋊C4C2211yescharacteristic
20C2×C42×C5C2211yescharacteristic
21C2×#685C2211yescharacteristic
22C2×#685C2211yescharacteristic
23C2×#685C2211yescharacteristic
24C2×#685C2211yescharacteristic
25C2×#685C2211yescharacteristic
26C2×#685C2211yescharacteristic
27C2×#685C2211yescharacteristic
28C2×C4⋊Dic5C2211yescharacteristic
29C2×C4⋊Dic5C2211yescharacteristic
30C2×#683C2211yescharacteristic
31C2×#683C2211yescharacteristic
32C2×#683C2211yescharacteristic
33C2×#683C2211yescharacteristic
34C2×#683C2211yescharacteristic
35C2×#683C2211yescharacteristic
36C2×#683C2211yescharacteristic
37C5×#95C2211yescharacteristic
38C5×#95C2211yescharacteristic
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#2836—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
67C5×C4⋊C4—22no—
68C5×C4⋊C4—41no—
69C5×C4⋊C4—41no—
70C5×C4⋊C4—41no—
71C42×C5—41no—
72#685—22no—
73#685—41no—
74#685—41no—
75#685—41no—
76#685—41no—
77#685—41no—
78#685—41no—
79C4⋊Dic5—41no—
80C4⋊Dic5—41no—
81#683—22no—
82#683—41no—
83#683—41no—
84#683—41no—
85#683—41no—
86#683—41no—
87#683—41no—
88#400—51no—
89#400—51no—
90#399—51no—
91#398—51no—
92#398—51no—
93#398—51no—
94#398—51no—
95#397—51no—
96#397—51no—
97#397—51no—
98#396—51no—
99#396—51no—
100#389D511yescharacteristic, complemented
101#388—51no—
102#387—51no—
103C23×C5C2411yescharacteristic
104C22×D5—21no—
105C22×D5—21no—
106C22×D5—21no—
107C22×D5—21no—
108C22×D5—21no—
109C22×D5—21no—
110C22×D5—21no—
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—21no—
153C2×C4⋊C4—51no—
154C2×C4⋊C4—51no—
155C2×C4⋊C4—51no—
156C2×C4⋊C4—51no—
157C2×C4⋊C4—51no—
158C2×C4⋊C4—51no—
159C2×C4⋊C4—51no—
160C2×C4⋊C4—51no—
161C2×C4⋊C4—51no—
162C2×C4⋊C4C2×D511yescharacteristic
163C2×C4⋊C4C2×D511yescharacteristic
164C2×C4⋊C4C2×D511yescharacteristic
165C2×C4⋊C4C2×D511yescharacteristic
166C2×C22⋊C4—51no—
167C2×C22⋊C4—51no—
168C2×C22⋊C4—51no—
169C2×C22⋊C4—51no—
170C2×C22⋊C4—51no—
171C2×C22⋊C4—51no—
172C2×C22⋊C4—51no—
173C2×C42C2×D511yescharacteristic
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#95—51no—
186#95C2×D511yescharacteristic
187#95C2×D511yescharacteristic
188C22×C5C2×#4111yescharacteristic
189C22×C5H(5,𝔽2)11yescharacteristic
190C22×C5H(5,𝔽2)11yescharacteristic
191C22×C5H(5,𝔽2)11yescharacteristic
192C22×C52−1+411yescharacteristic
193C22×C52−1+411yescharacteristic
194C22×C52−1+411yescharacteristic
195C2×D5—41no—
196C2×D5—41no—
197C2×D5—41no—
198C2×D5—41no—
199C2×D5—41no—
200C2×D5—41no—
201C2×D5—41no—
202C4×C5—22no—
203C4×C5—41no—
204C4×C5—41no—
205C4×C5—41no—
206C4×C5—41no—
207C4×C5—41no—
208C4×C5—41no—
209Dic5—41no—
210Dic5—41no—
211Dic5—41no—
212Dic5—41no—
213Dic5—41no—
214Dic5—41no—
215Dic5—41no—
216C24—51no—
217C22×C4—51no—
218C22×C4—51no—
219C22×C4—51no—
220C22×C4—51no—
221C22×C4—51no—
222C22×C4—51no—
223C22×C4—51no—
224C22×C4C22×D511yescharacteristic
225C22×C4C22×D511yescharacteristic
226C22×C4C22×D511yescharacteristic
227C22×C4C22×D511yescharacteristic
228C22×C4C22×D511yescharacteristic
229C22×C4C22×D511yescharacteristic
230C22×C4C22×D511yescharacteristic
231C4⋊C4—22no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—102no—
236C4⋊C4—201no—
237C4⋊C4—201no—
238C4⋊C4—201no—
239C4⋊C4—201no—
240C4⋊C4—201no—
241C4⋊C4—201no—
242C4⋊C4—201no—
243C4⋊C4—201no—
244C22⋊C4—102no—
245C22⋊C4—201no—
246C22⋊C4—201no—
247C22⋊C4—201no—
248C22⋊C4—201no—
249C22⋊C4—201no—
250C22⋊C4—201no—
251C42—41no—
252C2×C5#53911yescharacteristic
253C2×C5#54011yescharacteristic
254C2×C5#54111yescharacteristic
255C2×C5#56211yescharacteristic
256C2×C5#56211yescharacteristic
257C2×C5#56311yescharacteristic
258C2×C5#56311yescharacteristic
259D5—81no—
260C23—101no—
261C23—101no—
262C23—101no—
263C23—101no—
264C23—101no—
265C23—101no—
266C23—101no—
267C23C23×D511yescharacteristic
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
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—101no—
289C2×C4—101no—
290C2×C4—101no—
291C2×C4—101no—
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#70912yes—
310C5#283611yescharacteristic, complemented, Sylow
311C22—201no—
312C22—201no—
313C22—201no—
314C22—201no—
315C22—201no—
316C22—201no—
317C22—201no—
318C22C2×#70911yescharacteristic
319C22#414411yescharacteristic
320C22#414411yescharacteristic
321C22#414711yescharacteristic
322C22#414711yescharacteristic
323C22#414911yescharacteristic
324C22#415011yescharacteristic
325C4—22no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—201no—
333C4—201no—
334C4—201no—
335C4—201no—
336C4—201no—
337C4—201no—
338C4—201no—
339C2—401no—
340C2#6584911yescharacteristic
341C2#6589611yescharacteristic
342C2#6591711yescharacteristic
343C2#6595511yescharacteristic
344C2#6598111yescharacteristic
345C2#6603311yescharacteristic
346C2#6606911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#389C2
prime radicalC23×D5C23
hypercenter#389D5
hypocenterC5#2836
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C5×#389C2semidirect
6. #65275C2semidirect
7. #65272C2semidirect
8. #65271C2semidirect
9. #65269C2semidirect
11. #65222C2semidirect
14. #64946C2semidirect
15. #64946C2semidirect
100. #389D5semidirect
310. C5#2836semidirect

Maximal subgroups

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

subgroupindex
C5×#3892
#652832
#652822
#652812
#652752
#652722
#652712
#652692
#652292
#652222
#649642
#649462
#28365