Finite Group Databasebeta

← #10607293

Subgroups — #10607293

Order 640.

454 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4036C211yesmaximal, characteristic, complemented
2C2×#4025C211yesmaximal, characteristic
3C5×#388C211yesmaximal, characteristic
4#65272C211yesmaximal, characteristic, complemented
5#65240C211yesmaximal, characteristic
6#65238C211yesmaximal, characteristic
7#65237C211yesmaximal, characteristic
8#65234C211yesmaximal, characteristic
9#65233C211yesmaximal, characteristic
10#65225C211yesmaximal, characteristic, complemented
11C4×#683C211yesmaximal, characteristic, complemented
12#64946C211yesmaximal, characteristic, complemented
13#64941C211yesmaximal, characteristic, complemented
14#64938C211yesmaximal, characteristic, complemented
15#64936C211yesmaximal, characteristic, complemented
16C2×C5×C4⋊C4C2211yescharacteristic
17C2×C5×C22⋊C4C2211yescharacteristic
18C2×C5×C22⋊C4C2211yescharacteristic
19C2×C5×C22⋊C4C2211yescharacteristic
20C2×C42×C5C2211yescharacteristic
21C2×C22⋊Dic5C2211yescharacteristic
22C2×C22⋊Dic5C2211yescharacteristic
23C2×C22⋊Dic5C2211yescharacteristic
24C2×C22⋊Dic5C2211yescharacteristic
25C2×C4⋊Dic5C2211yescharacteristic
26C2×C4⋊Dic5C2211yescharacteristic
27C2×C4⋊Dic5C2211yescharacteristic
28C2×C4⋊Dic5C2211yescharacteristic
29C2×#683C2211yescharacteristic
30C2×#683C2211yescharacteristic
31C2×#683C2211yescharacteristic
32C2×#683C2211yescharacteristic
33C2×#683C2211yescharacteristic
34C2×#683C2211yescharacteristic
35C2×#683C2211yescharacteristic
36C2×#683C2211yescharacteristic
37C2×C4×Dic5C2211yescharacteristic
38C2×C4×Dic5C2211yescharacteristic
39C2×C4×Dic5C2211yescharacteristic
40C2×C4×Dic5C2211yescharacteristic
41#4036—24no—
42#4025—24no—
43C5×#95C2211yescharacteristic
44C5×#95C2211yescharacteristic
45#3963C2211yescharacteristic
46#3963C2211yescharacteristic
47#3963C2211yescharacteristic
48#3963C2211yescharacteristic
49#3963C2211yescharacteristic
50#3963C2211yescharacteristic
51#3963C2211yescharacteristic
52#3963C2211yescharacteristic
53#2519—51nomaximal, Sylow
54C24×C5C2311yescharacteristic
55C22×C4×C5C2311yescharacteristic
56C22×C4×C5C2311yescharacteristic
57C22×C4×C5C2311yescharacteristic
58C22×C4×C5C2311yescharacteristic
59C22×C4×C5C2311yescharacteristic
60C22×C4×C5C2311yescharacteristic
61C22×Dic5C2311yescharacteristic
62C22×Dic5C2311yescharacteristic
63C22×Dic5C2311yescharacteristic
64C22×Dic5C2311yescharacteristic
65C22×Dic5C2311yescharacteristic
66C22×Dic5C2311yescharacteristic
67C22×Dic5C2311yescharacteristic
68C22×Dic5C2311yescharacteristic
69C5×C4⋊C4—22no—
70C5×C22⋊C4—22no—
71C5×C22⋊C4—22no—
72C5×C22⋊C4—22no—
73C42×C5—22no—
74C22⋊Dic5—22no—
75C22⋊Dic5—22no—
76C22⋊Dic5—22no—
77C22⋊Dic5—22no—
78C4⋊Dic5—22no—
79C4⋊Dic5—22no—
80C4⋊Dic5—22no—
81C4⋊Dic5—22no—
82#683—22no—
83#683—22no—
84#683—22no—
85#683—22no—
86#683—22no—
87#683—22no—
88#683—22no—
89#683D414yes—
90C4×Dic5—22no—
91C4×Dic5—22no—
92C4×Dic5—22no—
93C4×Dic5—22no—
94C2×#126—51no—
95C2×#125—51no—
96#399—51no—
97#398—51no—
98#398—51no—
99#396—51no—
100#389—51no—
101#388—51no—
102#388—51no—
103#388—51no—
104#388D511yescharacteristic
105#387—51no—
106#382—51no—
107C4×C4⋊C4—51no—
108C4×C4⋊C4—51no—
109C23×C5—21no—
110C23×C5—21no—
111C23×C5—21no—
112C23×C5—21no—
113C23×C5—21no—
114C23×C5—21no—
115C23×C5—21no—
116C23×C5C2411yescharacteristic
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—21no—
132C2×C4×C5C2×D412yes—
133C2×C4×C5#4112yes—
134C2×C4×C5#4112yes—
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×Dic5—21no—
154C2×Dic5—21no—
155C2×Dic5C2×D412yes—
156C2×Dic5C2×D412yes—
157C2×Dic5#4112yes—
158C2×Dic5#4112yes—
159#126—104no—
160#125—104no—
161C2×C4⋊C4—51no—
162C2×C4⋊C4—51no—
163C2×C4⋊C4—51no—
164C2×C4⋊C4—51no—
165C2×C4⋊C4—51no—
166C2×C4⋊C4—51no—
167C2×C4⋊C4—51no—
168C2×C4⋊C4—51no—
169C2×C4⋊C4—51no—
170C2×C4⋊C4—51no—
171C2×C4⋊C4—51no—
172C2×C4⋊C4—51no—
173C2×C4⋊C4C2×D511yescharacteristic
174C2×C22⋊C4—51no—
175C2×C22⋊C4—51no—
176C2×C22⋊C4—51no—
177C2×C22⋊C4—51no—
178C2×C22⋊C4C2×D511yescharacteristic
179C2×C22⋊C4C2×D511yescharacteristic
180C2×C22⋊C4C2×D511yescharacteristic
181C2×C42—51no—
182C2×C42—51no—
183C2×C42—51no—
184C2×C42—51no—
185C2×C42C2×D511yescharacteristic
186#95—51no—
187#95—51no—
188#95—51no—
189#95—51no—
190#95—51no—
191#95—51no—
192#95—51no—
193#95—51no—
194#95C2×D511yescharacteristic
195#95C2×D511yescharacteristic
196C22×C5—41no—
197C22×C5—41no—
198C22×C5—41no—
199C22×C5—41no—
200C22×C5—41no—
201C22×C5—41no—
202C22×C5—41no—
203C22×C5C22×D411yescharacteristic
204C22×C5C2×#4111yescharacteristic
205C22×C5C2×#4111yescharacteristic
206C22×C5C2×#4111yescharacteristic
207C22×C5C2×#4111yescharacteristic
208C22×C52−1+411yescharacteristic
209C22×C52−1+411yescharacteristic
210C4×C5—22no—
211C4×C5—22no—
212C4×C5—22no—
213C4×C5—41no—
214C4×C5—41no—
215C4×C5—41no—
216Dic5—22no—
217Dic5—22no—
218Dic5—22no—
219Dic5—22no—
220Dic5—41no—
221Dic5—41no—
222Dic5—41no—
223Dic5—41no—
224C24C22×D511yescharacteristic
225C22×C4—51no—
226C22×C4—51no—
227C22×C4—51no—
228C22×C4—51no—
229C22×C4—51no—
230C22×C4—51no—
231C22×C4—51no—
232C22×C4—51no—
233C22×C4C22×D511yescharacteristic
234C22×C4C22×D511yescharacteristic
235C22×C4C22×D511yescharacteristic
236C22×C4C22×D511yescharacteristic
237C22×C4C22×D511yescharacteristic
238C22×C4C22×D511yescharacteristic
239C4⋊C4—22no—
240C4⋊C4—54no—
241C4⋊C4—102no—
242C4⋊C4—102no—
243C4⋊C4—102no—
244C4⋊C4—102no—
245C4⋊C4—102no—
246C4⋊C4—102no—
247C4⋊C4—102no—
248C4⋊C4—102no—
249C4⋊C4—102no—
250C4⋊C4—102no—
251C4⋊C4—102no—
252C22⋊C4—22no—
253C22⋊C4—22no—
254C22⋊C4—22no—
255C22⋊C4—102no—
256C22⋊C4—102no—
257C22⋊C4—102no—
258C22⋊C4—102no—
259C42—22no—
260C42—102no—
261C42—102no—
262C42—102no—
263C42—102no—
264C2×C5—81no—
265C2×C5#52911yescharacteristic
266C2×C5#53211yescharacteristic
267C2×C5#54111yescharacteristic
268C2×C5#54711yescharacteristic
269C2×C5#54811yescharacteristic
270C2×C5#55211yescharacteristic
271C2×C5#55211yescharacteristic
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23C23×D511yescharacteristic
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—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—52no—
296C2×C4—52no—
297C2×C4—52no—
298C2×C4—52no—
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—101no—
313C2×C4—101no—
314C2×C4—101no—
315C2×C4—101no—
316C2×C4—101no—
317C2×C4—101no—
318C2×C4—101no—
319C2×C4#70912yes—
320C2×C4D4×D512yes—
321C2×C4#71112yes—
322C5#251911yescharacteristic, complemented, Sylow
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22C2×#70911yescharacteristic
331C22C2×D4×D511yescharacteristic
332C22C2×#71111yescharacteristic
333C22D5×#4111yescharacteristic
334C22D5×#4111yescharacteristic
335C22#415011yescharacteristic
336C22#415011yescharacteristic
337C4—22no—
338C4—22no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—102no—
344C4—102no—
345C4—102no—
346C4—102no—
347C4—201no—
348C4—201no—
349C4—201no—
350C4—201no—
351C2—81no—
352C2#6586311yescharacteristic
353C2#6588611yescharacteristic
354C2#6589111yescharacteristic
355C2#6594511yescharacteristic
356C2#6598411yescharacteristic
357C2#6600211yescharacteristic
358C2#6603511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#388C2
prime radicalC24×C5C23
hypercenter#388D5
hypocenterC5#2519
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#4036C2semidirect
4. #65272C2semidirect
10. #65225C2semidirect
11. C4×#683C2semidirect
12. #64946C2semidirect
13. #64941C2semidirect
14. #64938C2semidirect
15. #64936C2semidirect
322. C5#2519semidirect

Maximal subgroups

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

subgroupindex
C2×#40362
C2×#40252
C5×#3882
#652722
#652402
#652382
#652372
#652342
#652332
#652252
C4×#6832
#649462
#649412
#649382
#649362
#25195