Finite Group Databasebeta

← #10614979

Subgroups — #10614979

Order 640.

450 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
1C2×C5×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×#4044C211yesmaximal, characteristic
3#65520C211yesmaximal, characteristic
4#65520C211yesmaximal, characteristic
5#65519C211yesmaximal, characteristic, complemented
6#65519C211yesmaximal, characteristic, complemented
7#65283C211yesmaximal, characteristic
8#65282C211yesmaximal, characteristic
9#65279C211yesmaximal, characteristic
10#65272C211yesmaximal, characteristic, complemented
11#65271C211yesmaximal, characteristic, complemented
12#65270C211yesmaximal, characteristic, complemented
13#65267C211yesmaximal, characteristic, complemented
14#65229C211yesmaximal, characteristic
15#65222C211yesmaximal, characteristic, complemented
16C22×C5×Q8C2211yescharacteristic
17C22×C5×Q8C2211yescharacteristic
18C5×C4⋊Q8—24no—
19C2×C5×C4⋊C4C2211yescharacteristic
20C2×C5×C4⋊C4C2211yescharacteristic
21C2×C5×C4⋊C4C2211yescharacteristic
22C2×C5×C4⋊C4C2211yescharacteristic
23C2×C42×C5C2211yescharacteristic
24C2×#685C2211yescharacteristic
25C2×#685C2211yescharacteristic
26C2×#685C2211yescharacteristic
27C2×#685C2211yescharacteristic
28C2×#685C2211yescharacteristic
29C2×#685C2211yescharacteristic
30C2×#685C2211yescharacteristic
31C2×C4⋊Dic5C2211yescharacteristic
32C2×C4⋊Dic5C2211yescharacteristic
33C2×#683C2211yescharacteristic
34C2×#683C2211yescharacteristic
35C2×#683C2211yescharacteristic
36C2×C4×Dic5C2211yescharacteristic
37C2×C4×Dic5C2211yescharacteristic
38#4044—24no—
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#3963C2211yescharacteristic
52#3963C2211yescharacteristic
53#2716—51nomaximal, Sylow
54C23×D5C2311yescharacteristic
55C2×C5×Q8—22no—
56C2×C5×Q8—22no—
57C2×C5×Q8—22no—
58C2×C5×Q8—22no—
59C2×C5×Q8—41no—
60C2×C5×Q8—41no—
61C22×C4×C5C2311yescharacteristic
62C22×C4×C5C2311yescharacteristic
63C22×C4×C5C2311yescharacteristic
64C22×C4×C5C2311yescharacteristic
65C22×C4×C5C2311yescharacteristic
66C22×C4×C5C2311yescharacteristic
67C22×C4×C5C2311yescharacteristic
68C22×Dic5C2311yescharacteristic
69C22×Dic5C2311yescharacteristic
70C22×Dic5C2311yescharacteristic
71C22×Dic5C2311yescharacteristic
72C22×Dic5C2311yescharacteristic
73C22×Dic5C2311yescharacteristic
74C22×Dic5C2311yescharacteristic
75C5×C4⋊C4—22no—
76C5×C4⋊C4—22no—
77C5×C4⋊C4—22no—
78C5×C4⋊C4D414yes—
79C42×C5—22no—
80#685—22no—
81#685—22no—
82#685—22no—
83#685—22no—
84#685—22no—
85#685—41no—
86#685—41no—
87C4⋊Dic5—22no—
88C4⋊Dic5—41no—
89#683—22no—
90#683—22no—
91#683—22no—
92C4×Dic5—22no—
93C4×Dic5—41no—
94C2×C4⋊Q8D511yescharacteristic, complemented
95C2×#126—51no—
96#400—51no—
97#398—51no—
98#397—51no—
99#396—51no—
100#393—51no—
101#393—51no—
102#391—51no—
103#391—51no—
104#388—51no—
105#388—51no—
106#387—51no—
107#387—51no—
108#387—51no—
109C23×C5C2411yescharacteristic
110C22×D5—21no—
111C22×D5—21no—
112C22×D5—21no—
113C22×D5—21no—
114C22×D5—21no—
115C22×D5—21no—
116C22×D5—21no—
117C5×Q8—44no—
118C5×Q8—44no—
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×C5—21no—
133C2×C4×C5—21no—
134C2×C4×C5—21no—
135C2×C4×C5C2×D412yes—
136C2×C4×C5C2×D412yes—
137C2×C4×C5C2×D412yes—
138C2×C4×C5#4112yes—
139C2×C4×C5#4112yes—
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×Dic5—21no—
156C2×Dic5—21no—
157C2×Dic5—21no—
158C2×Dic5—21no—
159C2×Dic5—21no—
160C2×Dic5—21no—
161C22×Q8C2×D511yescharacteristic
162C22×Q8C2×D511yescharacteristic
163C4⋊Q8—24no—
164#126—104no—
165C2×C4⋊C4—51no—
166C2×C4⋊C4—51no—
167C2×C4⋊C4—51no—
168C2×C4⋊C4—51no—
169C2×C4⋊C4—51no—
170C2×C4⋊C4C2×D511yescharacteristic
171C2×C4⋊C4C2×D511yescharacteristic
172C2×C4⋊C4C2×D511yescharacteristic
173C2×C4⋊C4C2×D511yescharacteristic
174C2×C22⋊C4—51no—
175C2×C22⋊C4—51no—
176C2×C22⋊C4—51no—
177C2×C22⋊C4—51no—
178C2×C22⋊C4—51no—
179C2×C22⋊C4—51no—
180C2×C22⋊C4—51no—
181C2×C42—51no—
182C2×C42—51no—
183C2×C42C2×D511yescharacteristic
184#95—51no—
185#95—51no—
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#95—51no—
195#95—51no—
196#95—51no—
197#95—51no—
198C22×C5C22×D411yescharacteristic
199C22×C5C2×#4111yescharacteristic
200C22×C5C2×#4111yescharacteristic
201C22×C5H(5,𝔽2)11yescharacteristic
202C22×C52−1+411yescharacteristic
203C22×C52−1+411yescharacteristic
204C22×C52−1+411yescharacteristic
205C2×D5—41no—
206C2×D5—41no—
207C2×D5—41no—
208C2×D5—41no—
209C2×D5—41no—
210C2×D5—41no—
211C2×D5—41no—
212C4×C5—22no—
213C4×C5—22no—
214C4×C5—22no—
215C4×C5—22no—
216C4×C5—22no—
217C4×C5—41no—
218C4×C5—41no—
219Dic5—41no—
220Dic5—41no—
221Dic5—41no—
222Dic5—41no—
223Dic5—41no—
224Dic5—41no—
225Dic5—41no—
226C24—51no—
227C2×Q8—22no—
228C2×Q8—22no—
229C2×Q8—22no—
230C2×Q8—22no—
231C2×Q8—41no—
232C2×Q8—41no—
233C22×C4—51no—
234C22×C4—51no—
235C22×C4—51no—
236C22×C4—51no—
237C22×C4—51no—
238C22×C4—51no—
239C22×C4—51no—
240C22×C4C22×D511yescharacteristic
241C22×C4C22×D511yescharacteristic
242C22×C4C22×D511yescharacteristic
243C22×C4C22×D511yescharacteristic
244C22×C4C22×D511yescharacteristic
245C22×C4C22×D511yescharacteristic
246C22×C4C22×D511yescharacteristic
247C4⋊C4—22no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—102no—
251C4⋊C4—102no—
252C4⋊C4—102no—
253C4⋊C4—102no—
254C4⋊C4—201no—
255C4⋊C4C22⋊D514yes—
256C22⋊C4—102no—
257C22⋊C4—102no—
258C22⋊C4—102no—
259C22⋊C4—102no—
260C22⋊C4—102no—
261C22⋊C4—201no—
262C22⋊C4—201no—
263C42—22no—
264C42—102no—
265C42—201no—
266C2×C5#53611yescharacteristic
267C2×C5#54111yescharacteristic
268C2×C5#54211yescharacteristic
269C2×C5#54611yescharacteristic
270C2×C5#54811yescharacteristic
271C2×C5#55611yescharacteristic
272C2×C5#56311yescharacteristic
273D5—81no—
274C23—101no—
275C23—101no—
276C23—101no—
277C23—101no—
278C23—101no—
279C23—101no—
280C23—101no—
281C23C23×D511yescharacteristic
282Q8—44no—
283Q8—44no—
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—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
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—101no—
320C2×C4—101no—
321C2×C4#71112yes—
322C2×C4#71312yes—
323C2×C4C2×C22⋊D512yes—
324C2×C4C2×C22⋊D512yes—
325C2×C4C2×C22⋊D512yes—
326C5#271611yescharacteristic, complemented, Sylow
327C22—201no—
328C22—201no—
329C22—201no—
330C22—201no—
331C22—201no—
332C22—201no—
333C22—201no—
334C22C2×#71111yescharacteristic
335C22#414411yescharacteristic
336C22C2×#71311yescharacteristic
337C22#414711yescharacteristic
338C22#414711yescharacteristic
339C22#414711yescharacteristic
340C22C22×C22⋊D511yescharacteristic
341C4—22no—
342C4—22no—
343C4—22no—
344C4—22no—
345C4—22no—
346C4—41no—
347C4—41no—
348C4—201no—
349C4—201no—
350C4—201no—
351C4—201no—
352C4—201no—
353C4—201no—
354C4—201no—
355C2—401no—
356C2#6606511yescharacteristic
357C2#6606611yescharacteristic
358C2#6606711yescharacteristic
359C2#6606911yescharacteristic
360C2#6614011yescharacteristic
361C2#6615011yescharacteristic
362C2#6615111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC2×C5×C4⋊Q8C2
prime radicalC23×D5C23
hypercenterC2×C4⋊Q8D5
hypocenterC5#2716
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C5×C4⋊Q8C2semidirect
5. #65519C2semidirect
6. #65519C2semidirect
10. #65272C2semidirect
11. #65271C2semidirect
12. #65270C2semidirect
13. #65267C2semidirect
15. #65222C2semidirect
94. C2×C4⋊Q8D5semidirect
326. C5#2716semidirect

Maximal subgroups

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

subgroupindex
C2×C5×C4⋊Q82
C2×#40442
#655202
#655192
#652832
#652822
#652792
#652722
#652712
#652702
#652672
#652292
#652222
#27165