Finite Group Databasebeta

← #10608524

Subgroups — #10608524

Order 640.

508 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4090C211yesmaximal, characteristic, complemented
2C2×#4024C211yesmaximal, characteristic
3C5×#393C211yesmaximal, characteristic
4#65519C211yesmaximal, characteristic, complemented
5#65236C211yesmaximal, characteristic
6#65234C211yesmaximal, characteristic
7#65233C211yesmaximal, characteristic
8#65231C211yesmaximal, characteristic
9C22⋊C4×Dic5C211yesmaximal, characteristic
10#64948C211yesmaximal, characteristic, complemented
11#64947C211yesmaximal, characteristic, complemented
12#64938C211yesmaximal, characteristic, complemented
13#64935C211yesmaximal, characteristic, complemented
14#64935C211yesmaximal, characteristic, complemented
15#64935C211yesmaximal, characteristic, complemented
16C22×C5×Q8C2211yescharacteristic
17C23×Dic5C2211yescharacteristic
18C22×Dic10C2211yescharacteristic
19C22×Dic10C2211yescharacteristic
20C2×C5×C22⋊C4C2211yescharacteristic
21C2×C5×C22⋊C4C2211yescharacteristic
22C2×C5×C22⋊C4C2211yescharacteristic
23C2×C22⋊Dic5C2211yescharacteristic
24C2×C22⋊Dic5C2211yescharacteristic
25C2×C22⋊Dic5C2211yescharacteristic
26#4090—24no—
27C2×C4⋊Dic5C2211yescharacteristic
28C2×#683C2211yescharacteristic
29C2×#683C2211yescharacteristic
30C2×#683C2211yescharacteristic
31C2×#683C2211yescharacteristic
32C2×#683C2211yescharacteristic
33C2×#683C2211yescharacteristic
34C2×C4×Dic5C2211yescharacteristic
35C2×C4×Dic5C2211yescharacteristic
36C2×C4×Dic5C2211yescharacteristic
37C2×C4×Dic5C2211yescharacteristic
38#4024—24no—
39C5×#95C2211yescharacteristic
40C5×#95C2211yescharacteristic
41C5×#95C2211yescharacteristic
42#3963C2211yescharacteristic
43#3963C2211yescharacteristic
44#3963C2211yescharacteristic
45#3963C2211yescharacteristic
46#3963C2211yescharacteristic
47#3963C2211yescharacteristic
48#3963C2211yescharacteristic
49#3963C2211yescharacteristic
50#3963C2211yescharacteristic
51#3963C2211yescharacteristic
52#3963C2211yescharacteristic
53#2492—51nomaximal, Sylow
54C24×C5C2311yescharacteristic
55C2×C5×Q8—22no—
56C2×C5×Q8—22no—
57C2×C5×Q8—41no—
58C22×C4×C5C2311yescharacteristic
59C22×C4×C5C2311yescharacteristic
60C22×C4×C5C2311yescharacteristic
61C22×C4×C5C2311yescharacteristic
62C22×C4×C5C2311yescharacteristic
63C22×C4×C5C2311yescharacteristic
64C22×Dic5—22no—
65C22×Dic5—22no—
66C22×Dic5—22no—
67C22×Dic5C2311yescharacteristic
68C22×Dic5C2311yescharacteristic
69C22×Dic5C2311yescharacteristic
70C22×Dic5C2311yescharacteristic
71C22×Dic5C2311yescharacteristic
72C22×Dic5C2311yescharacteristic
73C22×Dic5C2311yescharacteristic
74C22×Dic5C2311yescharacteristic
75C2×Dic10—22no—
76C2×Dic10—22no—
77C2×Dic10—22no—
78C2×Dic10—22no—
79C2×Dic10—22no—
80C2×Dic10—41no—
81C5×C22⋊C4—22no—
82C5×C22⋊C4—22no—
83C5×C22⋊C4—41no—
84C22⋊Dic5—22no—
85C22⋊Dic5—41no—
86C22⋊Dic5Q814yescomplemented
87C4⋊Dic5—22no—
88#683—22no—
89#683—22no—
90#683—22no—
91#683—22no—
92#683—22no—
93#683D414yes—
94C4×Dic5—22no—
95C4×Dic5—22no—
96C4×Dic5—41no—
97C4×Dic5—41no—
98C2×C4⋊Q8—51no—
99C2×C22⋊Q8—51no—
100#400—51no—
101#400—51no—
102#393—51no—
103#393D511yescharacteristic
104#391—51no—
105#391—51no—
106#391—51no—
107#391—51no—
108#388—51no—
109#388—51no—
110#380—51no—
111C4×C4⋊C4—51no—
112C4×C22⋊C4—51no—
113C23×C5—21no—
114C23×C5—21no—
115C23×C5—21no—
116C23×C5—21no—
117C23×C5—21no—
118C23×C5—21no—
119C23×C5C2×Q812yes—
120C23×C5C2411yescharacteristic
121C5×Q8—44no—
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×C5—21no—
136C2×C4×C5—21no—
137C2×C4×C5—21no—
138C2×C4×C5C2×D412yes—
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—44no—
159C2×Dic5C2×D412yes—
160C2×Dic5C2×D412yes—
161C2×Dic5C2×Q812yes—
162C2×Dic5C2×Q812yes—
163C2×Dic5#4112yes—
164C2×Dic5#4112yes—
165Dic10—44no—
166Dic10—44no—
167C22×Q8—51no—
168C22×Q8—51no—
169C22×Q8C2×D511yescharacteristic
170C23×C4—51no—
171C4⋊Q8—104no—
172C22⋊Q8—104no—
173C2×C4⋊C4—51no—
174C2×C4⋊C4—51no—
175C2×C4⋊C4—51no—
176C2×C4⋊C4—51no—
177C2×C4⋊C4—51no—
178C2×C4⋊C4—51no—
179C2×C4⋊C4—51no—
180C2×C22⋊C4—51no—
181C2×C22⋊C4—51no—
182C2×C22⋊C4—51no—
183C2×C22⋊C4C2×D511yescharacteristic
184C2×C22⋊C4C2×D511yescharacteristic
185C2×C22⋊C4C2×D511yescharacteristic
186C2×C42—51no—
187C2×C42—51no—
188C2×C42—51no—
189C2×C42—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—
198#95—51no—
199#95—51no—
200#95—51no—
201#95C2×D511yescharacteristic
202#95C2×D511yescharacteristic
203#95C2×D511yescharacteristic
204C22×C5—22no—
205C22×C5—22no—
206C22×C5—22no—
207C22×C5—41no—
208C22×C5—41no—
209C22×C5—41no—
210C22×C5—41no—
211C22×C5C22×D411yescharacteristic
212C22×C5C22×Q811yescharacteristic
213C22×C5C2×#4111yescharacteristic
214C22×C5C2×#4111yescharacteristic
215C22×C5C2×#4111yescharacteristic
216C22×C5H(5,𝔽2)11yescharacteristic
217C22×C52−1+411yescharacteristic
218C4×C5—22no—
219C4×C5—22no—
220C4×C5—41no—
221C4×C5—41no—
222C4×C5—41no—
223C4×C5—41no—
224Dic5—22no—
225Dic5—22no—
226Dic5—22no—
227Dic5—41no—
228Dic5—41no—
229Dic5—41no—
230Dic5—41no—
231Dic5#12414yes—
232C24C22×D511yescharacteristic
233C2×Q8—22no—
234C2×Q8—22no—
235C2×Q8—41no—
236C2×Q8—102no—
237C2×Q8—102no—
238C2×Q8—102no—
239C2×Q8—102no—
240C2×Q8—102no—
241C2×Q8—201no—
242C22×C4—51no—
243C22×C4—51no—
244C22×C4—51no—
245C22×C4—51no—
246C22×C4—51no—
247C22×C4—51no—
248C22×C4—51no—
249C22×C4—51no—
250C22×C4—102no—
251C22×C4—102no—
252C22×C4—102no—
253C22×C4C22×D511yescharacteristic
254C22×C4C22×D511yescharacteristic
255C22×C4C22×D511yescharacteristic
256C22×C4C22×D511yescharacteristic
257C22×C4C22×D511yescharacteristic
258C22×C4C22×D511yescharacteristic
259C4⋊C4—54no—
260C4⋊C4—102no—
261C4⋊C4—102no—
262C4⋊C4—102no—
263C4⋊C4—102no—
264C4⋊C4—102no—
265C4⋊C4—102no—
266C22⋊C4—22no—
267C22⋊C4—22no—
268C22⋊C4—41no—
269C22⋊C4—54no—
270C22⋊C4—102no—
271C22⋊C4—201no—
272C42—102no—
273C42—102no—
274C42—201no—
275C42—201no—
276C2×C5—42no—
277C2×C5C2×#12411yescharacteristic
278C2×C5#53311yescharacteristic
279C2×C5#54211yescharacteristic
280C2×C5#54611yescharacteristic
281C2×C5D4×Q811yescharacteristic
282C2×C5#55411yescharacteristic
283C2×C5#55611yescharacteristic
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23Q8×D512yes—
291C23C23×D511yescharacteristic
292Q8—44no—
293Q8—204no—
294Q8—204no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—52no—
312C2×C4—52no—
313C2×C4—52no—
314C2×C4—52no—
315C2×C4—52no—
316C2×C4—52no—
317C2×C4—101no—
318C2×C4—101no—
319C2×C4—101no—
320C2×C4—101no—
321C2×C4—101no—
322C2×C4—101no—
323C2×C4—101no—
324C2×C4—101no—
325C2×C4—101no—
326C2×C4—101no—
327C2×C4—101no—
328C2×C4—101no—
329C2×C4—101no—
330C2×C4—101no—
331C2×C4—101no—
332C2×C4—101no—
333C2×C4—101no—
334C2×C4—101no—
335C2×C4—204no—
336C2×C4D4×D512yes—
337C2×C4#71112yes—
338C5#249211yescharacteristic, complemented, Sylow
339C22—22no—
340C22—22no—
341C22—22no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22C2×D4×D511yescharacteristic
347C22C2×#71111yescharacteristic
348C22#414411yescharacteristic
349C22C2×Q8×D511yescharacteristic
350C22D5×#4111yescharacteristic
351C22D5×#4111yescharacteristic
352C22#415011yescharacteristic
353C4—22no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—54no—
360C4—102no—
361C4—102no—
362C4—102no—
363C4—201no—
364C4—201no—
365C4—201no—
366C4—201no—
367C2—42no—
368C2#6592511yescharacteristic
369C2#6595611yescharacteristic
370C2#6596611yescharacteristic
371C2#6597011yescharacteristic
372C2#6600311yescharacteristic
373C2#6600511yescharacteristic
374C2D5×#12411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#393C2
prime radicalC24×C5C23
hypercenter#393D5
hypocenterC5#2492
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#4090C2semidirect
4. #65519C2semidirect
10. #64948C2semidirect
11. #64947C2semidirect
12. #64938C2semidirect
13. #64935C2semidirect
14. #64935C2semidirect
15. #64935C2semidirect
86. C22⋊Dic5Q8semidirect
338. C5#2492semidirect

Maximal subgroups

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

subgroupindex
C2×#40902
C2×#40242
C5×#3932
#655192
#652362
#652342
#652332
#652312
C22⋊C4×Dic52
#649482
#649472
#649382
#649352
#24925