Finite Group Databasebeta

← #10608552

Subgroups — #10608552

Order 640.

424 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#393C211yesmaximal, characteristic
2#65519C211yesmaximal, characteristic, complemented
3#65518C211yesmaximal, characteristic, complemented
4#65237C211yesmaximal, characteristic
5#65237C211yesmaximal, characteristic
6#65236C211yesmaximal, characteristic
7#65232C211yesmaximal, characteristic
8#65231C211yesmaximal, characteristic
9C22⋊C4×Dic5C211yesmaximal, characteristic
10#64947C211yesmaximal, characteristic, complemented
11#64947C211yesmaximal, characteristic, complemented
12#64945C211yesmaximal, characteristic, complemented
13#64942C211yesmaximal, characteristic, complemented
14#64941C211yesmaximal, characteristic, complemented
15#64935C211yesmaximal, characteristic, complemented
16C22×C5×Q8C2211yescharacteristic
17C23×Dic5C2211yescharacteristic
18C22×Dic10C2211yescharacteristic
19C2×C5×C22⋊C4C2211yescharacteristic
20C2×C5×C22⋊C4C2211yescharacteristic
21C2×C5×C22⋊C4C2211yescharacteristic
22C2×C22⋊Dic5C2211yescharacteristic
23C2×C22⋊Dic5C2211yescharacteristic
24C2×C22⋊Dic5C2211yescharacteristic
25C2×C4⋊Dic5C2211yescharacteristic
26C2×C4⋊Dic5C2211yescharacteristic
27C2×#683C2211yescharacteristic
28C2×#683C2211yescharacteristic
29C2×#683C2211yescharacteristic
30C2×#683C2211yescharacteristic
31C2×#683C2211yescharacteristic
32C2×#683C2211yescharacteristic
33C2×C4×Dic5C2211yescharacteristic
34C2×C4×Dic5C2211yescharacteristic
35C5×#95C2211yescharacteristic
36C5×#95C2211yescharacteristic
37C5×#95C2211yescharacteristic
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#2665—51nomaximal, Sylow
52C24×C5C2311yescharacteristic
53C2×C5×Q8—22no—
54C2×C5×Q8—41no—
55C2×C5×Q8—41no—
56C22×C4×C5C2311yescharacteristic
57C22×C4×C5C2311yescharacteristic
58C22×C4×C5C2311yescharacteristic
59C22×C4×C5C2311yescharacteristic
60C22×C4×C5C2311yescharacteristic
61C22×C4×C5C2311yescharacteristic
62C22×Dic5—41no—
63C22×Dic5—41no—
64C22×Dic5Q814yescomplemented
65C22×Dic5C2311yescharacteristic
66C22×Dic5C2311yescharacteristic
67C22×Dic5C2311yescharacteristic
68C22×Dic5C2311yescharacteristic
69C22×Dic5C2311yescharacteristic
70C22×Dic5C2311yescharacteristic
71C22×Dic5C2311yescharacteristic
72C22×Dic5C2311yescharacteristic
73C2×Dic10—22no—
74C2×Dic10—41no—
75C2×Dic10—41no—
76C5×C22⋊C4—22no—
77C5×C22⋊C4—41no—
78C5×C22⋊C4—41no—
79C22⋊Dic5—22no—
80C22⋊Dic5—41no—
81C22⋊Dic5—41no—
82C4⋊Dic5—22no—
83C4⋊Dic5—41no—
84#683—22no—
85#683—41no—
86#683—41no—
87#683—41no—
88#683—41no—
89#683—41no—
90C4×Dic5—41no—
91C4×Dic5—41no—
92#400—51no—
93#400—51no—
94#396—51no—
95#396—51no—
96#395—51no—
97#395—51no—
98#393—51no—
99#393D511yescharacteristic
100#391—51no—
101#391—51no—
102#387—51no—
103#387—51no—
104#381—51no—
105#380—51no—
106C4×C22⋊C4—51no—
107C23×C5—21no—
108C23×C5—21no—
109C23×C5—21no—
110C23×C5—21no—
111C23×C5—21no—
112C23×C5—21no—
113C23×C5C2×Q812yes—
114C23×C5C2411yescharacteristic
115C5×Q8—44no—
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—21no—
132C2×C4×C5—21no—
133C2×C4×C5#4112yes—
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×Dic5—21no—
154C2×Dic5—21no—
155C2×Dic5—44no—
156C2×Dic5C2×Q812yes—
157C2×Dic5C2×Q812yes—
158C2×Dic5#4112yes—
159Dic10—44no—
160C22×Q8—51no—
161C22×Q8C2×D511yescharacteristic
162C23×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×C22⋊C4—51no—
172C2×C22⋊C4—51no—
173C2×C22⋊C4—51no—
174C2×C22⋊C4C2×D511yescharacteristic
175C2×C22⋊C4C2×D511yescharacteristic
176C2×C22⋊C4C2×D511yescharacteristic
177C2×C42—51no—
178C2×C42—51no—
179#95—51no—
180#95—51no—
181#95—51no—
182#95—51no—
183#95—51no—
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#95C2×D511yescharacteristic
193#95C2×D511yescharacteristic
194#95C2×D511yescharacteristic
195C22×C5—22no—
196C22×C5—22no—
197C22×C5—22no—
198C22×C5—41no—
199C22×C5—41no—
200C22×C5—41no—
201C22×C5—41no—
202C22×C5C22×Q811yescharacteristic
203C22×C5C2×#4111yescharacteristic
204C22×C5C2×#4111yescharacteristic
205C22×C5H(5,𝔽2)11yescharacteristic
206C22×C5H(5,𝔽2)11yescharacteristic
207C22×C5H(5,𝔽2)11yescharacteristic
208C22×C52−1+411yescharacteristic
209C4×C5—22no—
210C4×C5—41no—
211C4×C5—41no—
212C4×C5—41no—
213C4×C5—41no—
214C4×C5—41no—
215Dic5—22no—
216Dic5—22no—
217Dic5—22no—
218Dic5—41no—
219Dic5—41no—
220Dic5—41no—
221Dic5—41no—
222Dic5—41no—
223C24C22×D511yescharacteristic
224C2×Q8—22no—
225C2×Q8—41no—
226C2×Q8—41no—
227C2×Q8—102no—
228C2×Q8—201no—
229C2×Q8—201no—
230C22×C4—51no—
231C22×C4—51no—
232C22×C4—51no—
233C22×C4—54no—
234C22×C4—51no—
235C22×C4—51no—
236C22×C4—51no—
237C22×C4—51no—
238C22×C4—51no—
239C22×C4—201no—
240C22×C4—201no—
241C22×C4C22×D511yescharacteristic
242C22×C4C22×D511yescharacteristic
243C22×C4C22×D511yescharacteristic
244C22×C4C22×D511yescharacteristic
245C22×C4C22×D511yescharacteristic
246C22×C4C22×D511yescharacteristic
247C4⋊C4—102no—
248C4⋊C4—102no—
249C4⋊C4—201no—
250C4⋊C4—201no—
251C4⋊C4—201no—
252C4⋊C4—201no—
253C4⋊C4—201no—
254C4⋊C4—201no—
255C22⋊C4—22no—
256C22⋊C4—41no—
257C22⋊C4—41no—
258C22⋊C4—102no—
259C22⋊C4—201no—
260C22⋊C4—201no—
261C42—201no—
262C42—201no—
263C2×C5—42no—
264C2×C5#53311yescharacteristic
265C2×C5#53811yescharacteristic
266C2×C5#53811yescharacteristic
267C2×C5#54211yescharacteristic
268C2×C5#54211yescharacteristic
269C2×C5#54311yescharacteristic
270C2×C5#54411yescharacteristic
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23Q8×D512yes—
278C23C23×D511yescharacteristic
279Q8—44no—
280Q8—204no—
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—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—52no—
299C2×C4—52no—
300C2×C4—52no—
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—101no—
322C2×C4—204no—
323C2×C4#71112yes—
324C5#266511yescharacteristic, complemented, Sylow
325C22—22no—
326C22—22no—
327C22—22no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22C2×#71111yescharacteristic
333C22#414411yescharacteristic
334C22#414411yescharacteristic
335C22C2×Q8×D511yescharacteristic
336C22D5×#4111yescharacteristic
337C22#414911yescharacteristic
338C22#415011yescharacteristic
339C4—22no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—102no—
346C4—102no—
347C4—102no—
348C4—201no—
349C4—201no—
350C4—201no—
351C4—201no—
352C4—201no—
353C2—42no—
354C2#6592711yescharacteristic
355C2#6595611yescharacteristic
356C2#6595711yescharacteristic
357C2#6596811yescharacteristic
358C2#6600311yescharacteristic
359C2#6601211yescharacteristic
360C2#6601611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#393C2
prime radicalC24×C5C23
hypercenter#393D5
hypocenterC5#2665
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
2. #65519C2semidirect
3. #65518C2semidirect
10. #64947C2semidirect
11. #64947C2semidirect
12. #64945C2semidirect
13. #64942C2semidirect
14. #64941C2semidirect
15. #64935C2semidirect
64. C22×Dic5Q8semidirect
324. C5#2665semidirect

Maximal subgroups

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

subgroupindex
C5×#3932
#655192
#655182
#652372
#652362
#652322
#652312
C22⋊C4×Dic52
#649472
#649452
#649422
#649412
#649352
#26655