Finite Group Databasebeta

← #10609261

Subgroups — #10609261

Order 640.

398 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×#397C211yesmaximal, characteristic
2#65270C211yesmaximal, characteristic, complemented
3#65262C211yesmaximal, characteristic, complemented
4#65240C211yesmaximal, characteristic
5#65238C211yesmaximal, characteristic
6#65233C211yesmaximal, characteristic
7#65233C211yesmaximal, characteristic
8#65233C211yesmaximal, characteristic
9#65233C211yesmaximal, characteristic
10#64949C211yesmaximal, characteristic, complemented
11#64947C211yesmaximal, characteristic, complemented
12#64944C211yesmaximal, characteristic, complemented
13#64941C211yesmaximal, characteristic, complemented
14#64938C211yesmaximal, characteristic, complemented
15#64938C211yesmaximal, characteristic, complemented
16C2×C5×C4⋊C4C2211yescharacteristic
17C2×C5×C22⋊C4C2211yescharacteristic
18C2×C5×C22⋊C4C2211yescharacteristic
19C2×C5×C22⋊C4C2211yescharacteristic
20C2×C22⋊Dic5C2211yescharacteristic
21C2×C22⋊Dic5C2211yescharacteristic
22C2×C22⋊Dic5C2211yescharacteristic
23C2×C22⋊Dic5C2211yescharacteristic
24C2×C4⋊Dic5C2211yescharacteristic
25C2×C4⋊Dic5C2211yescharacteristic
26C2×#683C2211yescharacteristic
27C2×#683C2211yescharacteristic
28C2×#683C2211yescharacteristic
29C2×#683C2211yescharacteristic
30C2×#683C2211yescharacteristic
31C2×#683C2211yescharacteristic
32C2×C4×Dic5C2211yescharacteristic
33C2×C4×Dic5C2211yescharacteristic
34C2×C4×Dic5C2211yescharacteristic
35C2×C4×Dic5C2211yescharacteristic
36C2×C4×Dic5C2211yescharacteristic
37C5×#95C2211yescharacteristic
38C5×#95C2211yescharacteristic
39C5×#95C2211yescharacteristic
40#3963C2211yescharacteristic
41#3963C2211yescharacteristic
42#3963C2211yescharacteristic
43#3963C2211yescharacteristic
44#3963C2211yescharacteristic
45#3963C2211yescharacteristic
46#3963C2211yescharacteristic
47#3963C2211yescharacteristic
48#3963C2211yescharacteristic
49#3963C2211yescharacteristic
50#3963C2211yescharacteristic
51#2596—51nomaximal, Sylow
52C24×C5C2311yescharacteristic
53C22×C4×C5C2311yescharacteristic
54C22×C4×C5C2311yescharacteristic
55C22×C4×C5C2311yescharacteristic
56C22×C4×C5C2311yescharacteristic
57C22×C4×C5C2311yescharacteristic
58C22×C4×C5C2311yescharacteristic
59C22×Dic5C2311yescharacteristic
60C22×Dic5C2311yescharacteristic
61C22×Dic5C2311yescharacteristic
62C22×Dic5C2311yescharacteristic
63C22×Dic5C2311yescharacteristic
64C22×Dic5C2311yescharacteristic
65C22×Dic5C2311yescharacteristic
66C22×Dic5C2311yescharacteristic
67C5×C4⋊C4—22no—
68C5×C22⋊C4—22no—
69C5×C22⋊C4—41no—
70C5×C22⋊C4—41no—
71C22⋊Dic5—22no—
72C22⋊Dic5—22no—
73C22⋊Dic5—22no—
74C22⋊Dic5—22no—
75C4⋊Dic5—22no—
76C4⋊Dic5—41no—
77#683—22no—
78#683—22no—
79#683—22no—
80#683—22no—
81#683—22no—
82#683—22no—
83C4×Dic5—22no—
84C4×Dic5—22no—
85C4×Dic5—41no—
86C4×Dic5—41no—
87C4×Dic5—41no—
88#400—51no—
89#400—51no—
90#399—51no—
91#397D511yescharacteristic
92#389—51no—
93#388—51no—
94#388—51no—
95#388—51no—
96#388—51no—
97#388—51no—
98#387—51no—
99#387—51no—
100#387—51no—
101C4×C4⋊C4—51no—
102C4×C4⋊C4—51no—
103C23×C5—21no—
104C23×C5—21no—
105C23×C5—21no—
106C23×C5—21no—
107C23×C5—21no—
108C23×C5—21no—
109C23×C5—21no—
110C23×C5C2411yescharacteristic
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#4112yes—
129C2×Dic5—21no—
130C2×Dic5—21no—
131C2×Dic5—21no—
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#4112yes—
150C2×Dic5#4112yes—
151C2×Dic5#4112yes—
152C2×Dic5#4112yes—
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⋊C4C2×D511yescharacteristic
162C2×C22⋊C4—51no—
163C2×C22⋊C4—51no—
164C2×C22⋊C4—51no—
165C2×C22⋊C4—51no—
166C2×C22⋊C4C2×D511yescharacteristic
167C2×C22⋊C4C2×D511yescharacteristic
168C2×C22⋊C4C2×D511yescharacteristic
169C2×C42—51no—
170C2×C42—51no—
171C2×C42—51no—
172C2×C42—51no—
173C2×C42—51no—
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#95C2×D511yescharacteristic
186#95C2×D511yescharacteristic
187#95C2×D511yescharacteristic
188C22×C5—41no—
189C22×C5—41no—
190C22×C5—41no—
191C22×C5—41no—
192C22×C5—41no—
193C22×C5—41no—
194C22×C5—41no—
195C22×C5C2×#4111yescharacteristic
196C22×C5C2×#4111yescharacteristic
197C22×C5C2×#4111yescharacteristic
198C22×C5C2×#4111yescharacteristic
199C22×C5C2×#4111yescharacteristic
200C22×C5H(5,𝔽2)11yescharacteristic
201C22×C52−1+411yescharacteristic
202C4×C5—22no—
203C4×C5—41no—
204C4×C5—41no—
205C4×C5—41no—
206C4×C5—41no—
207C4×C5—41no—
208Dic5—22no—
209Dic5—22no—
210Dic5—22no—
211Dic5—22no—
212Dic5—41no—
213Dic5—41no—
214Dic5—41no—
215Dic5—41no—
216C24C22×D511yescharacteristic
217C22×C4—51no—
218C22×C4—51no—
219C22×C4—51no—
220C22×C4—51no—
221C22×C4—51no—
222C22×C4—51no—
223C22×C4—51no—
224C22×C4—51no—
225C22×C4C22×D511yescharacteristic
226C22×C4C22×D511yescharacteristic
227C22×C4C22×D511yescharacteristic
228C22×C4C22×D511yescharacteristic
229C22×C4C22×D511yescharacteristic
230C22×C4C22×D511yescharacteristic
231C4⋊C4—22no—
232C4⋊C4—102no—
233C4⋊C4—102no—
234C4⋊C4—102no—
235C4⋊C4—102no—
236C4⋊C4—102no—
237C4⋊C4—102no—
238C4⋊C4—102no—
239C4⋊C4—201no—
240C22⋊C4—22no—
241C22⋊C4—41no—
242C22⋊C4—41no—
243C22⋊C4—102no—
244C22⋊C4—102no—
245C22⋊C4—102no—
246C22⋊C4—102no—
247C42—102no—
248C42—102no—
249C42—201no—
250C42—201no—
251C42—201no—
252C2×C5—81no—
253C2×C5#52911yescharacteristic
254C2×C5#52911yescharacteristic
255C2×C5#53911yescharacteristic
256C2×C5#55211yescharacteristic
257C2×C5#55311yescharacteristic
258C2×C5#55611yescharacteristic
259C2×C5#55911yescharacteristic
260C23—21no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
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—52no—
286C2×C4—52no—
287C2×C4—52no—
288C2×C4—52no—
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#71112yes—
310C5#259611yescharacteristic, complemented, Sylow
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22C2×#71111yescharacteristic
319C22#414411yescharacteristic
320C22D5×#4111yescharacteristic
321C22D5×#4111yescharacteristic
322C22D5×#4111yescharacteristic
323C22D5×#4111yescharacteristic
324C22#415011yescharacteristic
325C4—22no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—102no—
332C4—102no—
333C4—102no—
334C4—102no—
335C4—201no—
336C4—201no—
337C4—201no—
338C4—201no—
339C2—81no—
340C2#6594811yescharacteristic
341C2#6598411yescharacteristic
342C2#6599411yescharacteristic
343C2#6599811yescharacteristic
344C2#6601411yescharacteristic
345C2#6603611yescharacteristic
346C2#6604011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#397C2
prime radicalC24×C5C23
hypercenter#397D5
hypocenterC5#2596
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. #65270C2semidirect
3. #65262C2semidirect
10. #64949C2semidirect
11. #64947C2semidirect
12. #64944C2semidirect
13. #64941C2semidirect
14. #64938C2semidirect
15. #64938C2semidirect
310. C5#2596semidirect

Maximal subgroups

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

subgroupindex
C5×#3972
#652702
#652622
#652402
#652382
#652332
#649492
#649472
#649442
#649412
#649382
#25965