Finite Group Databasebeta

← #10606830

Subgroups — #10606830

Order 640.

428 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#387C211yesmaximal, characteristic, complemented
2#65283C211yesmaximal, characteristic
3#65283C211yesmaximal, characteristic
4#65274C211yesmaximal, characteristic, complemented
5#65261C211yesmaximal, characteristic, complemented
6#65229C211yesmaximal, characteristic
7C4×C4⋊Dic5C211yesmaximal, characteristic, complemented
8#64958C211yesmaximal, characteristic
9#64957C211yesmaximal, characteristic
10#64957C211yesmaximal, characteristic
11#64955C211yesmaximal, characteristic
12#64947C211yesmaximal, characteristic, complemented
13#64946C211yesmaximal, characteristic, complemented
14#64943C211yesmaximal, characteristic, complemented
15#64936C211yesmaximal, characteristic, complemented
16C22×C4×D5C2211yescharacteristic
17C2×C5×C4⋊C4C2211yescharacteristic
18C2×C5×C4⋊C4C2211yescharacteristic
19C2×C42×C5C2211yescharacteristic
20C2×#685C2211yescharacteristic
21C2×#685C2211yescharacteristic
22C2×#685C2211yescharacteristic
23C2×#685C2211yescharacteristic
24C2×#685C2211yescharacteristic
25C2×#685C2211yescharacteristic
26C2×C4⋊Dic5C2211yescharacteristic
27C2×C4⋊Dic5C2211yescharacteristic
28C2×C4⋊Dic5C2211yescharacteristic
29C2×C4⋊Dic5C2211yescharacteristic
30C2×#683C2211yescharacteristic
31C2×#683C2211yescharacteristic
32C2×#683C2211yescharacteristic
33C2×#683C2211yescharacteristic
34C2×#683C2211yescharacteristic
35C2×#683C2211yescharacteristic
36C2×C4×Dic5C2211yescharacteristic
37C2×C4×Dic5C2211yescharacteristic
38C2×C4×Dic5C2211yescharacteristic
39C5×#95C2211yescharacteristic
40C5×#95C2211yescharacteristic
41C5×#95C2211yescharacteristic
42C5×#95C2211yescharacteristic
43#3963C2211yescharacteristic
44#3963C2211yescharacteristic
45#3963C2211yescharacteristic
46#3963C2211yescharacteristic
47#3963C2211yescharacteristic
48#3963C2211yescharacteristic
49#3963C2211yescharacteristic
50#3963C2211yescharacteristic
51#2587—51nomaximal, Sylow
52C23×D5C2311yescharacteristic
53C22×C4×C5C2311yescharacteristic
54C22×C4×C5C2311yescharacteristic
55C22×C4×C5C2311yescharacteristic
56C22×C4×C5C2311yescharacteristic
57C22×C4×C5C2311yescharacteristic
58C22×C4×C5C2311yescharacteristic
59C22×C4×C5C2311yescharacteristic
60C22×Dic5C2311yescharacteristic
61C22×Dic5C2311yescharacteristic
62C22×Dic5C2311yescharacteristic
63C22×Dic5C2311yescharacteristic
64C22×Dic5C2311yescharacteristic
65C22×Dic5C2311yescharacteristic
66C22×Dic5C2311yescharacteristic
67C2×C4×D5—22no—
68C2×C4×D5—41no—
69C2×C4×D5—41no—
70C5×C4⋊C4—22no—
71C5×C4⋊C4—22no—
72C42×C5—22no—
73#685—22no—
74#685—22no—
75#685—22no—
76#685—41no—
77#685—41no—
78#685Q814yes—
79C4⋊Dic5—22no—
80C4⋊Dic5—22no—
81C4⋊Dic5—22no—
82C4⋊Dic5—41no—
83#683—22no—
84#683—22no—
85#683—41no—
86#683—41no—
87#683—41no—
88#683—41no—
89C4×Dic5—41no—
90C4×Dic5—41no—
91C4×Dic5—41no—
92#400—51no—
93#398—51no—
94#396—51no—
95#396—51no—
96#389—51no—
97#389—51no—
98#389—51no—
99#388—51no—
100#388—51no—
101#387—51no—
102#387D511yescharacteristic, complemented
103#385—51no—
104#385—51no—
105C4×C4⋊C4—51no—
106C4×C22⋊C4—51no—
107C23×C5C2411yescharacteristic
108C22×D5—21no—
109C22×D5—21no—
110C22×D5—21no—
111C22×D5—21no—
112C22×D5—21no—
113C22×D5—21no—
114C22×D5C2×Q812yes—
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—21no—
129C2×C4×C5—21no—
130C2×C4×C5—21no—
131C2×C4×C5—21no—
132C2×C4×C5—21no—
133C2×C4×C5C2×Q812yes—
134C2×C4×C5#4112yes—
135C2×C4×C5#4112yes—
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×Dic5C2×Q812yes—
155C2×Dic5#4112yes—
156C2×Dic5#4112yes—
157C4×D5—44no—
158C23×C4—51no—
159C2×C4⋊C4—51no—
160C2×C4⋊C4—51no—
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⋊C4C2×D511yescharacteristic
170C2×C4⋊C4C2×D511yescharacteristic
171C2×C22⋊C4—51no—
172C2×C22⋊C4—51no—
173C2×C22⋊C4—51no—
174C2×C22⋊C4—51no—
175C2×C22⋊C4—51no—
176C2×C22⋊C4—51no—
177C2×C42—51no—
178C2×C42—51no—
179C2×C42—51no—
180C2×C42C2×D511yescharacteristic
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#95C2×D511yescharacteristic
190#95C2×D511yescharacteristic
191#95C2×D511yescharacteristic
192#95C2×D511yescharacteristic
193C22×C5C22×Q811yescharacteristic
194C22×C5C2×#4111yescharacteristic
195C22×C5C2×#4111yescharacteristic
196C22×C5C2×#4111yescharacteristic
197C22×C5C2×#4111yescharacteristic
198C22×C5H(5,𝔽2)11yescharacteristic
199C22×C5H(5,𝔽2)11yescharacteristic
200C2×D5—22no—
201C2×D5—22no—
202C2×D5—22no—
203C2×D5—41no—
204C2×D5—41no—
205C2×D5—41no—
206C2×D5—41no—
207C4×C5—22no—
208C4×C5—22no—
209C4×C5—22no—
210C4×C5—41no—
211C4×C5—41no—
212C4×C5—41no—
213C4×C5—41no—
214Dic5—22no—
215Dic5—22no—
216Dic5—22no—
217Dic5—41no—
218Dic5—41no—
219Dic5—41no—
220Dic5—41no—
221C24—51no—
222C22×C4—51no—
223C22×C4—51no—
224C22×C4—51no—
225C22×C4—51no—
226C22×C4—51no—
227C22×C4—51no—
228C22×C4—51no—
229C22×C4—102no—
230C22×C4—201no—
231C22×C4—201no—
232C22×C4C22×D511yescharacteristic
233C22×C4C22×D511yescharacteristic
234C22×C4C22×D511yescharacteristic
235C22×C4C22×D511yescharacteristic
236C22×C4C22×D511yescharacteristic
237C22×C4C22×D511yescharacteristic
238C22×C4C22×D511yescharacteristic
239C4⋊C4—22no—
240C4⋊C4—22no—
241C4⋊C4—102no—
242C4⋊C4—102no—
243C4⋊C4—102no—
244C4⋊C4—102no—
245C4⋊C4—102no—
246C4⋊C4—201no—
247C4⋊C4—201no—
248C4⋊C4—201no—
249C4⋊C4—201no—
250C4⋊C4—201no—
251C22⋊C4—54no—
252C22⋊C4—102no—
253C22⋊C4—102no—
254C22⋊C4—102no—
255C22⋊C4—201no—
256C22⋊C4—201no—
257C42—22no—
258C42—201no—
259C42—201no—
260C42—201no—
261C2×C5#52911yescharacteristic
262C2×C5#53311yescharacteristic
263C2×C5#53811yescharacteristic
264C2×C5#55311yescharacteristic
265C2×C5#55311yescharacteristic
266C2×C5#55411yescharacteristic
267C2×C5#55411yescharacteristic
268D5—42no—
269C23—52no—
270C23—101no—
271C23—101no—
272C23—101no—
273C23—101no—
274C23—101no—
275C23—101no—
276C23C23×D511yescharacteristic
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—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—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—101no—
310C2×C4—101no—
311C2×C4—101no—
312C2×C4—101no—
313C2×C4—101no—
314C2×C4—101no—
315C2×C4—101no—
316C2×C4—204no—
317C2×C4#70912yes—
318C2×C4#71112yes—
319C2×C4Q8×D512yes—
320C5#258711yescharacteristic, complemented, Sylow
321C22—102no—
322C22—102no—
323C22—102no—
324C22—201no—
325C22—201no—
326C22—201no—
327C22—201no—
328C22C2×#70911yescharacteristic
329C22C2×#71111yescharacteristic
330C22C2×Q8×D511yescharacteristic
331C22D5×#4111yescharacteristic
332C22D5×#4111yescharacteristic
333C22#414911yescharacteristic
334C22#414911yescharacteristic
335C4—22no—
336C4—22no—
337C4—22no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—102no—
343C4—102no—
344C4—102no—
345C4—201no—
346C4—201no—
347C4—201no—
348C4—201no—
349C2—202no—
350C2#6586411yescharacteristic
351C2#6589911yescharacteristic
352C2#6591211yescharacteristic
353C2#6596911yescharacteristic
354C2#6598311yescharacteristic
355C2#6602411yescharacteristic
356C2#6603811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#387C2
prime radicalC23×D5C23
hypercenter#387D5
hypocenterC5#2587
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
1. C5×#387C2semidirect
4. #65274C2semidirect
5. #65261C2semidirect
7. C4×C4⋊Dic5C2semidirect
12. #64947C2semidirect
13. #64946C2semidirect
14. #64943C2semidirect
15. #64936C2semidirect
102. #387D5semidirect
320. C5#2587semidirect

Maximal subgroups

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

subgroupindex
C5×#3872
#652832
#652742
#652612
#652292
C4×C4⋊Dic52
#649582
#649572
#649552
#649472
#649462
#649432
#649362
#25875