Finite Group Databasebeta

← #10609476

Subgroups — #10609476

Order 640.

608 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4043C211yesmaximal, characteristic
2C2×#4042C211yesmaximal, characteristic
3C2×D5×C4⋊C4C211yesmaximal, characteristic
4C2×#4034C211yesmaximal, characteristic, complemented
5C5×#398C211yesmaximal, characteristic, complemented
6#65278C211yesmaximal, characteristic
7#65268C211yesmaximal, characteristic, complemented
8#65265C211yesmaximal, characteristic, complemented
9#65261C211yesmaximal, characteristic, complemented
10#64957C211yesmaximal, characteristic
11#64956C211yesmaximal, characteristic
12#64955C211yesmaximal, characteristic
13#64950C211yesmaximal, characteristic, complemented
14#64945C211yesmaximal, characteristic, complemented
15#64936C211yesmaximal, characteristic, complemented
16C22×C4×D5C2211yescharacteristic
17C22×C4×D5C2211yescharacteristic
18C22×C4×D5C2211yescharacteristic
19C22×Dic10C2211yescharacteristic
20C22×Dic10C2211yescharacteristic
21C2×C5×C4⋊C4C2211yescharacteristic
22C2×C5×C4⋊C4C2211yescharacteristic
23C2×C5×C4⋊C4C2211yescharacteristic
24C2×C5×C4⋊C4C2211yescharacteristic
25C2×#685C2211yescharacteristic
26C2×#685C2211yescharacteristic
27C2×#685C2211yescharacteristic
28C2×#685C2211yescharacteristic
29C2×C4⋊Dic5C2211yescharacteristic
30C2×C4⋊Dic5C2211yescharacteristic
31C2×C4⋊Dic5C2211yescharacteristic
32C2×C4⋊Dic5C2211yescharacteristic
33C2×#683C2211yescharacteristic
34C2×#683C2211yescharacteristic
35C2×#683C2211yescharacteristic
36C2×#683C2211yescharacteristic
37C2×#683C2211yescharacteristic
38C2×#683C2211yescharacteristic
39C2×#683C2211yescharacteristic
40C2×#683C2211yescharacteristic
41C2×C4×Dic5C2211yescharacteristic
42C2×C4×Dic5C2211yescharacteristic
43#4043—24no—
44#4042—24no—
45D5×C4⋊C4—24no—
46#4034—24no—
47C5×#95C2211yescharacteristic
48C5×#95C2211yescharacteristic
49C5×#95C2211yescharacteristic
50#3963C2211yescharacteristic
51#3963C2211yescharacteristic
52#3963C2211yescharacteristic
53#3963C2211yescharacteristic
54#3963C2211yescharacteristic
55#2440—51nomaximal, Sylow
56C23×D5C2311yescharacteristic
57C22×C4×C5C2311yescharacteristic
58C22×C4×C5C2311yescharacteristic
59C22×C4×C5C2311yescharacteristic
60C22×C4×C5C2311yescharacteristic
61C22×C4×C5C2311yescharacteristic
62C22×C4×C5C2311yescharacteristic
63C22×C4×C5C2311yescharacteristic
64C22×Dic5C2311yescharacteristic
65C22×Dic5C2311yescharacteristic
66C22×Dic5C2311yescharacteristic
67C22×Dic5C2311yescharacteristic
68C22×Dic5C2311yescharacteristic
69C22×Dic5C2311yescharacteristic
70C22×Dic5C2311yescharacteristic
71C2×C4×D5—22no—
72C2×C4×D5—22no—
73C2×C4×D5—22no—
74C2×C4×D5—22no—
75C2×C4×D5—22no—
76C2×C4×D5—22no—
77C2×C4×D5—41no—
78C2×C4×D5—41no—
79C2×C4×D5Q814yescomplemented
80C2×Dic10—22no—
81C2×Dic10—22no—
82C2×Dic10—22no—
83C2×Dic10—22no—
84C2×Dic10—41no—
85C2×Dic10—41no—
86C5×C4⋊C4—22no—
87C5×C4⋊C4—22no—
88C5×C4⋊C4—22no—
89C5×C4⋊C4—22no—
90#685—22no—
91#685—22no—
92#685D414yes—
93#685Q814yescomplemented
94C4⋊Dic5—22no—
95C4⋊Dic5—22no—
96C4⋊Dic5—22no—
97C4⋊Dic5—22no—
98#683—22no—
99#683—22no—
100#683—22no—
101#683—22no—
102#683—22no—
103#683—41no—
104#683—41no—
105#683D414yes—
106C4×Dic5—22no—
107C4×Dic5—22no—
108C2×C4⋊Q8—51no—
109C2×C22⋊Q8—51no—
110C2×C22⋊Q8—51no—
111C22×C4⋊C4—51no—
112#398—51no—
113#398D511yescharacteristic, complemented
114#395—51no—
115#395—51no—
116#389—51no—
117#389—51no—
118#385—51no—
119#385—51no—
120#384—51no—
121#380—51no—
122C4×C22⋊C4—51no—
123C23×C5C2411yescharacteristic
124C22×D5—21no—
125C22×D5—21no—
126C22×D5—21no—
127C22×D5—21no—
128C22×D5C2×D412yes—
129C22×D5C2×Q812yes—
130C22×D5C2×Q812yes—
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×C5—21no—
139C2×C4×C5—21no—
140C2×C4×C5—21no—
141C2×C4×C5—21no—
142C2×C4×C5—21no—
143C2×C4×C5—21no—
144C2×C4×C5—21no—
145C2×C4×C5—21no—
146C2×C4×C5—21no—
147C2×C4×C5—21no—
148C2×C4×C5C2×D412yes—
149C2×C4×C5C2×D412yes—
150C2×C4×C5C2×Q812yes—
151C2×C4×C5C2×Q812yes—
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—
161C2×Dic5—21no—
162C2×Dic5—21no—
163C2×Dic5—21no—
164C2×Dic5—21no—
165C2×Dic5—21no—
166C2×Dic5—21no—
167C2×Dic5C2×D412yes—
168C2×Dic5C2×D412yes—
169C2×Dic5C2×D412yes—
170C2×Dic5C2×Q812yes—
171C2×Dic5C2×Q812yes—
172C2×Dic5#4112yes—
173C4×D5—28no—
174C4×D5—44no—
175C4×D5—44no—
176Dic10—44no—
177Dic10—44no—
178C22×Q8—51no—
179C22×Q8—51no—
180C23×C4—51no—
181C23×C4—51no—
182C23×C4—51no—
183C4⋊Q8—104no—
184C22⋊Q8—104no—
185C22⋊Q8—104no—
186C2×C4⋊C4—51no—
187C2×C4⋊C4—51no—
188C2×C4⋊C4—51no—
189C2×C4⋊C4—51no—
190C2×C4⋊C4—51no—
191C2×C4⋊C4—51no—
192C2×C4⋊C4—51no—
193C2×C4⋊C4—51no—
194C2×C4⋊C4—51no—
195C2×C4⋊C4—51no—
196C2×C4⋊C4—51no—
197C2×C4⋊C4—51no—
198C2×C4⋊C4—104no—
199C2×C4⋊C4C2×D511yescharacteristic
200C2×C4⋊C4C2×D511yescharacteristic
201C2×C4⋊C4C2×D511yescharacteristic
202C2×C4⋊C4C2×D511yescharacteristic
203C2×C22⋊C4—51no—
204C2×C22⋊C4—51no—
205C2×C22⋊C4—51no—
206C2×C22⋊C4—51no—
207C2×C42—51no—
208C2×C42—51no—
209#95—51no—
210#95—51no—
211#95—51no—
212#95—51no—
213#95—51no—
214#95C2×D511yescharacteristic
215#95C2×D511yescharacteristic
216#95C2×D511yescharacteristic
217C22×C5C22×D411yescharacteristic
218C22×C5C22×D411yescharacteristic
219C22×C5C22×Q811yescharacteristic
220C22×C5C22×Q811yescharacteristic
221C22×C5C2×#4111yescharacteristic
222C22×C5H(5,𝔽2)11yescharacteristic
223C22×C52−1+411yescharacteristic
224C2×D5—22no—
225C2×D5—22no—
226C2×D5—22no—
227C2×D5—22no—
228C2×D5—22no—
229C2×D5—22no—
230C2×D5C4⋊Q814yescomplemented
231C4×C5—22no—
232C4×C5—22no—
233C4×C5—22no—
234C4×C5—22no—
235C4×C5—41no—
236C4×C5—41no—
237C4×C5—41no—
238Dic5—22no—
239Dic5—22no—
240Dic5—22no—
241Dic5—41no—
242Dic5—41no—
243Dic5—41no—
244Dic5C22⋊Q814yescomplemented
245C24—51no—
246C2×Q8—102no—
247C2×Q8—102no—
248C2×Q8—102no—
249C2×Q8—102no—
250C2×Q8—201no—
251C2×Q8—201no—
252C22×C4—51no—
253C22×C4—51no—
254C22×C4—51no—
255C22×C4—51no—
256C22×C4—54no—
257C22×C4—51no—
258C22×C4—51no—
259C22×C4—51no—
260C22×C4—102no—
261C22×C4—102no—
262C22×C4—102no—
263C22×C4—102no—
264C22×C4—102no—
265C22×C4—102no—
266C22×C4—201no—
267C22×C4—201no—
268C22×C4C22×D511yescharacteristic
269C22×C4C22×D511yescharacteristic
270C22×C4C22×D511yescharacteristic
271C22×C4C22×D511yescharacteristic
272C22×C4C22×D511yescharacteristic
273C22×C4C22×D511yescharacteristic
274C22×C4C22×D511yescharacteristic
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—54no—
280C4⋊C4—102no—
281C4⋊C4—102no—
282C4⋊C4—102no—
283C4⋊C4—102no—
284C4⋊C4—102no—
285C4⋊C4—102no—
286C4⋊C4—102no—
287C4⋊C4—102no—
288C4⋊C4—102no—
289C4⋊C4—201no—
290C4⋊C4—201no—
291C22⋊C4—54no—
292C22⋊C4—54no—
293C22⋊C4—102no—
294C22⋊C4—102no—
295C42—102no—
296C42—102no—
297C2×C5C2×C22⋊Q811yescharacteristic
298C2×C5C2×C4⋊Q811yescharacteristic
299C2×C5#54411yescharacteristic
300C2×C5D4211yescharacteristic
301C2×C5#54711yescharacteristic
302C2×C5D4×Q811yescharacteristic
303C2×C5#55411yescharacteristic
304D5—24no—
305C23—52no—
306C23—52no—
307C23—52no—
308C23—101no—
309C23—101no—
310C23—101no—
311C23—101no—
312C23C23×D511yescharacteristic
313Q8—204no—
314Q8—204no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—52no—
333C2×C4—52no—
334C2×C4—52no—
335C2×C4—52no—
336C2×C4—52no—
337C2×C4—52no—
338C2×C4—108no—
339C2×C4—101no—
340C2×C4—101no—
341C2×C4—101no—
342C2×C4—101no—
343C2×C4—101no—
344C2×C4—101no—
345C2×C4—101no—
346C2×C4—101no—
347C2×C4—101no—
348C2×C4—101no—
349C2×C4—101no—
350C2×C4—101no—
351C2×C4—101no—
352C2×C4—101no—
353C2×C4—101no—
354C2×C4—204no—
355C2×C4—204no—
356C2×C4D4×D512yes—
357C2×C4D4×D512yes—
358C2×C4Q8×D512yes—
359C2×C4Q8×D512yes—
360C5#244011yescharacteristic, complemented, Sylow
361C22—54no—
362C22—102no—
363C22—102no—
364C22—102no—
365C22—102no—
366C22—102no—
367C22—102no—
368C22C2×D4×D511yescharacteristic
369C22C2×D4×D511yescharacteristic
370C22C2×Q8×D511yescharacteristic
371C22C2×Q8×D511yescharacteristic
372C22D5×#4111yescharacteristic
373C22#414911yescharacteristic
374C22#415011yescharacteristic
375C4—22no—
376C4—22no—
377C4—22no—
378C4—22no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—54no—
383C4—102no—
384C4—102no—
385C4—102no—
386C4—201no—
387C4—201no—
388C4—201no—
389C2—104no—
390C2#6594311yescharacteristic
391C2D5×C22⋊Q811yescharacteristic
392C2#6596611yescharacteristic
393C2#6598911yescharacteristic
394C2#6602311yescharacteristic
395C2#6602411yescharacteristic
396C2D5×C4⋊Q811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#398C2
prime radicalC23×D5C23
hypercenter#398D5
hypocenterC5#2440
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
4. C2×#4034C2semidirect
5. C5×#398C2semidirect
7. #65268C2semidirect
8. #65265C2semidirect
9. #65261C2semidirect
13. #64950C2semidirect
14. #64945C2semidirect
15. #64936C2semidirect
79. C2×C4×D5Q8semidirect
93. #685Q8semidirect
113. #398D5semidirect
230. C2×D5C4⋊Q8semidirect
244. Dic5C22⋊Q8semidirect
360. C5#2440semidirect

Maximal subgroups

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

subgroupindex
C2×#40432
C2×#40422
C2×D5×C4⋊C42
C2×#40342
C5×#3982
#652782
#652682
#652652
#652612
#649572
#649562
#649552
#649502
#649452
#649362
#24405