Finite Group Databasebeta

← #10605807

Subgroups — #10605807

Order 640.

546 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4075C211yesmaximal, characteristic
2C2×#4024C211yesmaximal, characteristic, complemented
3C5×#381C211yesmaximal, characteristic, complemented
4C2×#3963C211yesmaximal, characteristic, complemented
5#65247C211yesmaximal, characteristic
6#65247C211yesmaximal, characteristic
7C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
8#64964C211yesmaximal, characteristic, complemented
9#64962C211yesmaximal, characteristic, complemented
10#64959C211yesmaximal, characteristic, complemented
11#64958C211yesmaximal, characteristic, complemented
12#64949C211yesmaximal, characteristic, complemented
13#64947C211yesmaximal, characteristic, complemented
14#64939C211yesmaximal, characteristic, complemented
15#64935C211yesmaximal, characteristic, complemented
16C23×C4×C5C2211yescharacteristic
17C22×C22⋊D5C2211yescharacteristic
18C23×Dic5C2211yescharacteristic
19C23×Dic5C2211yescharacteristic
20C22×Dic10C2211yescharacteristic
21C2×C5×C22⋊C4C2211yescharacteristic
22C2×C5×C22⋊C4C2211yescharacteristic
23C2×C22⋊Dic5C2211yescharacteristic
24#4075—24no—
25C2×#685C2211yescharacteristic
26C2×#685C2211yescharacteristic
27C2×#685C2211yescharacteristic
28C2×#685C2211yescharacteristic
29C2×#685C2211yescharacteristic
30C2×#685C2211yescharacteristic
31C2×C4⋊Dic5C2211yescharacteristic
32C2×#683C2211yescharacteristic
33C2×#683C2211yescharacteristic
34C2×#683C2211yescharacteristic
35C2×#683C2211yescharacteristic
36C2×C4×Dic5C2211yescharacteristic
37C2×C4×Dic5C2211yescharacteristic
38#4024—24no—
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#3963C2211yescharacteristic
52#3963C2211yescharacteristic
53#2488—51nomaximal, Sylow
54C24×C5C2311yescharacteristic
55C23×D5C2311yescharacteristic
56C22×C4×C5—22no—
57C22×C4×C5—22no—
58C22×C4×C5—22no—
59C22×C4×C5C2311yescharacteristic
60C22×C4×C5C2311yescharacteristic
61C22×C4×C5C2311yescharacteristic
62C22×C4×C5C2311yescharacteristic
63C22×C4×C5C2311yescharacteristic
64C22×C4×C5C2311yescharacteristic
65C2×C22⋊D5—22no—
66C2×C22⋊D5—22no—
67C2×C22⋊D5—22no—
68C22×Dic5—22no—
69C22×Dic5—22no—
70C22×Dic5—22no—
71C22×Dic5—22no—
72C22×Dic5—41no—
73C22×Dic5—41no—
74C22×Dic5C2311yescharacteristic
75C22×Dic5C2311yescharacteristic
76C22×Dic5C2311yescharacteristic
77C22×Dic5C2311yescharacteristic
78C22×Dic5C2311yescharacteristic
79C22×Dic5C2311yescharacteristic
80C22×Dic5C2311yescharacteristic
81C2×Dic10—22no—
82C2×Dic10—22no—
83C2×Dic10—41no—
84C5×C22⋊C4—22no—
85C5×C22⋊C4—22no—
86C22⋊Dic5D414yes—
87#685—22no—
88#685—22no—
89#685—22no—
90#685—22no—
91#685—41no—
92#685—41no—
93C4⋊Dic5—22no—
94#683—22no—
95#683—22no—
96#683—22no—
97#683—22no—
98C4×Dic5—22no—
99C4×Dic5—41no—
100C2×#123—51no—
101C2×C22⋊Q8—51no—
102#400—51no—
103#400—51no—
104#397—51no—
105#393—51no—
106#391—51no—
107#388—51no—
108#388—51no—
109#386—51no—
110#386—51no—
111#382—51no—
112#381D511yescharacteristic, complemented
113C4×C22⋊C4—51no—
114C2×#95—51no—
115C23×C5—21no—
116C23×C5—21no—
117C23×C5—21no—
118C23×C5—21no—
119C23×C5C2×D412yes—
120C23×C5#4112yes—
121C23×C5#4112yes—
122C23×C5C2411yescharacteristic
123C22×D5—21no—
124C22×D5—21no—
125C22×D5—21no—
126C22×D5—21no—
127C22×D5—21no—
128C22×D5—21no—
129C22×D5—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×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×C5—44no—
149C22⋊D5—44no—
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—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×Dic5—44no—
168C2×Dic5—44no—
169C2×Dic5C2×D412yes—
170C2×Dic5C2×D412yes—
171C2×Dic5#4112yes—
172C2×Dic5#4112yes—
173Dic10—44no—
174C22×Q8—51no—
175C22×D4—51no—
176C23×C4—51no—
177C23×C4—51no—
178C23×C4C2×D511yescharacteristic
179#123—104no—
180C22⋊Q8—104no—
181C2×C4⋊C4—51no—
182C2×C4⋊C4—51no—
183C2×C4⋊C4—51no—
184C2×C4⋊C4—51no—
185C2×C4⋊C4—51no—
186C2×C22⋊C4—51no—
187C2×C22⋊C4—51no—
188C2×C22⋊C4—51no—
189C2×C22⋊C4—51no—
190C2×C22⋊C4—51no—
191C2×C22⋊C4—51no—
192C2×C22⋊C4—51no—
193C2×C22⋊C4C2×D511yescharacteristic
194C2×C22⋊C4C2×D511yescharacteristic
195C2×C42—51no—
196C2×C42—51no—
197#95—51no—
198#95—51no—
199#95—51no—
200#95—51no—
201#95—51no—
202#95—51no—
203#95—51no—
204#95—51no—
205#95—51no—
206#95—51no—
207#95C2×D511yescharacteristic
208#95C2×D511yescharacteristic
209#95C2×D511yescharacteristic
210#95C2×D511yescharacteristic
211C22×C5—22no—
212C22×C5—22no—
213C22×C5—22no—
214C22×C5—22no—
215C22×C5—22no—
216C22×C5—22no—
217C22×C5#12414yes—
218C22×C5C22×D411yescharacteristic
219C22×C5C2×#4111yescharacteristic
220C22×C5C2×#4111yescharacteristic
221C22×C5C2×#4111yescharacteristic
222C22×C5C2×#4111yescharacteristic
223C22×C5H(5,𝔽2)11yescharacteristic
224C22×C52−1+411yescharacteristic
225C2×D5—41no—
226C2×D5—41no—
227C2×D5—41no—
228C2×D5—41no—
229C2×D5—41no—
230C2×D5—41no—
231C2×D5—41no—
232C4×C5—41no—
233C4×C5—41no—
234C4×C5—41no—
235C4×C5—41no—
236C4×C5—41no—
237C4×C5—41no—
238Dic5—22no—
239Dic5—22no—
240Dic5—22no—
241Dic5—22no—
242Dic5—41no—
243Dic5—41no—
244Dic5—41no—
245C24—51no—
246C24C22×D511yescharacteristic
247C2×Q8—102no—
248C2×Q8—102no—
249C2×Q8—201no—
250C2×D4—102no—
251C2×D4—102no—
252C2×D4—102no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—51no—
257C22×C4—51no—
258C22×C4—51no—
259C22×C4—51no—
260C22×C4—51no—
261C22×C4—51no—
262C22×C4—51no—
263C22×C4—102no—
264C22×C4—102no—
265C22×C4—102no—
266C22×C4—102no—
267C22×C4—201no—
268C22×C4—201no—
269C22×C4C22×D511yescharacteristic
270C22×C4C22×D511yescharacteristic
271C22×C4C22×D511yescharacteristic
272C22×C4C22×D511yescharacteristic
273C22×C4C22×D511yescharacteristic
274C22×C4C22×D511yescharacteristic
275C4⋊C4—102no—
276C4⋊C4—102no—
277C4⋊C4—102no—
278C4⋊C4—102no—
279C4⋊C4—102no—
280C22⋊C4—22no—
281C22⋊C4—22no—
282C22⋊C4—54no—
283C22⋊C4—102no—
284C22⋊C4—102no—
285C22⋊C4—102no—
286C22⋊C4—102no—
287C22⋊C4—201no—
288C22⋊C4—201no—
289C42—102no—
290C42—201no—
291C2×C5—24no—
292C2×C5C2×#12411yescharacteristic
293C2×C5#52911yescharacteristic
294C2×C5#53911yescharacteristic
295C2×C5#54611yescharacteristic
296C2×C5#54711yescharacteristic
297C2×C5#55111yescharacteristic
298C2×C5#55211yescharacteristic
299D5—81no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—101no—
305C23—101no—
306C23—101no—
307C23—101no—
308C23—101no—
309C23—101no—
310C23—101no—
311C23#70912yes—
312C23D4×D512yes—
313C23#71112yes—
314C23C23×D511yescharacteristic
315Q8—204no—
316D4—204no—
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—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—44no—
336C2×C4—52no—
337C2×C4—52no—
338C2×C4—52no—
339C2×C4—52no—
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—101no—
355C2×C4—101no—
356C2×C4—101no—
357C2×C4—204no—
358C2×C4—204no—
359C5#248811yescharacteristic, complemented, Sylow
360C22—22no—
361C22—22no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22—201no—
367C22—201no—
368C22—201no—
369C22—201no—
370C22—201no—
371C22—201no—
372C22—201no—
373C22#403114yes—
374C22C2×#70911yescharacteristic
375C22C2×D4×D511yescharacteristic
376C22C2×#71111yescharacteristic
377C22D5×#4111yescharacteristic
378C22D5×#4111yescharacteristic
379C22#414911yescharacteristic
380C22#415011yescharacteristic
381C4—41no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—102no—
388C4—102no—
389C4—102no—
390C4—102no—
391C4—201no—
392C4—201no—
393C4—201no—
394C2—24no—
395C2—401no—
396C2C2×#403111yescharacteristic
397C2#6586111yescharacteristic
398C2#6586511yescharacteristic
399C2#6598311yescharacteristic
400C2#6598811yescharacteristic
401C2#6598911yescharacteristic
402C2#6599911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#381C2
prime radicalC22×C22⋊D5C22
hypercenter#381D5
hypocenterC5#2488
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#4024C2semidirect
3. C5×#381C2semidirect
4. C2×#3963C2semidirect
7. C22⋊C4×Dic5C2semidirect
8. #64964C2semidirect
9. #64962C2semidirect
10. #64959C2semidirect
11. #64958C2semidirect
12. #64949C2semidirect
13. #64947C2semidirect
14. #64939C2semidirect
15. #64935C2semidirect
112. #381D5semidirect
359. C5#2488semidirect

Maximal subgroups

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

subgroupindex
C2×#40752
C2×#40242
C5×#3812
C2×#39632
#652472
C22⋊C4×Dic52
#649642
#649622
#649592
#649582
#649492
#649472
#649392
#649352
#24885