Finite Group Databasebeta

← #13106023

Subgroups — #13106023

Order 1600.

548 conjugacy classes of subgroups.

The subgroup lattice has 441 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#87806C211yesmaximal, characteristic, complemented
2C4×C5×C22⋊D5C211yesmaximal, characteristic
3C5×#4070C211yesmaximal, characteristic, complemented
4#11717100C211yesmaximal, characteristic, complemented
5#11717100C211yesmaximal, characteristic, complemented
6#11717091C211yesmaximal, characteristic
7#11717091C211yesmaximal, characteristic
8#11717014C211yesmaximal, characteristic, complemented
9#11717006C211yesmaximal, characteristic, complemented
10D5×#683C211yesmaximal, characteristic, complemented
11#11716986C211yesmaximal, characteristic, complemented
12#11716969C211yesmaximal, characteristic, complemented
13#11716964C211yesmaximal, characteristic, complemented
14#11716957C211yesmaximal, characteristic, complemented
15#11716955C211yesmaximal, characteristic, complemented
16C22×C4×C52C2211yescharacteristic
17C22×#1039C2211yescharacteristic
18C22×#1039C2211yescharacteristic
19C2×C5×C22⋊D5C2211yescharacteristic
20C2×C4×C5×D5C2211yescharacteristic
21C2×C5×Dic10C2211yescharacteristic
22C2×#6039C2211yescharacteristic
23C2×#6039C2211yescharacteristic
24C2×D5×Dic5C2211yescharacteristic
25C2×D5×Dic5C2211yescharacteristic
26#87806C2211yescharacteristic
27#87806C2211yescharacteristic
28#87806C2211yescharacteristic
29#87806C2211yescharacteristic
30C5×C22⋊Dic5C2211yescharacteristic
31C5×C22⋊Dic5C2211yescharacteristic
32C5×C22⋊Dic5C2211yescharacteristic
33C5×#685C2211yescharacteristic
34C5×C4⋊Dic5C2211yescharacteristic
35C5×#683C2211yescharacteristic
36C5×#683C2211yescharacteristic
37C5×#683C2211yescharacteristic
38C4×C5×Dic5C2211yescharacteristic
39#87781C2211yescharacteristic
40#87781C2211yescharacteristic
41#87780C2211yescharacteristic
42#87780C2211yescharacteristic
43#87780C2211yescharacteristic
44#87780C2211yescharacteristic
45#87780C2211yescharacteristic
46#87780C2211yescharacteristic
47#87778C2211yescharacteristic
48#87778C2211yescharacteristic
49Dic52C2211yescharacteristic
50Dic52C2211yescharacteristic
51#65970—51nomaximal
52#65873—51nomaximal
53C23×C52C2311yescharacteristic
54C22×C5×D5C2311yescharacteristic
55C2×C4×C52—41no—
56C2×C4×C52C2311yescharacteristic
57C2×C4×C52C2311yescharacteristic
58C2×#1039—22no—
59C2×#1039—41no—
60C2×#1039C2311yescharacteristic
61C2×#1039C2311yescharacteristic
62C2×#1039C2311yescharacteristic
63C2×#1039C2311yescharacteristic
64C5×C22⋊D5Q814yescomplemented
65C2×C5×Dic5C2311yescharacteristic
66C2×C5×Dic5C2311yescharacteristic
67C2×C5×Dic5C2311yescharacteristic
68C2×C5×Dic5C2311yescharacteristic
69C2×C5×Dic5C2311yescharacteristic
70C2×C5×Dic5C2311yescharacteristic
71C2×C5×Dic5C2311yescharacteristic
72C4×C5×D5—41no—
73C5×Dic10—41no—
74#6039—22no—
75#6039—41no—
76D5×Dic5—22no—
77D5×Dic5—41no—
78C5×C22⋊Q8—51no—
79C4×C5×D4—51no—
80#4092—51no—
81#4090—51no—
82D4×Dic5—51no—
83D4×Dic5—51no—
84C4×C22⋊D5D511yescharacteristic
85#4070—51no—
86#4070D511yescharacteristic, complemented
87C2×#683—51no—
88C2×#683—51no—
89C2×#683—51no—
90C2×#683—102no—
91#4042—51no—
92#4042—51no—
93D5×C4⋊C4—51no—
94#4036—51no—
95#4035—51no—
96#4035—51no—
97#4034—51no—
98#4033—51no—
99#4027—51no—
100#4027—51no—
101#4024—51no—
102#4024—51no—
103#4024—51no—
104#4024—51no—
105#4024—51no—
106#4024—51no—
107#4016—51no—
108C4×Dic10—51no—
109C22×C52—21no—
110C22×C52—21no—
111C22×C52C2×Q812yes—
112C22×C52C2411yescharacteristic
113C2×C5×D5—21no—
114C2×C5×D5—21no—
115C2×C5×D5C2×Q812yes—
116C4×C52—21no—
117C4×C52—21no—
118#1039—21no—
119#1039—21no—
120#1039—21no—
121#1039#4112yes—
122C5×Dic5—21no—
123C5×Dic5—21no—
124C5×Dic5—21no—
125C5×Dic5—21no—
126C5×Dic5—21no—
127C5×Dic5—21no—
128C5×Dic5C2×Q812yes—
129C2×C5×Q8—51no—
130C2×C5×D4—51no—
131C22×C4×C5—22no—
132C22×C4×C5—51no—
133C22×C4×C5C2×D511yescharacteristic
134C22×C4×C5C2×D511yescharacteristic
135C2×C22⋊D5C2×D511yescharacteristic
136C22×Dic5—51no—
137C22×Dic5—51no—
138C22×Dic5—51no—
139C22×Dic5—51no—
140C22×Dic5—51no—
141C22×Dic5—51no—
142C22×Dic5—102no—
143C22×Dic5—102no—
144C2×C4×D5—51no—
145C2×C4×D5—51no—
146C2×C4×D5C2×D511yescharacteristic
147C2×Dic10—51no—
148C2×Dic10—51no—
149C2×Dic10—51no—
150C2×Dic10—51no—
151C2×Dic10C2×D511yescharacteristic
152C5×C4⋊C4—51no—
153C5×C4⋊C4—51no—
154C5×C4⋊C4—51no—
155C5×C4⋊C4—51no—
156C5×C22⋊C4—51no—
157C5×C22⋊C4—51no—
158C5×C22⋊C4—51no—
159C5×C22⋊C4—51no—
160C42×C5—51no—
161C22⋊Dic5—51no—
162C22⋊Dic5—51no—
163C22⋊Dic5C2×D511yescharacteristic
164C22⋊Dic5C2×D511yescharacteristic
165C22⋊Dic5C2×D511yescharacteristic
166#685—51no—
167#685—51no—
168#685C2×D511yescharacteristic
169C4⋊Dic5—51no—
170C4⋊Dic5—51no—
171C4⋊Dic5—51no—
172C4⋊Dic5—51no—
173C4⋊Dic5—51no—
174C4⋊Dic5—51no—
175C4⋊Dic5C2×D511yescharacteristic
176#683—51no—
177#683—51no—
178#683—51no—
179#683—51no—
180#683—51no—
181#683—51no—
182#683—51no—
183#683—51no—
184#683—51no—
185#683—51no—
186#683—51no—
187#683—51no—
188#683—51no—
189#683—51no—
190#683—51no—
191#683—51no—
192#683—51no—
193#683—51no—
194#683—102no—
195#683—102no—
196#683—102no—
197#683—102no—
198#683C2×D511yescharacteristic
199#683C2×D511yescharacteristic
200#683C2×D511yescharacteristic
201C4×Dic5—51no—
202C4×Dic5—51no—
203C4×Dic5—51no—
204C4×Dic5—51no—
205C4×Dic5C2×D511yescharacteristic
206#554—251noSylow
207C2×C52—22no—
208C2×C52C22×Q811yescharacteristic
209C2×C52C2×#4111yescharacteristic
210C2×C52H(5,𝔽2)11yescharacteristic
211C5×D5—22no—
212C23×C5—22no—
213C23×C5—51no—
214C23×C5C22×D511yescharacteristic
215C23×C5C22×D511yescharacteristic
216C22×D5C22×D511yescharacteristic
217C5×Q8—201no—
218C5×D4—54no—
219C2×C4×C5—22no—
220C2×C4×C5—22no—
221C2×C4×C5—41no—
222C2×C4×C5—41no—
223C2×C4×C5—44no—
224C2×C4×C5—51no—
225C2×C4×C5—51no—
226C2×C4×C5—51no—
227C2×C4×C5—51no—
228C2×C4×C5—51no—
229C2×C4×C5—51no—
230C2×C4×C5—51no—
231C2×C4×C5—201no—
232C2×C4×C5C22×D511yescharacteristic
233C2×C4×C5C22×D511yescharacteristic
234C2×C4×C5C22×D511yescharacteristic
235C2×C4×C5C22×D511yescharacteristic
236C22⋊D5Dic1014yescomplemented
237C2×Dic5—51no—
238C2×Dic5—51no—
239C2×Dic5—51no—
240C2×Dic5—51no—
241C2×Dic5—51no—
242C2×Dic5—51no—
243C2×Dic5—51no—
244C2×Dic5—51no—
245C2×Dic5—102no—
246C2×Dic5—102no—
247C2×Dic5—102no—
248C2×Dic5—102no—
249C2×Dic5—102no—
250C2×Dic5—102no—
251C2×Dic5—102no—
252C2×Dic5—108no—
253C2×Dic5—201no—
254C2×Dic5—201no—
255C2×Dic5—201no—
256C2×Dic5—204no—
257C2×Dic5C22×D511yescharacteristic
258C2×Dic5C22×D511yescharacteristic
259C2×Dic5C22×D511yescharacteristic
260C2×Dic5C22×D511yescharacteristic
261C2×Dic5C22×D511yescharacteristic
262C2×Dic5C22×D511yescharacteristic
263C2×Dic5C22×D511yescharacteristic
264C4×D5—41no—
265C4×D5—102no—
266C4×D5—201no—
267Dic10—41no—
268Dic10—102no—
269Dic10—102no—
270Dic10—201no—
271Dic10—201no—
272C4⋊Q8—251no—
273#125—251no—
274#125—251no—
275C22⋊Q8—51no—
276C22⋊Q8—251no—
277C22⋊Q8—251no—
278C22⋊Q8—251no—
279C22⋊Q8—251no—
280C22⋊Q8—251no—
281C4×Q8—251no—
282C4×D4—51no—
283C4×D4—251no—
284C4×D4—251no—
285C2×C4⋊C4—251no—
286C2×C4⋊C4—251no—
287C52#55411yescharacteristic, complemented, Sylow
288C22×C5—24no—
289C22×C5—24no—
290C22×C5—21no—
291C22×C5—21no—
292C22×C5—21no—
293C22×C5—21no—
294C22×C5—24no—
295C22×C5—22no—
296C22×C5—52no—
297C22×C5—101no—
298C22×C5—101no—
299C22×C5C2×Dic1012yes—
300C22×C5Q8×D512yes—
301C22×C5C23×D511yescharacteristic
302C22×C5C23×D511yescharacteristic
303C2×D5—21no—
304C2×D5—21no—
305C2×D5C2×Dic1012yes—
306C4×C5—21no—
307C4×C5—21no—
308C4×C5—21no—
309C4×C5—21no—
310C4×C5—42no—
311C4×C5—42no—
312C4×C5—52no—
313C4×C5—101no—
314C4×C5—101no—
315C4×C5—101no—
316C4×C5—101no—
317C4×C5—101no—
318C4×C5—101no—
319Dic5—21no—
320Dic5—21no—
321Dic5—21no—
322Dic5—21no—
323Dic5—21no—
324Dic5—21no—
325Dic5—52no—
326Dic5—52no—
327Dic5—104no—
328Dic5—104no—
329Dic5—101no—
330Dic5—101no—
331Dic5—101no—
332Dic5—101no—
333Dic5—101no—
334Dic5—101no—
335Dic5—202no—
336Dic5—202no—
337Dic5C2×Dic1012yes—
338C2×Q8—51no—
339C2×Q8—251no—
340C2×Q8—251no—
341C2×D4—51no—
342C22×C4—51no—
343C22×C4—251no—
344C22×C4—251no—
345C22×C4—251no—
346C22×C4—251no—
347C22×C4D5211yescharacteristic
348C4⋊C4—51no—
349C4⋊C4—51no—
350C4⋊C4—51no—
351C4⋊C4—51no—
352C4⋊C4—251no—
353C4⋊C4—251no—
354C4⋊C4—251no—
355C4⋊C4—251no—
356C4⋊C4—251no—
357C4⋊C4—251no—
358C4⋊C4—251no—
359C4⋊C4—251no—
360C4⋊C4—251no—
361C4⋊C4—251no—
362C4⋊C4—251no—
363C4⋊C4—251no—
364C22⋊C4—51no—
365C22⋊C4—51no—
366C22⋊C4—51no—
367C22⋊C4—51no—
368C22⋊C4—251no—
369C22⋊C4—251no—
370C42—51no—
371C42—251no—
372C42—251no—
373C2×C5—28no—
374C2×C5—22no—
375C2×C5—22no—
376C2×C5—22no—
377C2×C5—22no—
378C2×C5—22no—
379C2×C5—102no—
380C2×C5C22×Dic1011yescharacteristic
381C2×C5#414411yescharacteristic
382C2×C5#414411yescharacteristic
383C2×C5C2×Q8×D511yescharacteristic
384C2×C5D5×#4111yescharacteristic
385C2×C5D5×#4111yescharacteristic
386D5—22no—
387C23—51no—
388C23C2×D5211yescharacteristic
389Q8—201no—
390Q8—502no—
391Q8—1001no—
392D4—54no—
393C2×C4—41no—
394C2×C4—51no—
395C2×C4—51no—
396C2×C4—51no—
397C2×C4—51no—
398C2×C4—51no—
399C2×C4—51no—
400C2×C4—51no—
401C2×C4—201no—
402C2×C4—251no—
403C2×C4—251no—
404C2×C4—251no—
405C2×C4—251no—
406C2×C4—502no—
407C2×C4—502no—
408C2×C4—1001no—
409C2×C4—1001no—
410C2×C4C2×D5211yescharacteristic
411C2×C4C2×D5211yescharacteristic
412C5—22no—
413C5#6587311yescharacteristic, complemented
414C5#6597011yescharacteristic, complemented
415C22—21no—
416C22—21no—
417C22—52no—
418C22—101no—
419C22—101no—
420C22D5×Dic1012yes—
421C22C22×D5211yescharacteristic
422C4—21no—
423C4—21no—
424C4—52no—
425C4—101no—
426C4—101no—
427C4—101no—
428C4—101no—
429C4—101no—
430C4—101no—
431C4—252no—
432C4—501no—
433C4—501no—
434C4—501no—
435C2—22no—
436C2—102no—
437C2C2×D5×Dic1011yescharacteristic
438C2#1171747111yescharacteristic
439C2#1171749511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D52
commutator, socle, cosocleC22×C52C24
FittingC22×C4×C52C22
prime radicalC2×C5×C22⋊D5C22
hypercenterC22×C4D52
hypocenterC52#554
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×#87806C2semidirect
3. C5×#4070C2semidirect
4. #11717100C2semidirect
5. #11717100C2semidirect
8. #11717014C2semidirect
9. #11717006C2semidirect
10. D5×#683C2semidirect
11. #11716986C2semidirect
12. #11716969C2semidirect
13. #11716964C2semidirect
14. #11716957C2semidirect
15. #11716955C2semidirect
64. C5×C22⋊D5Q8semidirect
86. #4070D5semidirect
236. C22⋊D5Dic10semidirect
287. C52#554semidirect
413. C5#65873semidirect
414. C5#65970semidirect

Maximal subgroups

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

subgroupindex
C2×#878062
C4×C5×C22⋊D52
C5×#40702
#117171002
#117170912
#117170142
#117170062
D5×#6832
#117169862
#117169692
#117169642
#117169572
#117169552
#659705
#658735