Finite Group Databasebeta

← #13105994

Subgroups — #13105994

Order 1600.

544 conjugacy classes of subgroups.

The subgroup lattice has 447 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11717246C211yesmaximal, characteristic, complemented
2C4×C5×C22⋊D5C211yesmaximal, characteristic, complemented
3C4×C5×C22⋊D5C211yesmaximal, characteristic, complemented
4#11717088C211yesmaximal, characteristic
5#11717087C211yesmaximal, characteristic, complemented
6#11717077C211yesmaximal, characteristic, complemented
7#11717074C211yesmaximal, characteristic, complemented
8C4×#6039C211yesmaximal, characteristic, complemented
9C4×#6037C211yesmaximal, characteristic, complemented
10#11717007C211yesmaximal, characteristic, complemented
11#11717003C211yesmaximal, characteristic, complemented
12C4×D5×Dic5C211yesmaximal, characteristic, complemented
13#11716977C211yesmaximal, characteristic, complemented
14#11716973C211yesmaximal, characteristic, complemented
15#11716963C211yesmaximal, characteristic, complemented
16C22×C4×C52C2211yescharacteristic
17C2×C5×C22⋊D5C2211yescharacteristic
18C2×C5×C22⋊D5C2211yescharacteristic
19C2×C4×C5×D5C2211yescharacteristic
20C2×C4×C5×D5C2211yescharacteristic
21C2×#6039C2211yescharacteristic
22C2×#6037C2211yescharacteristic
23C2×D5×Dic5C2211yescharacteristic
24C2×D5×Dic5C2211yescharacteristic
25C22⋊#1039C2211yescharacteristic
26C22⋊#1039C2211yescharacteristic
27C4⋊#1039C2211yescharacteristic
28C4⋊#1039C2211yescharacteristic
29C4×#1039C2211yescharacteristic
30C4×#1039C2211yescharacteristic
31C5×C22⋊Dic5C2211yescharacteristic
32C5×C22⋊Dic5C2211yescharacteristic
33C5×#685C2211yescharacteristic
34C5×#685C2211yescharacteristic
35C5×#683C2211yescharacteristic
36C5×#683C2211yescharacteristic
37C4×C5×Dic5C2211yescharacteristic
38C4×C5×Dic5C2211yescharacteristic
39#87781C2211yescharacteristic
40#87781C2211yescharacteristic
41#87780C2211yescharacteristic
42#87780C2211yescharacteristic
43#87780C2211yescharacteristic
44#87780C2211yescharacteristic
45#87778C2211yescharacteristic
46#87778C2211yescharacteristic
47#87778C2211yescharacteristic
48#87778C2211yescharacteristic
49Dic52C2211yescharacteristic
50Dic52C2211yescharacteristic
51#65891—51nomaximal
52#65872—51nomaximal
53C23×C52C2311yescharacteristic
54C22×C5×D5C2311yescharacteristic
55C22×C5×D5C2311yescharacteristic
56C2×C4×C52—22no—
57C2×C4×C52C2311yescharacteristic
58C2×C4×C52C2311yescharacteristic
59C2×#1039C2311yescharacteristic
60C2×#1039C2311yescharacteristic
61C2×#1039C2311yescharacteristic
62C2×#1039C2311yescharacteristic
63C5×C22⋊D5—22no—
64C5×C22⋊D5—22no—
65C2×C5×Dic5C2311yescharacteristic
66C2×C5×Dic5C2311yescharacteristic
67C2×C5×Dic5C2311yescharacteristic
68C2×C5×Dic5C2311yescharacteristic
69C2×C5×Dic5C2311yescharacteristic
70C2×C5×Dic5C2311yescharacteristic
71C4×C5×D5—22no—
72C4×C5×D5—22no—
73#6039—22no—
74#6037—22no—
75D5×Dic5—22no—
76D5×Dic5—22no—
77C4×C5×D4—51no—
78C4×C5×D4—51no—
79#4085—51no—
80#4084—51no—
81#4082—51no—
82#4081—51no—
83C4×C22⋊D5—51no—
84C4×C22⋊D5—51no—
85C4×C22⋊D5D511yescharacteristic, complemented
86C4×C22⋊D5D511yescharacteristic, complemented
87#4072—51no—
88#4072—51no—
89#4072—51no—
90#4072—102no—
91C2×C4×Dic5—51no—
92#4044—51no—
93#4043—51no—
94#4036—51no—
95#4035—51no—
96#4032—51no—
97#4031—51no—
98#4029—51no—
99#4029—51no—
100#4025—51no—
101#4025—51no—
102#4025—51no—
103#4024—51no—
104#4018—51no—
105C42×D5—51no—
106C4×Dic10—51no—
107C4×Dic10—51no—
108C22×C52—21no—
109C22×C52—21no—
110C22×C52—21no—
111C22×C52C2411yescharacteristic
112C2×C5×D5—21no—
113C2×C5×D5—21no—
114C2×C5×D5—21no—
115C2×C5×D5—21no—
116C2×C5×D5—21no—
117C2×C5×D5#4112yes—
118C4×C52—21no—
119C4×C52#4112yes—
120#1039—21no—
121#1039—21no—
122#1039—21no—
123#1039—21no—
124C5×Dic5—21no—
125C5×Dic5—21no—
126C5×Dic5—21no—
127C5×Dic5—21no—
128C5×Dic5—21no—
129C5×Dic5#4112yes—
130C2×C5×D4—51no—
131C2×C5×D4—51no—
132C22×C4×C5—22no—
133C22×C4×C5—51no—
134C22×C4×C5—51no—
135C22×C4×C5C2×D511yescharacteristic
136C22×C4×C5C2×D511yescharacteristic
137C2×C22⋊D5—51no—
138C2×C22⋊D5—51no—
139C2×C22⋊D5C2×D511yescharacteristic
140C2×C22⋊D5C2×D511yescharacteristic
141C22×Dic5—51no—
142C22×Dic5—51no—
143C2×C4×D5—51no—
144C2×C4×D5—51no—
145C2×C4×D5C2×D511yescharacteristic
146C2×C4×D5C2×D511yescharacteristic
147C2×Dic10—51no—
148C2×Dic10—51no—
149C5×C4⋊C4—51no—
150C5×C4⋊C4—51no—
151C5×C22⋊C4—51no—
152C5×C22⋊C4—51no—
153C5×C22⋊C4—51no—
154C5×C22⋊C4—51no—
155C42×C5—51no—
156C42×C5—51no—
157C22⋊Dic5—51no—
158C22⋊Dic5—51no—
159C22⋊Dic5—51no—
160C22⋊Dic5—51no—
161C22⋊Dic5—51no—
162C22⋊Dic5—51no—
163C22⋊Dic5—51no—
164C22⋊Dic5—51no—
165C22⋊Dic5—102no—
166C22⋊Dic5—102no—
167C22⋊Dic5C2×D511yescharacteristic
168C22⋊Dic5C2×D511yescharacteristic
169#685—51no—
170#685—51no—
171#685—51no—
172#685—51no—
173#685C2×D511yescharacteristic
174#685C2×D511yescharacteristic
175C4⋊Dic5—51no—
176C4⋊Dic5—51no—
177C4⋊Dic5—51no—
178C4⋊Dic5—51no—
179C4⋊Dic5—51no—
180C4⋊Dic5—51no—
181C4⋊Dic5—51no—
182C4⋊Dic5—51no—
183C4⋊Dic5—102no—
184C4⋊Dic5—102no—
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#683C2×D511yescharacteristic
194#683C2×D511yescharacteristic
195C4×Dic5—51no—
196C4×Dic5—51no—
197C4×Dic5—51no—
198C4×Dic5—51no—
199C4×Dic5—51no—
200C4×Dic5—51no—
201C4×Dic5—51no—
202C4×Dic5—51no—
203C4×Dic5—102no—
204C4×Dic5—102no—
205C4×Dic5C2×D511yescharacteristic
206C4×Dic5C2×D511yescharacteristic
207#529—251noSylow
208C2×C52—41no—
209C2×C52C2×#4111yescharacteristic
210C2×C52C2×#4111yescharacteristic
211C2×C52C2×#4111yescharacteristic
212C5×D5—22no—
213C5×D5—41no—
214C23×C5—22no—
215C23×C5—51no—
216C23×C5—51no—
217C23×C5C22×D511yescharacteristic
218C23×C5C22×D511yescharacteristic
219C22×D5C22×D511yescharacteristic
220C22×D5C22×D511yescharacteristic
221C5×D4—102no—
222C5×D4—102no—
223C2×C4×C5—28no—
224C2×C4×C5—22no—
225C2×C4×C5—22no—
226C2×C4×C5—22no—
227C2×C4×C5—22no—
228C2×C4×C5—51no—
229C2×C4×C5—51no—
230C2×C4×C5—51no—
231C2×C4×C5—51no—
232C2×C4×C5—51no—
233C2×C4×C5—51no—
234C2×C4×C5—102no—
235C2×C4×C5—102no—
236C2×C4×C5C22×D511yescharacteristic
237C2×C4×C5C22×D511yescharacteristic
238C2×C4×C5C22×D511yescharacteristic
239C2×C4×C5C22×D511yescharacteristic
240C22⋊D5—22no—
241C22⋊D5—22no—
242C22⋊D5—102no—
243C22⋊D5—102no—
244C2×Dic5—51no—
245C2×Dic5—51no—
246C2×Dic5—51no—
247C2×Dic5—51no—
248C2×Dic5—51no—
249C2×Dic5—51no—
250C2×Dic5—51no—
251C2×Dic5—51no—
252C2×Dic5—102no—
253C2×Dic5—102no—
254C2×Dic5—102no—
255C2×Dic5—102no—
256C2×Dic5—102no—
257C2×Dic5—102no—
258C2×Dic5C22×D511yescharacteristic
259C2×Dic5C22×D511yescharacteristic
260C2×Dic5C22×D511yescharacteristic
261C2×Dic5C22×D511yescharacteristic
262C2×Dic5C22×D511yescharacteristic
263C2×Dic5C22×D511yescharacteristic
264C4×D5—22no—
265C4×D5—22no—
266C4×D5—102no—
267C4×D5—102no—
268Dic10—102no—
269Dic10—102no—
270#126—251no—
271#126—251no—
272#125—251no—
273#124—251no—
274#123—251no—
275#123—251no—
276C22⋊Q8—251no—
277#121—251no—
278C4×Q8—251no—
279C4×D4—51no—
280C4×D4—51no—
281C4×D4—251no—
282#117—251no—
283#117—251no—
284C2×C42—251no—
285C52#52911yescharacteristic, complemented, Sylow
286C22×C5—24no—
287C22×C5—21no—
288C22×C5—21no—
289C22×C5—21no—
290C22×C5—21no—
291C22×C5—21no—
292C22×C5—21no—
293C22×C5—22no—
294C22×C5—42no—
295C22×C5—42no—
296C22×C5—52no—
297C22×C5—101no—
298C22×C5—101no—
299C22×C5—101no—
300C22×C5—101no—
301C22×C5—101no—
302C22×C5C23×D511yescharacteristic
303C22×C5C23×D511yescharacteristic
304C2×D5—21no—
305C2×D5—21no—
306C2×D5—21no—
307C2×D5—21no—
308C2×D5—21no—
309C2×D5#70912yes—
310C4×C5—24no—
311C4×C5—21no—
312C4×C5—21no—
313C4×C5—24no—
314C4×C5—52no—
315C4×C5—101no—
316C4×C5—101no—
317C4×C5—101no—
318C4×C5—101no—
319C4×C5—101no—
320C4×C5#71112yes—
321C4×C5#71112yes—
322Dic5—21no—
323Dic5—21no—
324Dic5—21no—
325Dic5—21no—
326Dic5—21no—
327Dic5—101no—
328Dic5—101no—
329Dic5—101no—
330Dic5—101no—
331Dic5—101no—
332Dic5—101no—
333Dic5—101no—
334Dic5—101no—
335Dic5—202no—
336Dic5—202no—
337Dic5—202no—
338Dic5—202no—
339Dic5#70912yes—
340C2×Q8—251no—
341C2×D4—51no—
342C2×D4—51no—
343C2×D4—251no—
344C22×C4—51no—
345C22×C4—51no—
346C22×C4—251no—
347C22×C4—251no—
348C22×C4D5211yescharacteristic
349C4⋊C4—51no—
350C4⋊C4—51no—
351C4⋊C4—251no—
352C4⋊C4—251no—
353C4⋊C4—251no—
354C4⋊C4—251no—
355C4⋊C4—251no—
356C4⋊C4—251no—
357C4⋊C4—251no—
358C4⋊C4—251no—
359C22⋊C4—51no—
360C22⋊C4—51no—
361C22⋊C4—51no—
362C22⋊C4—51no—
363C22⋊C4—251no—
364C22⋊C4—251no—
365C22⋊C4—251no—
366C22⋊C4—251no—
367C22⋊C4—251no—
368C22⋊C4—251no—
369C42—51no—
370C42—51no—
371C42—251no—
372C42—251no—
373C42—251no—
374C42—251no—
375C2×C5—22no—
376C2×C5—22no—
377C2×C5—22no—
378C2×C5—44no—
379C2×C5—41no—
380C2×C5—41no—
381C2×C5—102no—
382C2×C5—201no—
383C2×C5C2×#70911yescharacteristic
384C2×C5C2×#70911yescharacteristic
385C2×C5C2×#71111yescharacteristic
386C2×C5C2×#71111yescharacteristic
387C2×C5D5×#4111yescharacteristic
388C2×C5D5×#4111yescharacteristic
389D5—22no—
390D5—41no—
391C23—51no—
392C23—51no—
393C23C2×D5211yescharacteristic
394Q8—502no—
395D4—102no—
396D4—102no—
397D4—502no—
398C2×C4—22no—
399C2×C4—51no—
400C2×C4—51no—
401C2×C4—51no—
402C2×C4—51no—
403C2×C4—51no—
404C2×C4—51no—
405C2×C4—102no—
406C2×C4—102no—
407C2×C4—251no—
408C2×C4—251no—
409C2×C4—251no—
410C2×C4—251no—
411C2×C4—502no—
412C2×C4—502no—
413C2×C4C2×D5211yescharacteristic
414C2×C4C2×D5211yescharacteristic
415C5—22no—
416C5#6587211yescharacteristic, complemented
417C5#6589111yescharacteristic, complemented
418C22—21no—
419C22—21no—
420C22—21no—
421C22—52no—
422C22—101no—
423C22—101no—
424C22—101no—
425C22—101no—
426C22—101no—
427C22C22×D5211yescharacteristic
428C4—21no—
429C4—52no—
430C4—101no—
431C4—101no—
432C4—101no—
433C4—101no—
434C4—101no—
435C4—501no—
436C4—501no—
437C4—501no—
438C4—501no—
439C4#8788012yes—
440C2—41no—
441C2—102no—
442C2—201no—
443C2D5×#70911yescharacteristic
444C2D5×#70911yescharacteristic
445C2C2×#8788011yescharacteristic
subgroupG/H
centerC2×C4C2×D52
commutator, socle, cosocleC22×C52C24
FrattiniC22C22×D52
FittingC22×C4×C52C22
prime radical#11717088C2
hypercenterC22×C4D52
hypocenterC52#529
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. #11717246C2semidirect
2. C4×C5×C22⋊D5C2semidirect
3. C4×C5×C22⋊D5C2semidirect
5. #11717087C2semidirect
6. #11717077C2semidirect
7. #11717074C2semidirect
8. C4×#6039C2semidirect
9. C4×#6037C2semidirect
10. #11717007C2semidirect
11. #11717003C2semidirect
12. C4×D5×Dic5C2semidirect
13. #11716977C2semidirect
14. #11716973C2semidirect
15. #11716963C2semidirect
85. C4×C22⋊D5D5semidirect
86. C4×C22⋊D5D5semidirect
285. C52#529semidirect
416. C5#65872semidirect
417. C5#65891semidirect

Maximal subgroups

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

subgroupindex
#117172462
C4×C5×C22⋊D52
#117170882
#117170872
#117170772
#117170742
C4×#60392
C4×#60372
#117170072
#117170032
C4×D5×Dic52
#117169772
#117169732
#117169632
#658915
#658725