Finite Group Databasebeta

← #13105152

Subgroups — #13105152

Order 1600.

528 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11717199C211yesmaximal, characteristic, complemented
2C5×#4030C211yesmaximal, characteristic
3C5×#4023C211yesmaximal, characteristic, complemented
4Dic5×C22⋊D5C211yesmaximal, characteristic, complemented
5Dic5×C22⋊D5C211yesmaximal, characteristic, complemented
6#11717087C211yesmaximal, characteristic, complemented
7#11717077C211yesmaximal, characteristic, complemented
8Dic5×D20C211yesmaximal, characteristic, complemented
9#11717002C211yesmaximal, characteristic, complemented
10#11716995C211yesmaximal, characteristic, complemented
11C4×D5×Dic5C211yesmaximal, characteristic, complemented
12#11716980C211yesmaximal, characteristic, complemented
13#11716969C211yesmaximal, characteristic, complemented
14#11716963C211yesmaximal, characteristic, complemented
15#11716955C211yesmaximal, characteristic, complemented
16C2×C5×C22⋊D5C2211yescharacteristic
17C2×C5×C22⋊D5C2211yescharacteristic
18C22×C5×Dic5C2211yescharacteristic
19C2×C5×D20C2211yescharacteristic
20C2×C4×C5×D5C2211yescharacteristic
21C2×#6039C2211yescharacteristic
22C2×D5×Dic5C2211yescharacteristic
23C2×D5×Dic5C2211yescharacteristic
24C2×D5×Dic5C2211yescharacteristic
25C52×C22⋊C4C2211yescharacteristic
26C22⋊#1039C2211yescharacteristic
27C22⋊#1039C2211yescharacteristic
28C4⋊#1039C2211yescharacteristic
29#87806C2211yescharacteristic
30#87806C2211yescharacteristic
31C4×#1039C2211yescharacteristic
32C5×C22⋊Dic5C2211yescharacteristic
33C5×#685C2211yescharacteristic
34C5×#683C2211yescharacteristic
35C5×#683C2211yescharacteristic
36C5×#683C2211yescharacteristic
37C4×C5×Dic5C2211yescharacteristic
38C4×C5×Dic5C2211yescharacteristic
39#87781C2211yescharacteristic
40#87780C2211yescharacteristic
41#87780C2211yescharacteristic
42#87780C2211yescharacteristic
43#87778C2211yescharacteristic
44#87778C2211yescharacteristic
45#87778C2211yescharacteristic
46#87778C2211yescharacteristic
47#87778C2211yescharacteristic
48Dic52C2211yescharacteristic
49Dic52C2211yescharacteristic
50Dic52C2211yescharacteristic
51#65934—51nomaximal
52#65862—51nomaximal
53C23×C52C2311yescharacteristic
54C22×C5×D5C2311yescharacteristic
55C22×C5×D5C2311yescharacteristic
56C2×C4×C52C2311yescharacteristic
57C2×C4×C52C2311yescharacteristic
58C2×#1039C2311yescharacteristic
59C2×#1039C2311yescharacteristic
60C2×#1039C2311yescharacteristic
61C2×#1039C2311yescharacteristic
62C5×C22⋊D5—22no—
63C5×C22⋊D5—22no—
64C2×C5×Dic5—22no—
65C2×C5×Dic5C2311yescharacteristic
66C2×C5×Dic5C2311yescharacteristic
67C2×C5×Dic5C2311yescharacteristic
68C2×C5×Dic5C2311yescharacteristic
69C2×C5×Dic5C2311yescharacteristic
70C2×C5×Dic5C2311yescharacteristic
71C5×D20—22no—
72C4×C5×D5—22no—
73#6039—22no—
74D5×Dic5—22no—
75D5×Dic5—22no—
76D5×Dic5—22no—
77C5×#121—51no—
78C5×#117—51no—
79#4082—51no—
80#4081—51no—
81#4081—51no—
82D4×Dic5—51no—
83D4×Dic5—51no—
84D4×Dic5—51no—
85C4×C22⋊D5—51no—
86C4×C22⋊D5—51no—
87#4070—51no—
88C2×C4×Dic5—51no—
89#4044—51no—
90#4042—51no—
91#4040—51no—
92#4036—51no—
93#4035—51no—
94#4033—51no—
95#4031—51no—
96#4030D511yescharacteristic
97#4029—51no—
98#4025—51no—
99#4025—51no—
100#4025—51no—
101#4025—102no—
102#4023—51no—
103#4023D511yescharacteristic, complemented
104C4×D20—51no—
105#4018—51no—
106C42×D5—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—21no—
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#4112yes—
129C5×Dic5#4112yes—
130C2×C5×D4—51no—
131C2×C5×D4—51no—
132C2×C5×D4—51no—
133C22×C4×C5—51no—
134C22×C4×C5—51no—
135C2×C22⋊D5C2×D511yescharacteristic
136C2×C22⋊D5C2×D511yescharacteristic
137C22×Dic5—51no—
138C22×Dic5—51no—
139C22×Dic5—51no—
140C22×Dic5C2×D511yescharacteristic
141C2×D20C2×D511yescharacteristic
142C2×C4×D5—51no—
143C2×C4×D5—51no—
144C2×C4×D5—51no—
145C2×C4×D5C2×D511yescharacteristic
146C2×Dic10—51no—
147C2×Dic10—51no—
148C5×C4⋊C4—51no—
149C5×C4⋊C4—51no—
150C5×C4⋊C4—51no—
151C5×C22⋊C4—22no—
152C5×C22⋊C4—51no—
153C5×C22⋊C4—51no—
154C5×C22⋊C4C2×D511yescharacteristic
155C5×C22⋊C4C2×D511yescharacteristic
156C42×C5—51no—
157C42×C5—51no—
158C22⋊Dic5—51no—
159C22⋊Dic5—51no—
160C22⋊Dic5—51no—
161C22⋊Dic5—51no—
162C22⋊Dic5—51no—
163C22⋊Dic5—51no—
164C22⋊Dic5—51no—
165C22⋊Dic5—51no—
166C22⋊Dic5—51no—
167C22⋊Dic5—102no—
168C22⋊Dic5—102no—
169C22⋊Dic5C2×D511yescharacteristic
170#685—51no—
171#685—51no—
172#685—51no—
173#685—51no—
174#685—51no—
175#685C2×D511yescharacteristic
176C4⋊Dic5—51no—
177C4⋊Dic5—51no—
178C4⋊Dic5—51no—
179C4⋊Dic5—51no—
180C4⋊Dic5—51no—
181C4⋊Dic5—102no—
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—102no—
192#683—102no—
193#683C2×D511yescharacteristic
194#683C2×D511yescharacteristic
195#683C2×D511yescharacteristic
196C4×Dic5—51no—
197C4×Dic5—51no—
198C4×Dic5—51no—
199C4×Dic5—51no—
200C4×Dic5—51no—
201C4×Dic5—51no—
202C4×Dic5—51no—
203C4×Dic5—51no—
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—
223C5×D4—102no—
224C2×C4×C5—22no—
225C2×C4×C5—22no—
226C2×C4×C5—51no—
227C2×C4×C5—51no—
228C2×C4×C5—51no—
229C2×C4×C5—51no—
230C2×C4×C5—51no—
231C2×C4×C5—51no—
232C2×C4×C5—102no—
233C2×C4×C5—102no—
234C2×C4×C5C22×D511yescharacteristic
235C2×C4×C5C22×D511yescharacteristic
236C2×C4×C5C22×D511yescharacteristic
237C2×C4×C5C22×D511yescharacteristic
238C22⋊D5—22no—
239C22⋊D5—22no—
240C2×Dic5—22no—
241C2×Dic5—51no—
242C2×Dic5—51no—
243C2×Dic5—51no—
244C2×Dic5—51no—
245C2×Dic5—51no—
246C2×Dic5—51no—
247C2×Dic5—51no—
248C2×Dic5—51no—
249C2×Dic5—102no—
250C2×Dic5—102no—
251C2×Dic5—102no—
252C2×Dic5—102no—
253C2×Dic5—102no—
254C2×Dic5—102no—
255C2×Dic5—102no—
256C2×Dic5C22×D511yescharacteristic
257C2×Dic5C22×D511yescharacteristic
258C2×Dic5C22×D511yescharacteristic
259C2×Dic5C22×D511yescharacteristic
260C2×Dic5C22×D511yescharacteristic
261C2×Dic5C22×D511yescharacteristic
262D20—22no—
263C4×D5—22no—
264C4×D5—102no—
265C4×D5—102no—
266C4×D5—102no—
267Dic10—102no—
268Dic10—102no—
269#126—251no—
270#126—251no—
271#125—251no—
272#124—251no—
273#123—251no—
274#123—251no—
275C22⋊Q8—251no—
276#121—51no—
277C4×Q8—251no—
278C4×D4—251no—
279C4×D4—251no—
280C4×D4—251no—
281#117—51no—
282#117—251no—
283C2×C42—251no—
284C52#52911yescharacteristic, complemented, Sylow
285C22×C5—21no—
286C22×C5—21no—
287C22×C5—21no—
288C22×C5—21no—
289C22×C5—21no—
290C22×C5—21no—
291C22×C5—22no—
292C22×C5—42no—
293C22×C5—42no—
294C22×C5—42no—
295C22×C5—52no—
296C22×C5—101no—
297C22×C5—101no—
298C22×C5—101no—
299C22×C5—101no—
300C22×C5—101no—
301C22×C5C23×D511yescharacteristic
302C22×C5C23×D511yescharacteristic
303C2×D5—21no—
304C2×D5—21no—
305C2×D5—21no—
306C2×D5—21no—
307C2×D5—21no—
308C2×D5#71112yes—
309C4×C5—21no—
310C4×C5—21no—
311C4×C5—21no—
312C4×C5—21no—
313C4×C5—42no—
314C4×C5—42no—
315C4×C5—52no—
316C4×C5—52no—
317C4×C5—101no—
318C4×C5—101no—
319C4×C5—101no—
320C4×C5—101no—
321Dic5—21no—
322Dic5—21no—
323Dic5—21no—
324Dic5—21no—
325Dic5—101no—
326Dic5—101no—
327Dic5—101no—
328Dic5—101no—
329Dic5—101no—
330Dic5—101no—
331Dic5—101no—
332Dic5—101no—
333Dic5—202no—
334Dic5—202no—
335Dic5—202no—
336Dic5—202no—
337Dic5#70912yes—
338Dic5#71112yes—
339C2×Q8—251no—
340C2×D4—51no—
341C2×D4—51no—
342C2×D4—51no—
343C22×C4—51no—
344C22×C4—51no—
345C22×C4—251no—
346C22×C4—251no—
347C22×C4—251no—
348C4⋊C4—51no—
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—
358C22⋊C4—51no—
359C22⋊C4—51no—
360C22⋊C4—251no—
361C22⋊C4—251no—
362C22⋊C4—251no—
363C22⋊C4—251no—
364C22⋊C4—251no—
365C22⋊C4—251no—
366C22⋊C4—251no—
367C22⋊C4D5211yescharacteristic
368C42—51no—
369C42—51no—
370C42—251no—
371C42—251no—
372C42—251no—
373C42—251no—
374C2×C5—22no—
375C2×C5—22no—
376C2×C5—22no—
377C2×C5—41no—
378C2×C5—41no—
379C2×C5—82no—
380C2×C5—102no—
381C2×C5—201no—
382C2×C5C2×#70911yescharacteristic
383C2×C5C2×#71111yescharacteristic
384C2×C5C2×#71111yescharacteristic
385C2×C5D5×#4111yescharacteristic
386C2×C5D5×#4111yescharacteristic
387C2×C5D5×#4111yescharacteristic
388D5—22no—
389D5—41no—
390C23—51no—
391C23—51no—
392C23C2×D5211yescharacteristic
393Q8—502no—
394D4—102no—
395D4—102no—
396D4—102no—
397C2×C4—51no—
398C2×C4—51no—
399C2×C4—51no—
400C2×C4—51no—
401C2×C4—51no—
402C2×C4—51no—
403C2×C4—102no—
404C2×C4—102no—
405C2×C4—251no—
406C2×C4—251no—
407C2×C4—251no—
408C2×C4—251no—
409C2×C4—502no—
410C2×C4—502no—
411C2×C4—502no—
412C2×C4C2×D5211yescharacteristic
413C2×C4C2×D5211yescharacteristic
414C5—22no—
415C5#6586211yescharacteristic, complemented
416C5#6593411yescharacteristic, complemented
417C22—21no—
418C22—21no—
419C22—21no—
420C22—52no—
421C22—101no—
422C22—101no—
423C22—101no—
424C22—101no—
425C22—101no—
426C22C22×D5211yescharacteristic
427C4—21no—
428C4—21no—
429C4—52no—
430C4—52no—
431C4—101no—
432C4—101no—
433C4—101no—
434C4—101no—
435C4—501no—
436C4—501no—
437C4—501no—
438C4—501no—
439C2—41no—
440C2—102no—
441C2—201no—
442C2D5×#70911yescharacteristic
443C2D5×#71111yescharacteristic
444C2D5×#71111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D52
commutator, socle, cosocleC22×C52C24
FittingC52×C22⋊C4C22
prime radicalC5×#4030C2
hypercenterC22⋊C4D52
hypocenterC52#529
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #11717199C2semidirect
3. C5×#4023C2semidirect
4. Dic5×C22⋊D5C2semidirect
5. Dic5×C22⋊D5C2semidirect
6. #11717087C2semidirect
7. #11717077C2semidirect
8. Dic5×D20C2semidirect
9. #11717002C2semidirect
10. #11716995C2semidirect
11. C4×D5×Dic5C2semidirect
12. #11716980C2semidirect
13. #11716969C2semidirect
14. #11716963C2semidirect
15. #11716955C2semidirect
103. #4023D5semidirect
284. C52#529semidirect
415. C5#65862semidirect
416. C5#65934semidirect

Maximal subgroups

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

subgroupindex
#117171992
C5×#40302
C5×#40232
Dic5×C22⋊D52
#117170872
#117170772
Dic5×D202
#117170022
#117169952
C4×D5×Dic52
#117169802
#117169692
#117169632
#117169552
#659345
#658625