Finite Group Databasebeta

← #13105516

Subgroups — #13105516

Order 1600.

520 conjugacy classes of subgroups.

The subgroup lattice has 425 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4⋊C4×C5⋊D5C211yesmaximal, characteristic, complemented
2C5×#4044C211yesmaximal, characteristic, complemented
3C5×#4035C211yesmaximal, characteristic, complemented
4#11717014C211yesmaximal, characteristic, complemented
5#11716999C211yesmaximal, characteristic
6#11716995C211yesmaximal, characteristic, complemented
7#11716992C211yesmaximal, characteristic, complemented
8#11716984C211yesmaximal, characteristic, complemented
9#11716977C211yesmaximal, characteristic, complemented
10#11716971C211yesmaximal, characteristic
11#11716971C211yesmaximal, characteristic
12#11716967C211yesmaximal, characteristic, complemented
13#11716965C211yesmaximal, characteristic, complemented
14#11716963C211yesmaximal, characteristic, complemented
15#11716955C211yesmaximal, characteristic, complemented
16C2×C4×C5⋊D5C2211yescharacteristic
17C2×C4×C5⋊D5C2211yescharacteristic
18C2×C4×C5⋊D5C2211yescharacteristic
19C2×#6039C2211yescharacteristic
20C2×#6038C2211yescharacteristic
21C2×D5×Dic5C2211yescharacteristic
22C52×C4⋊C4C2211yescharacteristic
23C4⋊#1039C2211yescharacteristic
24#87806C2211yescharacteristic
25#87806C2211yescharacteristic
26C5×#685C2211yescharacteristic
27C5×#685C2211yescharacteristic
28C5×#685C2211yescharacteristic
29C5×C4⋊Dic5C2211yescharacteristic
30C5×C4⋊Dic5C2211yescharacteristic
31C5×#683C2211yescharacteristic
32C5×#683C2211yescharacteristic
33C5×#683C2211yescharacteristic
34C5×#683C2211yescharacteristic
35C5×#683C2211yescharacteristic
36C4×C5×Dic5C2211yescharacteristic
37C4×C5×Dic5C2211yescharacteristic
38#87781C2211yescharacteristic
39#87781C2211yescharacteristic
40#87781C2211yescharacteristic
41#87780C2211yescharacteristic
42#87780C2211yescharacteristic
43#87779C2211yescharacteristic
44#87779C2211yescharacteristic
45#87779C2211yescharacteristic
46#87778C2211yescharacteristic
47#87778C2211yescharacteristic
48Dic52C2211yescharacteristic
49Dic52C2211yescharacteristic
50Dic52C2211yescharacteristic
51#66042—51nomaximal
52#66027—51nomaximal
53C22×C5⋊D5C2311yescharacteristic
54C22×C5×D5C2311yescharacteristic
55C2×C4×C52C2311yescharacteristic
56C2×C4×C52C2311yescharacteristic
57C2×C4×C52C2311yescharacteristic
58C2×#1039C2311yescharacteristic
59C2×#1039C2311yescharacteristic
60C2×#1039C2311yescharacteristic
61C4×C5⋊D5—22no—
62C4×C5⋊D5—22no—
63C4×C5⋊D5—22no—
64C2×C5×Dic5C2311yescharacteristic
65C2×C5×Dic5C2311yescharacteristic
66C2×C5×Dic5C2311yescharacteristic
67C2×C5×Dic5C2311yescharacteristic
68C2×C5×Dic5C2311yescharacteristic
69C2×C5×Dic5C2311yescharacteristic
70C2×C5×Dic5C2311yescharacteristic
71#6039—22no—
72#6038—22no—
73D5×Dic5—22no—
74C5×#126—51no—
75C5×#125—51no—
76#4044—51no—
77#4044D511yescharacteristic, complemented
78#4042—51no—
79#4042—51no—
80#4042—51no—
81#4040—51no—
82#4040—51no—
83#4039—51no—
84#4038—51no—
85#4038—51no—
86D5×C4⋊C4—51no—
87D5×C4⋊C4—51no—
88D5×C4⋊C4—102no—
89#4036—51no—
90#4035—51no—
91#4035—51no—
92#4035—51no—
93#4035D511yescharacteristic, complemented
94#4033—51no—
95#4029—51no—
96#4029—51no—
97#4027—51no—
98#4025—51no—
99#4024—51no—
100#4023—51no—
101#4018—51no—
102#4018—51no—
103#4018—51no—
104C4×Dic10—51no—
105C22×C52C2411yescharacteristic
106C2×C5⋊D5—21no—
107C2×C5⋊D5—21no—
108C2×C5⋊D5#4112yes—
109C2×C5×D5—21no—
110C2×C5×D5—21no—
111C2×C5×D5—21no—
112C4×C52—21no—
113C4×C52—21no—
114C4×C52—21no—
115#1039—21no—
116#1039—21no—
117#1039#4112yes—
118C5×Dic5—21no—
119C5×Dic5—21no—
120C5×Dic5—21no—
121C5×Dic5—21no—
122C5×Dic5—21no—
123C5×Dic5—21no—
124C5×Dic5—21no—
125C2×C22⋊D5—51no—
126C22×Dic5—51no—
127C2×D20—51no—
128C2×C4×D5—51no—
129C2×C4×D5—51no—
130C2×C4×D5—51no—
131C2×C4×D5—51no—
132C2×C4×D5—51no—
133C2×C4×D5—51no—
134C2×C4×D5—51no—
135C2×C4×D5—102no—
136C2×C4×D5—102no—
137C2×C4×D5—102no—
138C2×Dic10—51no—
139C2×Dic10—51no—
140C5×C4⋊C4—22no—
141C5×C4⋊C4—51no—
142C5×C4⋊C4—51no—
143C5×C4⋊C4—51no—
144C5×C4⋊C4—51no—
145C5×C4⋊C4—51no—
146C5×C4⋊C4—51no—
147C5×C4⋊C4—51no—
148C5×C4⋊C4C2×D511yescharacteristic
149C5×C4⋊C4C2×D511yescharacteristic
150C5×C22⋊C4—51no—
151C5×C22⋊C4—51no—
152C5×C22⋊C4—51no—
153C42×C5—51no—
154C42×C5—51no—
155C22⋊Dic5—51no—
156C22⋊Dic5—51no—
157#685—51no—
158#685—51no—
159#685—51no—
160#685—51no—
161#685—51no—
162#685—51no—
163#685—51no—
164#685—51no—
165#685C2×D511yescharacteristic
166#685C2×D511yescharacteristic
167#685C2×D511yescharacteristic
168C4⋊Dic5—51no—
169C4⋊Dic5—51no—
170C4⋊Dic5—51no—
171C4⋊Dic5—51no—
172C4⋊Dic5—102no—
173C4⋊Dic5C2×D511yescharacteristic
174C4⋊Dic5C2×D511yescharacteristic
175#683—51no—
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—102no—
188#683—102no—
189#683C2×D511yescharacteristic
190#683C2×D511yescharacteristic
191#683C2×D511yescharacteristic
192#683C2×D511yescharacteristic
193#683C2×D511yescharacteristic
194C4×Dic5—51no—
195C4×Dic5—51no—
196C4×Dic5—51no—
197C4×Dic5—51no—
198C4×Dic5—51no—
199C4×Dic5—51no—
200C4×Dic5C2×D511yescharacteristic
201C4×Dic5C2×D511yescharacteristic
202#552—251noSylow
203C2×C52C2×#4111yescharacteristic
204C2×C52C2×#4111yescharacteristic
205C2×C522−1+411yescharacteristic
206C5⋊D5—22no—
207C5×D5—41no—
208C23×C5—51no—
209C22×D5—51no—
210C22×D5—51no—
211C22×D5—102no—
212C22×D5C22×D511yescharacteristic
213C2×C4×C5—22no—
214C2×C4×C5—22no—
215C2×C4×C5—22no—
216C2×C4×C5—51no—
217C2×C4×C5—51no—
218C2×C4×C5—51no—
219C2×C4×C5—51no—
220C2×C4×C5—51no—
221C2×C4×C5—51no—
222C2×C4×C5—51no—
223C2×C4×C5C22×D511yescharacteristic
224C2×C4×C5C22×D511yescharacteristic
225C2×C4×C5C22×D511yescharacteristic
226C2×C4×C5C22×D511yescharacteristic
227C2×C4×C5C22×D511yescharacteristic
228C2×C4×C5C22×D511yescharacteristic
229C22⋊D5—102no—
230C2×Dic5—51no—
231C2×Dic5—51no—
232C2×Dic5—51no—
233C2×Dic5—51no—
234C2×Dic5—51no—
235C2×Dic5—51no—
236C2×Dic5—102no—
237C2×Dic5—102no—
238C2×Dic5—102no—
239C2×Dic5—102no—
240C2×Dic5C22×D511yescharacteristic
241C2×Dic5C22×D511yescharacteristic
242C2×Dic5C22×D511yescharacteristic
243C2×Dic5C22×D511yescharacteristic
244C2×Dic5C22×D511yescharacteristic
245C2×Dic5C22×D511yescharacteristic
246C2×Dic5C22×D511yescharacteristic
247D20—102no—
248C4×D5—102no—
249C4×D5—102no—
250C4×D5—102no—
251C4×D5—102no—
252C4×D5—102no—
253C4×D5—102no—
254C4×D5—102no—
255C4×D5—108no—
256C4×D5—204no—
257C4×D5—204no—
258Dic10—102no—
259Dic10—102no—
260#126—51no—
261#126—251no—
262#125—51no—
263#125—251no—
264#125—251no—
265#123—251no—
266#123—251no—
267C22⋊Q8—251no—
268C22⋊Q8—251no—
269C4×Q8—251no—
270C4×D4—251no—
271#117—251no—
272#117—251no—
273#117—251no—
274C2×C4⋊C4—251no—
275C52#55211yescharacteristic, complemented, Sylow
276C22×C5—22no—
277C22×C5—101no—
278C22×C5—101no—
279C22×C5—101no—
280C22×C5C23×D511yescharacteristic
281C22×C5C23×D511yescharacteristic
282C2×D5—21no—
283C2×D5—21no—
284C2×D5—21no—
285C2×D5—52no—
286C2×D5—52no—
287C2×D5—104no—
288C2×D5—104no—
289C2×D5—104no—
290C2×D5—101no—
291C2×D5—101no—
292C2×D5—101no—
293C2×D5—101no—
294C4×C5—24no—
295C4×C5—21no—
296C4×C5—21no—
297C4×C5—21no—
298C4×C5—21no—
299C4×C5—21no—
300C4×C5—21no—
301C4×C5—42no—
302C4×C5—42no—
303C4×C5—101no—
304C4×C5—101no—
305C4×C5—101no—
306C4×C5—101no—
307C4×C5—101no—
308C4×C5—101no—
309C4×C5—101no—
310Dic5—21no—
311Dic5—21no—
312Dic5—21no—
313Dic5—21no—
314Dic5—21no—
315Dic5—21no—
316Dic5—21no—
317Dic5—52no—
318Dic5—52no—
319Dic5—104no—
320Dic5—101no—
321Dic5—101no—
322Dic5—101no—
323Dic5—101no—
324Dic5—202no—
325Dic5—202no—
326C2×Q8—251no—
327C2×D4—251no—
328C22×C4—251no—
329C22×C4—251no—
330C22×C4—251no—
331C22×C4—251no—
332C4⋊C4—51no—
333C4⋊C4—51no—
334C4⋊C4—51no—
335C4⋊C4—51no—
336C4⋊C4—51no—
337C4⋊C4—51no—
338C4⋊C4—51no—
339C4⋊C4—251no—
340C4⋊C4—251no—
341C4⋊C4—251no—
342C4⋊C4—251no—
343C4⋊C4—251no—
344C4⋊C4—251no—
345C4⋊C4—251no—
346C4⋊C4—251no—
347C4⋊C4D5211yescharacteristic
348C22⋊C4—51no—
349C22⋊C4—51no—
350C22⋊C4—51no—
351C22⋊C4—251no—
352C22⋊C4—251no—
353C22⋊C4—251no—
354C22⋊C4—251no—
355C22⋊C4—251no—
356C42—51no—
357C42—51no—
358C42—251no—
359C42—251no—
360C42—251no—
361C2×C5—22no—
362C2×C5—22no—
363C2×C5—22no—
364C2×C5—201no—
365C2×C5#414711yescharacteristic
366C2×C5D5×#4111yescharacteristic
367C2×C5D5×#4111yescharacteristic
368C2×C5D5×#4111yescharacteristic
369C2×C5D5×#4111yescharacteristic
370C2×C5#415011yescharacteristic
371D5—41no—
372D5—108no—
373D5—102no—
374D5—102no—
375C23—51no—
376C23—251no—
377Q8—502no—
378D4—502no—
379C2×C4—51no—
380C2×C4—51no—
381C2×C4—51no—
382C2×C4—51no—
383C2×C4—51no—
384C2×C4—51no—
385C2×C4—51no—
386C2×C4—251no—
387C2×C4—251no—
388C2×C4—251no—
389C2×C4—502no—
390C2×C4—502no—
391C2×C4—502no—
392C2×C4—502no—
393C2×C4C2×D5211yescharacteristic
394C2×C4C2×D5211yescharacteristic
395C2×C4C2×D5211yescharacteristic
396C5—22no—
397C5#6602711yescharacteristic, complemented
398C5#6604211yescharacteristic, complemented
399C22—101no—
400C22—101no—
401C22—101no—
402C22—252no—
403C22—501no—
404C22—501no—
405C22C22×D5211yescharacteristic
406C4—21no—
407C4—21no—
408C4—21no—
409C4—101no—
410C4—101no—
411C4—101no—
412C4—101no—
413C4—101no—
414C4—101no—
415C4—101no—
416C4—252no—
417C4—501no—
418C4—501no—
419C2—201no—
420C2—502no—
421C2#1171747111yescharacteristic
422C2#1171747711yescharacteristic
423C2#1171748011yescharacteristic
subgroupG/H
center, FrattiniC22C22×D52
commutator, socle, cosocleC22×C52C24
FittingC52×C4⋊C4C22
prime radicalC2×#6038C22
hypercenterC4⋊C4D52
hypocenterC52#552
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C4⋊C4×C5⋊D5C2semidirect
2. C5×#4044C2semidirect
3. C5×#4035C2semidirect
4. #11717014C2semidirect
6. #11716995C2semidirect
7. #11716992C2semidirect
8. #11716984C2semidirect
9. #11716977C2semidirect
12. #11716967C2semidirect
13. #11716965C2semidirect
14. #11716963C2semidirect
15. #11716955C2semidirect
77. #4044D5semidirect
93. #4035D5semidirect
275. C52#552semidirect
397. C5#66027semidirect
398. C5#66042semidirect

Maximal subgroups

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

subgroupindex
C4⋊C4×C5⋊D52
C5×#40442
C5×#40352
#117170142
#117169992
#117169952
#117169922
#117169842
#117169772
#117169712
#117169672
#117169652
#117169632
#117169552
#660425
#660275