Finite Group Databasebeta

← #13104992

Subgroups — #13104992

Order 1600.

440 conjugacy classes of subgroups.

The subgroup lattice has 395 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11717190C211yesmaximal, characteristic, complemented
2C5×#4022C211yesmaximal, characteristic
3C4×C5×Dic10C211yesmaximal, characteristic, complemented
4#11717007C211yesmaximal, characteristic
5#11717006C211yesmaximal, characteristic
6#11716995C211yesmaximal, characteristic
7#11716986C211yesmaximal, characteristic, complemented
8#11716978C211yesmaximal, characteristic
9#11716977C211yesmaximal, characteristic
10#11716976C211yesmaximal, characteristic
11#11716965C211yesmaximal, characteristic, complemented
12#11716963C211yesmaximal, characteristic, complemented
13#11716963C211yesmaximal, characteristic, complemented
14#11716957C211yesmaximal, characteristic, complemented
15#11716955C211yesmaximal, characteristic, complemented
16C2×C5×Dic10C2211yescharacteristic
17C2×#6039C2211yescharacteristic
18C2×D5×Dic5C2211yescharacteristic
19C42×C52C2211yescharacteristic
20C4⋊#1039C2211yescharacteristic
21C4⋊#1039C2211yescharacteristic
22#87806C2211yescharacteristic
23#87806C2211yescharacteristic
24#87806C2211yescharacteristic
25#87806C2211yescharacteristic
26C5×#685C2211yescharacteristic
27C5×#685C2211yescharacteristic
28C5×#685C2211yescharacteristic
29C5×C4⋊Dic5C2211yescharacteristic
30C5×#683C2211yescharacteristic
31C5×#683C2211yescharacteristic
32C5×#683C2211yescharacteristic
33C5×#683C2211yescharacteristic
34C5×#683C2211yescharacteristic
35C4×C5×Dic5C2211yescharacteristic
36C4×C5×Dic5C2211yescharacteristic
37#87781C2211yescharacteristic
38#87781C2211yescharacteristic
39#87781C2211yescharacteristic
40#87780C2211yescharacteristic
41#87780C2211yescharacteristic
42#87780C2211yescharacteristic
43#87780C2211yescharacteristic
44#87780C2211yescharacteristic
45#87778C2211yescharacteristic
46#87778C2211yescharacteristic
47#87778C2211yescharacteristic
48Dic52C2211yescharacteristic
49Dic52C2211yescharacteristic
50Dic52C2211yescharacteristic
51#66035—51nomaximal
52#65917—51nomaximal
53C22×C5×D5C2311yescharacteristic
54C2×C4×C52C2311yescharacteristic
55C2×C4×C52C2311yescharacteristic
56C2×C4×C52C2311yescharacteristic
57C2×#1039C2311yescharacteristic
58C2×#1039C2311yescharacteristic
59C2×#1039C2311yescharacteristic
60C2×#1039C2311yescharacteristic
61C2×C5×Dic5C2311yescharacteristic
62C2×C5×Dic5C2311yescharacteristic
63C2×C5×Dic5C2311yescharacteristic
64C2×C5×Dic5C2311yescharacteristic
65C2×C5×Dic5C2311yescharacteristic
66C2×C5×Dic5C2311yescharacteristic
67C2×C5×Dic5C2311yescharacteristic
68C5×Dic10—22no—
69#6039—22no—
70D5×Dic5—22no—
71C5×#126—51no—
72C4×C5×Q8—51no—
73#4092—51no—
74#4090—51no—
75#4044—51no—
76#4044—51no—
77#4043—51no—
78#4036—51no—
79#4036—51no—
80#4035—51no—
81#4035—51no—
82#4035—51no—
83#4035—51no—
84#4035—51no—
85#4034—51no—
86#4033—51no—
87#4025—51no—
88#4025—51no—
89#4025—51no—
90#4024—51no—
91#4024—51no—
92#4023—51no—
93#4022—51no—
94#4022D511yescharacteristic
95#4018—51no—
96#4016—51no—
97#4016—51no—
98#4016—51no—
99#4016—102no—
100C4×Dic10—51no—
101C4×Dic10D511yescharacteristic, complemented
102C22×C52C2411yescharacteristic
103C2×C5×D5—21no—
104C2×C5×D5—21no—
105C2×C5×D5—21no—
106C4×C52—21no—
107C4×C52—21no—
108C4×C52—21no—
109#1039—21no—
110#1039—21no—
111#1039—21no—
112#1039—21no—
113C5×Dic5—21no—
114C5×Dic5—21no—
115C5×Dic5—21no—
116C5×Dic5—21no—
117C5×Dic5—21no—
118C5×Dic5—21no—
119C5×Dic5#4112yes—
120C2×C5×Q8—51no—
121C22×Dic5—51no—
122C2×C4×D5—51no—
123C2×Dic10—51no—
124C2×Dic10—51no—
125C2×Dic10C2×D511yescharacteristic
126C5×C4⋊C4—51no—
127C5×C4⋊C4—51no—
128C5×C4⋊C4—51no—
129C5×C4⋊C4—51no—
130C5×C4⋊C4—51no—
131C5×C4⋊C4—51no—
132C5×C22⋊C4—51no—
133C5×C22⋊C4—51no—
134C5×C22⋊C4—51no—
135C42×C5—22no—
136C42×C5—51no—
137C42×C5—51no—
138C42×C5C2×D511yescharacteristic
139C42×C5C2×D511yescharacteristic
140C22⋊Dic5—51no—
141C22⋊Dic5—51no—
142C22⋊Dic5—51no—
143#685—51no—
144#685—51no—
145#685—51no—
146#685C2×D511yescharacteristic
147#685C2×D511yescharacteristic
148#685C2×D511yescharacteristic
149C4⋊Dic5—51no—
150C4⋊Dic5—51no—
151C4⋊Dic5—51no—
152C4⋊Dic5—51no—
153C4⋊Dic5—51no—
154C4⋊Dic5—51no—
155C4⋊Dic5—51no—
156C4⋊Dic5—51no—
157C4⋊Dic5—51no—
158C4⋊Dic5—102no—
159C4⋊Dic5—102no—
160C4⋊Dic5C2×D511yescharacteristic
161#683—51no—
162#683—51no—
163#683—51no—
164#683—51no—
165#683—51no—
166#683—51no—
167#683—51no—
168#683—51no—
169#683—51no—
170#683—51no—
171#683—51no—
172#683—51no—
173#683—51no—
174#683—51no—
175#683—51no—
176#683—51no—
177#683—51no—
178#683—51no—
179#683—51no—
180#683—102no—
181#683—102no—
182#683—102no—
183#683—102no—
184#683C2×D511yescharacteristic
185#683C2×D511yescharacteristic
186#683C2×D511yescharacteristic
187#683C2×D511yescharacteristic
188#683C2×D511yescharacteristic
189C4×Dic5—51no—
190C4×Dic5—51no—
191C4×Dic5—51no—
192C4×Dic5—51no—
193C4×Dic5—51no—
194C4×Dic5—51no—
195C4×Dic5C2×D511yescharacteristic
196C4×Dic5C2×D511yescharacteristic
197#541—251noSylow
198C2×C52C2×#4111yescharacteristic
199C2×C522−1+411yescharacteristic
200C2×C522−1+411yescharacteristic
201C5×D5—41no—
202C23×C5—51no—
203C22×D5C22×D511yescharacteristic
204C5×Q8—102no—
205C2×C4×C5—22no—
206C2×C4×C5—22no—
207C2×C4×C5—22no—
208C2×C4×C5—51no—
209C2×C4×C5—51no—
210C2×C4×C5—51no—
211C2×C4×C5—51no—
212C2×C4×C5—51no—
213C2×C4×C5—51no—
214C2×C4×C5—51no—
215C2×C4×C5C22×D511yescharacteristic
216C2×C4×C5C22×D511yescharacteristic
217C2×C4×C5C22×D511yescharacteristic
218C2×C4×C5C22×D511yescharacteristic
219C2×C4×C5C22×D511yescharacteristic
220C2×C4×C5C22×D511yescharacteristic
221C2×Dic5—51no—
222C2×Dic5—51no—
223C2×Dic5—51no—
224C2×Dic5—51no—
225C2×Dic5—51no—
226C2×Dic5—51no—
227C2×Dic5—51no—
228C2×Dic5—51no—
229C2×Dic5—102no—
230C2×Dic5—102no—
231C2×Dic5—102no—
232C2×Dic5—102no—
233C2×Dic5—102no—
234C2×Dic5C22×D511yescharacteristic
235C2×Dic5C22×D511yescharacteristic
236C2×Dic5C22×D511yescharacteristic
237C2×Dic5C22×D511yescharacteristic
238C2×Dic5C22×D511yescharacteristic
239C2×Dic5C22×D511yescharacteristic
240C2×Dic5C22×D511yescharacteristic
241C4×D5—102no—
242Dic10—22no—
243Dic10—102no—
244Dic10—102no—
245C4⋊Q8—251no—
246#126—51no—
247#126—251no—
248#126—251no—
249#126—251no—
250#125—251no—
251#125—251no—
252#125—251no—
253#125—251no—
254#125—251no—
255C22⋊Q8—251no—
256C22⋊Q8—251no—
257C4×Q8—51no—
258C4×Q8—251no—
259#117—251no—
260C52#54111yescharacteristic, complemented, Sylow
261C22×C5—22no—
262C22×C5—101no—
263C22×C5—101no—
264C22×C5—101no—
265C22×C5C23×D511yescharacteristic
266C22×C5C23×D511yescharacteristic
267C2×D5—21no—
268C2×D5—21no—
269C2×D5—21no—
270C4×C5—24no—
271C4×C5—21no—
272C4×C5—21no—
273C4×C5—21no—
274C4×C5—21no—
275C4×C5—21no—
276C4×C5—21no—
277C4×C5—42no—
278C4×C5—42no—
279C4×C5—52no—
280C4×C5—101no—
281C4×C5—101no—
282C4×C5—101no—
283C4×C5—101no—
284C4×C5—101no—
285C4×C5—101no—
286Dic5—21no—
287Dic5—21no—
288Dic5—21no—
289Dic5—21no—
290Dic5—21no—
291Dic5—21no—
292Dic5—101no—
293Dic5—101no—
294Dic5—101no—
295Dic5—101no—
296Dic5—101no—
297Dic5—101no—
298Dic5—101no—
299Dic5—101no—
300Dic5—202no—
301Dic5—202no—
302Dic5—202no—
303Dic5—202no—
304Dic5#70912yes—
305C2×Q8—51no—
306C2×Q8—251no—
307C22×C4—251no—
308C4⋊C4—51no—
309C4⋊C4—51no—
310C4⋊C4—51no—
311C4⋊C4—51no—
312C4⋊C4—51no—
313C4⋊C4—51no—
314C4⋊C4—251no—
315C4⋊C4—251no—
316C4⋊C4—251no—
317C4⋊C4—251no—
318C4⋊C4—251no—
319C4⋊C4—251no—
320C4⋊C4—251no—
321C4⋊C4—251no—
322C4⋊C4—251no—
323C4⋊C4—251no—
324C4⋊C4—251no—
325C4⋊C4—251no—
326C4⋊C4—251no—
327C4⋊C4—251no—
328C22⋊C4—51no—
329C22⋊C4—51no—
330C22⋊C4—51no—
331C22⋊C4—251no—
332C22⋊C4—251no—
333C22⋊C4—251no—
334C42—51no—
335C42—51no—
336C42—251no—
337C42—251no—
338C42—251no—
339C42D5211yescharacteristic
340C2×C5—22no—
341C2×C5—22no—
342C2×C5—22no—
343C2×C5—201no—
344C2×C5C2×#70911yescharacteristic
345C2×C5#414711yescharacteristic
346C2×C5D5×#4111yescharacteristic
347C2×C5#415011yescharacteristic
348C2×C5#415011yescharacteristic
349C2×C5#415011yescharacteristic
350D5—41no—
351C23—51no—
352Q8—102no—
353Q8—502no—
354C2×C4—51no—
355C2×C4—51no—
356C2×C4—51no—
357C2×C4—51no—
358C2×C4—51no—
359C2×C4—51no—
360C2×C4—51no—
361C2×C4—251no—
362C2×C4—251no—
363C2×C4—251no—
364C2×C4—251no—
365C2×C4—502no—
366C2×C4C2×D5211yescharacteristic
367C2×C4C2×D5211yescharacteristic
368C2×C4C2×D5211yescharacteristic
369C5—22no—
370C5#6591711yescharacteristic, complemented
371C5#6603511yescharacteristic, complemented
372C22—101no—
373C22—101no—
374C22—101no—
375C22C22×D5211yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—52no—
380C4—101no—
381C4—101no—
382C4—101no—
383C4—101no—
384C4—101no—
385C4—101no—
386C4—501no—
387C4—501no—
388C4—501no—
389C4—501no—
390C2—201no—
391C2#1171746211yescharacteristic
392C2#1171746311yescharacteristic
393C2D5×#70911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D52
commutator, socle, cosocleC22×C52C24
FittingC42×C52C22
prime radicalC22×C5×D5C23
hypercenterC42D52
hypocenterC52#541
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. #11717190C2semidirect
3. C4×C5×Dic10C2semidirect
7. #11716986C2semidirect
11. #11716965C2semidirect
12. #11716963C2semidirect
13. #11716963C2semidirect
14. #11716957C2semidirect
15. #11716955C2semidirect
101. C4×Dic10D5semidirect
260. C52#541semidirect
370. C5#65917semidirect
371. C5#66035semidirect

Maximal subgroups

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

subgroupindex
#117171902
C5×#40222
C4×C5×Dic102
#117170072
#117170062
#117169952
#117169862
#117169782
#117169772
#117169762
#117169652
#117169632
#117169572
#117169552
#660355
#659175