Finite Group Databasebeta

← #13106009

Subgroups — #13106009

Order 1600.

504 conjugacy classes of subgroups.

The subgroup lattice has 423 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11717246C211yesmaximal, characteristic, complemented
2C5×#4075C211yesmaximal, characteristic
3C2×C5×#683C211yesmaximal, characteristic, complemented
4Dic5×C22⋊D5C211yesmaximal, characteristic
5#11717082C211yesmaximal, characteristic, complemented
6#11717079C211yesmaximal, characteristic
7#11717073C211yesmaximal, characteristic, complemented
8#11717007C211yesmaximal, characteristic, complemented
9#11716996C211yesmaximal, characteristic, complemented
10#11716989C211yesmaximal, characteristic, complemented
11#11716980C211yesmaximal, characteristic, complemented
12#11716977C211yesmaximal, characteristic, complemented
13#11716963C211yesmaximal, characteristic, complemented
14#11716963C211yesmaximal, characteristic, complemented
15#11716956C211yesmaximal, characteristic, complemented
16C22×C4×C52C2211yescharacteristic
17C2×C5×C22⋊D5C2211yescharacteristic
18C22×C5×Dic5C2211yescharacteristic
19C22×C5×Dic5C2211yescharacteristic
20C2×#6039C2211yescharacteristic
21C2×D5×Dic5C2211yescharacteristic
22C22⋊#1039C2211yescharacteristic
23C22⋊#1039C2211yescharacteristic
24C4⋊#1039C2211yescharacteristic
25C4⋊#1039C2211yescharacteristic
26C4×#1039C2211yescharacteristic
27C4×#1039C2211yescharacteristic
28C5×C22⋊Dic5C2211yescharacteristic
29C5×#685C2211yescharacteristic
30C5×#685C2211yescharacteristic
31C5×#683C2211yescharacteristic
32C5×#683C2211yescharacteristic
33C5×#683C2211yescharacteristic
34C5×#683C2211yescharacteristic
35C5×#683C2211yescharacteristic
36C5×#683C2211yescharacteristic
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#65984—51nomaximal
52#65847—51nomaximal
53C23×C52C2311yescharacteristic
54C22×C5×D5C2311yescharacteristic
55C2×C4×C52—22no—
56C2×C4×C52C2311yescharacteristic
57C2×C4×C52C2311yescharacteristic
58C2×#1039C2311yescharacteristic
59C2×#1039C2311yescharacteristic
60C2×#1039C2311yescharacteristic
61C2×#1039C2311yescharacteristic
62C5×C22⋊D5—22no—
63C2×C5×Dic5—22no—
64C2×C5×Dic5—22no—
65C2×C5×Dic5C2311yescharacteristic
66C2×C5×Dic5C2311yescharacteristic
67C2×C5×Dic5C2311yescharacteristic
68C2×C5×Dic5C2311yescharacteristic
69C2×C5×Dic5C2311yescharacteristic
70C2×C5×Dic5C2311yescharacteristic
71C2×C5×Dic5C2311yescharacteristic
72#6039—22no—
73D5×Dic5—22no—
74C5×#123—51no—
75C2×C5×C4⋊C4—51no—
76#4081—51no—
77D4×Dic5—51no—
78#4075—51no—
79#4075D511yescharacteristic
80C4×C22⋊D5—51no—
81#4072—51no—
82#4072—51no—
83#4072—51no—
84#4072—102no—
85#4070—51no—
86C2×#683D511yescharacteristic, complemented
87#4044—51no—
88#4044—51no—
89#4043—51no—
90#4038—51no—
91#4036—51no—
92#4036—51no—
93#4035—51no—
94#4035—51no—
95#4035—51no—
96#4035—51no—
97#4033—51no—
98#4033—51no—
99#4025—51no—
100#4025—51no—
101#4024—51no—
102#4024—51no—
103#4023—51no—
104#4023—51no—
105C22×C52—21no—
106C22×C52—21no—
107C22×C52#4112yes—
108C22×C52C2411yescharacteristic
109C2×C5×D5—21no—
110C2×C5×D5—21no—
111C2×C5×D5—21no—
112C4×C52—21no—
113C4×C52—21no—
114#1039—21no—
115#1039—21no—
116#1039—21no—
117#1039—21no—
118C5×Dic5—21no—
119C5×Dic5—21no—
120C5×Dic5—21no—
121C5×Dic5—21no—
122C5×Dic5—21no—
123C5×Dic5—21no—
124C5×Dic5#4112yes—
125C2×C5×D4—51no—
126C22×C4×C5—22no—
127C22×C4×C5—51no—
128C22×C4×C5—51no—
129C22×C4×C5C2×D511yescharacteristic
130C22×C4×C5C2×D511yescharacteristic
131C2×C22⋊D5C2×D511yescharacteristic
132C22×Dic5—51no—
133C22×Dic5C2×D511yescharacteristic
134C22×Dic5C2×D511yescharacteristic
135C2×C4×D5—51no—
136C2×Dic10—51no—
137C2×Dic10—51no—
138C5×C4⋊C4—51no—
139C5×C4⋊C4—51no—
140C5×C4⋊C4—51no—
141C5×C4⋊C4—51no—
142C5×C4⋊C4—51no—
143C5×C4⋊C4—51no—
144C5×C22⋊C4—51no—
145C5×C22⋊C4—51no—
146C5×C22⋊C4—51no—
147C22⋊Dic5—51no—
148C22⋊Dic5—51no—
149C22⋊Dic5—51no—
150C22⋊Dic5—51no—
151C22⋊Dic5—51no—
152C22⋊Dic5—51no—
153C22⋊Dic5—51no—
154C22⋊Dic5—102no—
155C22⋊Dic5—102no—
156C22⋊Dic5C2×D511yescharacteristic
157#685—51no—
158#685—51no—
159#685—51no—
160#685C2×D511yescharacteristic
161#685C2×D511yescharacteristic
162C4⋊Dic5—51no—
163C4⋊Dic5—51no—
164C4⋊Dic5—51no—
165C4⋊Dic5—51no—
166C4⋊Dic5—51no—
167C4⋊Dic5—51no—
168C4⋊Dic5—51no—
169C4⋊Dic5—51no—
170C4⋊Dic5—51no—
171C4⋊Dic5—102no—
172C4⋊Dic5—102no—
173#683—51no—
174#683—51no—
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#683C2×D511yescharacteristic
185#683C2×D511yescharacteristic
186#683C2×D511yescharacteristic
187#683C2×D511yescharacteristic
188#683C2×D511yescharacteristic
189#683C2×D511yescharacteristic
190C4×Dic5—51no—
191C4×Dic5—51no—
192C4×Dic5—51no—
193C4×Dic5—51no—
194C4×Dic5—51no—
195C4×Dic5—51no—
196C4×Dic5—51no—
197C4×Dic5—51no—
198C4×Dic5—51no—
199C4×Dic5—51no—
200C4×Dic5—102no—
201C4×Dic5—102no—
202#552—251noSylow
203C2×C52—22no—
204C2×C52C2×#4111yescharacteristic
205C2×C52C2×#4111yescharacteristic
206C2×C522−1+411yescharacteristic
207C5×D5—41no—
208C23×C5—22no—
209C23×C5—51no—
210C23×C5C22×D511yescharacteristic
211C23×C5C22×D511yescharacteristic
212C22×D5C22×D511yescharacteristic
213C5×D4—102no—
214C2×C4×C5—28no—
215C2×C4×C5—22no—
216C2×C4×C5—22no—
217C2×C4×C5—22no—
218C2×C4×C5—22no—
219C2×C4×C5—51no—
220C2×C4×C5—51no—
221C2×C4×C5—51no—
222C2×C4×C5—51no—
223C2×C4×C5—51no—
224C2×C4×C5—51no—
225C2×C4×C5—51no—
226C2×C4×C5—102no—
227C2×C4×C5—102no—
228C2×C4×C5C22×D511yescharacteristic
229C2×C4×C5C22×D511yescharacteristic
230C2×C4×C5C22×D511yescharacteristic
231C2×C4×C5C22×D511yescharacteristic
232C22⋊D5—22no—
233C2×Dic5—22no—
234C2×Dic5—22no—
235C2×Dic5—51no—
236C2×Dic5—51no—
237C2×Dic5—51no—
238C2×Dic5—51no—
239C2×Dic5—51no—
240C2×Dic5—51no—
241C2×Dic5—51no—
242C2×Dic5—51no—
243C2×Dic5—102no—
244C2×Dic5—102no—
245C2×Dic5—102no—
246C2×Dic5—102no—
247C2×Dic5—102no—
248C2×Dic5C22×D511yescharacteristic
249C2×Dic5C22×D511yescharacteristic
250C2×Dic5C22×D511yescharacteristic
251C2×Dic5C22×D511yescharacteristic
252C2×Dic5C22×D511yescharacteristic
253C2×Dic5C22×D511yescharacteristic
254C2×Dic5C22×D511yescharacteristic
255C4×D5—102no—
256Dic10—102no—
257Dic10—102no—
258#126—251no—
259#126—251no—
260#125—251no—
261#125—251no—
262#125—251no—
263#123—51no—
264#123—251no—
265C22⋊Q8—251no—
266C22⋊Q8—251no—
267C4×Q8—251no—
268C4×D4—251no—
269#117—251no—
270#117—251no—
271#117—251no—
272C2×C4⋊C4—51no—
273C52#55211yescharacteristic, complemented, Sylow
274C22×C5—21no—
275C22×C5—21no—
276C22×C5—21no—
277C22×C5—21no—
278C22×C5—24no—
279C22×C5—22no—
280C22×C5—42no—
281C22×C5—42no—
282C22×C5—101no—
283C22×C5—101no—
284C22×C5—101no—
285C22×C5#71112yes—
286C22×C5#71112yes—
287C22×C5C23×D511yescharacteristic
288C22×C5C23×D511yescharacteristic
289C2×D5—21no—
290C2×D5—21no—
291C2×D5—21no—
292C4×C5—24no—
293C4×C5—24no—
294C4×C5—21no—
295C4×C5—21no—
296C4×C5—21no—
297C4×C5—21no—
298C4×C5—52no—
299C4×C5—101no—
300C4×C5—101no—
301C4×C5—101no—
302C4×C5—101no—
303C4×C5—101no—
304C4×C5—101no—
305Dic5—21no—
306Dic5—21no—
307Dic5—21no—
308Dic5—21no—
309Dic5—21no—
310Dic5—21no—
311Dic5—101no—
312Dic5—101no—
313Dic5—101no—
314Dic5—101no—
315Dic5—101no—
316Dic5—101no—
317Dic5—101no—
318Dic5—101no—
319Dic5—202no—
320Dic5—202no—
321Dic5—202no—
322Dic5—202no—
323Dic5#70912yes—
324C2×Q8—251no—
325C2×D4—51no—
326C22×C4—51no—
327C22×C4—51no—
328C22×C4—251no—
329C22×C4D5211yescharacteristic
330C4⋊C4—51no—
331C4⋊C4—51no—
332C4⋊C4—51no—
333C4⋊C4—51no—
334C4⋊C4—51no—
335C4⋊C4—51no—
336C4⋊C4—251no—
337C4⋊C4—251no—
338C4⋊C4—251no—
339C4⋊C4—251no—
340C4⋊C4—251no—
341C4⋊C4—251no—
342C4⋊C4—251no—
343C4⋊C4—251no—
344C4⋊C4—251no—
345C4⋊C4—251no—
346C22⋊C4—51no—
347C22⋊C4—51no—
348C22⋊C4—51no—
349C22⋊C4—251no—
350C22⋊C4—251no—
351C22⋊C4—251no—
352C22⋊C4—251no—
353C22⋊C4—251no—
354C42—251no—
355C42—251no—
356C42—251no—
357C42—251no—
358C42—251no—
359C2×C5—22no—
360C2×C5—22no—
361C2×C5—22no—
362C2×C5—22no—
363C2×C5—22no—
364C2×C5—44no—
365C2×C5—201no—
366C2×C5C2×#70911yescharacteristic
367C2×C5C2×#71111yescharacteristic
368C2×C5C2×#71111yescharacteristic
369C2×C5#414711yescharacteristic
370C2×C5D5×#4111yescharacteristic
371C2×C5#415011yescharacteristic
372D5—41no—
373C23—51no—
374C23C2×D5211yescharacteristic
375Q8—502no—
376D4—102no—
377C2×C4—22no—
378C2×C4—51no—
379C2×C4—51no—
380C2×C4—51no—
381C2×C4—51no—
382C2×C4—51no—
383C2×C4—51no—
384C2×C4—51no—
385C2×C4—102no—
386C2×C4—102no—
387C2×C4—251no—
388C2×C4—251no—
389C2×C4—251no—
390C2×C4—251no—
391C2×C4—502no—
392C2×C4C2×D5211yescharacteristic
393C2×C4C2×D5211yescharacteristic
394C5—22no—
395C5#6584711yescharacteristic, complemented
396C5#6598411yescharacteristic, complemented
397C22—21no—
398C22—21no—
399C22—101no—
400C22—101no—
401C22—101no—
402C22#8788012yes—
403C22C22×D5211yescharacteristic
404C4—21no—
405C4—21no—
406C4—52no—
407C4—101no—
408C4—101no—
409C4—101no—
410C4—101no—
411C4—101no—
412C4—101no—
413C4—501no—
414C4—501no—
415C4—501no—
416C4—501no—
417C2—22no—
418C2—201no—
419C2#1171746211yescharacteristic
420C2D5×#70911yescharacteristic
421C2C2×#8788011yescharacteristic
subgroupG/H
center, FrattiniC22C22×D52
commutator, socle, cosocleC22×C52C24
FittingC22×C4×C52C22
prime radicalC2×C5×C22⋊D5C22
hypercenterC22×C4D52
hypocenterC52#552
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. #11717246C2semidirect
3. C2×C5×#683C2semidirect
5. #11717082C2semidirect
7. #11717073C2semidirect
8. #11717007C2semidirect
9. #11716996C2semidirect
10. #11716989C2semidirect
11. #11716980C2semidirect
12. #11716977C2semidirect
13. #11716963C2semidirect
14. #11716963C2semidirect
15. #11716956C2semidirect
86. C2×#683D5semidirect
273. C52#552semidirect
395. C5#65847semidirect
396. C5#65984semidirect

Maximal subgroups

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

subgroupindex
#117172462
C5×#40752
C2×C5×#6832
Dic5×C22⋊D52
#117170822
#117170792
#117170732
#117170072
#117169962
#117169892
#117169802
#117169772
#117169632
#117169562
#659845
#658475