Finite Group Databasebeta

← C4×#87879 #13105933

Subgroups — C4×#87879 #13105933

Order 1600.

714 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#87879C211yesmaximal, characteristic
2C4×C22⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
3C4×C5×C22⋊D5C211yesmaximal, characteristic, complemented
4C2×C4×C5×Dic5C211yesmaximal, characteristic, complemented
5Dic5×C22⋊D5C211yesmaximal, characteristic, complemented
6#11717073C211yesmaximal, characteristic, complemented
7#11717070C211yesmaximal, characteristic, complemented
8C4×#6039C211yesmaximal, characteristic, complemented
9C4×#6038C211yesmaximal, characteristic, complemented
10C4×#6036C211yesmaximal, characteristic, complemented
11#11716998C211yesmaximal, characteristic, complemented
12#11716995C211yesmaximal, characteristic, complemented
13C4×D5×Dic5C211yesmaximal, characteristic, complemented
14#11716955C211yesmaximal, characteristic, complemented
15#11716954C211yesmaximal, characteristic, complemented
16C22×C4×C52C2211yescharacteristic
17C2×C22⋊(C5⋊D5)C2211yescharacteristic
18C2×C4×C5⋊D5C2211yescharacteristic
19C2×C5×C22⋊D5C2211yescharacteristic
20C22×C5×Dic5C2211yescharacteristic
21C22×C5×Dic5C2211yescharacteristic
22C2×C4×C5×D5C2211yescharacteristic
23C2×#6039C2211yescharacteristic
24C2×#6038C2211yescharacteristic
25C2×#6036C2211yescharacteristic
26C2×#6036C2211yescharacteristic
27#87879C418yesdirect product factor
28C2×D5×Dic5C2211yescharacteristic
29C2×D5×Dic5C2211yescharacteristic
30C22⋊#1039C2211yescharacteristic
31#87808C2211yescharacteristic
32#87806C2211yescharacteristic
33C4×#1039C2211yescharacteristic
34C5×C22⋊Dic5C2211yescharacteristic
35C5×#685C2211yescharacteristic
36C5×#683C2211yescharacteristic
37C4×C5×Dic5C2211yescharacteristic
38C4×C5×Dic5C2211yescharacteristic
39C4×C5×Dic5C2211yescharacteristic
40C4×C5×Dic5C2211yescharacteristic
41C4×C5×Dic5C2211yescharacteristic
42#87781C2211yescharacteristic
43#87780C2211yescharacteristic
44#87780C2211yescharacteristic
45#87780C2211yescharacteristic
46#87779C2211yescharacteristic
47#87778C2211yescharacteristic
48Dic52C2211yescharacteristic
49Dic52C2211yescharacteristic
50Dic52C2211yescharacteristic
51Dic52C2211yescharacteristic
52C4×#711—51nomaximal
53C4×#709—51nomaximal
54C23×C52C2311yescharacteristic
55C22×C5⋊D5C2311yescharacteristic
56C22×C5×D5C2311yescharacteristic
57C2×C4×C52—22no—
58C2×C4×C52C2311yescharacteristic
59C2×C4×C52C2311yescharacteristic
60C22⋊(C5⋊D5)C2×C414yescomplemented
61C2×#1039C2311yescharacteristic
62C2×#1039C2311yescharacteristic
63C2×#1039C2311yescharacteristic
64C4×C5⋊D5—22no—
65C5×C22⋊D5C2×C414yescomplemented
66C2×C5×Dic5—22no—
67C2×C5×Dic5C2×C414yescomplemented
68C2×C5×Dic5C2311yescharacteristic
69C2×C5×Dic5C2311yescharacteristic
70C2×C5×Dic5C2311yescharacteristic
71C2×C5×Dic5C2311yescharacteristic
72C2×C5×Dic5C2311yescharacteristic
73C2×C5×Dic5C2311yescharacteristic
74C2×C5×Dic5C2311yescharacteristic
75C4×C5×D5—22no—
76#6039C2×C414yescomplemented
77#6038C2×C414yescomplemented
78#6036—22no—
79#6036C2×C414yescomplemented
80D5×Dic5—22no—
81D5×Dic5C2×C414yescomplemented
82C2×#711—51no—
83C2×#709—51no—
84C4×C5×D4—51no—
85C2×C42×C5—51no—
86D4×Dic5—51no—
87C4×C22⋊D5—51no—
88C4×C22⋊D5—51no—
89C4×C22⋊D5—51no—
90C4×C22⋊D5—51no—
91C4×C22⋊D5—51no—
92C4×C22⋊D5—102no—
93C4×C22⋊D5D511yescharacteristic, complemented
94#4072—51no—
95C2×C4×Dic5—51no—
96C2×C4×Dic5D511yescharacteristic, complemented
97#4038—51no—
98#4033—51no—
99#4027—51no—
100#4027—51no—
101#4023—51no—
102#4023—51no—
103C4×D20—51no—
104C4×D20—51no—
105#4018—51no—
106#4018—51no—
107C42×D5—51no—
108C42×D5—51no—
109C42×D5—51no—
110C4×Dic10—51no—
111C4×Dic10—51no—
112C4×Dic10—51no—
113C22×C52—21no—
114C22×C52—21no—
115C22×C52C22×C412yes—
116C22×C52C2411yescharacteristic
117C2×C5⋊D5—21no—
118C2×C5⋊D5—21no—
119C2×C5⋊D5C22×C412yes—
120C2×C5×D5—21no—
121C2×C5×D5—21no—
122C2×C5×D5C22×C412yes—
123C4×C52—21no—
124C4×C52#4112yescomplemented
125#1039—21no—
126#1039—21no—
127#1039C22×C412yes—
128C5×Dic5—21no—
129C5×Dic5—21no—
130C5×Dic5—21no—
131C5×Dic5C22×C412yes—
132C5×Dic5C22×C412yes—
133C5×Dic5C22×C412yes—
134C5×Dic5#4112yescomplemented
135C2×C5×D4—51no—
136C22×C4×C5—22no—
137C22×C4×C5—51no—
138C22×C4×C5—51no—
139C22×C4×C5—51no—
140C22×C4×C5C2×D511yescharacteristic
141C22×C4×C5C2×D511yescharacteristic
142C2×C22⋊D5—51no—
143C2×C22⋊D5—51no—
144C2×C22⋊D5—51no—
145C2×C22⋊D5—102no—
146C2×C22⋊D5C2×D511yescharacteristic
147C22×Dic5—51no—
148C22×Dic5—51no—
149C22×Dic5C2×D511yescharacteristic
150C22×Dic5C2×D511yescharacteristic
151#711—58no—
152#709—58no—
153C2×D20—51no—
154C2×C4×D5—51no—
155C2×C4×D5—51no—
156C2×C4×D5—51no—
157C2×C4×D5—51no—
158C2×C4×D5—51no—
159C2×C4×D5—51no—
160C2×C4×D5—51no—
161C2×C4×D5—51no—
162C2×C4×D5—102no—
163C2×C4×D5C2×D511yescharacteristic
164C2×Dic10—51no—
165C2×Dic10—51no—
166C5×C4⋊C4—51no—
167C5×C22⋊C4—51no—
168C5×C22⋊C4—51no—
169C42×C5—51no—
170C42×C5—51no—
171C42×C5—51no—
172C42×C5—51no—
173C42×C5—51no—
174C22⋊Dic5—51no—
175C22⋊Dic5—51no—
176C22⋊Dic5—51no—
177C22⋊Dic5—102no—
178C22⋊Dic5C2×D511yescharacteristic
179#685—51no—
180#685—51no—
181#685—51no—
182#685—51no—
183#685—51no—
184#685—102no—
185#685C2×D511yescharacteristic
186C4⋊Dic5—51no—
187C4⋊Dic5—51no—
188C4⋊Dic5—51no—
189#683—51no—
190#683—51no—
191#683—51no—
192#683—51no—
193#683—51no—
194#683—51no—
195#683—51no—
196#683—102no—
197#683C2×D511yescharacteristic
198C4×Dic5—51no—
199C4×Dic5—51no—
200C4×Dic5—51no—
201C4×Dic5—51no—
202C4×Dic5—51no—
203C4×Dic5—51no—
204C4×Dic5—51no—
205C4×Dic5—51no—
206C4×Dic5—51no—
207C4×Dic5—51no—
208C4×Dic5—102no—
209C4×Dic5C2×D511yescharacteristic
210C4×Dic5C2×D511yescharacteristic
211C4×Dic5C2×D511yescharacteristic
212C4×Dic5C2×D511yescharacteristic
213C4×Dic5C2×D511yescharacteristic
214C4×#41—251noSylow
215C2×C52—22no—
216C2×C52C23×C411yescharacteristic
217C2×C52C2×#4111yescharacteristic
218C2×C52C2×#4111yescharacteristic
219C5⋊D5—22no—
220C5×D5—22no—
221C23×C5—22no—
222C23×C5—51no—
223C23×C5C22×D511yescharacteristic
224C23×C5C22×D511yescharacteristic
225C22×D5—51no—
226C22×D5—51no—
227C22×D5—102no—
228C22×D5C22×D511yescharacteristic
229C5×D4—54no—
230C2×C4×C5—22no—
231C2×C4×C5—22no—
232C2×C4×C5—22no—
233C2×C4×C5—22no—
234C2×C4×C5—44no—
235C2×C4×C5—54no—
236C2×C4×C5—51no—
237C2×C4×C5—51no—
238C2×C4×C5—51no—
239C2×C4×C5—51no—
240C2×C4×C5—51no—
241C2×C4×C5—51no—
242C2×C4×C5—51no—
243C2×C4×C5—102no—
244C2×C4×C5—102no—
245C2×C4×C5C22×D511yescharacteristic
246C2×C4×C5C22×D511yescharacteristic
247C2×C4×C5C22×D511yescharacteristic
248C2×C4×C5C22×D511yescharacteristic
249C22⋊D5—54no—
250C22⋊D5—54no—
251C22⋊D5—54no—
252C22⋊D5—108no—
253C22⋊D5C4×D514yescomplemented
254C2×Dic5—22no—
255C2×Dic5—51no—
256C2×Dic5—51no—
257C2×Dic5—54no—
258C2×Dic5—51no—
259C2×Dic5—51no—
260C2×Dic5—51no—
261C2×Dic5—51no—
262C2×Dic5—102no—
263C2×Dic5—102no—
264C2×Dic5—102no—
265C2×Dic5—102no—
266C2×Dic5C4×D514yescomplemented
267C2×Dic5C22×D511yescharacteristic
268C2×Dic5C22×D511yescharacteristic
269C2×Dic5C22×D511yescharacteristic
270C2×Dic5C22×D511yescharacteristic
271C2×Dic5C22×D511yescharacteristic
272C2×Dic5C22×D511yescharacteristic
273C2×Dic5C22×D511yescharacteristic
274D20—54no—
275C4×D5—22no—
276C4×D5—54no—
277C4×D5—54no—
278C4×D5—54no—
279C4×D5—102no—
280C4×D5—102no—
281C4×D5—102no—
282C4×D5—102no—
283C4×D5—102no—
284C4×D5—204no—
285Dic10—54no—
286Dic10—54no—
287C2×#41—251no—
288C4×Q8—251no—
289C4×Q8—251no—
290C4×D4—51no—
291C4×D4—251no—
292C4×D4—251no—
293C4×D4—251no—
294C4×D4—251no—
295C4×D4—251no—
296#117—251no—
297#117—251no—
298#117—251no—
299C2×C42—51no—
300C2×C42—251no—
301C2×C42—251no—
302C52C4×#4111yescharacteristic, complemented, Sylow
303C22×C5—21no—
304C22×C5—21no—
305C22×C5—21no—
306C22×C5—21no—
307C22×C5—24no—
308C22×C5—22no—
309C22×C5—42no—
310C22×C5—42no—
311C22×C5—52no—
312C22×C5—101no—
313C22×C5—101no—
314C22×C5C2×C4×D512yes—
315C22×C5C2×C4×D512yes—
316C22×C5C23×D511yescharacteristic
317C22×C5C23×D511yescharacteristic
318C2×D5—21no—
319C2×D5—21no—
320C2×D5—52no—
321C2×D5—52no—
322C2×D5—104no—
323C2×D5—101no—
324C2×D5—101no—
325C2×D5—101no—
326C2×D5—101no—
327C2×D5—202no—
328C2×D5—202no—
329C2×D5C2×C4×D512yes—
330C4×C5—21no—
331C4×C5—21no—
332C4×C5—24no—
333C4×C5—42no—
334C4×C5—52no—
335C4×C5—52no—
336C4×C5—52no—
337C4×C5—52no—
338C4×C5—101no—
339C4×C5—101no—
340C4×C5—101no—
341C4×C5#70912yescomplemented
342C4×C5#71112yescomplemented
343Dic5—21no—
344Dic5—21no—
345Dic5—21no—
346Dic5—52no—
347Dic5—52no—
348Dic5—104no—
349Dic5—101no—
350Dic5—101no—
351Dic5—101no—
352Dic5—101no—
353Dic5—202no—
354Dic5—202no—
355Dic5C2×C4×D512yes—
356Dic5C2×C4×D512yes—
357Dic5C2×C4×D512yes—
358Dic5#70912yescomplemented
359#41—258no—
360C2×Q8—251no—
361C2×D4—51no—
362C2×D4—251no—
363C2×D4—251no—
364C22×C4—51no—
365C22×C4—51no—
366C22×C4—51no—
367C22×C4—251no—
368C22×C4—251no—
369C22×C4—251no—
370C22×C4—251no—
371C22×C4—251no—
372C22×C4D5211yescharacteristic
373C4⋊C4—51no—
374C4⋊C4—251no—
375C4⋊C4—251no—
376C4⋊C4—251no—
377C4⋊C4—251no—
378C4⋊C4—251no—
379C22⋊C4—51no—
380C22⋊C4—51no—
381C22⋊C4—251no—
382C22⋊C4—251no—
383C22⋊C4—251no—
384C22⋊C4—251no—
385C42—51no—
386C42—51no—
387C42—51no—
388C42—51no—
389C42—51no—
390C42—251no—
391C42—251no—
392C42—251no—
393C42—251no—
394C42—251no—
395C2×C5—22no—
396C2×C5—22no—
397C2×C5—22no—
398C2×C5—22no—
399C2×C5—22no—
400C2×C5—44no—
401C2×C5—102no—
402C2×C5C22×C4×D511yescharacteristic
403C2×C5C22×C4×D511yescharacteristic
404C2×C5C2×#70911yescharacteristic
405C2×C5C2×#70911yescharacteristic
406C2×C5C2×#71111yescharacteristic
407C2×C5D5×#4111yescharacteristic
408D5—22no—
409D5—102no—
410D5—102no—
411D5—204no—
412C23—51no—
413C23—251no—
414C23C2×D5211yescharacteristic
415Q8—254no—
416D4—54no—
417D4—254no—
418D4—254no—
419C2×C4—22no—
420C2×C4—54no—
421C2×C4—51no—
422C2×C4—51no—
423C2×C4—51no—
424C2×C4—51no—
425C2×C4—51no—
426C2×C4—51no—
427C2×C4—51no—
428C2×C4—102no—
429C2×C4—102no—
430C2×C4—254no—
431C2×C4—254no—
432C2×C4—251no—
433C2×C4—251no—
434C2×C4—251no—
435C2×C4—502no—
436C2×C4—502no—
437C2×C4—502no—
438C2×C4C2×D5211yescharacteristic
439C2×C4C2×D5211yescharacteristic
440C5—22no—
441C5C4×#70911yescharacteristic, complemented
442C5C4×#71111yescharacteristic, complemented
443C22—21no—
444C22—21no—
445C22—52no—
446C22—101no—
447C22—101no—
448C22—252no—
449C22—501no—
450C22—501no—
451C22C4×D5212yes—
452C22C22×D5211yescharacteristic
453C4—21no—
454C4—52no—
455C4—52no—
456C4—52no—
457C4—52no—
458C4—101no—
459C4—101no—
460C4—101no—
461C4—252no—
462C4—501no—
463C4—501no—
464C4#8787912yesdirect product factor
465C2—22no—
466C2—102no—
467C2—502no—
468C2C2×C4×D5211yescharacteristic
469C2D5×#70911yescharacteristic
470C2C2×#8787911yescharacteristic
subgroupG/H
centerC2×C4C2×D52
commutatorC2×C52C23×C4
FrattiniC22C22×D52
FittingC22×C4×C52C22
socle, cosocleC22×C52C24
prime radicalC2×#87879C2
hypercenterC22×C4D52
hypocenterC52C4×#41
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊(C5⋊D5)C2semidirect
3. C4×C5×C22⋊D5C2semidirect
4. C2×C4×C5×Dic5C2semidirect
5. Dic5×C22⋊D5C2semidirect
6. #11717073C2semidirect
7. #11717070C2semidirect
8. C4×#6039C2semidirect
9. C4×#6038C2semidirect
10. C4×#6036C2semidirect
11. #11716998C2semidirect
12. #11716995C2semidirect
13. C4×D5×Dic5C2semidirect
14. #11716955C2semidirect
15. #11716954C2semidirect
27. #87879C4direct (N × H)
60. C22⋊(C5⋊D5)C2×C4semidirect
65. C5×C22⋊D5C2×C4semidirect
67. C2×C5×Dic5C2×C4semidirect
76. #6039C2×C4semidirect
77. #6038C2×C4semidirect
79. #6036C2×C4semidirect
81. D5×Dic5C2×C4semidirect
93. C4×C22⋊D5D5semidirect
96. C2×C4×Dic5D5semidirect
124. C4×C52#41semidirect
134. C5×Dic5#41semidirect
253. C22⋊D5C4×D5semidirect
266. C2×Dic5C4×D5semidirect
302. C52C4×#41semidirect
341. C4×C5#709semidirect
342. C4×C5#711semidirect
358. Dic5#709semidirect
441. C5C4×#709semidirect
442. C5C4×#711semidirect
464. C4#87879direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#878792
C4×C22⋊(C5⋊D5)2
C4×C5×C22⋊D52
C2×C4×C5×Dic52
Dic5×C22⋊D52
#117170732
#117170702
C4×#60392
C4×#60382
C4×#60362
#117169982
#117169952
C4×D5×Dic52
#117169552
#117169542
C4×#7115
C4×#7095