Finite Group Databasebeta

← C5×#9786 #11932506

Subgroups — C5×#9786 #11932506

Order 1280.

552 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#465C211yesmaximal, characteristic
2C5×#1996C211yesmaximal, characteristic, complemented
3C5×#1964C211yesmaximal, characteristic
4C5×#1808C211yesmaximal, characteristic, complemented
5C5×#1752C211yesmaximal, characteristic, complemented
6C5×#1520C211yesmaximal, characteristic, complemented
7C5×#1519C211yesmaximal, characteristic
8C22×C5×SD16C411yescharacteristic, complemented
9C23×C5×C8C2211yescharacteristic
10C2×C5×C22⋊Q8C2211yescharacteristic
11C2×C5×#121C2211yescharacteristic
12C5×#465—21no—
13C5×#465—21no—
14C5×#465—21no—
15C5×#465—21no—
16C2×C5×#107—21no—
17C2×C5×#106C411yescharacteristic, complemented
18C2×C5×#103C411yescharacteristic, complemented
19C2×C5×#102C411yescharacteristic, complemented
20C2×C5×#99—22no—
21C2×C5×C22⋊C8C2211yescharacteristic
22C2×C5×#97—21no—
23C5×#380C2211yescharacteristic
24C5×#380C2211yescharacteristic
25C4×C5×C22⋊C4C2211yescharacteristic
26C5×#342—22no—
27C5×#340—21no—
28C5×#336—21no—
29C5×#328—22no—
30C5×#327—22no—
31#9786C511yesmaximal, characteristic, direct product factor, Sylow
32C22×C5×Q8C2×C411yescharacteristic
33C22×C5×D4—21no—
34C22×C5×D4C2×C411yescharacteristic
35C23×C4×C5C2311yescharacteristic
36C2×C5×SD16—21no—
37C2×C5×SD16—21no—
38C2×C5×SD16—42no—
39C22×C5×C8—21no—
40C22×C5×C8—42no—
41C22×C5×C8C2×C411yescharacteristic
42C22×C5×C8C2×C411yescharacteristic
43C22×C5×C8D411yescharacteristic
44C22×C5×C8D411yescharacteristic
45C22×C5×C8D411yescharacteristic
46C22×C5×C8D411yescharacteristic
47C5×C22⋊Q8—21no—
48C5×C22⋊Q8—21no—
49C5×C22⋊Q8—21no—
50C5×C22⋊Q8—21no—
51C5×#121—21no—
52C5×#121—21no—
53C5×#121—21no—
54C5×#121—21no—
55C2×C5×C4⋊C4—21no—
56C2×C5×C4⋊C4—21no—
57C2×C5×C4⋊C4—21no—
58C2×C5×C4⋊C4C2×C411yescharacteristic
59C2×C5×C4⋊C4C2×C411yescharacteristic
60C2×C5×C22⋊C4—21no—
61C2×C5×C22⋊C4—21no—
62C2×C5×C22⋊C4—21no—
63C2×C5×C22⋊C4—21no—
64C2×C5×C22⋊C4D412yes—
65C2×C42×C5—21no—
66C5×#107—42no—
67C5×#106—21no—
68C5×#106—21no—
69C5×#103—21no—
70C5×#103—21no—
71C5×#102—21no—
72C5×#102—21no—
73C5×#99—44no—
74C5×C22⋊C8—21no—
75C5×C22⋊C8D412yes—
76C5×#97—42no—
77C5×#95—21no—
78C5×#95—21no—
79C5×#95—21no—
80C2×#465C2×C511yescharacteristic
81#1996C2×C511yescharacteristic, complemented
82#1964C2×C511yescharacteristic
83#1808C2×C511yescharacteristic, complemented
84#1752C2×C511yescharacteristic, complemented
85#1520C2×C511yescharacteristic, complemented
86#1519C2×C511yescharacteristic
87C24×C5—21no—
88C24×C5C2×D411yescharacteristic
89C2×C5×Q8—21no—
90C2×C5×Q8—21no—
91C2×C5×Q8—41no—
92C2×C5×Q8—41no—
93C2×C5×D4—21no—
94C2×C5×D4—21no—
95C2×C5×D4—41no—
96C2×C5×D4—41no—
97C2×C5×D4—41no—
98C2×C5×D4—41no—
99C2×C5×D4—42no—
100C2×C5×D4—42no—
101C22×C4×C5—21no—
102C22×C4×C5—22no—
103C22×C4×C5—21no—
104C22×C4×C5—21no—
105C22×C4×C5—41no—
106C22×C4×C5—41no—
107C22×C4×C5—41no—
108C22×C4×C5—41no—
109C22×C4×C5C22×C411yescharacteristic
110C22×C4×C5C2×D411yescharacteristic
111C22×C4×C5C2×D411yescharacteristic
112C22×C4×C5C2×D411yescharacteristic
113C22×C4×C5#4111yescharacteristic
114C22×C4×C5#4111yescharacteristic
115C5×SD16—42no—
116C5×SD16—42no—
117C2×C5×C8—22no—
118C2×C5×C8—22no—
119C2×C5×C8—22no—
120C2×C5×C8—22no—
121C2×C5×C8—41no—
122C2×C5×C8—41no—
123C2×C5×C8—41no—
124C2×C5×C8—41no—
125C2×C5×C8—41no—
126C2×C5×C8C22⋊C411yescharacteristic
127C2×C5×C8C22⋊C411yescharacteristic
128C2×C5×C8C22⋊C411yescharacteristic
129C2×C5×C8C22⋊C411yescharacteristic
130C5×C4⋊C4—21no—
131C5×C4⋊C4—21no—
132C5×C4⋊C4—21no—
133C5×C4⋊C4—21no—
134C5×C4⋊C4—41no—
135C5×C4⋊C4—41no—
136C5×C4⋊C4—41no—
137C5×C4⋊C4—41no—
138C5×C4⋊C4—41no—
139C5×C4⋊C4—41no—
140C5×C22⋊C4—22no—
141C5×C22⋊C4—22no—
142C5×C22⋊C4—41no—
143C5×C22⋊C4—41no—
144C5×C22⋊C4—41no—
145C5×C22⋊C4—41no—
146C5×C22⋊C4—42no—
147C5×C22⋊C4—42no—
148C42×C5—41no—
149C42×C5—41no—
150C22×SD16C4×C511yescharacteristic, complemented
151C23×C8C22×C511yescharacteristic
152C2×C22⋊Q8C22×C511yescharacteristic
153C2×#121C22×C511yescharacteristic
154#465—21no—
155#465—21no—
156#465—21no—
157#465—21no—
158C2×#107—21no—
159C2×#106C4×C511yescharacteristic, complemented
160C2×#103C4×C511yescharacteristic, complemented
161C2×#102C4×C511yescharacteristic, complemented
162C2×#99—22no—
163C2×C22⋊C8C22×C511yescharacteristic
164C2×#97—21no—
165#380C22×C511yescharacteristic
166#380C22×C511yescharacteristic
167C4×C22⋊C4C22×C511yescharacteristic
168#342—22no—
169#340—21no—
170#336—21no—
171#328—22no—
172#327—22no—
173C23×C5—41no—
174C23×C5—41no—
175C23×C5—41no—
176C23×C5—42no—
177C23×C5—81no—
178C23×C5—81no—
179C23×C5C4×D411yescharacteristic
180C23×C5#12111yescharacteristic
181C23×C5#12711yescharacteristic
182C23×C5AGL(1,ℤ/8)12yes—
183C23×C5#13712yes—
184C5×Q8—41no—
185C5×Q8—41no—
186C5×Q8—81no—
187C5×D4—41no—
188C5×D4—41no—
189C5×D4—81no—
190C5×D4—82no—
191C5×D4—81no—
192C5×D4—81no—
193C2×C4×C5—21no—
194C2×C4×C5—21no—
195C2×C4×C5—21no—
196C2×C4×C5—21no—
197C2×C4×C5—21no—
198C2×C4×C5—21no—
199C2×C4×C5—41no—
200C2×C4×C5—41no—
201C2×C4×C5—41no—
202C2×C4×C5—42no—
203C2×C4×C5—42no—
204C2×C4×C5—41no—
205C2×C4×C5—41no—
206C2×C4×C5—41no—
207C2×C4×C5—42no—
208C2×C4×C5—42no—
209C2×C4×C5—81no—
210C2×C4×C5—81no—
211C2×C4×C5—81no—
212C2×C4×C5—81no—
213C2×C4×C5—81no—
214C2×C4×C5—81no—
215C2×C4×C5—81no—
216C2×C4×C5—81no—
217C2×C4×C5C2×C22⋊C411yescharacteristic
218C2×C4×C5C4×D411yescharacteristic
219C2×C4×C5#12111yescharacteristic
220C2×C4×C5#12411yescharacteristic
221C5×C8—21no—
222C5×C8—21no—
223C5×C8—21no—
224C5×C8—42no—
225C5×C8#9912yescomplemented
226C22×Q8C2×C4×C511yescharacteristic
227C22×D4—21no—
228C22×D4C2×C4×C511yescharacteristic
229C23×C4C23×C511yescharacteristic
230C2×SD16—21no—
231C2×SD16—21no—
232C2×SD16—42no—
233C22×C8—21no—
234C22×C8—42no—
235C22×C8C2×C4×C511yescharacteristic
236C22×C8C2×C4×C511yescharacteristic
237C22×C8C5×D411yescharacteristic
238C22×C8C5×D411yescharacteristic
239C22×C8C5×D411yescharacteristic
240C22×C8C5×D411yescharacteristic
241C22⋊Q8—21no—
242C22⋊Q8—21no—
243C22⋊Q8—21no—
244C22⋊Q8—21no—
245#121—21no—
246#121—21no—
247#121—21no—
248#121—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4C2×C4×C511yescharacteristic
253C2×C4⋊C4C2×C4×C511yescharacteristic
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4C5×D412yes—
259C2×C42—21no—
260#107—42no—
261#106—21no—
262#106—21no—
263#103—21no—
264#103—21no—
265#102—21no—
266#102—21no—
267#99—44no—
268C22⋊C8—21no—
269C22⋊C8C5×D412yes—
270#97—42no—
271#95—21no—
272#95—21no—
273#95—21no—
274C22×C5—21no—
275C22×C5—21no—
276C22×C5—21no—
277C22×C5—21no—
278C22×C5—21no—
279C22×C5—21no—
280C22×C5—42no—
281C22×C5—42no—
282C22×C5—81no—
283C22×C5—81no—
284C22×C5—81no—
285C22×C5—162no—
286C22×C5#39011yescharacteristic
287C22×C5#44012yes—
288C22×C5#46812yes—
289C22×C5#49611yescharacteristic
290C22×C5#49711yescharacteristic
291C4×C5—21no—
292C4×C5—21no—
293C4×C5—21no—
294C4×C5—82no—
295C4×C5—81no—
296C4×C5—81no—
297C4×C5—81no—
298C4×C5—161no—
299C4×C5—161no—
300C4×C5C2×#9911yescharacteristic
301C4×C5#41011yescharacteristic
302C24—21no—
303C24C2×C5×D411yescharacteristic
304C2×Q8—21no—
305C2×Q8—21no—
306C2×Q8—41no—
307C2×Q8—41no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—42no—
315C2×D4—42no—
316C22×C4—21no—
317C22×C4—22no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4C22×C4×C511yescharacteristic
325C22×C4C2×C5×D411yescharacteristic
326C22×C4C2×C5×D411yescharacteristic
327C22×C4C2×C5×D411yescharacteristic
328C22×C4C5×#4111yescharacteristic
329C22×C4C5×#4111yescharacteristic
330SD16—42no—
331SD16—42no—
332C2×C8—22no—
333C2×C8—22no—
334C2×C8—22no—
335C2×C8—22no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8C5×C22⋊C411yescharacteristic
342C2×C8C5×C22⋊C411yescharacteristic
343C2×C8C5×C22⋊C411yescharacteristic
344C2×C8C5×C22⋊C411yescharacteristic
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C4⋊C4—41no—
355C22⋊C4—22no—
356C22⋊C4—22no—
357C22⋊C4—41no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C22⋊C4—41no—
361C22⋊C4—42no—
362C22⋊C4—42no—
363C42—41no—
364C42—41no—
365C2×C5—22no—
366C2×C5—21no—
367C2×C5—22no—
368C2×C5—21no—
369C2×C5—161no—
370C2×C5#196411yescharacteristic
371C2×C5#197311yescharacteristic
372C2×C5#197611yescharacteristic
373C23—41no—
374C23—41no—
375C23—41no—
376C23—42no—
377C23—81no—
378C23—81no—
379C23C4×C5×D411yescharacteristic
380C23C5×#12111yescharacteristic
381C23C5×#12711yescharacteristic
382C23C5×AGL(1,ℤ/8)12yes—
383C23C5×#13712yes—
384Q8—41no—
385Q8—41no—
386Q8—81no—
387D4—41no—
388D4—41no—
389D4—81no—
390D4—82no—
391D4—81no—
392D4—81no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—81no—
410C2×C4—81no—
411C2×C4—81no—
412C2×C4—81no—
413C2×C4—81no—
414C2×C4—81no—
415C2×C4—81no—
416C2×C4—81no—
417C2×C4C2×C5×C22⋊C411yescharacteristic
418C2×C4C4×C5×D411yescharacteristic
419C2×C4C5×#12111yescharacteristic
420C2×C4C5×#12411yescharacteristic
421C8—21no—
422C8—21no—
423C8—21no—
424C8—42no—
425C8C5×#9912yescomplemented
426C5#978611yescharacteristic, direct product factor, Sylow
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—42no—
434C22—42no—
435C22—81no—
436C22—81no—
437C22—81no—
438C22—162no—
439C22C5×#39011yescharacteristic
440C22C5×#44012yes—
441C22C5×#46812yes—
442C22C5×#49611yescharacteristic
443C22C5×#49711yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—82no—
448C4—81no—
449C4—81no—
450C4—81no—
451C4—161no—
452C4—161no—
453C4C2×C5×#9911yescharacteristic
454C4C5×#41011yescharacteristic
455C2—22no—
456C2—21no—
457C2—22no—
458C2—21no—
459C2—161no—
460C2C5×#196411yescharacteristic
461C2C5×#197311yescharacteristic
462C2C5×#197611yescharacteristic
subgroupG/H
center, socleC22×C5#390
commutatorC22×C4C22×C4×C5
Frattini, cosocleC23×C4C23×C5
prime radicalC2×C5×#121C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#1996C2semidirect
4. C5×#1808C2semidirect
5. C5×#1752C2semidirect
6. C5×#1520C2semidirect
8. C22×C5×SD16C4semidirect
17. C2×C5×#106C4semidirect
18. C2×C5×#103C4semidirect
19. C2×C5×#102C4semidirect
31. #9786C5direct (N × H)
81. #1996C2×C5semidirect
83. #1808C2×C5semidirect
84. #1752C2×C5semidirect
85. #1520C2×C5semidirect
150. C22×SD16C4×C5semidirect
159. C2×#106C4×C5semidirect
160. C2×#103C4×C5semidirect
161. C2×#102C4×C5semidirect
225. C5×C8#99semidirect
425. C8C5×#99semidirect
426. C5#9786direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4652
C5×#19962
C5×#19642
C5×#18082
C5×#17522
C5×#15202
C5×#15192
#97865