Finite Group Databasebeta

← C5×#8989 #11931709

Subgroups — C5×#8989 #11931709

Order 1280.

540 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
1C5×#3101C211yesmaximal, characteristic
2C5×D4×M16C211yesmaximal, characteristic
3C5×#1986C211yesmaximal, characteristic, complemented
4C4×C5×#102C211yesmaximal, characteristic
5C5×#1493C211yesmaximal, characteristic, complemented
6C5×#1303C211yesmaximal, characteristic, complemented
7C5×#1278C211yesmaximal, characteristic, complemented
8C22×C5×M16—21no—
9C5×#533C2211yescharacteristic
10C2×C4×C5×D4C2211yescharacteristic
11C5×#483—21no—
12C5×#476C411yescharacteristic, complemented
13C5×#476C411yescharacteristic, complemented
14C5×#461C411yescharacteristic, complemented
15C5×#461C411yescharacteristic, complemented
16C5×#450—21no—
17C4×C5×SD16—21no—
18C4×C5×SD16—21no—
19C5×#436—21no—
20C5×#435—22no—
21C5×C8×D4—21no—
22C5×#431C2211yescharacteristic
23C5×#423C2211yescharacteristic
24C2×C5×#102—21no—
25C5×#407—21no—
26C4×C5×M16C2211yescharacteristic
27C2×C4×C5×C8C2211yescharacteristic
28C4×C5×C4⋊C4C2211yescharacteristic
29C5×#340—21no—
30C5×#339—21no—
31C5×#339—21no—
32C5×Q8⋊C8—22no—
33#8989C511yesmaximal, characteristic, direct product factor, Sylow
34C22×C5×D4D411yescharacteristic
35C23×C4×C5—21no—
36C2×C5×SD16—21no—
37C2×C5×SD16—21no—
38C2×C5×M16—22no—
39C2×C5×M16—21no—
40C2×C5×M16—42no—
41C2×C5×M16—42no—
42C2×C5×M16D411yescharacteristic
43C2×C5×M16D411yescharacteristic
44C22×C5×C8—22no—
45C22×C5×C8—21no—
46C5×C4⋊Q8C2×C411yescharacteristic
47C5×C4⋊Q8C2×C411yescharacteristic
48C5×#125—21no—
49C5×C22⋊Q8—21no—
50C5×C22⋊Q8—21no—
51C4×C5×Q8—21no—
52C4×C5×Q8—21no—
53C4×C5×D4—21no—
54C4×C5×D4—21no—
55C4×C5×D4C2×C411yescharacteristic
56C4×C5×D4C2×C411yescharacteristic
57C4×C5×D4D411yescharacteristic
58C4×C5×D4D411yescharacteristic
59C5×#117—21no—
60C2×C5×C4⋊C4—21no—
61C2×C5×C4⋊C4D411yescharacteristic
62C2×C5×C22⋊C4—21no—
63C2×C42×C5—21no—
64C2×C42×C5C2311yescharacteristic
65C5×#106—21no—
66C5×#106—21no—
67C5×C4⋊C8—21no—
68C5×C4⋊C8C2×C411yescharacteristic
69C5×C4⋊C8C2×C411yescharacteristic
70C5×C4⋊C8D412yes—
71C5×#103—21no—
72C5×#103—21no—
73C5×#102—24no—
74C5×#102—21no—
75C5×#102—21no—
76C5×C22⋊C8—22no—
77C5×C22⋊C8—22no—
78C5×C22⋊C8—21no—
79C5×#97—21no—
80C4×C5×C8—21no—
81C4×C5×C8—21no—
82C4×C5×C8—21no—
83C4×C5×C8—21no—
84C5×#95—21no—
85#3101C2×C511yescharacteristic
86D4×M16C2×C511yescharacteristic
87#1986C2×C511yescharacteristic, complemented
88C4×#102C2×C511yescharacteristic
89#1493C2×C511yescharacteristic, complemented
90#1303C2×C511yescharacteristic, complemented
91#1278C2×C511yescharacteristic, complemented
92C24×C5—21no—
93C2×C5×Q8—21no—
94C2×C5×Q8—21no—
95C2×C5×D4—22no—
96C2×C5×D4—21no—
97C2×C5×D4—41no—
98C2×C5×D4C22⋊C411yescharacteristic
99C2×C5×D4C22⋊C411yescharacteristic
100C22×C4×C5—21no—
101C22×C4×C5—21no—
102C22×C4×C5—21no—
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×C5—41no—
110C22×C4×C5C2×D411yescharacteristic
111C22×C4×C5C2×D411yescharacteristic
112C22×C4×C5#4111yescharacteristic
113C5×SD16—42no—
114C5×SD16—42no—
115C5×M16—21no—
116C5×M16—21no—
117C5×M16—21no—
118C5×M16—44no—
119C5×M16—41no—
120C5×M16—41no—
121C5×M16SD1612yescomplemented
122C2×C5×C8—21no—
123C2×C5×C8—22no—
124C2×C5×C8—21no—
125C2×C5×C8—21no—
126C2×C5×C8—22no—
127C2×C5×C8—21no—
128C2×C5×C8—44no—
129C2×C5×C8—41no—
130C2×C5×C8—41no—
131C5×C4⋊C4—21no—
132C5×C4⋊C4—22no—
133C5×C4⋊C4—21no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4—21no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4—41no—
138C5×C4⋊C4—41no—
139C5×C4⋊C4—41no—
140C5×C4⋊C4C22⋊C411yescharacteristic
141C5×C4⋊C4C22⋊C411yescharacteristic
142C5×C22⋊C4—21no—
143C5×C22⋊C4—21no—
144C5×C22⋊C4—21no—
145C5×C22⋊C4—21no—
146C5×C22⋊C4—41no—
147C42×C5—41no—
148C42×C5—41no—
149C42×C5—41no—
150C42×C5C22×C411yescharacteristic
151C42×C5C2×D411yescharacteristic
152C42×C5C2×D411yescharacteristic
153C42×C5#4111yescharacteristic
154C22×M16—21no—
155#533C22×C511yescharacteristic
156C2×C4×D4C22×C511yescharacteristic
157#483—21no—
158#476C4×C511yescharacteristic, complemented
159#476C4×C511yescharacteristic, complemented
160#461C4×C511yescharacteristic, complemented
161#461C4×C511yescharacteristic, complemented
162#450—21no—
163C4×SD16—21no—
164C4×SD16—21no—
165#436—21no—
166#435—22no—
167C8×D4—21no—
168#431C22×C511yescharacteristic
169#423C22×C511yescharacteristic
170C2×#102—21no—
171#407—21no—
172C4×M16C22×C511yescharacteristic
173C2×C4×C8C22×C511yescharacteristic
174C4×C4⋊C4C22×C511yescharacteristic
175#340—21no—
176#339—21no—
177#339—21no—
178Q8⋊C8—22no—
179C23×C5—21no—
180C23×C5—21no—
181C23×C5—42no—
182C23×C5—41no—
183C23×C5—41no—
184C23×C5—81no—
185C23×C5#12111yescharacteristic
186C5×Q8—42no—
187C5×Q8—41no—
188C5×Q8—41no—
189C5×D4—21no—
190C5×D4—21no—
191C5×D4—21no—
192C5×D4—42no—
193C5×D4#10412yes—
194C2×C4×C5—21no—
195C2×C4×C5—21no—
196C2×C4×C5—21no—
197C2×C4×C5—21no—
198C2×C4×C5—41no—
199C2×C4×C5—41no—
200C2×C4×C5—41no—
201C2×C4×C5—41no—
202C2×C4×C5—41no—
203C2×C4×C5—41no—
204C2×C4×C5—41no—
205C2×C4×C5—41no—
206C2×C4×C5—41no—
207C2×C4×C5—41no—
208C2×C4×C5—41no—
209C2×C4×C5—42no—
210C2×C4×C5—41no—
211C2×C4×C5—41no—
212C2×C4×C5—81no—
213C2×C4×C5—81no—
214C2×C4×C5C2×C22⋊C411yescharacteristic
215C2×C4×C5C4×D411yescharacteristic
216C2×C4×C5C4×D411yescharacteristic
217C2×C4×C5#12011yescharacteristic
218C2×C4×C5#12111yescharacteristic
219C2×C4×C5#12311yescharacteristic
220C2×C4×C5C2×SD1611yescharacteristic
221C2×C4×C5#13511yescharacteristic
222C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
223C2×C4×C5#13711yescharacteristic
224C5×C8—22no—
225C5×C8—42no—
226C5×C8—41no—
227C5×C8—41no—
228C5×C8—42no—
229C5×C8—41no—
230C22×D4C5×D411yescharacteristic
231C23×C4—21no—
232C2×SD16—21no—
233C2×SD16—21no—
234C2×M16—22no—
235C2×M16—21no—
236C2×M16—42no—
237C2×M16—42no—
238C2×M16C5×D411yescharacteristic
239C2×M16C5×D411yescharacteristic
240C22×C8—22no—
241C22×C8—21no—
242C4⋊Q8C2×C4×C511yescharacteristic
243C4⋊Q8C2×C4×C511yescharacteristic
244#125—21no—
245C22⋊Q8—21no—
246C22⋊Q8—21no—
247C4×Q8—21no—
248C4×Q8—21no—
249C4×D4—21no—
250C4×D4—21no—
251C4×D4C2×C4×C511yescharacteristic
252C4×D4C2×C4×C511yescharacteristic
253C4×D4C5×D411yescharacteristic
254C4×D4C5×D411yescharacteristic
255#117—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4C5×D411yescharacteristic
258C2×C22⋊C4—21no—
259C2×C42—21no—
260C2×C42C23×C511yescharacteristic
261#106—21no—
262#106—21no—
263C4⋊C8—21no—
264C4⋊C8C2×C4×C511yescharacteristic
265C4⋊C8C2×C4×C511yescharacteristic
266C4⋊C8C5×D412yes—
267#103—21no—
268#103—21no—
269#102—24no—
270#102—21no—
271#102—21no—
272C22⋊C8—22no—
273C22⋊C8—22no—
274C22⋊C8—21no—
275#97—21no—
276C4×C8—21no—
277C4×C8—21no—
278C4×C8—21no—
279C4×C8—21no—
280#95—21no—
281C22×C5—21no—
282C22×C5—21no—
283C22×C5—22no—
284C22×C5—41no—
285C22×C5—41no—
286C22×C5—41no—
287C22×C5—41no—
288C22×C5—41no—
289C22×C5—82no—
290C22×C5—82no—
291C22×C5#38611yescharacteristic
292C22×C5#46111yescharacteristic
293C22×C5#46311yescharacteristic
294C4×C5—21no—
295C4×C5—21no—
296C4×C5—21no—
297C4×C5—41no—
298C4×C5—41no—
299C4×C5—82no—
300C4×C5—81no—
301C4×C5—81no—
302C4×C5C2×#10411yescharacteristic
303C4×C5#42111yescharacteristic
304C4×C5C4×SD1611yescharacteristic
305C4×C5#44011yescharacteristic
306C4×C5#45011yescharacteristic
307C4×C5#45211yescharacteristic
308C24—21no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×D4—22no—
312C2×D4—21no—
313C2×D4—41no—
314C2×D4C5×C22⋊C411yescharacteristic
315C2×D4C5×C22⋊C411yescharacteristic
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4C2×C5×D411yescharacteristic
327C22×C4C2×C5×D411yescharacteristic
328C22×C4C5×#4111yescharacteristic
329SD16—42no—
330SD16—42no—
331M16—21no—
332M16—21no—
333M16—21no—
334M16—44no—
335M16—41no—
336M16—41no—
337M16C5×SD1612yescomplemented
338C2×C8—21no—
339C2×C8—22no—
340C2×C8—21no—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—22no—
344C2×C8—44no—
345C2×C8—41no—
346C2×C8—41no—
347C4⋊C4—21no—
348C4⋊C4—22no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—41no—
354C4⋊C4—41no—
355C4⋊C4—41no—
356C4⋊C4C5×C22⋊C411yescharacteristic
357C4⋊C4C5×C22⋊C411yescharacteristic
358C22⋊C4—21no—
359C22⋊C4—21no—
360C22⋊C4—21no—
361C22⋊C4—21no—
362C22⋊C4—41no—
363C42—41no—
364C42—41no—
365C42—41no—
366C42C22×C4×C511yescharacteristic
367C42C2×C5×D411yescharacteristic
368C42C2×C5×D411yescharacteristic
369C42C5×#4111yescharacteristic
370C2×C5—21no—
371C2×C5—21no—
372C2×C5—42no—
373C2×C5—81no—
374C2×C5#187111yescharacteristic
375C2×C5#187711yescharacteristic
376C2×C5#188111yescharacteristic
377C23—21no—
378C23—21no—
379C23—42no—
380C23—41no—
381C23—41no—
382C23—81no—
383C23C5×#12111yescharacteristic
384Q8—42no—
385Q8—41no—
386Q8—41no—
387D4—21no—
388D4—21no—
389D4—21no—
390D4—42no—
391D4C5×#10412yes—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—81no—
411C2×C4—81no—
412C2×C4C2×C5×C22⋊C411yescharacteristic
413C2×C4C4×C5×D411yescharacteristic
414C2×C4C4×C5×D411yescharacteristic
415C2×C4C5×#12011yescharacteristic
416C2×C4C5×#12111yescharacteristic
417C2×C4C5×#12311yescharacteristic
418C2×C4C2×C5×SD1611yescharacteristic
419C2×C4C5×#13511yescharacteristic
420C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
421C2×C4C5×#13711yescharacteristic
422C8—22no—
423C8—42no—
424C8—41no—
425C8—41no—
426C8—42no—
427C8—41no—
428C5#898911yescharacteristic, direct product factor, Sylow
429C22—21no—
430C22—21no—
431C22—22no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—82no—
438C22—82no—
439C22C5×#38611yescharacteristic
440C22C5×#46111yescharacteristic
441C22C5×#46311yescharacteristic
442C4—21no—
443C4—21no—
444C4—21no—
445C4—41no—
446C4—41no—
447C4—82no—
448C4—81no—
449C4—81no—
450C4C2×C5×#10411yescharacteristic
451C4C5×#42111yescharacteristic
452C4C4×C5×SD1611yescharacteristic
453C4C5×#44011yescharacteristic
454C4C5×#45011yescharacteristic
455C4C5×#45211yescharacteristic
456C2—21no—
457C2—21no—
458C2—42no—
459C2—81no—
460C2C5×#187111yescharacteristic
461C2C5×#187711yescharacteristic
462C2C5×#188111yescharacteristic
subgroupG/H
centerC2×C4×C5#120
commutatorC42C22×C4×C5
Frattini, cosocleC2×C42C23×C5
socleC22×C5#386
prime radicalC22×C5×D4D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
3. C5×#1986C2semidirect
5. C5×#1493C2semidirect
6. C5×#1303C2semidirect
7. C5×#1278C2semidirect
12. C5×#476C4semidirect
13. C5×#476C4semidirect
14. C5×#461C4semidirect
15. C5×#461C4semidirect
33. #8989C5direct (N × H)
87. #1986C2×C5semidirect
89. #1493C2×C5semidirect
90. #1303C2×C5semidirect
91. #1278C2×C5semidirect
121. C5×M16SD16semidirect
158. #476C4×C5semidirect
159. #476C4×C5semidirect
160. #461C4×C5semidirect
161. #461C4×C5semidirect
337. M16C5×SD16semidirect
428. C5#8989direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#31012
C5×D4×M162
C5×#19862
C4×C5×#1022
C5×#14932
C5×#13032
C5×#12782
#89895