Finite Group Databasebeta

← C5×#32871 #11955591

Subgroups — C5×#32871 #11955591

Order 1280.

492 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2103C211yesmaximal, characteristic, complemented
2C5×#2103C211yesmaximal, characteristic, complemented
3C5×#2098C211yesmaximal, characteristic, complemented
4C5×#2082C211yesmaximal, characteristic, complemented
5C5×#2081C211yesmaximal, characteristic, complemented
6C5×#2070C211yesmaximal, characteristic, complemented
7C5×#2069C211yesmaximal, characteristic, complemented
8C5×#2049C211yesmaximal, characteristic, complemented
9C5×#2048C211yesmaximal, characteristic
10C5×#2046C211yesmaximal, characteristic, complemented
11C5×#2046C211yesmaximal, characteristic, complemented
12C5×#2019C211yesmaximal, characteristic
13C5×#1903C211yesmaximal, characteristic
14C5×#1902C211yesmaximal, characteristic, complemented
15C5×#1858C211yesmaximal, characteristic, complemented
16C2×C5×#137C2211yescharacteristic
17C2×C5×AGL(1,ℤ/8)C2211yescharacteristic
18C22×C5×SD16C2211yescharacteristic
19C5×#568C2211yescharacteristic
20C5×#430C2211yescharacteristic
21C5×#430C2211yescharacteristic
22C5×#430C2211yescharacteristic
23C5×#430C2211yescharacteristic
24C5×#430C2211yescharacteristic
25C5×#424C2211yescharacteristic
26C5×#424C2211yescharacteristic
27C5×#421C2211yescharacteristic
28C5×#421C2211yescharacteristic
29C5×#419C2211yescharacteristic
30C5×#419C2211yescharacteristic
31C5×#418C2211yescharacteristic
32C5×#418C2211yescharacteristic
33C5×#413C2211yescharacteristic
34C2×C5×#101C2211yescharacteristic
35C2×C5×#101C2211yescharacteristic
36C2×C5×#101C2211yescharacteristic
37C2×C5×#100C2211yescharacteristic
38C2×C5×#100C2211yescharacteristic
39C2×C5×#100C2211yescharacteristic
40C5×#408C2211yescharacteristic
41C5×#344C2211yescharacteristic
42C5×#344C2211yescharacteristic
43C5×#344C2211yescharacteristic
44C5×#344C2211yescharacteristic
45C5×#341C2211yescharacteristic
46C5×#341C2211yescharacteristic
47C5×#341C2211yescharacteristic
48C5×#338C2211yescharacteristic
49C5×#338C2211yescharacteristic
50C5×H(3,ℤ/4)C2211yescharacteristic
51#32871C511yesmaximal, characteristic, direct product factor, Sylow
52C2×C5×#41C2311yescharacteristic
53C22×C5×Q8C2311yescharacteristic
54C22×C5×D4C2311yescharacteristic
55C5×#137—41no—
56C5×#137—41no—
57C5×AGL(1,ℤ/8)—41no—
58C5×AGL(1,ℤ/8)—41no—
59C2×C5×Q16—21no—
60C2×C5×SD16—21no—
61C2×C5×SD16—21no—
62C2×C5×SD16—41no—
63C2×C5×SD16—41no—
64C2×C5×SD16—41no—
65C2×C5×D8—21no—
66C5×#131—41no—
67C5×#131—41no—
68C2×C5×M16—41no—
69C2×C5×M16C2311yescharacteristic
70C2×C5×M16C2311yescharacteristic
71C2×C5×M16C2311yescharacteristic
72C2×C5×M16C2311yescharacteristic
73C2×C5×M16C2311yescharacteristic
74C2×C5×M16C2311yescharacteristic
75C2×C5×M16C2311yescharacteristic
76C2×C5×M16C2311yescharacteristic
77C2×C5×M16C2311yescharacteristic
78C22×C5×C8C2311yescharacteristic
79C5×#117C2311yescharacteristic
80C5×#117C2311yescharacteristic
81C5×#108—41no—
82C5×#108—41no—
83C5×#108—41no—
84C5×#108—41no—
85C5×#108—41no—
86C5×C4⋊C8—41no—
87C5×C4⋊C8—41no—
88C5×#104—41no—
89C5×#104—41no—
90C5×#103—41no—
91C5×#103—41no—
92C5×#102—41no—
93C5×#102—41no—
94C5×#101—21no—
95C5×#101—41no—
96C5×#101—41no—
97C5×#101—41no—
98C5×#100—21no—
99C5×#100—41no—
100C5×#100—41no—
101C5×#100—41no—
102C5×C22⋊C8—41no—
103#2103C2×C511yescharacteristic, complemented
104#2103C2×C511yescharacteristic, complemented
105#2098C2×C511yescharacteristic, complemented
106#2082C2×C511yescharacteristic, complemented
107#2081C2×C511yescharacteristic, complemented
108#2070C2×C511yescharacteristic, complemented
109#2069C2×C511yescharacteristic, complemented
110#2049C2×C511yescharacteristic, complemented
111#2048C2×C511yescharacteristic
112#2046C2×C511yescharacteristic, complemented
113#2046C2×C511yescharacteristic, complemented
114#2019C2×C511yescharacteristic
115#1903C2×C511yescharacteristic
116#1902C2×C511yescharacteristic, complemented
117#1858C2×C511yescharacteristic, complemented
118C24×C5—21no—
119C5×#41—21no—
120C5×#41—21no—
121C5×#41—21no—
122C5×#41—21no—
123C2×C5×Q8—21no—
124C2×C5×Q8—21no—
125C2×C5×Q8—21no—
126C2×C5×Q8—21no—
127C2×C5×Q8—21no—
128C2×C5×Q8—21no—
129C2×C5×Q8#4111yescharacteristic
130C2×C5×D4—21no—
131C2×C5×D4—21no—
132C2×C5×D4—21no—
133C2×C5×D4—21no—
134C2×C5×D4—21no—
135C2×C5×D4—21no—
136C2×C5×D4—21no—
137C2×C5×D4#4111yescharacteristic
138C22×C4×C5—21no—
139C22×C4×C5—21no—
140C22×C4×C5C2411yescharacteristic
141C5×Q16—42no—
142C5×SD16—42no—
143C5×SD16—42no—
144C5×SD16—44no—
145C5×D8—42no—
146C5×M16—21no—
147C5×M16—21no—
148C5×M16—21no—
149C5×M16—21no—
150C5×M16—21no—
151C5×M16—21no—
152C5×M16—21no—
153C5×M16—21no—
154C5×M16—21no—
155C5×M16—21no—
156C5×M16—21no—
157C5×M16—21no—
158C5×M16—21no—
159C5×M16—21no—
160C5×M16—21no—
161C5×M16—21no—
162C5×M16—21no—
163C5×M16—21no—
164C5×M16—42no—
165C2×C5×C8—21no—
166C2×C5×C8—21no—
167C2×C5×C8—21no—
168C2×C5×C8—21no—
169C2×C5×C8—21no—
170C2×C5×C8—21no—
171C2×C5×C8—21no—
172C2×C5×C8—21no—
173C2×C5×C8—21no—
174C2×C5×C8—21no—
175C2×C5×C8—21no—
176C2×C5×C8—21no—
177C2×C5×C8—42no—
178C5×C4⋊C4—21no—
179C5×C4⋊C4—21no—
180C5×C22⋊C4—21no—
181C5×C22⋊C4—21no—
182C42×C5—21no—
183C42×C5—21no—
184C2×#137C22×C511yescharacteristic
185C2×AGL(1,ℤ/8)C22×C511yescharacteristic
186C22×SD16C22×C511yescharacteristic
187#568C22×C511yescharacteristic
188#430C22×C511yescharacteristic
189#430C22×C511yescharacteristic
190#430C22×C511yescharacteristic
191#430C22×C511yescharacteristic
192#430C22×C511yescharacteristic
193#424C22×C511yescharacteristic
194#424C22×C511yescharacteristic
195#421C22×C511yescharacteristic
196#421C22×C511yescharacteristic
197#419C22×C511yescharacteristic
198#419C22×C511yescharacteristic
199#418C22×C511yescharacteristic
200#418C22×C511yescharacteristic
201#413C22×C511yescharacteristic
202C2×#101C22×C511yescharacteristic
203C2×#101C22×C511yescharacteristic
204C2×#101C22×C511yescharacteristic
205C2×#100C22×C511yescharacteristic
206C2×#100C22×C511yescharacteristic
207C2×#100C22×C511yescharacteristic
208#408C22×C511yescharacteristic
209#344C22×C511yescharacteristic
210#344C22×C511yescharacteristic
211#344C22×C511yescharacteristic
212#344C22×C511yescharacteristic
213#341C22×C511yescharacteristic
214#341C22×C511yescharacteristic
215#341C22×C511yescharacteristic
216#338C22×C511yescharacteristic
217#338C22×C511yescharacteristic
218H(3,ℤ/4)C22×C511yescharacteristic
219C23×C5—21no—
220C23×C5—41no—
221C23×C5—41no—
222C23×C5—41no—
223C23×C5—161no—
224C23×C52−1+411yescharacteristic
225C5×Q8—21no—
226C5×Q8—21no—
227C5×Q8—41no—
228C5×Q8—41no—
229C5×Q8—41no—
230C5×Q8—41no—
231C5×D4—21no—
232C5×D4—21no—
233C5×D4—41no—
234C5×D4—41no—
235C5×D4—41no—
236C5×D4—41no—
237C5×D4—41no—
238C5×D4—41no—
239C2×C4×C5—21no—
240C2×C4×C5—41no—
241C2×C4×C5—41no—
242C2×C4×C5—41no—
243C2×C4×C5—41no—
244C2×C4×C5—41no—
245C2×C4×C5—41no—
246C2×C4×C5—41no—
247C2×C4×C5C2×#4111yescharacteristic
248C2×C4×C5H(5,𝔽2)11yescharacteristic
249C2×C4×C5H(5,𝔽2)11yescharacteristic
250C2×C4×C5H(5,𝔽2)11yescharacteristic
251C2×C4×C5H(5,𝔽2)11yescharacteristic
252C2×C4×C5H(5,𝔽2)11yescharacteristic
253C5×C8—41no—
254C5×C8—41no—
255C5×C8—41no—
256C5×C8—41no—
257C5×C8—41no—
258C5×C8—41no—
259C5×C8—41no—
260C5×C8—41no—
261C5×C8—41no—
262C5×C8—41no—
263C2×#41C23×C511yescharacteristic
264C22×Q8C23×C511yescharacteristic
265C22×D4C23×C511yescharacteristic
266#137—41no—
267#137—41no—
268AGL(1,ℤ/8)—41no—
269AGL(1,ℤ/8)—41no—
270C2×Q16—21no—
271C2×SD16—21no—
272C2×SD16—21no—
273C2×SD16—41no—
274C2×SD16—41no—
275C2×SD16—41no—
276C2×D8—21no—
277#131—41no—
278#131—41no—
279C2×M16—41no—
280C2×M16C23×C511yescharacteristic
281C2×M16C23×C511yescharacteristic
282C2×M16C23×C511yescharacteristic
283C2×M16C23×C511yescharacteristic
284C2×M16C23×C511yescharacteristic
285C2×M16C23×C511yescharacteristic
286C2×M16C23×C511yescharacteristic
287C2×M16C23×C511yescharacteristic
288C2×M16C23×C511yescharacteristic
289C22×C8C23×C511yescharacteristic
290#117C23×C511yescharacteristic
291#117C23×C511yescharacteristic
292#108—41no—
293#108—41no—
294#108—41no—
295#108—41no—
296#108—41no—
297C4⋊C8—41no—
298C4⋊C8—41no—
299#104—41no—
300#104—41no—
301#103—41no—
302#103—41no—
303#102—41no—
304#102—41no—
305#101—21no—
306#101—41no—
307#101—41no—
308#101—41no—
309#100—21no—
310#100—41no—
311#100—41no—
312#100—41no—
313C22⋊C8—41no—
314C22×C5—41no—
315C22×C5—41no—
316C22×C5—81no—
317C22×C5—81no—
318C22×C5—161no—
319C22×C5—161no—
320C22×C5—161no—
321C22×C5#53911yescharacteristic
322C22×C5#56211yescharacteristic
323C22×C5#56211yescharacteristic
324C4×C5—41no—
325C4×C5—81no—
326C4×C5—81no—
327C4×C5—81no—
328C4×C5#53811yescharacteristic
329C4×C5#53811yescharacteristic
330C4×C5#56011yescharacteristic
331C4×C5#56011yescharacteristic
332C24—21no—
333#41—21no—
334#41—21no—
335#41—21no—
336#41—21no—
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8C5×#4111yescharacteristic
344C2×D4—21no—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4C5×#4111yescharacteristic
352C22×C4—21no—
353C22×C4—21no—
354C22×C4C24×C511yescharacteristic
355Q16—42no—
356SD16—42no—
357SD16—42no—
358SD16—44no—
359D8—42no—
360M16—21no—
361M16—21no—
362M16—21no—
363M16—21no—
364M16—21no—
365M16—21no—
366M16—21no—
367M16—21no—
368M16—21no—
369M16—21no—
370M16—21no—
371M16—21no—
372M16—21no—
373M16—21no—
374M16—21no—
375M16—21no—
376M16—21no—
377M16—21no—
378M16—42no—
379C2×C8—21no—
380C2×C8—21no—
381C2×C8—21no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—21no—
385C2×C8—21no—
386C2×C8—21no—
387C2×C8—21no—
388C2×C8—21no—
389C2×C8—21no—
390C2×C8—21no—
391C2×C8—42no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C22⋊C4—21no—
395C22⋊C4—21no—
396C42—21no—
397C42—21no—
398C2×C5—21no—
399C2×C5—21no—
400C2×C5—21no—
401C2×C5—81no—
402C2×C5—161no—
403C2×C5#282611yescharacteristic
404C23—21no—
405C23—41no—
406C23—41no—
407C23—41no—
408C23—161no—
409C23C5×2−1+411yescharacteristic
410Q8—21no—
411Q8—21no—
412Q8—41no—
413Q8—41no—
414Q8—41no—
415Q8—41no—
416D4—21no—
417D4—21no—
418D4—41no—
419D4—41no—
420D4—41no—
421D4—41no—
422D4—41no—
423D4—41no—
424C2×C4—21no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4C2×C5×#4111yescharacteristic
433C2×C4C5×H(5,𝔽2)11yescharacteristic
434C2×C4C5×H(5,𝔽2)11yescharacteristic
435C2×C4C5×H(5,𝔽2)11yescharacteristic
436C2×C4C5×H(5,𝔽2)11yescharacteristic
437C2×C4C5×H(5,𝔽2)11yescharacteristic
438C8—41no—
439C8—41no—
440C8—41no—
441C8—41no—
442C8—41no—
443C8—41no—
444C8—41no—
445C8—41no—
446C8—41no—
447C8—41no—
448C5#3287111yescharacteristic, direct product factor, Sylow
449C22—41no—
450C22—41no—
451C22—81no—
452C22—81no—
453C22—161no—
454C22—161no—
455C22—161no—
456C22C5×#53911yescharacteristic
457C22C5×#56211yescharacteristic
458C22C5×#56211yescharacteristic
459C4—41no—
460C4—81no—
461C4—81no—
462C4—81no—
463C4C5×#53811yescharacteristic
464C4C5×#53811yescharacteristic
465C4C5×#56011yescharacteristic
466C4C5×#56011yescharacteristic
467C2—21no—
468C2—21no—
469C2—21no—
470C2—81no—
471C2—161no—
472C2C5×#282611yescharacteristic
subgroupG/H
center, socleC2×C5#2826
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC2×C5×AGL(1,ℤ/8)C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C5 ◁ C22×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#2103C2semidirect
2. C5×#2103C2semidirect
3. C5×#2098C2semidirect
4. C5×#2082C2semidirect
5. C5×#2081C2semidirect
6. C5×#2070C2semidirect
7. C5×#2069C2semidirect
8. C5×#2049C2semidirect
10. C5×#2046C2semidirect
11. C5×#2046C2semidirect
14. C5×#1902C2semidirect
15. C5×#1858C2semidirect
51. #32871C5direct (N × H)
103. #2103C2×C5semidirect
104. #2103C2×C5semidirect
105. #2098C2×C5semidirect
106. #2082C2×C5semidirect
107. #2081C2×C5semidirect
108. #2070C2×C5semidirect
109. #2069C2×C5semidirect
110. #2049C2×C5semidirect
112. #2046C2×C5semidirect
113. #2046C2×C5semidirect
116. #1902C2×C5semidirect
117. #1858C2×C5semidirect
448. C5#32871direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#21032
C5×#20982
C5×#20822
C5×#20812
C5×#20702
C5×#20692
C5×#20492
C5×#20482
C5×#20462
C5×#20192
C5×#19032
C5×#19022
C5×#18582
#328715