Finite Group Databasebeta

← C5×#19062 #11941782

Subgroups — C5×#19062 #11941782

Order 1280.

874 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3550C211yesmaximal, characteristic, complemented
2C5×#3235C211yesmaximal, characteristic, complemented
3C5×#3214C211yesmaximal, characteristic
4C5×#3135C211yesmaximal, characteristic, complemented
5C5×#1664C214yesmaximal, complemented
6C5×#1657C214yesmaximal, complemented
7C5×#1537C211yesmaximal, characteristic, complemented
8C5×#1531C211yesmaximal, characteristic, complemented
9C5×#1530C211yesmaximal, characteristic, complemented
10C5×#563C2214yes—
11C5×#559—21no—
12C5×Q82—21no—
13C5×#556—21no—
14C5×#556—21no—
15C5×D4×Q8—21no—
16C5×D4×Q8—21no—
17C5×#542—22no—
18C5×#542—22no—
19C5×#536—22no—
20C5×#533C2211yescharacteristic
21C5×#533C2211yescharacteristic
22C5×#532C2211yescharacteristic
23C5×#532C2211yescharacteristic
24C5×#501C2212yes—
25C5×#496C2212yes—
26C5×#491C2212yes—
27C5×#490C2212yes—
28C5×#490C2212yes—
29C5×#489—21no—
30C5×#489—21no—
31C5×#489C2212yes—
32C5×#482—22no—
33C5×#476—21no—
34C5×#474—21no—
35C5×#461—21no—
36C5×#459—21no—
37C5×#449—22no—
38C5×#432C2211yescharacteristic
39C5×#432C2211yescharacteristic
40C5×#416—22no—
41C2×C5×#97C2211yescharacteristic
42C5×#330C2214yes—
43C5×#330C2214yes—
44C5×#329C2214yes—
45#19062C511yesmaximal, characteristic, direct product factor, Sylow
46C2×C5×#41—21no—
47C2×C5×#41D412yes—
48C22×C5×Q8—22no—
49C2×C5×SD16—22no—
50C2×C5×D8—22no—
51C22×C5×C8—21no—
52C5×C4⋊Q8—22no—
53C5×C4⋊Q8—22no—
54C5×C4⋊Q8—24no—
55C5×C4⋊Q8D411yescharacteristic
56C5×C4⋊Q8D411yescharacteristic
57C5×C4⋊Q8D411yescharacteristic
58C5×C4⋊Q8D411yescharacteristic
59C5×C4⋊Q8D411yescharacteristic
60C5×C4⋊Q8C2311yescharacteristic
61C5×#127D411yescharacteristic
62C5×#127C2311yescharacteristic
63C5×#126—24no—
64C5×#126—24no—
65C5×#125C2312yes—
66C5×#125C2312yes—
67C5×#124—24no—
68C5×#124—22no—
69C5×#124—22no—
70C5×#124—21no—
71C5×#124C2312yes—
72C5×#123—24no—
73C5×#123—24no—
74C5×C22⋊Q8—22no—
75C5×C22⋊Q8—22no—
76C5×C22⋊Q8—21no—
77C5×C22⋊Q8—21no—
78C5×C22⋊Q8—21no—
79C5×C22⋊Q8—21no—
80C5×C22⋊Q8—24no—
81C5×C22⋊Q8—24no—
82C5×#121—21no—
83C5×#121—21no—
84C5×#121—21no—
85C5×#121—21no—
86C4×C5×Q8—22no—
87C4×C5×Q8—22no—
88C4×C5×Q8—21no—
89C4×C5×Q8—21no—
90C4×C5×Q8—21no—
91C4×C5×Q8—21no—
92C4×C5×D4—22no—
93C4×C5×D4—22no—
94C4×C5×D4—21no—
95C4×C5×D4—21no—
96C4×C5×D4—21no—
97C4×C5×D4—21no—
98C5×#117—22no—
99C5×#117D412yes—
100C5×#117D412yes—
101C2×C42×C5C2311yescharacteristic
102C5×#107—22no—
103C5×#106—22no—
104C5×C4⋊C8—21no—
105C5×C4⋊C8—21no—
106C5×#103—22no—
107C5×#103—22no—
108C5×#103—22no—
109C5×#102—22no—
110C5×#102—22no—
111C5×#102—22no—
112C5×#102—22no—
113C5×#102—22no—
114C5×C22⋊C8—21no—
115C5×C22⋊C8—21no—
116C5×#97—21no—
117C5×#97C2312yes—
118C5×#97C2312yes—
119C5×#97C2312yes—
120#3550C2×C511yescharacteristic, complemented
121#3235C2×C511yescharacteristic, complemented
122#3214C2×C511yescharacteristic
123#3135C2×C511yescharacteristic, complemented
124#1664C2×C514yescomplemented
125#1657C2×C514yescomplemented
126#1537C2×C511yescharacteristic, complemented
127#1531C2×C511yescharacteristic, complemented
128#1530C2×C511yescharacteristic, complemented
129C5×#41—44no—
130C5×#41—82no—
131C2×C5×Q8—24no—
132C2×C5×Q8—21no—
133C2×C5×Q8—21no—
134C2×C5×Q8—21no—
135C2×C5×Q8—21no—
136C2×C5×Q8—21no—
137C2×C5×Q8—84no—
138C2×C5×Q8C2×D412yes—
139C2×C5×D4—22no—
140C2×C5×D4—21no—
141C2×C5×D4—21no—
142C2×C5×D4—21no—
143C2×C5×D4—21no—
144C2×C5×D4—21no—
145C2×C5×D4—41no—
146C2×C5×D4C2×D412yes—
147C22×C4×C5—24no—
148C22×C4×C5—22no—
149C22×C4×C5—41no—
150C22×C4×C5C2×D411yescharacteristic
151C22×C4×C5C2×D411yescharacteristic
152C22×C4×C5C2×D411yescharacteristic
153C5×SD16—82no—
154C5×D8—82no—
155C2×C5×C8—22no—
156C2×C5×C8—22no—
157C2×C5×C8—22no—
158C2×C5×C8—42no—
159C5×C4⋊C4—24no—
160C5×C4⋊C4—24no—
161C5×C4⋊C4—21no—
162C5×C4⋊C4—21no—
163C5×C4⋊C4—21no—
164C5×C4⋊C4—21no—
165C5×C4⋊C4—21no—
166C5×C4⋊C4—21no—
167C5×C4⋊C4—22no—
168C5×C4⋊C4—22no—
169C5×C4⋊C4—22no—
170C5×C4⋊C4—22no—
171C5×C4⋊C4—21no—
172C5×C4⋊C4—21no—
173C5×C4⋊C4C2×D412yes—
174C5×C4⋊C4C2×D412yes—
175C5×C4⋊C4C2×D412yes—
176C5×C4⋊C4C2×D412yes—
177C5×C22⋊C4—24no—
178C5×C22⋊C4—24no—
179C5×C22⋊C4—24no—
180C5×C22⋊C4—22no—
181C5×C22⋊C4—22no—
182C5×C22⋊C4—22no—
183C5×C22⋊C4—22no—
184C5×C22⋊C4—41no—
185C5×C22⋊C4—41no—
186C42×C5—24no—
187C42×C5—22no—
188C42×C5—22no—
189C42×C5C2×D411yescharacteristic
190C42×C5C2×D411yescharacteristic
191C42×C5C2×D411yescharacteristic
192C42×C5C2411yescharacteristic
193#563C22×C514yes—
194#559—21no—
195Q82—21no—
196#556—21no—
197#556—21no—
198D4×Q8—21no—
199D4×Q8—21no—
200#542—22no—
201#542—22no—
202#536—22no—
203#533C22×C511yescharacteristic
204#533C22×C511yescharacteristic
205#532C22×C511yescharacteristic
206#532C22×C511yescharacteristic
207#501C22×C512yes—
208#496C22×C512yes—
209#491C22×C512yes—
210#490C22×C512yes—
211#490C22×C512yes—
212#489—21no—
213#489—21no—
214#489C22×C512yes—
215#482—22no—
216#476—21no—
217#474—21no—
218#461—21no—
219#459—21no—
220#449—22no—
221#432C22×C511yescharacteristic
222#432C22×C511yescharacteristic
223#416—22no—
224C2×#97C22×C511yescharacteristic
225#330C22×C514yes—
226#330C22×C514yes—
227#329C22×C514yes—
228C23×C5—22no—
229C23×C5—41no—
230C23×C5#12011yescharacteristic
231C5×Q8—42no—
232C5×Q8—42no—
233C5×Q8—42no—
234C5×Q8—42no—
235C5×Q8—42no—
236C5×Q8—42no—
237C5×Q8—84no—
238C5×D4—42no—
239C5×D4—42no—
240C5×D4—41no—
241C5×D4—41no—
242C5×D4—42no—
243C5×D4—42no—
244C5×D4—42no—
245C5×D4—82no—
246C5×D4—82no—
247C2×C4×C5—22no—
248C2×C4×C5—22no—
249C2×C4×C5—22no—
250C2×C4×C5—22no—
251C2×C4×C5—22no—
252C2×C4×C5—22no—
253C2×C4×C5—41no—
254C2×C4×C5—41no—
255C2×C4×C5—44no—
256C2×C4×C5—41no—
257C2×C4×C5—84no—
258C2×C4×C5—82no—
259C2×C4×C5#12011yescharacteristic
260C2×C4×C5#12011yescharacteristic
261C2×C4×C5#12011yescharacteristic
262C2×C4×C5C22×D411yescharacteristic
263C2×C4×C5C22×D411yescharacteristic
264C2×C4×C5C22×D411yescharacteristic
265C5×C8—42no—
266C5×C8—42no—
267C5×C8—42no—
268C2×#41—21no—
269C2×#41C5×D412yes—
270C22×Q8—22no—
271C2×SD16—22no—
272C2×D8—22no—
273C22×C8—21no—
274C4⋊Q8—22no—
275C4⋊Q8—22no—
276C4⋊Q8—24no—
277C4⋊Q8C5×D411yescharacteristic
278C4⋊Q8C5×D411yescharacteristic
279C4⋊Q8C5×D411yescharacteristic
280C4⋊Q8C5×D411yescharacteristic
281C4⋊Q8C5×D411yescharacteristic
282C4⋊Q8C23×C511yescharacteristic
283#127C5×D411yescharacteristic
284#127C23×C511yescharacteristic
285#126—24no—
286#126—24no—
287#125C23×C512yes—
288#125C23×C512yes—
289#124—24no—
290#124—22no—
291#124—22no—
292#124—21no—
293#124C23×C512yes—
294#123—24no—
295#123—24no—
296C22⋊Q8—22no—
297C22⋊Q8—22no—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301C22⋊Q8—21no—
302C22⋊Q8—24no—
303C22⋊Q8—24no—
304#121—21no—
305#121—21no—
306#121—21no—
307#121—21no—
308C4×Q8—22no—
309C4×Q8—22no—
310C4×Q8—21no—
311C4×Q8—21no—
312C4×Q8—21no—
313C4×Q8—21no—
314C4×D4—22no—
315C4×D4—22no—
316C4×D4—21no—
317C4×D4—21no—
318C4×D4—21no—
319C4×D4—21no—
320#117—22no—
321#117C5×D412yes—
322#117C5×D412yes—
323C2×C42C23×C511yescharacteristic
324#107—22no—
325#106—22no—
326C4⋊C8—21no—
327C4⋊C8—21no—
328#103—22no—
329#103—22no—
330#103—22no—
331#102—22no—
332#102—22no—
333#102—22no—
334#102—22no—
335#102—22no—
336C22⋊C8—21no—
337C22⋊C8—21no—
338#97—21no—
339#97C23×C512yes—
340#97C23×C512yes—
341#97C23×C512yes—
342C22×C5—21no—
343C22×C5—21no—
344C22×C5—21no—
345C22×C5—42no—
346C22×C5—42no—
347C22×C5—42no—
348C22×C5—81no—
349C22×C5—81no—
350C22×C5—81no—
351C22×C5C2×#12011yescharacteristic
352C4×C5—21no—
353C4×C5—21no—
354C4×C5—21no—
355C4×C5—21no—
356C4×C5—21no—
357C4×C5—42no—
358C4×C5—42no—
359C4×C5—42no—
360C4×C5—42no—
361C4×C5—42no—
362C4×C5—81no—
363C4×C5#45412yes—
364#41—44no—
365#41—82no—
366C2×Q8—24no—
367C2×Q8—21no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—21no—
371C2×Q8—21no—
372C2×Q8—84no—
373C2×Q8C2×C5×D412yes—
374C2×D4—22no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—21no—
379C2×D4—21no—
380C2×D4—41no—
381C2×D4C2×C5×D412yes—
382C22×C4—24no—
383C22×C4—22no—
384C22×C4—41no—
385C22×C4C2×C5×D411yescharacteristic
386C22×C4C2×C5×D411yescharacteristic
387C22×C4C2×C5×D411yescharacteristic
388SD16—82no—
389D8—82no—
390C2×C8—22no—
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—42no—
394C4⋊C4—24no—
395C4⋊C4—24no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4C2×C5×D412yes—
409C4⋊C4C2×C5×D412yes—
410C4⋊C4C2×C5×D412yes—
411C4⋊C4C2×C5×D412yes—
412C22⋊C4—24no—
413C22⋊C4—24no—
414C22⋊C4—24no—
415C22⋊C4—22no—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C22⋊C4—22no—
419C22⋊C4—41no—
420C22⋊C4—41no—
421C42—24no—
422C42—22no—
423C42—22no—
424C42C2×C5×D411yescharacteristic
425C42C2×C5×D411yescharacteristic
426C42C2×C5×D411yescharacteristic
427C42C24×C511yescharacteristic
428C2×C5—41no—
429C2×C5—82no—
430C2×C5—161no—
431C2×C5C2×#45411yescharacteristic
432C2×C5#301911yescharacteristic
433C2×C5#302011yescharacteristic
434C23—22no—
435C23—41no—
436C23C5×#12011yescharacteristic
437Q8—42no—
438Q8—42no—
439Q8—42no—
440Q8—42no—
441Q8—42no—
442Q8—42no—
443Q8—84no—
444D4—42no—
445D4—42no—
446D4—41no—
447D4—41no—
448D4—42no—
449D4—42no—
450D4—42no—
451D4—82no—
452D4—82no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—44no—
462C2×C4—41no—
463C2×C4—84no—
464C2×C4—82no—
465C2×C4C5×#12011yescharacteristic
466C2×C4C5×#12011yescharacteristic
467C2×C4C5×#12011yescharacteristic
468C2×C4C22×C5×D411yescharacteristic
469C2×C4C22×C5×D411yescharacteristic
470C2×C4C22×C5×D411yescharacteristic
471C8—42no—
472C8—42no—
473C8—42no—
474C5#1906211yescharacteristic, direct product factor, Sylow
475C22—21no—
476C22—21no—
477C22—21no—
478C22—42no—
479C22—42no—
480C22—42no—
481C22—81no—
482C22—81no—
483C22—81no—
484C22C2×C5×#12011yescharacteristic
485C4—21no—
486C4—21no—
487C4—21no—
488C4—21no—
489C4—21no—
490C4—42no—
491C4—42no—
492C4—42no—
493C4—42no—
494C4—42no—
495C4—81no—
496C4C5×#45412yes—
497C2—41no—
498C2—82no—
499C2—161no—
500C2C2×C5×#45411yescharacteristic
501C2C5×#301911yescharacteristic
502C2C5×#302011yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
prime radicalC5×#3214C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#3550C2semidirect
2. C5×#3235C2semidirect
4. C5×#3135C2semidirect
5. C5×#1664C2semidirect
6. C5×#1657C2semidirect
7. C5×#1537C2semidirect
8. C5×#1531C2semidirect
9. C5×#1530C2semidirect
45. #19062C5direct (N × H)
120. #3550C2×C5semidirect
121. #3235C2×C5semidirect
123. #3135C2×C5semidirect
124. #1664C2×C5semidirect
125. #1657C2×C5semidirect
126. #1537C2×C5semidirect
127. #1531C2×C5semidirect
128. #1530C2×C5semidirect
474. C5#19062direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35502
C5×#32352
C5×#32142
C5×#31352
C5×#16642
C5×#16572
C5×#15372
C5×#15312
C5×#15302
#190625