Finite Group Databasebeta

← C5×#19032 #11941752

Subgroups — C5×#19032 #11941752

Order 1280.

896 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3561C211yesmaximal, characteristic
2C5×#3218C211yesmaximal, characteristic, complemented
3C5×#3165C211yesmaximal, characteristic, complemented
4C2×C5×#489C211yesmaximal, characteristic, complemented
5C5×#1664C214yesmaximal, complemented
6C5×#1661C214yesmaximal, complemented
7C5×#1531C211yesmaximal, characteristic, complemented
8C5×#1527C211yesmaximal, characteristic, complemented
9C5×#1524C211yesmaximal, characteristic, complemented
10C5×#563C2212yes—
11C5×#562C2212yes—
12C5×#556—21no—
13C5×#551—22no—
14C5×D4×Q8—21no—
15C5×#548—21no—
16C5×#546—21no—
17C5×#543—21no—
18C5×#542—21no—
19C5×#542—22no—
20C5×#538—21no—
21C5×#536—21no—
22C5×#533C2211yescharacteristic
23C2×C5×C4⋊Q8C2211yescharacteristic
24C5×#529C2211yescharacteristic
25C2×C5×#124C2211yescharacteristic
26C5×#501C2214yescomplemented
27C5×#500—21no—
28C5×#498—21no—
29C5×#497C2212yescomplemented
30C5×#491C2212yescomplemented
31C5×#489—22no—
32C5×#489C2214yes—
33C5×#462—21no—
34C5×#461—21no—
35C5×#451—21no—
36C5×#448—21no—
37C5×#432C2211yescharacteristic
38C5×#428—22no—
39C2×C5×#103—21no—
40C2×C5×#102—21no—
41C4×C5×M16C2211yescharacteristic
42C2×C5×#97C2211yescharacteristic
43C5×#330C2212yescomplemented
44C5×#330C2214yescomplemented
45C5×#329C2214yes—
46C5×#329C2212yescomplemented
47#19032C511yesmaximal, characteristic, direct product factor, Sylow
48C2×C5×#41—21no—
49C22×C5×Q8—21no—
50C22×C5×Q8—21no—
51C22×C5×Q8D411yescharacteristic
52C22×C5×D4D411yescharacteristic
53C2×C5×Q16—22no—
54C2×C5×SD16—22no—
55C2×C5×M16—21no—
56C22×C5×C8—21no—
57C5×C4⋊Q8—21no—
58C5×C4⋊Q8—22no—
59C5×C4⋊Q8—21no—
60C5×C4⋊Q8—21no—
61C5×C4⋊Q8—21no—
62C5×C4⋊Q8D411yescharacteristic
63C5×C4⋊Q8D411yescharacteristic
64C5×C4⋊Q8C2312yes—
65C5×#126—22no—
66C5×#126—22no—
67C5×#126—22no—
68C5×#126—21no—
69C5×#125C2311yescharacteristic
70C5×#125C2312yes—
71C5×#124—21no—
72C5×#124—22no—
73C5×#124—22no—
74C5×#124—21no—
75C5×#124—21no—
76C5×#124D412yes—
77C5×#124C2312yes—
78C5×#124C2311yescharacteristic
79C5×#123—22no—
80C5×#123—22no—
81C5×#123—21no—
82C5×#123—22no—
83C5×#123—22no—
84C5×C22⋊Q8—22no—
85C5×C22⋊Q8—22no—
86C5×C22⋊Q8—21no—
87C5×C22⋊Q8—22no—
88C5×C22⋊Q8—22no—
89C5×C22⋊Q8—22no—
90C5×C22⋊Q8—21no—
91C5×C22⋊Q8—21no—
92C5×C22⋊Q8—22no—
93C5×C22⋊Q8—22no—
94C5×C22⋊Q8D411yescharacteristic
95C5×#121—21no—
96C5×#121—22no—
97C5×#121—22no—
98C5×#121D411yescharacteristic
99C5×#120—22no—
100C4×C5×Q8—21no—
101C4×C5×Q8—21no—
102C4×C5×Q8—21no—
103C4×C5×Q8D411yescharacteristic
104C4×C5×D4—22no—
105C4×C5×D4—21no—
106C4×C5×D4—22no—
107C4×C5×D4—21no—
108C4×C5×D4D411yescharacteristic
109C5×#117—22no—
110C5×#117—21no—
111C5×#117D412yes—
112C2×C5×C4⋊C4—21no—
113C2×C5×C4⋊C4—21no—
114C2×C5×C22⋊C4—22no—
115C2×C5×C22⋊C4—21no—
116C2×C5×C22⋊C4—21no—
117C2×C42×C5C2311yescharacteristic
118C5×#107—24no—
119C5×#106—24no—
120C5×C4⋊C8—21no—
121C5×#103—24no—
122C5×#103—22no—
123C5×#103—22no—
124C5×#102—24no—
125C5×C22⋊C8—21no—
126C5×#97—21no—
127C5×#97C2312yes—
128C5×#97C2312yes—
129C5×#97C2312yes—
130C4×C5×C8—21no—
131#3561C2×C511yescharacteristic
132#3218C2×C511yescharacteristic, complemented
133#3165C2×C511yescharacteristic, complemented
134C2×#489C2×C511yescharacteristic, complemented
135#1664C2×C514yescomplemented
136#1661C2×C514yescomplemented
137#1531C2×C511yescharacteristic, complemented
138#1527C2×C511yescharacteristic, complemented
139#1524C2×C511yescharacteristic, complemented
140C24×C5—21no—
141C5×#41—82no—
142C2×C5×Q8—22no—
143C2×C5×Q8—21no—
144C2×C5×Q8—21no—
145C2×C5×Q8—21no—
146C2×C5×Q8—22no—
147C2×C5×Q8—42no—
148C2×C5×Q8—41no—
149C2×C5×Q8—82no—
150C2×C5×Q8—82no—
151C2×C5×Q8C2×D411yescharacteristic
152C2×C5×Q8C2×D412yes—
153C2×C5×D4—21no—
154C2×C5×D4—22no—
155C2×C5×D4—22no—
156C2×C5×D4—21no—
157C2×C5×D4—42no—
158C2×C5×D4C2×D411yescharacteristic
159C2×C5×D4C2×D412yes—
160C22×C4×C5—22no—
161C22×C4×C5—22no—
162C22×C4×C5—22no—
163C22×C4×C5—21no—
164C22×C4×C5—21no—
165C22×C4×C5—41no—
166C22×C4×C5C2×D411yescharacteristic
167C22×C4×C5C2×D411yescharacteristic
168C22×C4×C5C2×D411yescharacteristic
169C5×Q16—82no—
170C5×SD16—82no—
171C5×M16—24no—
172C2×C5×C8—22no—
173C2×C5×C8—22no—
174C2×C5×C8—22no—
175C2×C5×C8—42no—
176C5×C4⋊C4—22no—
177C5×C4⋊C4—22no—
178C5×C4⋊C4—22no—
179C5×C4⋊C4—22no—
180C5×C4⋊C4—21no—
181C5×C4⋊C4—21no—
182C5×C4⋊C4—21no—
183C5×C4⋊C4—21no—
184C5×C4⋊C4—21no—
185C5×C4⋊C4—21no—
186C5×C4⋊C4—22no—
187C5×C4⋊C4—22no—
188C5×C4⋊C4—22no—
189C5×C4⋊C4—22no—
190C5×C4⋊C4—41no—
191C5×C4⋊C4—41no—
192C5×C4⋊C4C2×D412yes—
193C5×C4⋊C4C2×D412yes—
194C5×C4⋊C4C2×D411yescharacteristic
195C5×C4⋊C4C2×D411yescharacteristic
196C5×C22⋊C4—22no—
197C5×C22⋊C4—22no—
198C5×C22⋊C4—22no—
199C5×C22⋊C4—22no—
200C5×C22⋊C4—22no—
201C5×C22⋊C4—21no—
202C5×C22⋊C4—22no—
203C5×C22⋊C4—22no—
204C5×C22⋊C4—22no—
205C5×C22⋊C4—21no—
206C5×C22⋊C4—21no—
207C5×C22⋊C4—22no—
208C5×C22⋊C4—22no—
209C5×C22⋊C4—21no—
210C5×C22⋊C4—21no—
211C42×C5—22no—
212C42×C5—22no—
213C42×C5—21no—
214C42×C5C2×D411yescharacteristic
215C42×C5C2×D411yescharacteristic
216C42×C5C2×D411yescharacteristic
217C42×C5C2411yescharacteristic
218#563C22×C512yes—
219#562C22×C512yes—
220#556—21no—
221#551—22no—
222D4×Q8—21no—
223#548—21no—
224#546—21no—
225#543—21no—
226#542—21no—
227#542—22no—
228#538—21no—
229#536—21no—
230#533C22×C511yescharacteristic
231C2×C4⋊Q8C22×C511yescharacteristic
232#529C22×C511yescharacteristic
233C2×#124C22×C511yescharacteristic
234#501C22×C514yescomplemented
235#500—21no—
236#498—21no—
237#497C22×C512yescomplemented
238#491C22×C512yescomplemented
239#489—22no—
240#489C22×C514yes—
241#462—21no—
242#461—21no—
243#451—21no—
244#448—21no—
245#432C22×C511yescharacteristic
246#428—22no—
247C2×#103—21no—
248C2×#102—21no—
249C4×M16C22×C511yescharacteristic
250C2×#97C22×C511yescharacteristic
251#330C22×C514yescomplemented
252#330C22×C512yescomplemented
253#329C22×C514yes—
254#329C22×C512yescomplemented
255C23×C5—22no—
256C23×C5—21no—
257C23×C5—42no—
258C23×C5—81no—
259C23×C5—81no—
260C23×C5#12011yescharacteristic
261C5×Q8—41no—
262C5×Q8—42no—
263C5×Q8—42no—
264C5×Q8—42no—
265C5×Q8—42no—
266C5×Q8—42no—
267C5×Q8—81no—
268C5×Q8—82no—
269C5×Q8—82no—
270C5×D4—41no—
271C5×D4—42no—
272C5×D4—42no—
273C5×D4—42no—
274C5×D4—82no—
275C5×D4—82no—
276C2×C4×C5—22no—
277C2×C4×C5—22no—
278C2×C4×C5—21no—
279C2×C4×C5—22no—
280C2×C4×C5—21no—
281C2×C4×C5—22no—
282C2×C4×C5—22no—
283C2×C4×C5—21no—
284C2×C4×C5—41no—
285C2×C4×C5—42no—
286C2×C4×C5—42no—
287C2×C4×C5—81no—
288C2×C4×C5—82no—
289C2×C4×C5—82no—
290C2×C4×C5—82no—
291C2×C4×C5—82no—
292C2×C4×C5#12011yescharacteristic
293C2×C4×C5#12011yescharacteristic
294C2×C4×C5#12011yescharacteristic
295C2×C4×C5C22×D411yescharacteristic
296C2×C4×C5C22×D411yescharacteristic
297C2×C4×C5C22×D411yescharacteristic
298C5×C8—24no—
299C5×C8—42no—
300C5×C8—42no—
301C2×#41—21no—
302C22×Q8—21no—
303C22×Q8—21no—
304C22×Q8C5×D411yescharacteristic
305C22×D4C5×D411yescharacteristic
306C2×Q16—22no—
307C2×SD16—22no—
308C2×M16—21no—
309C22×C8—21no—
310C4⋊Q8—21no—
311C4⋊Q8—22no—
312C4⋊Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8C5×D411yescharacteristic
316C4⋊Q8C5×D411yescharacteristic
317C4⋊Q8C23×C512yes—
318#126—22no—
319#126—22no—
320#126—22no—
321#126—21no—
322#125C23×C511yescharacteristic
323#125C23×C512yes—
324#124—21no—
325#124—22no—
326#124—22no—
327#124—21no—
328#124—21no—
329#124C5×D412yes—
330#124C23×C512yes—
331#124C23×C511yescharacteristic
332#123—22no—
333#123—22no—
334#123—21no—
335#123—22no—
336#123—22no—
337C22⋊Q8—22no—
338C22⋊Q8—22no—
339C22⋊Q8—21no—
340C22⋊Q8—22no—
341C22⋊Q8—22no—
342C22⋊Q8—22no—
343C22⋊Q8—21no—
344C22⋊Q8—21no—
345C22⋊Q8—22no—
346C22⋊Q8—22no—
347C22⋊Q8C5×D411yescharacteristic
348#121—21no—
349#121—22no—
350#121—22no—
351#121C5×D411yescharacteristic
352#120—22no—
353C4×Q8—21no—
354C4×Q8—21no—
355C4×Q8—21no—
356C4×Q8C5×D411yescharacteristic
357C4×D4—22no—
358C4×D4—21no—
359C4×D4—22no—
360C4×D4—21no—
361C4×D4C5×D411yescharacteristic
362#117—22no—
363#117—21no—
364#117C5×D412yes—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C42C23×C511yescharacteristic
371#107—24no—
372#106—24no—
373C4⋊C8—21no—
374#103—24no—
375#103—22no—
376#103—22no—
377#102—24no—
378C22⋊C8—21no—
379#97—21no—
380#97C23×C512yes—
381#97C23×C512yes—
382#97C23×C512yes—
383C4×C8—21no—
384C22×C5—21no—
385C22×C5—21no—
386C22×C5—41no—
387C22×C5—42no—
388C22×C5—41no—
389C22×C5—42no—
390C22×C5—42no—
391C22×C5—41no—
392C22×C5—162no—
393C22×C5#45612yes—
394C22×C5C2×#12011yescharacteristic
395C4×C5—21no—
396C4×C5—21no—
397C4×C5—21no—
398C4×C5—21no—
399C4×C5—21no—
400C4×C5—41no—
401C4×C5—42no—
402C4×C5—42no—
403C4×C5—41no—
404C4×C5—41no—
405C4×C5—42no—
406C4×C5—82no—
407C4×C5#45512yes—
408C24—21no—
409#41—82no—
410C2×Q8—22no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—22no—
415C2×Q8—42no—
416C2×Q8—41no—
417C2×Q8—82no—
418C2×Q8—82no—
419C2×Q8C2×C5×D412yes—
420C2×Q8C2×C5×D411yescharacteristic
421C2×D4—21no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—21no—
425C2×D4—42no—
426C2×D4C2×C5×D412yes—
427C2×D4C2×C5×D411yescharacteristic
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—41no—
434C22×C4C2×C5×D411yescharacteristic
435C22×C4C2×C5×D411yescharacteristic
436C22×C4C2×C5×D411yescharacteristic
437Q16—82no—
438SD16—82no—
439M16—24no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—42no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4C2×C5×D411yescharacteristic
461C4⋊C4C2×C5×D411yescharacteristic
462C4⋊C4C2×C5×D412yes—
463C4⋊C4C2×C5×D412yes—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—21no—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C42—22no—
480C42—22no—
481C42—21no—
482C42C2×C5×D411yescharacteristic
483C42C2×C5×D411yescharacteristic
484C42C2×C5×D411yescharacteristic
485C42C24×C511yescharacteristic
486C2×C5—22no—
487C2×C5—81no—
488C2×C5—82no—
489C2×C5C2×#45511yescharacteristic
490C2×C5C2×#45611yescharacteristic
491C2×C5#302111yescharacteristic
492C23—22no—
493C23—21no—
494C23—42no—
495C23—81no—
496C23—81no—
497C23C5×#12011yescharacteristic
498Q8—41no—
499Q8—42no—
500Q8—42no—
501Q8—42no—
502Q8—42no—
503Q8—42no—
504Q8—81no—
505Q8—82no—
506Q8—82no—
507D4—41no—
508D4—42no—
509D4—42no—
510D4—42no—
511D4—82no—
512D4—82no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—81no—
525C2×C4—82no—
526C2×C4—82no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4C5×#12011yescharacteristic
530C2×C4C5×#12011yescharacteristic
531C2×C4C5×#12011yescharacteristic
532C2×C4C22×C5×D411yescharacteristic
533C2×C4C22×C5×D411yescharacteristic
534C2×C4C22×C5×D411yescharacteristic
535C8—24no—
536C8—42no—
537C8—42no—
538C5#1903211yescharacteristic, direct product factor, Sylow
539C22—21no—
540C22—21no—
541C22—41no—
542C22—42no—
543C22—41no—
544C22—42no—
545C22—42no—
546C22—41no—
547C22—162no—
548C22C5×#45612yes—
549C22C2×C5×#12011yescharacteristic
550C4—21no—
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—41no—
556C4—42no—
557C4—42no—
558C4—41no—
559C4—41no—
560C4—42no—
561C4—82no—
562C4C5×#45512yes—
563C2—22no—
564C2—82no—
565C2—81no—
566C2C2×C5×#45511yescharacteristic
567C2C2×C5×#45611yescharacteristic
568C2C5×#302111yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
prime radicalC5×#3561C2
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
2. C5×#3218C2semidirect
3. C5×#3165C2semidirect
4. C2×C5×#489C2semidirect
5. C5×#1664C2semidirect
6. C5×#1661C2semidirect
7. C5×#1531C2semidirect
8. C5×#1527C2semidirect
9. C5×#1524C2semidirect
26. C5×#501C22semidirect
29. C5×#497C22semidirect
30. C5×#491C22semidirect
43. C5×#330C22semidirect
44. C5×#330C22semidirect
46. C5×#329C22semidirect
47. #19032C5direct (N × H)
132. #3218C2×C5semidirect
133. #3165C2×C5semidirect
134. C2×#489C2×C5semidirect
135. #1664C2×C5semidirect
136. #1661C2×C5semidirect
137. #1531C2×C5semidirect
138. #1527C2×C5semidirect
139. #1524C2×C5semidirect
234. #501C22×C5semidirect
237. #497C22×C5semidirect
238. #491C22×C5semidirect
251. #330C22×C5semidirect
252. #330C22×C5semidirect
254. #329C22×C5semidirect
538. C5#19032direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35612
C5×#32182
C5×#31652
C2×C5×#4892
C5×#16642
C5×#16612
C5×#15312
C5×#15272
C5×#15242
#190325