Finite Group Databasebeta

← C5×#19381 #11942101

Subgroups — C5×#19381 #11942101

Order 1280.

572 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3252C211yesmaximal, characteristic
2C5×#3239C211yesmaximal, characteristic
3C5×#3139C211yesmaximal, characteristic, complemented
4C5×#2969C211yesmaximal, characteristic
5C5×#1704C211yesmaximal, characteristic, complemented
6C5×#1703C211yesmaximal, characteristic, complemented
7C5×#1700C211yesmaximal, characteristic, complemented
8C5×#1699C211yesmaximal, characteristic, complemented
9C5×#1684C211yesmaximal, characteristic, complemented
10C5×#1683C211yesmaximal, characteristic, complemented
11C5×#1680C211yesmaximal, characteristic, complemented
12C5×#1679C211yesmaximal, characteristic, complemented
13C5×#1569C211yesmaximal, characteristic, complemented
14C5×#1554C211yesmaximal, characteristic, complemented
15C5×#1549C211yesmaximal, characteristic, complemented
16C5×#533C2211yescharacteristic
17C2×C5×C4⋊Q8C2211yescharacteristic
18C5×#529C2211yescharacteristic
19C5×#501—21no—
20C5×#491—21no—
21C5×#491—21no—
22C5×#489—21no—
23C5×#487C2211yescharacteristic
24C5×#487C2211yescharacteristic
25C5×#487C2211yescharacteristic
26C5×#487C2211yescharacteristic
27C5×#484—21no—
28C5×#481—21no—
29C5×#479—21no—
30C5×#477C2211yescharacteristic
31C5×#476C2211yescharacteristic
32C5×#475C2211yescharacteristic
33C5×#475C2211yescharacteristic
34C5×#474C2211yescharacteristic
35C5×#474C2211yescharacteristic
36C5×#470—21no—
37C5×#468—21no—
38C5×#464—21no—
39C5×#462C2211yescharacteristic
40C5×#461C2211yescharacteristic
41C5×#446C2211yescharacteristic
42C5×C8×Q8C2211yescharacteristic
43C5×#436—21no—
44C5×#436C2211yescharacteristic
45C5×#435—21no—
46C5×C8×D4C2211yescharacteristic
47C5×#433—21no—
48C5×#432C2211yescharacteristic
49C5×#431C2211yescharacteristic
50C5×#423C2211yescharacteristic
51C5×#419—21no—
52C5×#419—21no—
53C5×#405—21no—
54C4×C5×M16C2211yescharacteristic
55C5×#335C2211yescharacteristic
56C5×#335C2211yescharacteristic
57C5×#334C2211yescharacteristic
58C5×#334C2211yescharacteristic
59C5×#333C2211yescharacteristic
60C5×#333C2211yescharacteristic
61C5×#332C2211yescharacteristic
62C5×#332C2211yescharacteristic
63C5×#332C2211yescharacteristic
64C5×#332C2211yescharacteristic
65C5×#332C2211yescharacteristic
66C5×#332C2211yescharacteristic
67#19381C511yesmaximal, characteristic, direct product factor, Sylow
68C22×C5×Q8—21no—
69C2×C5×Q16—21no—
70C2×C5×SD16—21no—
71C2×C5×M16—21no—
72C2×C5×M16—21no—
73C2×C5×M16D411yescharacteristic
74C2×C5×M16D411yescharacteristic
75C22×C5×C8—21no—
76C5×C4⋊Q8—21no—
77C5×C4⋊Q8—21no—
78C5×C4⋊Q8—21no—
79C5×C4⋊Q8C2311yescharacteristic
80C5×C4⋊Q8C2311yescharacteristic
81C5×C4⋊Q8C2311yescharacteristic
82C5×C4⋊Q8C2311yescharacteristic
83C5×#126—21no—
84C5×#125—21no—
85C5×#125D411yescharacteristic
86C5×#124D411yescharacteristic
87C5×#123—21no—
88C5×C22⋊Q8—21no—
89C5×C22⋊Q8—21no—
90C5×C22⋊Q8D411yescharacteristic
91C5×#121D411yescharacteristic
92C4×C5×Q8—21no—
93C4×C5×Q8—21no—
94C4×C5×Q8C2311yescharacteristic
95C4×C5×D4—21no—
96C4×C5×D4C2311yescharacteristic
97C5×#117—21no—
98C5×#117—21no—
99C2×C5×C4⋊C4—21no—
100C2×C5×C4⋊C4—21no—
101C2×C42×C5C2311yescharacteristic
102C5×#107—21no—
103C5×#107—21no—
104C5×#107—21no—
105C5×#106—21no—
106C5×#106—21no—
107C5×#106—21no—
108C5×C4⋊C8—21no—
109C5×C4⋊C8—21no—
110C5×C4⋊C8—21no—
111C5×C4⋊C8C2311yescharacteristic
112C5×C4⋊C8C2311yescharacteristic
113C5×C4⋊C8C2311yescharacteristic
114C5×C4⋊C8C2311yescharacteristic
115C5×C4⋊C8C2311yescharacteristic
116C5×C4⋊C8C2311yescharacteristic
117C5×#103—21no—
118C5×#103—21no—
119C5×#103—21no—
120C5×#103—21no—
121C5×#103—21no—
122C5×#103—21no—
123C5×#103—21no—
124C5×#103—21no—
125C5×#103—21no—
126C5×#103—21no—
127C5×#103—21no—
128C5×#103—21no—
129C5×#103—21no—
130C5×#102—21no—
131C5×#102—21no—
132C5×#102—21no—
133C5×C22⋊C8—21no—
134C5×C22⋊C8—21no—
135C5×C22⋊C8—21no—
136C5×C22⋊C8—21no—
137C5×#97—21no—
138C5×#97—21no—
139C5×#97D411yescharacteristic
140C5×#97D411yescharacteristic
141C4×C5×C8—21no—
142C4×C5×C8—21no—
143C4×C5×C8C2311yescharacteristic
144C4×C5×C8C2311yescharacteristic
145#3252C2×C511yescharacteristic
146#3239C2×C511yescharacteristic
147#3139C2×C511yescharacteristic, complemented
148#2969C2×C511yescharacteristic
149#1704C2×C511yescharacteristic, complemented
150#1703C2×C511yescharacteristic, complemented
151#1700C2×C511yescharacteristic, complemented
152#1699C2×C511yescharacteristic, complemented
153#1684C2×C511yescharacteristic, complemented
154#1683C2×C511yescharacteristic, complemented
155#1680C2×C511yescharacteristic, complemented
156#1679C2×C511yescharacteristic, complemented
157#1569C2×C511yescharacteristic, complemented
158#1554C2×C511yescharacteristic, complemented
159#1549C2×C511yescharacteristic, complemented
160C2×C5×Q8—21no—
161C2×C5×Q8—21no—
162C2×C5×Q8—21no—
163C2×C5×Q8—21no—
164C2×C5×Q8—42no—
165C2×C5×Q8—42no—
166C2×C5×Q8—41no—
167C2×C5×Q8C2×D411yescharacteristic
168C2×C5×D4—21no—
169C2×C5×D4C2×D411yescharacteristic
170C22×C4×C5—21no—
171C22×C4×C5—41no—
172C22×C4×C5C2×D411yescharacteristic
173C22×C4×C5C2×D411yescharacteristic
174C22×C4×C5#4111yescharacteristic
175C5×Q16—81no—
176C5×SD16—81no—
177C5×M16—41no—
178C5×M16—41no—
179C5×M16—42no—
180C5×M16—81no—
181C2×C5×C8—21no—
182C2×C5×C8—21no—
183C2×C5×C8—21no—
184C2×C5×C8—21no—
185C2×C5×C8—21no—
186C2×C5×C8—21no—
187C2×C5×C8—42no—
188C2×C5×C8C2×D411yescharacteristic
189C2×C5×C8C2×D411yescharacteristic
190C2×C5×C8C2×D411yescharacteristic
191C2×C5×C8C2×D411yescharacteristic
192C5×C4⋊C4—21no—
193C5×C4⋊C4—21no—
194C5×C4⋊C4—21no—
195C5×C4⋊C4—21no—
196C5×C4⋊C4—21no—
197C5×C4⋊C4—21no—
198C5×C4⋊C4—21no—
199C5×C4⋊C4—21no—
200C5×C4⋊C4—21no—
201C5×C4⋊C4—21no—
202C5×C4⋊C4—21no—
203C5×C4⋊C4—21no—
204C5×C4⋊C4—41no—
205C5×C4⋊C4—41no—
206C5×C4⋊C4—41no—
207C5×C4⋊C4—41no—
208C5×C4⋊C4C2×D411yescharacteristic
209C5×C4⋊C4C2×D411yescharacteristic
210C5×C22⋊C4—21no—
211C5×C22⋊C4—21no—
212C5×C22⋊C4—21no—
213C5×C22⋊C4—21no—
214C5×C22⋊C4—21no—
215C5×C22⋊C4—41no—
216C42×C5—21no—
217C42×C5—41no—
218C42×C5C2×D411yescharacteristic
219C42×C5C2×D411yescharacteristic
220C42×C5#4111yescharacteristic
221C42×C5C2411yescharacteristic
222#533C22×C511yescharacteristic
223C2×C4⋊Q8C22×C511yescharacteristic
224#529C22×C511yescharacteristic
225#501—21no—
226#491—21no—
227#491—21no—
228#489—21no—
229#487C22×C511yescharacteristic
230#487C22×C511yescharacteristic
231#487C22×C511yescharacteristic
232#487C22×C511yescharacteristic
233#484—21no—
234#481—21no—
235#479—21no—
236#477C22×C511yescharacteristic
237#476C22×C511yescharacteristic
238#475C22×C511yescharacteristic
239#475C22×C511yescharacteristic
240#474C22×C511yescharacteristic
241#474C22×C511yescharacteristic
242#470—21no—
243#468—21no—
244#464—21no—
245#462C22×C511yescharacteristic
246#461C22×C511yescharacteristic
247#446C22×C511yescharacteristic
248C8×Q8C22×C511yescharacteristic
249#436—21no—
250#436C22×C511yescharacteristic
251#435—21no—
252C8×D4C22×C511yescharacteristic
253#433—21no—
254#432C22×C511yescharacteristic
255#431C22×C511yescharacteristic
256#423C22×C511yescharacteristic
257#419—21no—
258#419—21no—
259#405—21no—
260C4×M16C22×C511yescharacteristic
261#335C22×C511yescharacteristic
262#335C22×C511yescharacteristic
263#334C22×C511yescharacteristic
264#334C22×C511yescharacteristic
265#333C22×C511yescharacteristic
266#333C22×C511yescharacteristic
267#332C22×C511yescharacteristic
268#332C22×C511yescharacteristic
269#332C22×C511yescharacteristic
270#332C22×C511yescharacteristic
271#332C22×C511yescharacteristic
272#332C22×C511yescharacteristic
273C23×C5—21no—
274C23×C5#12111yescharacteristic
275C5×Q8—21no—
276C5×Q8—21no—
277C5×Q8—41no—
278C5×Q8—41no—
279C5×Q8—41no—
280C5×Q8—41no—
281C5×Q8—41no—
282C5×Q8—41no—
283C5×Q8—81no—
284C5×Q8—82no—
285C5×D4—21no—
286C5×D4—21no—
287C5×D4—81no—
288C2×C4×C5—21no—
289C2×C4×C5—21no—
290C2×C4×C5—21no—
291C2×C4×C5—21no—
292C2×C4×C5—21no—
293C2×C4×C5—21no—
294C2×C4×C5—21no—
295C2×C4×C5—41no—
296C2×C4×C5—41no—
297C2×C4×C5—41no—
298C2×C4×C5—41no—
299C2×C4×C5—41no—
300C2×C4×C5—41no—
301C2×C4×C5—41no—
302C2×C4×C5—82no—
303C2×C4×C5#12111yescharacteristic
304C2×C4×C5#12111yescharacteristic
305C2×C4×C5#12111yescharacteristic
306C2×C4×C5C22×D411yescharacteristic
307C2×C4×C5C22×D411yescharacteristic
308C2×C4×C5C2×#4111yescharacteristic
309C5×C8—21no—
310C5×C8—21no—
311C5×C8—21no—
312C5×C8—21no—
313C5×C8—41no—
314C5×C8—41no—
315C5×C8—41no—
316C5×C8—41no—
317C5×C8—41no—
318C5×C8—41no—
319C22×Q8—21no—
320C2×Q16—21no—
321C2×SD16—21no—
322C2×M16—21no—
323C2×M16—21no—
324C2×M16C5×D411yescharacteristic
325C2×M16C5×D411yescharacteristic
326C22×C8—21no—
327C4⋊Q8—21no—
328C4⋊Q8—21no—
329C4⋊Q8—21no—
330C4⋊Q8C23×C511yescharacteristic
331C4⋊Q8C23×C511yescharacteristic
332C4⋊Q8C23×C511yescharacteristic
333C4⋊Q8C23×C511yescharacteristic
334#126—21no—
335#125—21no—
336#125C5×D411yescharacteristic
337#124C5×D411yescharacteristic
338#123—21no—
339C22⋊Q8—21no—
340C22⋊Q8—21no—
341C22⋊Q8C5×D411yescharacteristic
342#121C5×D411yescharacteristic
343C4×Q8—21no—
344C4×Q8—21no—
345C4×Q8C23×C511yescharacteristic
346C4×D4—21no—
347C4×D4C23×C511yescharacteristic
348#117—21no—
349#117—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C42C23×C511yescharacteristic
353#107—21no—
354#107—21no—
355#107—21no—
356#106—21no—
357#106—21no—
358#106—21no—
359C4⋊C8—21no—
360C4⋊C8—21no—
361C4⋊C8—21no—
362C4⋊C8C23×C511yescharacteristic
363C4⋊C8C23×C511yescharacteristic
364C4⋊C8C23×C511yescharacteristic
365C4⋊C8C23×C511yescharacteristic
366C4⋊C8C23×C511yescharacteristic
367C4⋊C8C23×C511yescharacteristic
368#103—21no—
369#103—21no—
370#103—21no—
371#103—21no—
372#103—21no—
373#103—21no—
374#103—21no—
375#103—21no—
376#103—21no—
377#103—21no—
378#103—21no—
379#103—21no—
380#103—21no—
381#102—21no—
382#102—21no—
383#102—21no—
384C22⋊C8—21no—
385C22⋊C8—21no—
386C22⋊C8—21no—
387C22⋊C8—21no—
388#97—21no—
389#97—21no—
390#97C5×D411yescharacteristic
391#97C5×D411yescharacteristic
392C4×C8—21no—
393C4×C8—21no—
394C4×C8C23×C511yescharacteristic
395C4×C8C23×C511yescharacteristic
396C22×C5—21no—
397C22×C5—21no—
398C22×C5—21no—
399C22×C5—41no—
400C22×C5—41no—
401C22×C5—41no—
402C22×C5C2×#12111yescharacteristic
403C4×C5—21no—
404C4×C5—21no—
405C4×C5—21no—
406C4×C5—21no—
407C4×C5—41no—
408C4×C5—41no—
409C4×C5—41no—
410C4×C5—81no—
411C4×C5—81no—
412C4×C5—81no—
413C4×C5—81no—
414C4×C5#57511yescharacteristic
415C4×C5#57511yescharacteristic
416C4×C5#57711yescharacteristic
417C4×C5#57811yescharacteristic
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—42no—
423C2×Q8—42no—
424C2×Q8—41no—
425C2×Q8C2×C5×D411yescharacteristic
426C2×D4—21no—
427C2×D4C2×C5×D411yescharacteristic
428C22×C4—21no—
429C22×C4—41no—
430C22×C4C2×C5×D411yescharacteristic
431C22×C4C2×C5×D411yescharacteristic
432C22×C4C5×#4111yescharacteristic
433Q16—81no—
434SD16—81no—
435M16—41no—
436M16—41no—
437M16—42no—
438M16—81no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—42no—
446C2×C8C2×C5×D411yescharacteristic
447C2×C8C2×C5×D411yescharacteristic
448C2×C8C2×C5×D411yescharacteristic
449C2×C8C2×C5×D411yescharacteristic
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4C2×C5×D411yescharacteristic
467C4⋊C4C2×C5×D411yescharacteristic
468C22⋊C4—21no—
469C22⋊C4—21no—
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—41no—
474C42—21no—
475C42—41no—
476C42C2×C5×D411yescharacteristic
477C42C2×C5×D411yescharacteristic
478C42C5×#4111yescharacteristic
479C42C24×C511yescharacteristic
480C2×C5—41no—
481C2×C5—81no—
482C2×C5#304011yescharacteristic
483C2×C5#306311yescharacteristic
484C2×C5#306911yescharacteristic
485C23—21no—
486C23C5×#12111yescharacteristic
487Q8—21no—
488Q8—21no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—81no—
496Q8—82no—
497D4—21no—
498D4—21no—
499D4—81no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—82no—
515C2×C4C5×#12111yescharacteristic
516C2×C4C5×#12111yescharacteristic
517C2×C4C5×#12111yescharacteristic
518C2×C4C22×C5×D411yescharacteristic
519C2×C4C22×C5×D411yescharacteristic
520C2×C4C2×C5×#4111yescharacteristic
521C8—21no—
522C8—21no—
523C8—21no—
524C8—21no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—41no—
531C5#1938111yescharacteristic, direct product factor, Sylow
532C22—21no—
533C22—21no—
534C22—21no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22C2×C5×#12111yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—81no—
547C4—81no—
548C4—81no—
549C4—81no—
550C4C5×#57511yescharacteristic
551C4C5×#57511yescharacteristic
552C4C5×#57711yescharacteristic
553C4C5×#57811yescharacteristic
554C2—41no—
555C2—81no—
556C2C5×#304011yescharacteristic
557C2C5×#306311yescharacteristic
558C2C5×#306911yescharacteristic
subgroupG/H
center, socleC22×C5C2×#121
commutator, Frattini, cosocleC42C24×C5
prime radicalC5×#121D4
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
3. C5×#3139C2semidirect
5. C5×#1704C2semidirect
6. C5×#1703C2semidirect
7. C5×#1700C2semidirect
8. C5×#1699C2semidirect
9. C5×#1684C2semidirect
10. C5×#1683C2semidirect
11. C5×#1680C2semidirect
12. C5×#1679C2semidirect
13. C5×#1569C2semidirect
14. C5×#1554C2semidirect
15. C5×#1549C2semidirect
67. #19381C5direct (N × H)
147. #3139C2×C5semidirect
149. #1704C2×C5semidirect
150. #1703C2×C5semidirect
151. #1700C2×C5semidirect
152. #1699C2×C5semidirect
153. #1684C2×C5semidirect
154. #1683C2×C5semidirect
155. #1680C2×C5semidirect
156. #1679C2×C5semidirect
157. #1569C2×C5semidirect
158. #1554C2×C5semidirect
159. #1549C2×C5semidirect
531. C5#19381direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#32522
C5×#32392
C5×#31392
C5×#29692
C5×#17042
C5×#17032
C5×#17002
C5×#16992
C5×#16842
C5×#16832
C5×#16802
C5×#16792
C5×#15692
C5×#15542
C5×#15492
#193815