Finite Group Databasebeta

← C5×#19579 #11942299

Subgroups — C5×#19579 #11942299

Order 1280.

584 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3251C211yesmaximal, characteristic
2C5×#3233C211yesmaximal, characteristic, complemented
3C5×#3210C211yesmaximal, characteristic, complemented
4C5×#2994C211yesmaximal, characteristic, complemented
5C5×#1703C211yesmaximal, characteristic, complemented
6C5×#1698C211yesmaximal, characteristic, complemented
7C5×#1690C211yesmaximal, characteristic, complemented
8C5×#1685C211yesmaximal, characteristic, complemented
9C5×#1684C211yesmaximal, characteristic, complemented
10C5×#1677C211yesmaximal, characteristic, complemented
11C5×#1669C211yesmaximal, characteristic, complemented
12C5×#1666C211yesmaximal, characteristic, complemented
13C5×#1574C211yesmaximal, characteristic, complemented
14C5×#1550C211yesmaximal, characteristic, complemented
15C5×#1540C211yesmaximal, characteristic, complemented
16C5×#533C2211yescharacteristic
17C5×#532C2211yescharacteristic
18C5×#529C2211yescharacteristic
19C5×#499—21no—
20C5×#494C2211yescharacteristic
21C5×#492C2211yescharacteristic
22C5×#488—21no—
23C5×#487C2211yescharacteristic
24C5×#486C2211yescharacteristic
25C5×#485—21no—
26C5×#482—21no—
27C5×#478—21no—
28C5×#477C2211yescharacteristic
29C5×#476C2211yescharacteristic
30C5×#475C2211yescharacteristic
31C5×#475C2211yescharacteristic
32C5×#474C2211yescharacteristic
33C5×#474C2211yescharacteristic
34C5×#469—21no—
35C5×#468—21no—
36C5×#464—21no—
37C5×#464—21no—
38C5×#463—21no—
39C5×#460C2211yescharacteristic
40C5×#459C2211yescharacteristic
41C5×#452—21no—
42C5×#452—21no—
43C5×#446C2211yescharacteristic
44C5×C8×Q8C2211yescharacteristic
45C5×#436C2211yescharacteristic
46C5×#435—21no—
47C5×C8×D4—21no—
48C5×C8×D4C2211yescharacteristic
49C5×#433—21no—
50C5×#431C2211yescharacteristic
51C5×#431C2211yescharacteristic
52C5×#424—21no—
53C5×#423C2211yescharacteristic
54C2×C5×C4⋊C8C2211yescharacteristic
55C5×#335C2211yescharacteristic
56C5×#335C2211yescharacteristic
57C5×#334C2211yescharacteristic
58C5×#334C2211yescharacteristic
59C5×#333C2211yescharacteristic
60C5×#333C2211yescharacteristic
61C5×#332C2211yescharacteristic
62C5×#332C2211yescharacteristic
63C5×#332C2211yescharacteristic
64C5×#332C2211yescharacteristic
65C5×#331C2211yescharacteristic
66C5×#331C2211yescharacteristic
67#19579C511yesmaximal, characteristic, direct product factor, Sylow
68C2×C5×#41—21no—
69C2×C5×Q16—21no—
70C2×C5×Q16—21no—
71C2×C5×SD16—21no—
72C2×C5×SD16—21no—
73C2×C5×SD16—21no—
74C2×C5×D8—21no—
75C2×C5×M16—21no—
76C2×C5×M16—21no—
77C22×C5×C8—21no—
78C22×C5×C8—21no—
79C5×C4⋊Q8C2311yescharacteristic
80C5×C4⋊Q8C2311yescharacteristic
81C5×C4⋊Q8C2311yescharacteristic
82C5×#127C2311yescharacteristic
83C5×#126—21no—
84C5×#125—21no—
85C5×#125D411yescharacteristic
86C5×#124—21no—
87C5×#124D411yescharacteristic
88C5×#123—21no—
89C5×C22⋊Q8—21no—
90C5×C22⋊Q8—21no—
91C5×C22⋊Q8D411yescharacteristic
92C5×#121—21no—
93C5×#121—21no—
94C5×#121D411yescharacteristic
95C4×C5×Q8—21no—
96C4×C5×Q8—21no—
97C4×C5×Q8C2311yescharacteristic
98C4×C5×D4—21no—
99C4×C5×D4—21no—
100C4×C5×D4—21no—
101C4×C5×D4C2311yescharacteristic
102C5×#117—21no—
103C5×#117—21no—
104C2×C42×C5C2311yescharacteristic
105C5×#107—21no—
106C5×#107—21no—
107C5×#107—21no—
108C5×#106—21no—
109C5×#106—21no—
110C5×#106—21no—
111C5×C4⋊C8—21no—
112C5×C4⋊C8—21no—
113C5×C4⋊C8—21no—
114C5×C4⋊C8—21no—
115C5×C4⋊C8D411yescharacteristic
116C5×C4⋊C8D411yescharacteristic
117C5×C4⋊C8C2311yescharacteristic
118C5×C4⋊C8C2311yescharacteristic
119C5×C4⋊C8C2311yescharacteristic
120C5×C4⋊C8C2311yescharacteristic
121C5×C4⋊C8C2311yescharacteristic
122C5×C4⋊C8C2311yescharacteristic
123C5×#103—21no—
124C5×#103—21no—
125C5×#103—21no—
126C5×#103—21no—
127C5×#103—21no—
128C5×#102—21no—
129C5×#102—21no—
130C5×#102—21no—
131C5×#102—21no—
132C5×#102—21no—
133C5×#102—21no—
134C5×#102—21no—
135C5×C22⋊C8—21no—
136C5×C22⋊C8—21no—
137C5×C22⋊C8—21no—
138C5×C22⋊C8D411yescharacteristic
139C5×C22⋊C8D411yescharacteristic
140C5×#97—21no—
141C4×C5×C8—21no—
142C4×C5×C8—21no—
143C4×C5×C8C2311yescharacteristic
144C4×C5×C8C2311yescharacteristic
145#3251C2×C511yescharacteristic
146#3233C2×C511yescharacteristic, complemented
147#3210C2×C511yescharacteristic, complemented
148#2994C2×C511yescharacteristic, complemented
149#1703C2×C511yescharacteristic, complemented
150#1698C2×C511yescharacteristic, complemented
151#1690C2×C511yescharacteristic, complemented
152#1685C2×C511yescharacteristic, complemented
153#1684C2×C511yescharacteristic, complemented
154#1677C2×C511yescharacteristic, complemented
155#1669C2×C511yescharacteristic, complemented
156#1666C2×C511yescharacteristic, complemented
157#1574C2×C511yescharacteristic, complemented
158#1550C2×C511yescharacteristic, complemented
159#1540C2×C511yescharacteristic, complemented
160C5×#41—81no—
161C5×#41—81no—
162C2×C5×Q8—21no—
163C2×C5×Q8—21no—
164C2×C5×Q8—21no—
165C2×C5×Q8C2×D411yescharacteristic
166C2×C5×D4—21no—
167C2×C5×D4—21no—
168C2×C5×D4—21no—
169C2×C5×D4—21no—
170C2×C5×D4—41no—
171C2×C5×D4C2×D411yescharacteristic
172C22×C4×C5—21no—
173C22×C4×C5—41no—
174C22×C4×C5C2×D411yescharacteristic
175C22×C4×C5C2×D411yescharacteristic
176C22×C4×C5#4111yescharacteristic
177C5×Q16—81no—
178C5×Q16—81no—
179C5×SD16—81no—
180C5×SD16—81no—
181C5×SD16—81no—
182C5×D8—81no—
183C5×M16—81no—
184C5×M16—81no—
185C2×C5×C8—21no—
186C2×C5×C8—21no—
187C2×C5×C8—21no—
188C2×C5×C8—21no—
189C2×C5×C8—21no—
190C2×C5×C8—21no—
191C2×C5×C8—81no—
192C2×C5×C8—81no—
193C2×C5×C8C2×D411yescharacteristic
194C2×C5×C8C2×D411yescharacteristic
195C2×C5×C8C2×D411yescharacteristic
196C2×C5×C8C2×D411yescharacteristic
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—21no—
205C5×C4⋊C4—21no—
206C5×C4⋊C4—21no—
207C5×C4⋊C4—41no—
208C5×C4⋊C4—41no—
209C5×C4⋊C4C2×D411yescharacteristic
210C5×C4⋊C4C2×D411yescharacteristic
211C5×C22⋊C4—21no—
212C5×C22⋊C4—21no—
213C5×C22⋊C4—21no—
214C5×C22⋊C4—21no—
215C5×C22⋊C4—21no—
216C5×C22⋊C4—41no—
217C5×C22⋊C4—41no—
218C5×C22⋊C4—41no—
219C42×C5—21no—
220C42×C5—41no—
221C42×C5C2×D411yescharacteristic
222C42×C5C2×D411yescharacteristic
223C42×C5#4111yescharacteristic
224C42×C5C2411yescharacteristic
225#533C22×C511yescharacteristic
226#532C22×C511yescharacteristic
227#529C22×C511yescharacteristic
228#499—21no—
229#494C22×C511yescharacteristic
230#492C22×C511yescharacteristic
231#488—21no—
232#487C22×C511yescharacteristic
233#486C22×C511yescharacteristic
234#485—21no—
235#482—21no—
236#478—21no—
237#477C22×C511yescharacteristic
238#476C22×C511yescharacteristic
239#475C22×C511yescharacteristic
240#475C22×C511yescharacteristic
241#474C22×C511yescharacteristic
242#474C22×C511yescharacteristic
243#469—21no—
244#468—21no—
245#464—21no—
246#464—21no—
247#463—21no—
248#460C22×C511yescharacteristic
249#459C22×C511yescharacteristic
250#452—21no—
251#452—21no—
252#446C22×C511yescharacteristic
253C8×Q8C22×C511yescharacteristic
254#436C22×C511yescharacteristic
255#435—21no—
256C8×D4—21no—
257C8×D4C22×C511yescharacteristic
258#433—21no—
259#431C22×C511yescharacteristic
260#431C22×C511yescharacteristic
261#424—21no—
262#423C22×C511yescharacteristic
263C2×C4⋊C8C22×C511yescharacteristic
264#335C22×C511yescharacteristic
265#335C22×C511yescharacteristic
266#334C22×C511yescharacteristic
267#334C22×C511yescharacteristic
268#333C22×C511yescharacteristic
269#333C22×C511yescharacteristic
270#332C22×C511yescharacteristic
271#332C22×C511yescharacteristic
272#332C22×C511yescharacteristic
273#332C22×C511yescharacteristic
274#331C22×C511yescharacteristic
275#331C22×C511yescharacteristic
276C23×C5—21no—
277C23×C5—41no—
278C23×C5#12111yescharacteristic
279C5×Q8—21no—
280C5×Q8—21no—
281C5×Q8—41no—
282C5×Q8—41no—
283C5×Q8—41no—
284C5×Q8—41no—
285C5×Q8—81no—
286C5×D4—21no—
287C5×D4—21no—
288C5×D4—42no—
289C5×D4—41no—
290C5×D4—41no—
291C5×D4—41no—
292C5×D4—41no—
293C5×D4—81no—
294C5×D4—82no—
295C2×C4×C5—21no—
296C2×C4×C5—21no—
297C2×C4×C5—21no—
298C2×C4×C5—21no—
299C2×C4×C5—21no—
300C2×C4×C5—21no—
301C2×C4×C5—21no—
302C2×C4×C5—41no—
303C2×C4×C5—41no—
304C2×C4×C5—41no—
305C2×C4×C5—41no—
306C2×C4×C5—41no—
307C2×C4×C5—41no—
308C2×C4×C5—82no—
309C2×C4×C5#12111yescharacteristic
310C2×C4×C5#12111yescharacteristic
311C2×C4×C5#12111yescharacteristic
312C2×C4×C5C22×D411yescharacteristic
313C2×C4×C5C22×D411yescharacteristic
314C2×C4×C5C2×#4111yescharacteristic
315C5×C8—21no—
316C5×C8—21no—
317C5×C8—21no—
318C5×C8—21no—
319C5×C8—41no—
320C5×C8—41no—
321C5×C8—41no—
322C5×C8—41no—
323C5×C8—41no—
324C5×C8—41no—
325C2×#41—21no—
326C2×Q16—21no—
327C2×Q16—21no—
328C2×SD16—21no—
329C2×SD16—21no—
330C2×SD16—21no—
331C2×D8—21no—
332C2×M16—21no—
333C2×M16—21no—
334C22×C8—21no—
335C22×C8—21no—
336C4⋊Q8C23×C511yescharacteristic
337C4⋊Q8C23×C511yescharacteristic
338C4⋊Q8C23×C511yescharacteristic
339#127C23×C511yescharacteristic
340#126—21no—
341#125—21no—
342#125C5×D411yescharacteristic
343#124—21no—
344#124C5×D411yescharacteristic
345#123—21no—
346C22⋊Q8—21no—
347C22⋊Q8—21no—
348C22⋊Q8C5×D411yescharacteristic
349#121—21no—
350#121—21no—
351#121C5×D411yescharacteristic
352C4×Q8—21no—
353C4×Q8—21no—
354C4×Q8C23×C511yescharacteristic
355C4×D4—21no—
356C4×D4—21no—
357C4×D4—21no—
358C4×D4C23×C511yescharacteristic
359#117—21no—
360#117—21no—
361C2×C42C23×C511yescharacteristic
362#107—21no—
363#107—21no—
364#107—21no—
365#106—21no—
366#106—21no—
367#106—21no—
368C4⋊C8—21no—
369C4⋊C8—21no—
370C4⋊C8—21no—
371C4⋊C8—21no—
372C4⋊C8C5×D411yescharacteristic
373C4⋊C8C5×D411yescharacteristic
374C4⋊C8C23×C511yescharacteristic
375C4⋊C8C23×C511yescharacteristic
376C4⋊C8C23×C511yescharacteristic
377C4⋊C8C23×C511yescharacteristic
378C4⋊C8C23×C511yescharacteristic
379C4⋊C8C23×C511yescharacteristic
380#103—21no—
381#103—21no—
382#103—21no—
383#103—21no—
384#103—21no—
385#102—21no—
386#102—21no—
387#102—21no—
388#102—21no—
389#102—21no—
390#102—21no—
391#102—21no—
392C22⋊C8—21no—
393C22⋊C8—21no—
394C22⋊C8—21no—
395C22⋊C8C5×D411yescharacteristic
396C22⋊C8C5×D411yescharacteristic
397#97—21no—
398C4×C8—21no—
399C4×C8—21no—
400C4×C8C23×C511yescharacteristic
401C4×C8C23×C511yescharacteristic
402C22×C5—21no—
403C22×C5—21no—
404C22×C5—21no—
405C22×C5—41no—
406C22×C5—41no—
407C22×C5—41no—
408C22×C5—81no—
409C22×C5—81no—
410C22×C5—81no—
411C22×C5C2×#12111yescharacteristic
412C4×C5—21no—
413C4×C5—21no—
414C4×C5—21no—
415C4×C5—21no—
416C4×C5—41no—
417C4×C5—41no—
418C4×C5—41no—
419C4×C5—81no—
420C4×C5—81no—
421C4×C5—81no—
422C4×C5#57611yescharacteristic
423C4×C5#57711yescharacteristic
424C4×C5#57711yescharacteristic
425C4×C5#57811yescharacteristic
426#41—81no—
427#41—81no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8C2×C5×D411yescharacteristic
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—41no—
437C2×D4C2×C5×D411yescharacteristic
438C22×C4—21no—
439C22×C4—41no—
440C22×C4C2×C5×D411yescharacteristic
441C22×C4C2×C5×D411yescharacteristic
442C22×C4C5×#4111yescharacteristic
443Q16—81no—
444Q16—81no—
445SD16—81no—
446SD16—81no—
447SD16—81no—
448D8—81no—
449M16—81no—
450M16—81no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—81no—
458C2×C8—81no—
459C2×C8C2×C5×D411yescharacteristic
460C2×C8C2×C5×D411yescharacteristic
461C2×C8C2×C5×D411yescharacteristic
462C2×C8C2×C5×D411yescharacteristic
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4C2×C5×D411yescharacteristic
476C4⋊C4C2×C5×D411yescharacteristic
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C42—21no—
486C42—41no—
487C42C2×C5×D411yescharacteristic
488C42C2×C5×D411yescharacteristic
489C42C5×#4111yescharacteristic
490C42C24×C511yescharacteristic
491C2×C5—41no—
492C2×C5—81no—
493C2×C5—161no—
494C2×C5#304511yescharacteristic
495C2×C5#306311yescharacteristic
496C2×C5#306711yescharacteristic
497C23—21no—
498C23—41no—
499C23C5×#12111yescharacteristic
500Q8—21no—
501Q8—21no—
502Q8—41no—
503Q8—41no—
504Q8—41no—
505Q8—41no—
506Q8—81no—
507D4—21no—
508D4—21no—
509D4—42no—
510D4—41no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—81no—
515D4—82no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—82no—
530C2×C4C5×#12111yescharacteristic
531C2×C4C5×#12111yescharacteristic
532C2×C4C5×#12111yescharacteristic
533C2×C4C22×C5×D411yescharacteristic
534C2×C4C22×C5×D411yescharacteristic
535C2×C4C2×C5×#4111yescharacteristic
536C8—21no—
537C8—21no—
538C8—21no—
539C8—21no—
540C8—41no—
541C8—41no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—41no—
546C5#1957911yescharacteristic, direct product factor, Sylow
547C22—21no—
548C22—21no—
549C22—21no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22C2×C5×#12111yescharacteristic
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—81no—
565C4—81no—
566C4—81no—
567C4C5×#57611yescharacteristic
568C4C5×#57711yescharacteristic
569C4C5×#57711yescharacteristic
570C4C5×#57811yescharacteristic
571C2—41no—
572C2—81no—
573C2—161no—
574C2C5×#304511yescharacteristic
575C2C5×#306311yescharacteristic
576C2C5×#306711yescharacteristic
subgroupG/H
center, socleC22×C5C2×#121
commutator, Frattini, cosocleC42C24×C5
prime radicalC5×#3251C2
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×#3233C2semidirect
3. C5×#3210C2semidirect
4. C5×#2994C2semidirect
5. C5×#1703C2semidirect
6. C5×#1698C2semidirect
7. C5×#1690C2semidirect
8. C5×#1685C2semidirect
9. C5×#1684C2semidirect
10. C5×#1677C2semidirect
11. C5×#1669C2semidirect
12. C5×#1666C2semidirect
13. C5×#1574C2semidirect
14. C5×#1550C2semidirect
15. C5×#1540C2semidirect
67. #19579C5direct (N × H)
146. #3233C2×C5semidirect
147. #3210C2×C5semidirect
148. #2994C2×C5semidirect
149. #1703C2×C5semidirect
150. #1698C2×C5semidirect
151. #1690C2×C5semidirect
152. #1685C2×C5semidirect
153. #1684C2×C5semidirect
154. #1677C2×C5semidirect
155. #1669C2×C5semidirect
156. #1666C2×C5semidirect
157. #1574C2×C5semidirect
158. #1550C2×C5semidirect
159. #1540C2×C5semidirect
546. C5#19579direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#32512
C5×#32332
C5×#32102
C5×#29942
C5×#17032
C5×#16982
C5×#16902
C5×#16852
C5×#16842
C5×#16772
C5×#16692
C5×#16662
C5×#15742
C5×#15502
C5×#15402
#195795