Finite Group Databasebeta

← C5×#19030 #11941750

Subgroups — C5×#19030 #11941750

Order 1280.

902 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3559C211yesmaximal, characteristic, complemented
2C5×#3214C211yesmaximal, characteristic, complemented
3C5×#3171C211yesmaximal, characteristic, complemented
4C5×#3142C211yesmaximal, characteristic, complemented
5C5×#1664C212yesmaximal, complemented
6C5×#1662C212yesmaximal, complemented
7C5×#1657C212yesmaximal, complemented
8C5×#1656C212yesmaximal, complemented
9C5×#1529C211yesmaximal, characteristic, complemented
10C5×#1528C211yesmaximal, characteristic, complemented
11C5×#1525C211yesmaximal, characteristic, complemented
12C5×#563C2212yes—
13C5×#562C2212yes—
14C5×#554—21no—
15C5×#553—21no—
16C5×#553—21no—
17C5×#547—22no—
18C5×#547—21no—
19C5×#544—21no—
20C5×#540—21no—
21C5×#539—22no—
22C5×#539—21no—
23C5×#537—21no—
24C5×#532C2211yescharacteristic
25C5×#532C2211yescharacteristic
26C5×#529C2211yescharacteristic
27C2×C5×#125C2211yescharacteristic
28C5×#501C2211yescharacteristic
29C5×#496C2211yescharacteristic
30C5×#496C2212yes—
31C5×#491C2212yes—
32C5×#490C2212yes—
33C5×#490C2211yescharacteristic
34C5×#489C2211yescharacteristic
35C5×#489C2212yes—
36C5×#488—22no—
37C5×#469—21no—
38C5×#468—21no—
39C5×#461—21no—
40C5×#459—21no—
41C5×#449—22no—
42C4×C5×SD16—21no—
43C4×C5×D8—21no—
44C5×#432C2211yescharacteristic
45C5×#417—21no—
46C5×#417—21no—
47C4×C5×M16C2211yescharacteristic
48C4×C5×M16C2211yescharacteristic
49C5×#330C2212yes—
50C5×#330C2212yes—
51C5×#330C2212yes—
52C5×#329C2212yes—
53C5×#329C2212yes—
54C5×#329C2212yes—
55#19030C511yesmaximal, characteristic, direct product factor, Sylow
56C2×C5×#41—22no—
57C2×C5×#41—21no—
58C2×C5×#41D412yes—
59C2×C5×SD16—21no—
60C2×C5×SD16—22no—
61C2×C5×D8—21no—
62C2×C5×D8—22no—
63C2×C5×M16—21no—
64C2×C5×M16—21no—
65C5×C4⋊Q8—21no—
66C5×C4⋊Q8—22no—
67C5×C4⋊Q8D411yescharacteristic
68C5×C4⋊Q8C2311yescharacteristic
69C5×#127D411yescharacteristic
70C5×#127C2311yescharacteristic
71C5×#126—22no—
72C5×#126—22no—
73C5×#126—21no—
74C5×#125—22no—
75C5×#125—21no—
76C5×#125—21no—
77C5×#125—21no—
78C5×#125D412yes—
79C5×#125C2312yes—
80C5×#125C2311yescharacteristic
81C5×#124—21no—
82C5×#124C2311yescharacteristic
83C5×#124C2312yes—
84C5×#123—22no—
85C5×#123—22no—
86C5×#123—22no—
87C5×#123—22no—
88C5×#123—21no—
89C5×#123—22no—
90C5×#123—22no—
91C5×C22⋊Q8—22no—
92C5×C22⋊Q8—22no—
93C5×C22⋊Q8—22no—
94C5×C22⋊Q8—22no—
95C5×C22⋊Q8—22no—
96C5×C22⋊Q8—22no—
97C5×C22⋊Q8D411yescharacteristic
98C5×#121—22no—
99C5×#121—22no—
100C5×#121—21no—
101C5×#121—21no—
102C5×#121—22no—
103C5×#121—22no—
104C5×#121—21no—
105C5×#121—21no—
106C5×#121—21no—
107C5×#121—21no—
108C5×#121D411yescharacteristic
109C4×C5×Q8D411yescharacteristic
110C4×C5×D4—22no—
111C4×C5×D4—22no—
112C4×C5×D4—21no—
113C4×C5×D4—21no—
114C4×C5×D4—21no—
115C4×C5×D4—21no—
116C4×C5×D4—21no—
117C4×C5×D4—21no—
118C4×C5×D4—21no—
119C4×C5×D4D411yescharacteristic
120C5×#117—21no—
121C5×#117—21no—
122C2×C5×C4⋊C4—22no—
123C2×C5×C4⋊C4—21no—
124C2×C5×C4⋊C4—21no—
125C2×C5×C4⋊C4—21no—
126C2×C5×C4⋊C4D411yescharacteristic
127C2×C5×C4⋊C4D411yescharacteristic
128C2×C42×C5C2311yescharacteristic
129C5×#107—21no—
130C5×#106—21no—
131C5×C4⋊C8—21no—
132C5×#103—21no—
133C5×#103—22no—
134C5×#103—22no—
135C5×#103—22no—
136C5×#102—21no—
137C5×#102—22no—
138C5×#102—22no—
139C5×#102—22no—
140C5×#102—21no—
141C5×#102—21no—
142C5×C22⋊C8—21no—
143C5×#97C2312yes—
144C5×#97C2311yescharacteristic
145C5×#97C2311yescharacteristic
146C5×#97C2312yes—
147C4×C5×C8—21no—
148C4×C5×C8—21no—
149#3559C2×C511yescharacteristic, complemented
150#3214C2×C511yescharacteristic, complemented
151#3171C2×C511yescharacteristic, complemented
152#3142C2×C511yescharacteristic, complemented
153#1664C2×C512yescomplemented
154#1662C2×C512yescomplemented
155#1657C2×C512yescomplemented
156#1656C2×C512yescomplemented
157#1529C2×C511yescharacteristic, complemented
158#1528C2×C511yescharacteristic, complemented
159#1525C2×C511yescharacteristic, complemented
160C5×#41—44no—
161C5×#41—84no—
162C5×#41—82no—
163C2×C5×Q8—22no—
164C2×C5×Q8—21no—
165C2×C5×Q8C2×D411yescharacteristic
166C2×C5×Q8C2×D412yes—
167C2×C5×D4—22no—
168C2×C5×D4—21no—
169C2×C5×D4—22no—
170C2×C5×D4—22no—
171C2×C5×D4—21no—
172C2×C5×D4—21no—
173C2×C5×D4—21no—
174C2×C5×D4—21no—
175C2×C5×D4—21no—
176C2×C5×D4—41no—
177C2×C5×D4C2×D411yescharacteristic
178C2×C5×D4C2×D412yes—
179C22×C4×C5—21no—
180C22×C4×C5—22no—
181C22×C4×C5—22no—
182C22×C4×C5—22no—
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—22no—
186C22×C4×C5—41no—
187C22×C4×C5C2×D411yescharacteristic
188C22×C4×C5C2×D411yescharacteristic
189C22×C4×C5C2×D411yescharacteristic
190C5×SD16—42no—
191C5×SD16—82no—
192C5×D8—42no—
193C5×D8—82no—
194C5×M16—42no—
195C5×M16—42no—
196C2×C5×C8—21no—
197C2×C5×C8—21no—
198C2×C5×C8—22no—
199C2×C5×C8—22no—
200C5×C4⋊C4—22no—
201C5×C4⋊C4—22no—
202C5×C4⋊C4—22no—
203C5×C4⋊C4—22no—
204C5×C4⋊C4—22no—
205C5×C4⋊C4—21no—
206C5×C4⋊C4—21no—
207C5×C4⋊C4—21no—
208C5×C4⋊C4—22no—
209C5×C4⋊C4—21no—
210C5×C4⋊C4—21no—
211C5×C4⋊C4—21no—
212C5×C4⋊C4—22no—
213C5×C4⋊C4—22no—
214C5×C4⋊C4—21no—
215C5×C4⋊C4—21no—
216C5×C4⋊C4—21no—
217C5×C4⋊C4—21no—
218C5×C4⋊C4C2×D412yes—
219C5×C4⋊C4C2×D412yes—
220C5×C4⋊C4C2×D411yescharacteristic
221C5×C4⋊C4C2×D411yescharacteristic
222C5×C22⋊C4—22no—
223C5×C22⋊C4—22no—
224C5×C22⋊C4—22no—
225C5×C22⋊C4—22no—
226C5×C22⋊C4—22no—
227C5×C22⋊C4—21no—
228C5×C22⋊C4—21no—
229C5×C22⋊C4—21no—
230C5×C22⋊C4—21no—
231C5×C22⋊C4—22no—
232C5×C22⋊C4—22no—
233C5×C22⋊C4—21no—
234C5×C22⋊C4—41no—
235C5×C22⋊C4—41no—
236C42×C5—22no—
237C42×C5—21no—
238C42×C5C2×D411yescharacteristic
239C42×C5C2×D411yescharacteristic
240C42×C5C2×D411yescharacteristic
241C42×C5C2411yescharacteristic
242#563C22×C512yes—
243#562C22×C512yes—
244#554—21no—
245#553—21no—
246#553—21no—
247#547—22no—
248#547—21no—
249#544—21no—
250#540—21no—
251#539—22no—
252#539—21no—
253#537—21no—
254#532C22×C511yescharacteristic
255#532C22×C511yescharacteristic
256#529C22×C511yescharacteristic
257C2×#125C22×C511yescharacteristic
258#501C22×C511yescharacteristic
259#496C22×C511yescharacteristic
260#496C22×C512yes—
261#491C22×C512yes—
262#490C22×C512yes—
263#490C22×C511yescharacteristic
264#489C22×C511yescharacteristic
265#489C22×C512yes—
266#488—22no—
267#469—21no—
268#468—21no—
269#461—21no—
270#459—21no—
271#449—22no—
272C4×SD16—21no—
273C4×D8—21no—
274#432C22×C511yescharacteristic
275#417—21no—
276#417—21no—
277C4×M16C22×C511yescharacteristic
278C4×M16C22×C511yescharacteristic
279#330C22×C512yes—
280#330C22×C512yes—
281#330C22×C512yes—
282#329C22×C512yes—
283#329C22×C512yes—
284#329C22×C512yes—
285C23×C5—21no—
286C23×C5—22no—
287C23×C5—41no—
288C23×C5#12011yescharacteristic
289C5×Q8—41no—
290C5×Q8—42no—
291C5×Q8—42no—
292C5×Q8—82no—
293C5×D4—41no—
294C5×D4—42no—
295C5×D4—41no—
296C5×D4—41no—
297C5×D4—41no—
298C5×D4—41no—
299C5×D4—42no—
300C5×D4—44no—
301C5×D4—42no—
302C5×D4—42no—
303C5×D4—81no—
304C5×D4—82no—
305C5×D4—82no—
306C5×D4—82no—
307C2×C4×C5—22no—
308C2×C4×C5—21no—
309C2×C4×C5—21no—
310C2×C4×C5—22no—
311C2×C4×C5—22no—
312C2×C4×C5—21no—
313C2×C4×C5—22no—
314C2×C4×C5—41no—
315C2×C4×C5—41no—
316C2×C4×C5—42no—
317C2×C4×C5—42no—
318C2×C4×C5—41no—
319C2×C4×C5—82no—
320C2×C4×C5—81no—
321C2×C4×C5—82no—
322C2×C4×C5—82no—
323C2×C4×C5—82no—
324C2×C4×C5—82no—
325C2×C4×C5#12011yescharacteristic
326C2×C4×C5#12011yescharacteristic
327C2×C4×C5#12011yescharacteristic
328C2×C4×C5C22×D411yescharacteristic
329C2×C4×C5C22×D411yescharacteristic
330C2×C4×C5C22×D411yescharacteristic
331C5×C8—22no—
332C5×C8—42no—
333C5×C8—41no—
334C5×C8—42no—
335C2×#41—22no—
336C2×#41—21no—
337C2×#41C5×D412yes—
338C2×SD16—21no—
339C2×SD16—22no—
340C2×D8—21no—
341C2×D8—22no—
342C2×M16—21no—
343C2×M16—21no—
344C4⋊Q8—21no—
345C4⋊Q8—22no—
346C4⋊Q8C5×D411yescharacteristic
347C4⋊Q8C23×C511yescharacteristic
348#127C5×D411yescharacteristic
349#127C23×C511yescharacteristic
350#126—22no—
351#126—22no—
352#126—21no—
353#125—22no—
354#125—21no—
355#125—21no—
356#125—21no—
357#125C5×D412yes—
358#125C23×C512yes—
359#125C23×C511yescharacteristic
360#124—21no—
361#124C23×C511yescharacteristic
362#124C23×C512yes—
363#123—22no—
364#123—22no—
365#123—22no—
366#123—22no—
367#123—21no—
368#123—22no—
369#123—22no—
370C22⋊Q8—22no—
371C22⋊Q8—22no—
372C22⋊Q8—22no—
373C22⋊Q8—22no—
374C22⋊Q8—22no—
375C22⋊Q8—22no—
376C22⋊Q8C5×D411yescharacteristic
377#121—22no—
378#121—22no—
379#121—21no—
380#121—21no—
381#121—22no—
382#121—22no—
383#121—21no—
384#121—21no—
385#121—21no—
386#121—21no—
387#121C5×D411yescharacteristic
388C4×Q8C5×D411yescharacteristic
389C4×D4—22no—
390C4×D4—22no—
391C4×D4—21no—
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4C5×D411yescharacteristic
399#117—21no—
400#117—21no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4C5×D411yescharacteristic
406C2×C4⋊C4C5×D411yescharacteristic
407C2×C42C23×C511yescharacteristic
408#107—21no—
409#106—21no—
410C4⋊C8—21no—
411#103—21no—
412#103—22no—
413#103—22no—
414#103—22no—
415#102—21no—
416#102—22no—
417#102—22no—
418#102—22no—
419#102—21no—
420#102—21no—
421C22⋊C8—21no—
422#97C23×C512yes—
423#97C23×C511yescharacteristic
424#97C23×C511yescharacteristic
425#97C23×C512yes—
426C4×C8—21no—
427C4×C8—21no—
428C22×C5—21no—
429C22×C5—21no—
430C22×C5—21no—
431C22×C5—41no—
432C22×C5—42no—
433C22×C5—42no—
434C22×C5—41no—
435C22×C5—42no—
436C22×C5—41no—
437C22×C5—81no—
438C22×C5—81no—
439C22×C5—81no—
440C22×C5C2×#12011yescharacteristic
441C4×C5—21no—
442C4×C5—21no—
443C4×C5—21no—
444C4×C5—21no—
445C4×C5—21no—
446C4×C5—41no—
447C4×C5—42no—
448C4×C5—41no—
449C4×C5—42no—
450C4×C5—42no—
451C4×C5—41no—
452C4×C5—81no—
453C4×C5#45412yes—
454#41—44no—
455#41—84no—
456#41—82no—
457C2×Q8—22no—
458C2×Q8—21no—
459C2×Q8C2×C5×D411yescharacteristic
460C2×Q8C2×C5×D412yes—
461C2×D4—22no—
462C2×D4—21no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—41no—
471C2×D4C2×C5×D411yescharacteristic
472C2×D4C2×C5×D412yes—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—41no—
481C22×C4C2×C5×D411yescharacteristic
482C22×C4C2×C5×D411yescharacteristic
483C22×C4C2×C5×D411yescharacteristic
484SD16—42no—
485SD16—82no—
486D8—42no—
487D8—82no—
488M16—42no—
489M16—42no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—22no—
493C2×C8—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—22no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4C2×C5×D412yes—
513C4⋊C4C2×C5×D412yes—
514C4⋊C4C2×C5×D411yescharacteristic
515C4⋊C4C2×C5×D411yescharacteristic
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—21no—
528C22⋊C4—41no—
529C22⋊C4—41no—
530C42—22no—
531C42—21no—
532C42C2×C5×D411yescharacteristic
533C42C2×C5×D411yescharacteristic
534C42C2×C5×D411yescharacteristic
535C42C24×C511yescharacteristic
536C2×C5—41no—
537C2×C5—81no—
538C2×C5—82no—
539C2×C5—161no—
540C2×C5C2×#45411yescharacteristic
541C2×C5#301811yescharacteristic
542C2×C5#301911yescharacteristic
543C23—21no—
544C23—22no—
545C23—41no—
546C23C5×#12011yescharacteristic
547Q8—41no—
548Q8—42no—
549Q8—42no—
550Q8—82no—
551D4—41no—
552D4—42no—
553D4—41no—
554D4—41no—
555D4—41no—
556D4—41no—
557D4—42no—
558D4—44no—
559D4—42no—
560D4—42no—
561D4—81no—
562D4—82no—
563D4—82no—
564D4—82no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—41no—
577C2×C4—82no—
578C2×C4—81no—
579C2×C4—82no—
580C2×C4—82no—
581C2×C4—82no—
582C2×C4—82no—
583C2×C4C5×#12011yescharacteristic
584C2×C4C5×#12011yescharacteristic
585C2×C4C5×#12011yescharacteristic
586C2×C4C22×C5×D411yescharacteristic
587C2×C4C22×C5×D411yescharacteristic
588C2×C4C22×C5×D411yescharacteristic
589C8—22no—
590C8—42no—
591C8—41no—
592C8—42no—
593C5#1903011yescharacteristic, direct product factor, Sylow
594C22—21no—
595C22—21no—
596C22—21no—
597C22—41no—
598C22—42no—
599C22—42no—
600C22—41no—
601C22—42no—
602C22—41no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22C2×C5×#12011yescharacteristic
607C4—21no—
608C4—21no—
609C4—21no—
610C4—21no—
611C4—21no—
612C4—41no—
613C4—42no—
614C4—41no—
615C4—42no—
616C4—42no—
617C4—41no—
618C4—81no—
619C4C5×#45412yes—
620C2—41no—
621C2—81no—
622C2—82no—
623C2—161no—
624C2C2×C5×#45411yescharacteristic
625C2C5×#301811yescharacteristic
626C2C5×#301911yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
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×#3559C2semidirect
2. C5×#3214C2semidirect
3. C5×#3171C2semidirect
4. C5×#3142C2semidirect
5. C5×#1664C2semidirect
6. C5×#1662C2semidirect
7. C5×#1657C2semidirect
8. C5×#1656C2semidirect
9. C5×#1529C2semidirect
10. C5×#1528C2semidirect
11. C5×#1525C2semidirect
55. #19030C5direct (N × H)
149. #3559C2×C5semidirect
150. #3214C2×C5semidirect
151. #3171C2×C5semidirect
152. #3142C2×C5semidirect
153. #1664C2×C5semidirect
154. #1662C2×C5semidirect
155. #1657C2×C5semidirect
156. #1656C2×C5semidirect
157. #1529C2×C5semidirect
158. #1528C2×C5semidirect
159. #1525C2×C5semidirect
593. C5#19030direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35592
C5×#32142
C5×#31712
C5×#31422
C5×#16642
C5×#16622
C5×#16572
C5×#16562
C5×#15292
C5×#15282
C5×#15252
#190305