Finite Group Databasebeta

← C5×#18593 #11941313

Subgroups — C5×#18593 #11941313

Order 1280.

916 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3511C211yesmaximal, characteristic
2C5×#3254C211yesmaximal, characteristic, complemented
3C5×#3165C211yesmaximal, characteristic, complemented
4C5×#3107C211yesmaximal, characteristic, complemented
5C5×#1654C212yesmaximal, complemented
6C5×#1652C212yesmaximal, complemented
7C5×#1650C212yesmaximal, complemented
8C5×#1647C212yesmaximal, complemented
9C5×#1546C211yesmaximal, characteristic, complemented
10C5×#1489C211yesmaximal, characteristic, complemented
11C5×#1484C211yesmaximal, characteristic, complemented
12C5×#556C2212yes—
13C5×#555—21no—
14C5×#554—21no—
15C5×#553—22no—
16C5×#548—22no—
17C5×#547C2212yes—
18C5×#542—22no—
19C5×#537—21no—
20C5×#533—21no—
21C5×#533C2211yescharacteristic
22C5×#532—21no—
23C5×#532C2211yescharacteristic
24C2×C5×C4⋊Q8C2211yescharacteristic
25C5×#520—21no—
26C4×C5×#41C2211yescharacteristic
27C5×#501—22no—
28C5×#500C2212yes—
29C5×#498C2212yes—
30C5×#485—21no—
31C5×#477—21no—
32C5×#475C2211yescharacteristic
33C5×#474C2212yes—
34C5×#474C2211yescharacteristic
35C5×#468—22no—
36C5×#462C2211yescharacteristic
37C5×#461C2212yes—
38C5×#461C2211yescharacteristic
39C5×#460—21no—
40C5×#452—21no—
41C4×C5×Q16—21no—
42C4×C5×SD16—21no—
43C5×#431C2211yescharacteristic
44C5×#428—22no—
45C5×#423C2211yescharacteristic
46C4×C5×M16C2211yescharacteristic
47C5×#332C2212yes—
48C5×#332C2212yes—
49C5×Q8⋊C8C2212yes—
50C5×D4⋊C8C2212yes—
51C5×D4⋊C8C2212yes—
52C5×D4⋊C8C2212yes—
53#18593C511yesmaximal, characteristic, direct product factor, Sylow
54C2×C5×#41—22no—
55C2×C5×#41—21no—
56C2×C5×#41D411yescharacteristic
57C22×C5×Q8—21no—
58C2×C5×Q16—21no—
59C2×C5×SD16—21no—
60C2×C5×SD16—22no—
61C2×C5×M16—21no—
62C2×C5×M16—21no—
63C5×C4⋊Q8—21no—
64C5×C4⋊Q8—21no—
65C5×C4⋊Q8D411yescharacteristic
66C5×C4⋊Q8D412yes—
67C5×C4⋊Q8C2311yescharacteristic
68C5×C4⋊Q8C2311yescharacteristic
69C5×C4⋊Q8C2312yes—
70C5×#127D411yescharacteristic
71C5×#126—24no—
72C5×#125—22no—
73C5×#125—21no—
74C5×#124—24no—
75C5×#124—22no—
76C5×#124—21no—
77C5×#123—24no—
78C5×C22⋊Q8—22no—
79C5×C22⋊Q8—24no—
80C5×C22⋊Q8—22no—
81C5×C22⋊Q8—22no—
82C5×C22⋊Q8—21no—
83C5×C22⋊Q8—21no—
84C5×#121—22no—
85C5×#121—22no—
86C5×#121—24no—
87C5×#121—22no—
88C5×#121—21no—
89C5×#121D412yes—
90C4×C5×Q8—22no—
91C4×C5×Q8—22no—
92C4×C5×Q8—21no—
93C4×C5×Q8—21no—
94C4×C5×Q8D411yescharacteristic
95C4×C5×Q8C2311yescharacteristic
96C4×C5×D4—22no—
97C4×C5×D4—24no—
98C4×C5×D4—22no—
99C4×C5×D4—21no—
100C4×C5×D4—21no—
101C4×C5×D4—21no—
102C4×C5×D4D411yescharacteristic
103C4×C5×D4C2311yescharacteristic
104C4×C5×D4C2312yes—
105C5×#117—22no—
106C5×#117—22no—
107C5×#117—21no—
108C5×#117—21no—
109C5×#117D411yescharacteristic
110C2×C5×C4⋊C4—21no—
111C2×C5×C4⋊C4—22no—
112C2×C5×C4⋊C4D412yes—
113C2×C42×C5—21no—
114C2×C42×C5C2311yescharacteristic
115C5×#107—24no—
116C5×#107—21no—
117C5×#107—22no—
118C5×#106—24no—
119C5×#106—21no—
120C5×C4⋊C8—21no—
121C5×C4⋊C8C2311yescharacteristic
122C5×C4⋊C8C2311yescharacteristic
123C5×C4⋊C8C2312yes—
124C5×#103—21no—
125C5×#103—21no—
126C5×#103—21no—
127C5×#103—22no—
128C5×#102—21no—
129C5×#102—22no—
130C5×C22⋊C8—21no—
131C5×#97—21no—
132C4×C5×C8—21no—
133C4×C5×C8C2312yes—
134#3511C2×C511yescharacteristic
135#3254C2×C511yescharacteristic, complemented
136#3165C2×C511yescharacteristic, complemented
137#3107C2×C511yescharacteristic, complemented
138#1654C2×C512yescomplemented
139#1652C2×C512yescomplemented
140#1650C2×C512yescomplemented
141#1647C2×C512yescomplemented
142#1546C2×C511yescharacteristic, complemented
143#1489C2×C511yescharacteristic, complemented
144#1484C2×C511yescharacteristic, complemented
145C5×#41—41no—
146C5×#41—41no—
147C5×#41—42no—
148C5×#41—42no—
149C5×#41—82no—
150C5×#41—82no—
151C2×C5×Q8—21no—
152C2×C5×Q8—22no—
153C2×C5×Q8—22no—
154C2×C5×Q8—21no—
155C2×C5×Q8—21no—
156C2×C5×Q8—81no—
157C2×C5×Q8—81no—
158C2×C5×Q8C2×D411yescharacteristic
159C2×C5×D4—21no—
160C2×C5×D4—22no—
161C2×C5×D4—24no—
162C2×C5×D4—21no—
163C2×C5×D4—21no—
164C2×C5×D4C2×D411yescharacteristic
165C2×C5×D4C2×D412yes—
166C22×C4×C5—24no—
167C22×C4×C5—22no—
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5—22no—
172C22×C4×C5C2×D411yescharacteristic
173C22×C4×C5C2×D411yescharacteristic
174C22×C4×C5C2×D411yescharacteristic
175C5×Q16—42no—
176C5×SD16—42no—
177C5×SD16—82no—
178C5×M16—24no—
179C5×M16—81no—
180C2×C5×C8—22no—
181C2×C5×C8—22no—
182C2×C5×C8—21no—
183C2×C5×C8—21no—
184C5×C4⋊C4—24no—
185C5×C4⋊C4—24no—
186C5×C4⋊C4—22no—
187C5×C4⋊C4—22no—
188C5×C4⋊C4—21no—
189C5×C4⋊C4—21no—
190C5×C4⋊C4—22no—
191C5×C4⋊C4—21no—
192C5×C4⋊C4—21no—
193C5×C4⋊C4—21no—
194C5×C4⋊C4—21no—
195C5×C4⋊C4—21no—
196C5×C4⋊C4—41no—
197C5×C4⋊C4—41no—
198C5×C4⋊C4C2×D411yescharacteristic
199C5×C4⋊C4C2×D414yes—
200C5×C4⋊C4C2×D411yescharacteristic
201C5×C4⋊C4C2×D412yes—
202C5×C22⋊C4—24no—
203C5×C22⋊C4—24no—
204C5×C22⋊C4—24no—
205C5×C22⋊C4—21no—
206C5×C22⋊C4—21no—
207C5×C22⋊C4—22no—
208C5×C22⋊C4—21no—
209C5×C22⋊C4—22no—
210C5×C22⋊C4—41no—
211C42×C5—24no—
212C42×C5—21no—
213C42×C5—21no—
214C42×C5—21no—
215C42×C5—41no—
216C42×C5C2×D411yescharacteristic
217C42×C5C2×D411yescharacteristic
218C42×C5C2×D411yescharacteristic
219C42×C5C2411yescharacteristic
220#556C22×C512yes—
221#555—21no—
222#554—21no—
223#553—22no—
224#548—22no—
225#547C22×C512yes—
226#542—22no—
227#537—21no—
228#533—21no—
229#533C22×C511yescharacteristic
230#532—21no—
231#532C22×C511yescharacteristic
232C2×C4⋊Q8C22×C511yescharacteristic
233#520—21no—
234C4×#41C22×C511yescharacteristic
235#501—22no—
236#500C22×C512yes—
237#498C22×C512yes—
238#485—21no—
239#477—21no—
240#475C22×C511yescharacteristic
241#474C22×C511yescharacteristic
242#474C22×C512yes—
243#468—22no—
244#462C22×C511yescharacteristic
245#461C22×C511yescharacteristic
246#461C22×C512yes—
247#460—21no—
248#452—21no—
249C4×Q16—21no—
250C4×SD16—21no—
251#431C22×C511yescharacteristic
252#428—22no—
253#423C22×C511yescharacteristic
254C4×M16C22×C511yescharacteristic
255#332C22×C512yes—
256#332C22×C512yes—
257Q8⋊C8C22×C512yes—
258D4⋊C8C22×C512yes—
259D4⋊C8C22×C512yes—
260D4⋊C8C22×C512yes—
261C23×C5—21no—
262C23×C5—22no—
263C23×C5#12011yescharacteristic
264C5×Q8—21no—
265C5×Q8—21no—
266C5×Q8—42no—
267C5×Q8—42no—
268C5×Q8—42no—
269C5×Q8—41no—
270C5×Q8—41no—
271C5×Q8—41no—
272C5×Q8—41no—
273C5×Q8—82no—
274C5×D4—21no—
275C5×D4—21no—
276C5×D4—22no—
277C5×D4—22no—
278C5×D4—42no—
279C5×D4—42no—
280C5×D4—44no—
281C5×D4—42no—
282C5×D4—84no—
283C2×C4×C5—21no—
284C2×C4×C5—21no—
285C2×C4×C5—21no—
286C2×C4×C5—21no—
287C2×C4×C5—22no—
288C2×C4×C5—21no—
289C2×C4×C5—21no—
290C2×C4×C5—22no—
291C2×C4×C5—21no—
292C2×C4×C5—24no—
293C2×C4×C5—42no—
294C2×C4×C5—42no—
295C2×C4×C5—42no—
296C2×C4×C5—41no—
297C2×C4×C5—41no—
298C2×C4×C5—42no—
299C2×C4×C5—41no—
300C2×C4×C5—41no—
301C2×C4×C5—82no—
302C2×C4×C5—84no—
303C2×C4×C5#12011yescharacteristic
304C2×C4×C5#12011yescharacteristic
305C2×C4×C5#12011yescharacteristic
306C2×C4×C5C22×D411yescharacteristic
307C2×C4×C5C22×D411yescharacteristic
308C2×C4×C5C22×D411yescharacteristic
309C5×C8—24no—
310C5×C8—41no—
311C5×C8—41no—
312C5×C8—42no—
313C2×#41—22no—
314C2×#41—21no—
315C2×#41C5×D411yescharacteristic
316C22×Q8—21no—
317C2×Q16—21no—
318C2×SD16—21no—
319C2×SD16—22no—
320C2×M16—21no—
321C2×M16—21no—
322C4⋊Q8—21no—
323C4⋊Q8—21no—
324C4⋊Q8C5×D412yes—
325C4⋊Q8C5×D411yescharacteristic
326C4⋊Q8C23×C511yescharacteristic
327C4⋊Q8C23×C511yescharacteristic
328C4⋊Q8C23×C512yes—
329#127C5×D411yescharacteristic
330#126—24no—
331#125—22no—
332#125—21no—
333#124—24no—
334#124—22no—
335#124—21no—
336#123—24no—
337C22⋊Q8—22no—
338C22⋊Q8—24no—
339C22⋊Q8—22no—
340C22⋊Q8—22no—
341C22⋊Q8—21no—
342C22⋊Q8—21no—
343#121—22no—
344#121—22no—
345#121—24no—
346#121—22no—
347#121—21no—
348#121C5×D412yes—
349C4×Q8—22no—
350C4×Q8—22no—
351C4×Q8—21no—
352C4×Q8—21no—
353C4×Q8C5×D411yescharacteristic
354C4×Q8C23×C511yescharacteristic
355C4×D4—22no—
356C4×D4—24no—
357C4×D4—22no—
358C4×D4—21no—
359C4×D4—21no—
360C4×D4—21no—
361C4×D4C5×D411yescharacteristic
362C4×D4C23×C511yescharacteristic
363C4×D4C23×C512yes—
364#117—22no—
365#117—22no—
366#117—21no—
367#117—21no—
368#117C5×D411yescharacteristic
369C2×C4⋊C4—21no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4C5×D412yes—
372C2×C42—21no—
373C2×C42C23×C511yescharacteristic
374#107—24no—
375#107—21no—
376#107—22no—
377#106—24no—
378#106—21no—
379C4⋊C8—21no—
380C4⋊C8C23×C511yescharacteristic
381C4⋊C8C23×C511yescharacteristic
382C4⋊C8C23×C512yes—
383#103—21no—
384#103—21no—
385#103—21no—
386#103—22no—
387#102—21no—
388#102—22no—
389C22⋊C8—21no—
390#97—21no—
391C4×C8—21no—
392C4×C8C23×C512yes—
393C22×C5—21no—
394C22×C5—21no—
395C22×C5—21no—
396C22×C5—41no—
397C22×C5—42no—
398C22×C5—41no—
399C22×C5—42no—
400C22×C5—41no—
401C22×C5—42no—
402C22×C5C2×#12011yescharacteristic
403C4×C5—21no—
404C4×C5—21no—
405C4×C5—21no—
406C4×C5—41no—
407C4×C5—42no—
408C4×C5—41no—
409C4×C5—44no—
410C4×C5—41no—
411C4×C5—81no—
412C4×C5—81no—
413C4×C5#45612yes—
414C4×C5#57511yescharacteristic
415C4×C5#57511yescharacteristic
416C4×C5#57611yescharacteristic
417C4×C5#57711yescharacteristic
418#41—41no—
419#41—41no—
420#41—42no—
421#41—42no—
422#41—82no—
423#41—82no—
424C2×Q8—21no—
425C2×Q8—22no—
426C2×Q8—22no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—81no—
430C2×Q8—81no—
431C2×Q8C2×C5×D411yescharacteristic
432C2×D4—21no—
433C2×D4—22no—
434C2×D4—24no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4C2×C5×D411yescharacteristic
438C2×D4C2×C5×D412yes—
439C22×C4—24no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4C2×C5×D411yescharacteristic
446C22×C4C2×C5×D411yescharacteristic
447C22×C4C2×C5×D411yescharacteristic
448Q16—42no—
449SD16—42no—
450SD16—82no—
451M16—24no—
452M16—81no—
453C2×C8—22no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—22no—
457C4⋊C4—24no—
458C4⋊C4—24no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—22no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4C2×C5×D411yescharacteristic
472C4⋊C4C2×C5×D411yescharacteristic
473C4⋊C4C2×C5×D412yes—
474C4⋊C4C2×C5×D414yes—
475C22⋊C4—24no—
476C22⋊C4—24no—
477C22⋊C4—24no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—22no—
481C22⋊C4—21no—
482C22⋊C4—22no—
483C22⋊C4—41no—
484C42—24no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—41no—
489C42C2×C5×D411yescharacteristic
490C42C2×C5×D411yescharacteristic
491C42C2×C5×D411yescharacteristic
492C42C24×C511yescharacteristic
493C2×C5—41no—
494C2×C5—81no—
495C2×C5—82no—
496C2×C5#300511yescharacteristic
497C2×C5#301211yescharacteristic
498C2×C5C2×#45611yescharacteristic
499C23—21no—
500C23—22no—
501C23C5×#12011yescharacteristic
502Q8—21no—
503Q8—21no—
504Q8—42no—
505Q8—42no—
506Q8—42no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—82no—
512D4—21no—
513D4—21no—
514D4—22no—
515D4—22no—
516D4—42no—
517D4—42no—
518D4—44no—
519D4—42no—
520D4—84no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—21no—
530C2×C4—24no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—82no—
540C2×C4—84no—
541C2×C4C5×#12011yescharacteristic
542C2×C4C5×#12011yescharacteristic
543C2×C4C5×#12011yescharacteristic
544C2×C4C22×C5×D411yescharacteristic
545C2×C4C22×C5×D411yescharacteristic
546C2×C4C22×C5×D411yescharacteristic
547C8—24no—
548C8—41no—
549C8—41no—
550C8—42no—
551C5#1859311yescharacteristic, direct product factor, Sylow
552C22—21no—
553C22—21no—
554C22—21no—
555C22—41no—
556C22—42no—
557C22—41no—
558C22—42no—
559C22—41no—
560C22—42no—
561C22C2×C5×#12011yescharacteristic
562C4—21no—
563C4—21no—
564C4—21no—
565C4—41no—
566C4—42no—
567C4—41no—
568C4—44no—
569C4—41no—
570C4—81no—
571C4—81no—
572C4C5×#45612yes—
573C4C5×#57511yescharacteristic
574C4C5×#57511yescharacteristic
575C4C5×#57611yescharacteristic
576C4C5×#57711yescharacteristic
577C2—41no—
578C2—81no—
579C2—82no—
580C2C5×#300511yescharacteristic
581C2C5×#301211yescharacteristic
582C2C2×C5×#45611yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
prime radicalC5×#3511C2
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×#3254C2semidirect
3. C5×#3165C2semidirect
4. C5×#3107C2semidirect
5. C5×#1654C2semidirect
6. C5×#1652C2semidirect
7. C5×#1650C2semidirect
8. C5×#1647C2semidirect
9. C5×#1546C2semidirect
10. C5×#1489C2semidirect
11. C5×#1484C2semidirect
53. #18593C5direct (N × H)
135. #3254C2×C5semidirect
136. #3165C2×C5semidirect
137. #3107C2×C5semidirect
138. #1654C2×C5semidirect
139. #1652C2×C5semidirect
140. #1650C2×C5semidirect
141. #1647C2×C5semidirect
142. #1546C2×C5semidirect
143. #1489C2×C5semidirect
144. #1484C2×C5semidirect
551. C5#18593direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35112
C5×#32542
C5×#31652
C5×#31072
C5×#16542
C5×#16522
C5×#16502
C5×#16472
C5×#15462
C5×#14892
C5×#14842
#185935