Finite Group Databasebeta

← C13×#8419 #15694758

Subgroups — C13×#8419 #15694758

Order 3328.

778 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3522C211yesmaximal, characteristic
2C13×#1980C211yesmaximal, characteristic, complemented
3C13×#1763C211yesmaximal, characteristic, complemented
4C13×#1530C211yesmaximal, characteristic, complemented
5C13×#1524C211yesmaximal, characteristic, complemented
6C13×#1509C211yesmaximal, characteristic, complemented
7C13×#1491C211yesmaximal, characteristic, complemented
8C13×#559—21no—
9C13×#559C411yescharacteristic, complemented
10Q82×C13C411yescharacteristic, complemented
11C13×#554—21no—
12C13×#554C411yescharacteristic, complemented
13C13×#550C411yescharacteristic, complemented
14C13×#548—21no—
15C13×#547—22no—
16C13×#547—21no—
17C13×#542—22no—
18C13×#542—21no—
19C13×#532—21no—
20C13×#532C2211yescharacteristic
21C13×#529—21no—
22C13×#529C2211yescharacteristic
23C13×#520—21no—
24C2×C4×Q8×C13C2211yescharacteristic
25C13×#432C2211yescharacteristic
26C2×C13×#104—22no—
27C2×C13×#103—21no—
28C4×C13×M16C2211yescharacteristic
29C2×C13×#97C2211yescharacteristic
30C4×C13×C4⋊C4C2211yescharacteristic
31C13×#340—21no—
32C13×#330—21no—
33C13×#329—21no—
34C13×#329—22no—
35C13×#328—21no—
36C13×#327—21no—
37C13×Q8⋊C8—21no—
38C13×Q8⋊C8—21no—
39C2×C13×#41—22no—
40C2×C13×#41—21no—
41C2×C13×#41D412yes—
42C22×Q8×C13D411yescharacteristic
43C2×C13×M16—21no—
44C22×C8×C13—21no—
45C13×C4⋊Q8—22no—
46C13×C4⋊Q8—21no—
47C13×C4⋊Q8—21no—
48C13×C4⋊Q8C2×C411yescharacteristic
49C13×#127—21no—
50C13×#127C2×C411yescharacteristic
51C13×#126—22no—
52C13×#126—21no—
53C13×#125—21no—
54C13×#125D411yescharacteristic
55C13×#124—22no—
56C13×#124—22no—
57C13×#124—21no—
58C13×#124—21no—
59C13×#124D411yescharacteristic
60C13×#124D412yes—
61C13×#123—22no—
62C13×#123—22no—
63C13×#123—22no—
64C13×#123—22no—
65C13×#123—21no—
66C13×C22⋊Q8—22no—
67C13×C22⋊Q8—22no—
68C13×C22⋊Q8—22no—
69C13×C22⋊Q8—22no—
70C13×C22⋊Q8—21no—
71C13×C22⋊Q8D411yescharacteristic
72C13×#121—22no—
73C13×#121—22no—
74C13×#121—21no—
75C13×#121—21no—
76C13×#121—21no—
77C13×#121D411yescharacteristic
78C4×Q8×C13—21no—
79C4×Q8×C13—21no—
80C4×Q8×C13—21no—
81C4×Q8×C13—21no—
82C4×Q8×C13C2×C411yescharacteristic
83C4×Q8×C13C2×C411yescharacteristic
84C4×Q8×C13C2×C411yescharacteristic
85C4×Q8×C13D411yescharacteristic
86C4×Q8×C13D411yescharacteristic
87C4×D4×C13—22no—
88C4×D4×C13—22no—
89C4×D4×C13—22no—
90C4×D4×C13—21no—
91C4×D4×C13—21no—
92C4×D4×C13—21no—
93C4×D4×C13—21no—
94C4×D4×C13—21no—
95C4×D4×C13—21no—
96C4×D4×C13—21no—
97C4×D4×C13C2×C411yescharacteristic
98C13×#117—22no—
99C13×#117—21no—
100C2×C13×C4⋊C4—22no—
101C2×C13×C4⋊C4—21no—
102C2×C13×C4⋊C4—21no—
103C2×C13×C4⋊C4—21no—
104C2×C13×C4⋊C4D411yescharacteristic
105C2×C42×C13—21no—
106C2×C42×C13—21no—
107C2×C42×C13C2311yescharacteristic
108C13×C4⋊C8—21no—
109C13×#104—44no—
110C13×#103—24no—
111C13×C22⋊C8—21no—
112C13×#97—21no—
113C13×#97—21no—
114C13×#97—21no—
115C13×#97—21no—
116C4×C8×C13—21no—
117C13×#95—21no—
118#8419C1311yesmaximal, characteristic, direct product factor, Sylow
119C13×#41—42no—
120C13×#41—42no—
121C13×#41—42no—
122C13×#41—42no—
123C13×#41—82no—
124C13×#41—82no—
125C2×Q8×C13—22no—
126C2×Q8×C13—21no—
127C2×Q8×C13—22no—
128C2×Q8×C13—41no—
129C2×Q8×C13C22⋊C411yescharacteristic
130C2×Q8×C13C22⋊C411yescharacteristic
131C2×Q8×C13C22⋊C411yescharacteristic
132C2×Q8×C13C22⋊C412yes—
133C2×D4×C13—22no—
134C2×D4×C13—22no—
135C2×D4×C13—21no—
136C2×D4×C13—22no—
137C2×D4×C13—21no—
138C2×D4×C13—21no—
139C2×D4×C13C22⋊C411yescharacteristic
140C2×D4×C13C22⋊C412yes—
141C22×C4×C13—22no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—22no—
145C22×C4×C13—22no—
146C22×C4×C13—21no—
147C22×C4×C13—22no—
148C22×C4×C13—41no—
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C13×M16—22no—
153C13×M16—41no—
154C2×C8×C13—22no—
155C2×C8×C13—41no—
156C2×C8×C13—41no—
157C2×C8×C13—41no—
158C2×C8×C13—41no—
159C13×C4⋊C4—22no—
160C13×C4⋊C4—22no—
161C13×C4⋊C4—22no—
162C13×C4⋊C4—22no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—22no—
175C13×C4⋊C4—41no—
176C13×C4⋊C4C22⋊C411yescharacteristic
177C13×C4⋊C4C22⋊C411yescharacteristic
178C13×C4⋊C4C22⋊C411yescharacteristic
179C13×C4⋊C4C22⋊C411yescharacteristic
180C13×C22⋊C4—22no—
181C13×C22⋊C4—22no—
182C13×C22⋊C4—22no—
183C13×C22⋊C4—22no—
184C13×C22⋊C4—22no—
185C13×C22⋊C4—21no—
186C13×C22⋊C4—21no—
187C13×C22⋊C4—22no—
188C13×C22⋊C4—21no—
189C13×C22⋊C4—21no—
190C13×C22⋊C4—22no—
191C13×C22⋊C4—21no—
192C42×C13—22no—
193C42×C13—21no—
194C42×C13—21no—
195C42×C13—21no—
196C42×C13—21no—
197C42×C13—21no—
198C42×C13—42no—
199C42×C13C22×C411yescharacteristic
200C42×C13C2×D411yescharacteristic
201C42×C13C2×D411yescharacteristic
202C42×C13C2×D411yescharacteristic
203#3522C2×C1311yescharacteristic
204#1980C2×C1311yescharacteristic, complemented
205#1763C2×C1311yescharacteristic, complemented
206#1530C2×C1311yescharacteristic, complemented
207#1524C2×C1311yescharacteristic, complemented
208#1509C2×C1311yescharacteristic, complemented
209#1491C2×C1311yescharacteristic, complemented
210C23×C13—22no—
211C23×C13—21no—
212C23×C13#12011yescharacteristic
213Q8×C13—21no—
214Q8×C13—21no—
215Q8×C13—21no—
216Q8×C13—42no—
217Q8×C13—41no—
218Q8×C13—42no—
219Q8×C13—82no—
220Q8×C13#10412yescomplemented
221D4×C13—42no—
222D4×C13—44no—
223D4×C13—41no—
224D4×C13—42no—
225D4×C13—42no—
226D4×C13—41no—
227D4×C13—42no—
228D4×C13—41no—
229D4×C13—41no—
230D4×C13—41no—
231D4×C13—82no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—22no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—41no—
245C2×C4×C13—42no—
246C2×C4×C13—44no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—42no—
252C2×C4×C13—82no—
253C2×C4×C13—82no—
254C2×C4×C13—82no—
255C2×C4×C13—81no—
256C2×C4×C13—81no—
257C2×C4×C13C2×C22⋊C411yescharacteristic
258C2×C4×C13C2×C22⋊C411yescharacteristic
259C2×C4×C13C2×C22⋊C411yescharacteristic
260C2×C4×C13#12011yescharacteristic
261C2×C4×C13#12011yescharacteristic
262C2×C4×C13#12011yescharacteristic
263C8×C13—42no—
264C8×C13—42no—
265C8×C13—81no—
266#559—21no—
267#559C4×C1311yescharacteristic, complemented
268Q82C4×C1311yescharacteristic, complemented
269#554—21no—
270#554C4×C1311yescharacteristic, complemented
271#550C4×C1311yescharacteristic, complemented
272#548—21no—
273#547—22no—
274#547—21no—
275#542—22no—
276#542—21no—
277#532—21no—
278#532C22×C1311yescharacteristic
279#529—21no—
280#529C22×C1311yescharacteristic
281#520—21no—
282C2×C4×Q8C22×C1311yescharacteristic
283#432C22×C1311yescharacteristic
284C2×#104—22no—
285C2×#103—21no—
286C4×M16C22×C1311yescharacteristic
287C2×#97C22×C1311yescharacteristic
288C4×C4⋊C4C22×C1311yescharacteristic
289#340—21no—
290#330—21no—
291#329—21no—
292#329—22no—
293#328—21no—
294#327—21no—
295Q8⋊C8—21no—
296Q8⋊C8—21no—
297C22×C13—21no—
298C22×C13—21no—
299C22×C13—42no—
300C22×C13—41no—
301C22×C13—42no—
302C22×C13—41no—
303C22×C13—42no—
304C22×C13—41no—
305C22×C13#37911yescharacteristic
306C22×C13#45311yescharacteristic
307C22×C13#45511yescharacteristic
308C4×C13—21no—
309C4×C13—21no—
310C4×C13—21no—
311C4×C13—21no—
312C4×C13—21no—
313C4×C13—22no—
314C4×C13—41no—
315C4×C13—41no—
316C4×C13—42no—
317C4×C13—41no—
318C4×C13—41no—
319C4×C13—41no—
320C4×C13—41no—
321C4×C13—82no—
322C4×C13C2×#10411yescharacteristic
323C4×C13#42111yescharacteristic
324C2×#41—22no—
325C2×#41—21no—
326C2×#41D4×C1312yes—
327C22×Q8D4×C1311yescharacteristic
328C2×M16—21no—
329C22×C8—21no—
330C4⋊Q8—22no—
331C4⋊Q8—21no—
332C4⋊Q8—21no—
333C4⋊Q8C2×C4×C1311yescharacteristic
334#127—21no—
335#127C2×C4×C1311yescharacteristic
336#126—22no—
337#126—21no—
338#125—21no—
339#125D4×C1311yescharacteristic
340#124—22no—
341#124—22no—
342#124—21no—
343#124—21no—
344#124D4×C1311yescharacteristic
345#124D4×C1312yes—
346#123—22no—
347#123—22no—
348#123—22no—
349#123—22no—
350#123—21no—
351C22⋊Q8—22no—
352C22⋊Q8—22no—
353C22⋊Q8—22no—
354C22⋊Q8—22no—
355C22⋊Q8—21no—
356C22⋊Q8D4×C1311yescharacteristic
357#121—22no—
358#121—22no—
359#121—21no—
360#121—21no—
361#121—21no—
362#121D4×C1311yescharacteristic
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8C2×C4×C1311yescharacteristic
368C4×Q8C2×C4×C1311yescharacteristic
369C4×Q8C2×C4×C1311yescharacteristic
370C4×Q8D4×C1311yescharacteristic
371C4×Q8D4×C1311yescharacteristic
372C4×D4—22no—
373C4×D4—22no—
374C4×D4—22no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4C2×C4×C1311yescharacteristic
383#117—22no—
384#117—21no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4D4×C1311yescharacteristic
390C2×C42—21no—
391C2×C42—21no—
392C2×C42C23×C1311yescharacteristic
393C4⋊C8—21no—
394#104—44no—
395#103—24no—
396C22⋊C8—21no—
397#97—21no—
398#97—21no—
399#97—21no—
400#97—21no—
401C4×C8—21no—
402#95—21no—
403C2×C13—21no—
404C2×C13—21no—
405C2×C13—82no—
406C2×C13—81no—
407C2×C13#178911yescharacteristic
408C2×C13#179211yescharacteristic
409C2×C13#179611yescharacteristic
410#41—42no—
411#41—42no—
412#41—42no—
413#41—42no—
414#41—82no—
415#41—82no—
416C2×Q8—22no—
417C2×Q8—21no—
418C2×Q8—22no—
419C2×Q8—41no—
420C2×Q8C13×C22⋊C411yescharacteristic
421C2×Q8C13×C22⋊C411yescharacteristic
422C2×Q8C13×C22⋊C411yescharacteristic
423C2×Q8C13×C22⋊C412yes—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—21no—
427C2×D4—22no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4C13×C22⋊C411yescharacteristic
431C2×D4C13×C22⋊C412yes—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—41no—
440C22×C4C2×D4×C1311yescharacteristic
441C22×C4C2×D4×C1311yescharacteristic
442C22×C4C2×D4×C1311yescharacteristic
443M16—22no—
444M16—41no—
445C2×C8—22no—
446C2×C8—41no—
447C2×C8—41no—
448C2×C8—41no—
449C2×C8—41no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—22no—
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—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—22no—
466C4⋊C4—41no—
467C4⋊C4C13×C22⋊C411yescharacteristic
468C4⋊C4C13×C22⋊C411yescharacteristic
469C4⋊C4C13×C22⋊C411yescharacteristic
470C4⋊C4C13×C22⋊C411yescharacteristic
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—22no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—22no—
482C22⋊C4—21no—
483C42—22no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—42no—
490C42C22×C4×C1311yescharacteristic
491C42C2×D4×C1311yescharacteristic
492C42C2×D4×C1311yescharacteristic
493C42C2×D4×C1311yescharacteristic
494C13#841911yescharacteristic, direct product factor, Sylow
495C23—22no—
496C23—21no—
497C23C13×#12011yescharacteristic
498Q8—21no—
499Q8—21no—
500Q8—21no—
501Q8—42no—
502Q8—42no—
503Q8—41no—
504Q8—82no—
505Q8C13×#10412yescomplemented
506D4—41no—
507D4—42no—
508D4—42no—
509D4—44no—
510D4—42no—
511D4—41no—
512D4—42no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—82no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—44no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—82no—
538C2×C4—82no—
539C2×C4—82no—
540C2×C4—81no—
541C2×C4—81no—
542C2×C4C2×C13×C22⋊C411yescharacteristic
543C2×C4C2×C13×C22⋊C411yescharacteristic
544C2×C4C2×C13×C22⋊C411yescharacteristic
545C2×C4C13×#12011yescharacteristic
546C2×C4C13×#12011yescharacteristic
547C2×C4C13×#12011yescharacteristic
548C8—42no—
549C8—42no—
550C8—81no—
551C22—21no—
552C22—21no—
553C22—42no—
554C22—41no—
555C22—42no—
556C22—41no—
557C22—42no—
558C22—41no—
559C22C13×#37911yescharacteristic
560C22C13×#45311yescharacteristic
561C22C13×#45511yescharacteristic
562C4—21no—
563C4—22no—
564C4—21no—
565C4—21no—
566C4—21no—
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—42no—
573C4—41no—
574C4—41no—
575C4—82no—
576C4C2×C13×#10411yescharacteristic
577C4C13×#42111yescharacteristic
578C2—21no—
579C2—21no—
580C2—82no—
581C2—81no—
582C2C13×#178911yescharacteristic
583C2C13×#179211yescharacteristic
584C2C13×#179611yescharacteristic
subgroupG/H
center, socleC22×C13#379
commutatorC42C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC13×#3522C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C13×#1980C2semidirect
3. C13×#1763C2semidirect
4. C13×#1530C2semidirect
5. C13×#1524C2semidirect
6. C13×#1509C2semidirect
7. C13×#1491C2semidirect
9. C13×#559C4semidirect
10. Q82×C13C4semidirect
12. C13×#554C4semidirect
13. C13×#550C4semidirect
118. #8419C13direct (N × H)
204. #1980C2×C13semidirect
205. #1763C2×C13semidirect
206. #1530C2×C13semidirect
207. #1524C2×C13semidirect
208. #1509C2×C13semidirect
209. #1491C2×C13semidirect
220. Q8×C13#104semidirect
267. #559C4×C13semidirect
268. Q82C4×C13semidirect
270. #554C4×C13semidirect
271. #550C4×C13semidirect
494. C13#8419direct (N × H)
505. Q8C13×#104semidirect

Maximal subgroups

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

subgroupindex
C13×#35222
C13×#19802
C13×#17632
C13×#15302
C13×#15242
C13×#15092
C13×#14912
#841913