Finite Group Databasebeta

← C13×#19838 #15706177

Subgroups — C13×#19838 #15706177

Order 3328.

574 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3383C211yesmaximal, characteristic, complemented
2C13×#3372C211yesmaximal, characteristic
3C13×#3359C211yesmaximal, characteristic
4C13×#3299C211yesmaximal, characteristic
5C13×#1718C211yesmaximal, characteristic, complemented
6C13×#1700C211yesmaximal, characteristic, complemented
7C13×#1684C211yesmaximal, characteristic, complemented
8C13×#1684C211yesmaximal, characteristic, complemented
9C13×#1673C211yesmaximal, characteristic
10C13×#1653C211yesmaximal, characteristic, complemented
11C13×#1651C211yesmaximal, characteristic
12C13×#1643C211yesmaximal, characteristic
13C13×#1636C211yesmaximal, characteristic, complemented
14C13×#1584C211yesmaximal, characteristic, complemented
15C13×SD16⋊C8C211yesmaximal, characteristic
16C13×#557C2211yescharacteristic
17C13×#557C2211yescharacteristic
18C13×#554C2211yescharacteristic
19D4×Q8×C13C2211yescharacteristic
20C13×#500C2211yescharacteristic
21C13×#499—21no—
22C13×#498C2211yescharacteristic
23C13×#491—21no—
24C13×#487—21no—
25C13×#487C2211yescharacteristic
26C13×#487C2211yescharacteristic
27C13×#487C2211yescharacteristic
28C13×#487C2211yescharacteristic
29C13×#484—21no—
30C13×#479—21no—
31C13×#479—21no—
32C13×#479—21no—
33C13×#477C2211yescharacteristic
34C13×#477C2211yescharacteristic
35C13×#475—21no—
36C13×#475C2211yescharacteristic
37C13×#475C2211yescharacteristic
38C13×#475C2211yescharacteristic
39C13×#467—21no—
40C13×#462C2211yescharacteristic
41C13×#461—21no—
42C13×#461—21no—
43C13×#461C2211yescharacteristic
44C13×#461C2211yescharacteristic
45C13×#451—21no—
46C13×#446C2211yescharacteristic
47C8×Q8×C13C2211yescharacteristic
48C8×Q8×C13C2211yescharacteristic
49C13×#440—21no—
50C4×C13×Q16—21no—
51C4×C13×Q16C2211yescharacteristic
52C4×C13×SD16—21no—
53C4×C13×SD16C2211yescharacteristic
54C8×D4×C13C2211yescharacteristic
55C2×C13×#103—21no—
56C13×#335C2211yescharacteristic
57C13×#335C2211yescharacteristic
58C13×#333C2211yescharacteristic
59C13×#332C2211yescharacteristic
60C13×#332C2211yescharacteristic
61C13×#332C2211yescharacteristic
62C13×Q8⋊C8C2211yescharacteristic
63C13×Q8⋊C8C2211yescharacteristic
64C13×Q8⋊C8C2211yescharacteristic
65C13×D4⋊C8C2211yescharacteristic
66C13×#322C2211yescharacteristic
67C22×Q8×C13—21no—
68C2×C13×Q16—21no—
69C2×C13×Q16D411yescharacteristic
70C2×C13×SD16—21no—
71C2×C13×SD16—21no—
72C2×C13×SD16D411yescharacteristic
73C22×C8×C13—21no—
74C13×C4⋊Q8—21no—
75C13×C4⋊Q8—21no—
76C13×C4⋊Q8—21no—
77C13×C4⋊Q8C2311yescharacteristic
78C13×C4⋊Q8C2311yescharacteristic
79C13×C4⋊Q8C2311yescharacteristic
80C13×C4⋊Q8C2311yescharacteristic
81C13×#125—21no—
82C13×#125—21no—
83C13×#125—21no—
84C13×#125—41no—
85C13×#125—41no—
86C13×C22⋊Q8—21no—
87C13×C22⋊Q8—21no—
88C13×C22⋊Q8—41no—
89C13×C22⋊Q8—41no—
90C4×Q8×C13—21no—
91C4×Q8×C13—21no—
92C4×Q8×C13—21no—
93C4×Q8×C13—21no—
94C4×Q8×C13C2311yescharacteristic
95C4×Q8×C13C2311yescharacteristic
96C4×Q8×C13C2311yescharacteristic
97C4×D4×C13—21no—
98C4×D4×C13—21no—
99C4×D4×C13C2311yescharacteristic
100C2×C13×C4⋊C4—21no—
101C13×#107—21no—
102C13×#107—21no—
103C13×#107—21no—
104C13×#107—21no—
105C13×#107D411yescharacteristic
106C13×#106—21no—
107C13×#106—21no—
108C13×#106—21no—
109C13×#106—41no—
110C13×#106D411yescharacteristic
111C13×C4⋊C8—21no—
112C13×C4⋊C8—21no—
113C13×C4⋊C8—21no—
114C13×C4⋊C8C2311yescharacteristic
115C13×C4⋊C8C2311yescharacteristic
116C13×C4⋊C8C2311yescharacteristic
117C13×C4⋊C8C2311yescharacteristic
118C13×#103—21no—
119C13×#103—21no—
120C13×#103—21no—
121C13×#103—21no—
122C13×#103—21no—
123C13×#103—21no—
124C13×#103—21no—
125C13×#103—21no—
126C13×#103—21no—
127C13×#103—21no—
128C13×#103—21no—
129C13×#103—21no—
130C13×#103—21no—
131C13×#103—21no—
132C13×#103—41no—
133C13×#103D411yescharacteristic
134C13×#103D411yescharacteristic
135C13×#103D411yescharacteristic
136C13×#102D411yescharacteristic
137C13×C22⋊C8—21no—
138C13×#97—21no—
139C4×C8×C13—21no—
140C4×C8×C13—21no—
141C4×C8×C13C2311yescharacteristic
142C4×C8×C13C2311yescharacteristic
143C4×C8×C13C2311yescharacteristic
144#19838C1311yesmaximal, characteristic, direct product factor, Sylow
145C2×Q8×C13—21no—
146C2×Q8×C13—21no—
147C2×Q8×C13—21no—
148C2×Q8×C13—21no—
149C2×Q8×C13—41no—
150C2×Q8×C13—42no—
151C2×Q8×C13—81no—
152C2×Q8×C13C2×D411yescharacteristic
153C2×Q8×C13C2×D411yescharacteristic
154C2×Q8×C13C2×D411yescharacteristic
155C2×D4×C13C2×D411yescharacteristic
156C22×C4×C13—21no—
157C22×C4×C13—41no—
158C22×C4×C13—41no—
159C13×Q16—22no—
160C13×Q16—81no—
161C13×SD16—22no—
162C13×SD16—42no—
163C13×SD16—42no—
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—81no—
170C2×C8×C13C2×D411yescharacteristic
171C2×C8×C13C2×D411yescharacteristic
172C2×C8×C13C2×D411yescharacteristic
173C2×C8×C13C2×D411yescharacteristic
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—21no—
185C13×C4⋊C4—41no—
186C13×C4⋊C4—41no—
187C13×C4⋊C4—41no—
188C13×C4⋊C4—41no—
189C13×C4⋊C4—41no—
190C13×C4⋊C4—41no—
191C13×C4⋊C4—41no—
192C13×C4⋊C4—41no—
193C13×C4⋊C4—41no—
194C13×C4⋊C4C2×D411yescharacteristic
195C13×C4⋊C4C2×D411yescharacteristic
196C13×C4⋊C4C2×D411yescharacteristic
197C13×C4⋊C4C2×D411yescharacteristic
198C13×C22⋊C4—21no—
199C13×C22⋊C4—41no—
200C13×C22⋊C4—41no—
201C42×C13—21no—
202C42×C13—21no—
203C42×C13—21no—
204C42×C13—41no—
205C42×C13—41no—
206C42×C13C2411yescharacteristic
207#3383C2×C1311yescharacteristic, complemented
208#3372C2×C1311yescharacteristic
209#3359C2×C1311yescharacteristic
210#3299C2×C1311yescharacteristic
211#1718C2×C1311yescharacteristic, complemented
212#1700C2×C1311yescharacteristic, complemented
213#1684C2×C1311yescharacteristic, complemented
214#1684C2×C1311yescharacteristic, complemented
215#1673C2×C1311yescharacteristic
216#1653C2×C1311yescharacteristic, complemented
217#1651C2×C1311yescharacteristic
218#1643C2×C1311yescharacteristic
219#1636C2×C1311yescharacteristic, complemented
220#1584C2×C1311yescharacteristic, complemented
221SD16⋊C8C2×C1311yescharacteristic
222C23×C13—21no—
223Q8×C13—21no—
224Q8×C13—21no—
225Q8×C13—21no—
226Q8×C13—21no—
227Q8×C13—21no—
228Q8×C13—41no—
229Q8×C13—41no—
230Q8×C13—41no—
231Q8×C13—41no—
232Q8×C13—41no—
233Q8×C13—41no—
234Q8×C13—82no—
235Q8×C13—81no—
236Q8×C13#13712yes—
237D4×C13—21no—
238D4×C13#13512yes—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—82no—
253C2×C4×C13—161no—
254C2×C4×C13C22×D411yescharacteristic
255C2×C4×C13C22×D411yescharacteristic
256C2×C4×C13H(5,𝔽2)11yescharacteristic
257C8×C13—21no—
258C8×C13—21no—
259C8×C13—21no—
260C8×C13—21no—
261C8×C13—41no—
262C8×C13—41no—
263C8×C13—41no—
264C8×C13—41no—
265C8×C13—41no—
266#557C22×C1311yescharacteristic
267#557C22×C1311yescharacteristic
268#554C22×C1311yescharacteristic
269D4×Q8C22×C1311yescharacteristic
270#500C22×C1311yescharacteristic
271#499—21no—
272#498C22×C1311yescharacteristic
273#491—21no—
274#487—21no—
275#487C22×C1311yescharacteristic
276#487C22×C1311yescharacteristic
277#487C22×C1311yescharacteristic
278#487C22×C1311yescharacteristic
279#484—21no—
280#479—21no—
281#479—21no—
282#479—21no—
283#477C22×C1311yescharacteristic
284#477C22×C1311yescharacteristic
285#475—21no—
286#475C22×C1311yescharacteristic
287#475C22×C1311yescharacteristic
288#475C22×C1311yescharacteristic
289#467—21no—
290#462C22×C1311yescharacteristic
291#461—21no—
292#461—21no—
293#461C22×C1311yescharacteristic
294#461C22×C1311yescharacteristic
295#451—21no—
296#446C22×C1311yescharacteristic
297C8×Q8C22×C1311yescharacteristic
298C8×Q8C22×C1311yescharacteristic
299#440—21no—
300C4×Q16—21no—
301C4×Q16C22×C1311yescharacteristic
302C4×SD16—21no—
303C4×SD16C22×C1311yescharacteristic
304C8×D4C22×C1311yescharacteristic
305C2×#103—21no—
306#335C22×C1311yescharacteristic
307#335C22×C1311yescharacteristic
308#333C22×C1311yescharacteristic
309#332C22×C1311yescharacteristic
310#332C22×C1311yescharacteristic
311#332C22×C1311yescharacteristic
312Q8⋊C8C22×C1311yescharacteristic
313Q8⋊C8C22×C1311yescharacteristic
314Q8⋊C8C22×C1311yescharacteristic
315D4⋊C8C22×C1311yescharacteristic
316#322C22×C1311yescharacteristic
317C22×C13—22no—
318C22×C13—41no—
319C22×C13—41no—
320C22×C13D4211yescharacteristic
321C4×C13—22no—
322C4×C13—21no—
323C4×C13—41no—
324C4×C13—41no—
325C4×C13—41no—
326C4×C13—41no—
327C4×C13—41no—
328C4×C13—41no—
329C4×C13—81no—
330C4×C13—81no—
331C4×C13—81no—
332C4×C13—81no—
333C4×C13C2×#13511yescharacteristic
334C4×C13C2×#13711yescharacteristic
335C4×C13#57711yescharacteristic
336C4×C13#57811yescharacteristic
337C22×Q8—21no—
338C2×Q16—21no—
339C2×Q16D4×C1311yescharacteristic
340C2×SD16—21no—
341C2×SD16—21no—
342C2×SD16D4×C1311yescharacteristic
343C22×C8—21no—
344C4⋊Q8—21no—
345C4⋊Q8—21no—
346C4⋊Q8—21no—
347C4⋊Q8C23×C1311yescharacteristic
348C4⋊Q8C23×C1311yescharacteristic
349C4⋊Q8C23×C1311yescharacteristic
350C4⋊Q8C23×C1311yescharacteristic
351#125—21no—
352#125—21no—
353#125—21no—
354#125—41no—
355#125—41no—
356C22⋊Q8—21no—
357C22⋊Q8—21no—
358C22⋊Q8—41no—
359C22⋊Q8—41no—
360C4×Q8—21no—
361C4×Q8—21no—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8C23×C1311yescharacteristic
365C4×Q8C23×C1311yescharacteristic
366C4×Q8C23×C1311yescharacteristic
367C4×D4—21no—
368C4×D4—21no—
369C4×D4C23×C1311yescharacteristic
370C2×C4⋊C4—21no—
371#107—21no—
372#107—21no—
373#107—21no—
374#107—21no—
375#107D4×C1311yescharacteristic
376#106—21no—
377#106—21no—
378#106—21no—
379#106—41no—
380#106D4×C1311yescharacteristic
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8C23×C1311yescharacteristic
385C4⋊C8C23×C1311yescharacteristic
386C4⋊C8C23×C1311yescharacteristic
387C4⋊C8C23×C1311yescharacteristic
388#103—21no—
389#103—21no—
390#103—21no—
391#103—21no—
392#103—21no—
393#103—21no—
394#103—21no—
395#103—21no—
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—41no—
403#103D4×C1311yescharacteristic
404#103D4×C1311yescharacteristic
405#103D4×C1311yescharacteristic
406#102D4×C1311yescharacteristic
407C22⋊C8—21no—
408#97—21no—
409C4×C8—21no—
410C4×C8—21no—
411C4×C8C23×C1311yescharacteristic
412C4×C8C23×C1311yescharacteristic
413C4×C8C23×C1311yescharacteristic
414C2×C13—42no—
415C2×C13#326611yescharacteristic
416C2×C13#328511yescharacteristic
417C2×C13#328911yescharacteristic
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—41no—
423C2×Q8—42no—
424C2×Q8—81no—
425C2×Q8C2×D4×C1311yescharacteristic
426C2×Q8C2×D4×C1311yescharacteristic
427C2×Q8C2×D4×C1311yescharacteristic
428C2×D4C2×D4×C1311yescharacteristic
429C22×C4—21no—
430C22×C4—41no—
431C22×C4—41no—
432Q16—22no—
433Q16—81no—
434SD16—22no—
435SD16—42no—
436SD16—42no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—81no—
443C2×C8C2×D4×C1311yescharacteristic
444C2×C8C2×D4×C1311yescharacteristic
445C2×C8C2×D4×C1311yescharacteristic
446C2×C8C2×D4×C1311yescharacteristic
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
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—41no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4C2×D4×C1311yescharacteristic
468C4⋊C4C2×D4×C1311yescharacteristic
469C4⋊C4C2×D4×C1311yescharacteristic
470C4⋊C4C2×D4×C1311yescharacteristic
471C22⋊C4—21no—
472C22⋊C4—41no—
473C22⋊C4—41no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—41no—
478C42—41no—
479C42C24×C1311yescharacteristic
480C13#1983811yescharacteristic, direct product factor, Sylow
481C23—21no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—21no—
486Q8—21no—
487Q8—41no—
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—41no—
493Q8—82no—
494Q8—81no—
495Q8C13×#13712yes—
496D4—21no—
497D4C13×#13512yes—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—82no—
512C2×C4—161no—
513C2×C4C22×D4×C1311yescharacteristic
514C2×C4C22×D4×C1311yescharacteristic
515C2×C4C13×H(5,𝔽2)11yescharacteristic
516C8—21no—
517C8—21no—
518C8—21no—
519C8—21no—
520C8—41no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8—41no—
525C22—22no—
526C22—41no—
527C22—41no—
528C22D42×C1311yescharacteristic
529C4—22no—
530C4—21no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—81no—
538C4—81no—
539C4—81no—
540C4—81no—
541C4C2×C13×#13511yescharacteristic
542C4C2×C13×#13711yescharacteristic
543C4C13×#57711yescharacteristic
544C4C13×#57811yescharacteristic
545C2—42no—
546C2C13×#326611yescharacteristic
547C2C13×#328511yescharacteristic
548C2C13×#328911yescharacteristic
subgroupG/H
center, socleC22×C13D42
commutator, Frattini, cosocleC42C24×C13
prime radicalC2×D4×C13C2×D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3383C2semidirect
5. C13×#1718C2semidirect
6. C13×#1700C2semidirect
7. C13×#1684C2semidirect
8. C13×#1684C2semidirect
10. C13×#1653C2semidirect
13. C13×#1636C2semidirect
14. C13×#1584C2semidirect
144. #19838C13direct (N × H)
207. #3383C2×C13semidirect
211. #1718C2×C13semidirect
212. #1700C2×C13semidirect
213. #1684C2×C13semidirect
214. #1684C2×C13semidirect
216. #1653C2×C13semidirect
219. #1636C2×C13semidirect
220. #1584C2×C13semidirect
480. C13#19838direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#33832
C13×#33722
C13×#33592
C13×#32992
C13×#17182
C13×#17002
C13×#16842
C13×#16732
C13×#16532
C13×#16512
C13×#16432
C13×#16362
C13×#15842
C13×SD16⋊C82
#1983813