Finite Group Databasebeta

← C13×#19881 #15706220

Subgroups — C13×#19881 #15706220

Order 3328.

562 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3395C211yesmaximal, characteristic, complemented
2C13×#3381C211yesmaximal, characteristic
3C13×#3364C211yesmaximal, characteristic
4C13×#3356C211yesmaximal, characteristic
5C13×#1716C211yesmaximal, characteristic, complemented
6C13×#1689C211yesmaximal, characteristic
7C13×#1680C211yesmaximal, characteristic, complemented
8C13×#1672C211yesmaximal, characteristic, complemented
9C13×#1672C211yesmaximal, characteristic, complemented
10C13×#1653C211yesmaximal, characteristic, complemented
11C13×#1652C211yesmaximal, characteristic
12C13×#1644C211yesmaximal, characteristic
13C13×#1636C211yesmaximal, characteristic, complemented
14C13×#1583C211yesmaximal, characteristic
15C13×#1579C211yesmaximal, characteristic, complemented
16C13×#557C2211yescharacteristic
17C13×#557C2211yescharacteristic
18C13×#556C2211yescharacteristic
19C13×#554C2211yescharacteristic
20C13×#499—21no—
21C13×#498C2211yescharacteristic
22C13×#498C2211yescharacteristic
23C13×#498C2211yescharacteristic
24C13×#494—21no—
25C13×#494C2211yescharacteristic
26C13×#488—21no—
27C13×#487C2211yescharacteristic
28C13×#487C2211yescharacteristic
29C13×#485—21no—
30C13×#483—21no—
31C13×#479—21no—
32C13×#479—21no—
33C13×#478—21no—
34C13×#477C2211yescharacteristic
35C13×#477C2211yescharacteristic
36C13×#475C2211yescharacteristic
37C13×#474C2211yescharacteristic
38C13×#474C2211yescharacteristic
39C13×#470—21no—
40C13×#464—21no—
41C13×#462—21no—
42C13×#462—21no—
43C13×#462C2211yescharacteristic
44C13×#462C2211yescharacteristic
45C13×#462C2211yescharacteristic
46C8×Q8×C13C2211yescharacteristic
47C8×Q8×C13C2211yescharacteristic
48C8×Q8×C13C2211yescharacteristic
49C4×C13×Q16—21no—
50C4×C13×Q16—21no—
51C4×C13×Q16C2211yescharacteristic
52C4×C13×SD16—21no—
53C4×C13×SD16C2211yescharacteristic
54C13×#436C2211yescharacteristic
55C13×#428—21no—
56C13×#334C2211yescharacteristic
57C13×#334C2211yescharacteristic
58C13×#333C2211yescharacteristic
59C13×#332C2211yescharacteristic
60C13×#332C2211yescharacteristic
61C13×#332C2211yescharacteristic
62C13×Q8⋊C8C2211yescharacteristic
63C13×Q8⋊C8C2211yescharacteristic
64C13×Q8⋊C8C2211yescharacteristic
65C13×D4⋊C8C2211yescharacteristic
66C13×#322C2211yescharacteristic
67C2×C13×Q16—21no—
68C2×C13×Q16—21no—
69C2×C13×Q16—21no—
70C2×C13×Q16—21no—
71C2×C13×Q16—21no—
72C2×C13×Q16D411yescharacteristic
73C2×C13×SD16D411yescharacteristic
74C2×C13×M16—21no—
75C13×C4⋊Q8—21no—
76C13×C4⋊Q8—21no—
77C13×C4⋊Q8C2311yescharacteristic
78C13×C4⋊Q8C2311yescharacteristic
79C13×C4⋊Q8C2311yescharacteristic
80C13×C4⋊Q8C2311yescharacteristic
81C13×#126—41no—
82C13×#125—21no—
83C13×#125—21no—
84C13×#125—21no—
85C13×#125—41no—
86C13×#125—41no—
87C13×#124—21no—
88C13×C22⋊Q8—21no—
89C13×C22⋊Q8—21no—
90C13×C22⋊Q8—41no—
91C4×Q8×C13—21no—
92C4×Q8×C13—21no—
93C4×Q8×C13—21no—
94C4×Q8×C13—21no—
95C4×Q8×C13—21no—
96C4×Q8×C13C2311yescharacteristic
97C4×Q8×C13C2311yescharacteristic
98C4×Q8×C13C2311yescharacteristic
99C4×D4×C13—21no—
100C4×D4×C13C2311yescharacteristic
101C13×#117—21no—
102C2×C13×C4⋊C4—21no—
103C13×#107—21no—
104C13×#107—21no—
105C13×#107—21no—
106C13×#107—21no—
107C13×#107D411yescharacteristic
108C13×#106—21no—
109C13×#106—21no—
110C13×#106—21no—
111C13×#106—21no—
112C13×#106—21no—
113C13×#106—41no—
114C13×#106D411yescharacteristic
115C13×C4⋊C8—21no—
116C13×C4⋊C8—21no—
117C13×C4⋊C8—21no—
118C13×C4⋊C8C2311yescharacteristic
119C13×C4⋊C8C2311yescharacteristic
120C13×C4⋊C8C2311yescharacteristic
121C13×C4⋊C8C2311yescharacteristic
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—41no—
131C13×#103D411yescharacteristic
132C13×#103D411yescharacteristic
133C13×#103D411yescharacteristic
134C13×#102—21no—
135C13×#102—21no—
136C13×#102D411yescharacteristic
137C13×C22⋊C8—21no—
138C4×C8×C13—21no—
139C4×C8×C13—21no—
140C4×C8×C13—21no—
141C4×C8×C13C2311yescharacteristic
142C4×C8×C13C2311yescharacteristic
143C4×C8×C13C2311yescharacteristic
144#19881C1311yesmaximal, characteristic, direct product factor, Sylow
145C2×Q8×C13—21no—
146C2×Q8×C13—21no—
147C2×Q8×C13—21no—
148C2×Q8×C13—21no—
149C2×Q8×C13C2×D411yescharacteristic
150C2×Q8×C13C2×D411yescharacteristic
151C2×Q8×C13C2×D411yescharacteristic
152C2×D4×C13C2×D411yescharacteristic
153C22×C4×C13—21no—
154C22×C4×C13—41no—
155C13×Q16—22no—
156C13×Q16—42no—
157C13×Q16—42no—
158C13×Q16—81no—
159C13×Q16—81no—
160C13×Q16—81no—
161C13×SD16—22no—
162C13×M16—42no—
163C2×C8×C13—21no—
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13C2×D411yescharacteristic
169C2×C8×C13C2×D411yescharacteristic
170C2×C8×C13C2×D411yescharacteristic
171C2×C8×C13C2×D411yescharacteristic
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
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—41no—
184C13×C4⋊C4—41no—
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⋊C4C2×D411yescharacteristic
193C13×C4⋊C4C2×D411yescharacteristic
194C13×C4⋊C4C2×D411yescharacteristic
195C13×C4⋊C4C2×D411yescharacteristic
196C13×C22⋊C4—21no—
197C13×C22⋊C4—41no—
198C13×C22⋊C4—41no—
199C13×C22⋊C4—41no—
200C42×C13—21no—
201C42×C13—21no—
202C42×C13—21no—
203C42×C13—41no—
204C42×C13—41no—
205C42×C13—41no—
206C42×C13C2411yescharacteristic
207#3395C2×C1311yescharacteristic, complemented
208#3381C2×C1311yescharacteristic
209#3364C2×C1311yescharacteristic
210#3356C2×C1311yescharacteristic
211#1716C2×C1311yescharacteristic, complemented
212#1689C2×C1311yescharacteristic
213#1680C2×C1311yescharacteristic, complemented
214#1672C2×C1311yescharacteristic, complemented
215#1672C2×C1311yescharacteristic, complemented
216#1653C2×C1311yescharacteristic, complemented
217#1652C2×C1311yescharacteristic
218#1644C2×C1311yescharacteristic
219#1636C2×C1311yescharacteristic, complemented
220#1583C2×C1311yescharacteristic
221#1579C2×C1311yescharacteristic, complemented
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—81no—
235Q8×C13#13712yes—
236D4×C13—21no—
237D4×C13—21no—
238C2×C4×C13—21no—
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—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—161no—
252C2×C4×C13C22×D411yescharacteristic
253C2×C4×C13C22×D411yescharacteristic
254C2×C4×C13H(5,𝔽2)11yescharacteristic
255C8×C13—21no—
256C8×C13—21no—
257C8×C13—21no—
258C8×C13—41no—
259C8×C13—41no—
260C8×C13—41no—
261C8×C13—41no—
262C8×C13—41no—
263C8×C13#13512yes—
264#557C22×C1311yescharacteristic
265#557C22×C1311yescharacteristic
266#556C22×C1311yescharacteristic
267#554C22×C1311yescharacteristic
268#499—21no—
269#498C22×C1311yescharacteristic
270#498C22×C1311yescharacteristic
271#498C22×C1311yescharacteristic
272#494—21no—
273#494C22×C1311yescharacteristic
274#488—21no—
275#487C22×C1311yescharacteristic
276#487C22×C1311yescharacteristic
277#485—21no—
278#483—21no—
279#479—21no—
280#479—21no—
281#478—21no—
282#477C22×C1311yescharacteristic
283#477C22×C1311yescharacteristic
284#475C22×C1311yescharacteristic
285#474C22×C1311yescharacteristic
286#474C22×C1311yescharacteristic
287#470—21no—
288#464—21no—
289#462—21no—
290#462—21no—
291#462C22×C1311yescharacteristic
292#462C22×C1311yescharacteristic
293#462C22×C1311yescharacteristic
294C8×Q8C22×C1311yescharacteristic
295C8×Q8C22×C1311yescharacteristic
296C8×Q8C22×C1311yescharacteristic
297C4×Q16—21no—
298C4×Q16—21no—
299C4×Q16C22×C1311yescharacteristic
300C4×SD16—21no—
301C4×SD16C22×C1311yescharacteristic
302#436C22×C1311yescharacteristic
303#428—21no—
304#334C22×C1311yescharacteristic
305#334C22×C1311yescharacteristic
306#333C22×C1311yescharacteristic
307#332C22×C1311yescharacteristic
308#332C22×C1311yescharacteristic
309#332C22×C1311yescharacteristic
310Q8⋊C8C22×C1311yescharacteristic
311Q8⋊C8C22×C1311yescharacteristic
312Q8⋊C8C22×C1311yescharacteristic
313D4⋊C8C22×C1311yescharacteristic
314#322C22×C1311yescharacteristic
315C22×C13—41no—
316C22×C13—41no—
317C22×C13—41no—
318C22×C13D4211yescharacteristic
319C4×C13—22no—
320C4×C13—21no—
321C4×C13—41no—
322C4×C13—41no—
323C4×C13—41no—
324C4×C13—41no—
325C4×C13—41no—
326C4×C13—41no—
327C4×C13—81no—
328C4×C13—81no—
329C4×C13—81no—
330C4×C13—81no—
331C4×C13C2×#13511yescharacteristic
332C4×C13C2×#13711yescharacteristic
333C4×C13#57711yescharacteristic
334C4×C13#57811yescharacteristic
335C2×Q16—21no—
336C2×Q16—21no—
337C2×Q16—21no—
338C2×Q16—21no—
339C2×Q16—21no—
340C2×Q16D4×C1311yescharacteristic
341C2×SD16D4×C1311yescharacteristic
342C2×M16—21no—
343C4⋊Q8—21no—
344C4⋊Q8—21no—
345C4⋊Q8C23×C1311yescharacteristic
346C4⋊Q8C23×C1311yescharacteristic
347C4⋊Q8C23×C1311yescharacteristic
348C4⋊Q8C23×C1311yescharacteristic
349#126—41no—
350#125—21no—
351#125—21no—
352#125—21no—
353#125—41no—
354#125—41no—
355#124—21no—
356C22⋊Q8—21no—
357C22⋊Q8—21no—
358C22⋊Q8—41no—
359C4×Q8—21no—
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×D4C23×C1311yescharacteristic
369#117—21no—
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—21no—
380#106—21no—
381#106—41no—
382#106D4×C1311yescharacteristic
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8C23×C1311yescharacteristic
387C4⋊C8C23×C1311yescharacteristic
388C4⋊C8C23×C1311yescharacteristic
389C4⋊C8C23×C1311yescharacteristic
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—41no—
399#103D4×C1311yescharacteristic
400#103D4×C1311yescharacteristic
401#103D4×C1311yescharacteristic
402#102—21no—
403#102—21no—
404#102D4×C1311yescharacteristic
405C22⋊C8—21no—
406C4×C8—21no—
407C4×C8—21no—
408C4×C8—21no—
409C4×C8C23×C1311yescharacteristic
410C4×C8C23×C1311yescharacteristic
411C4×C8C23×C1311yescharacteristic
412C2×C13—81no—
413C2×C13#327011yescharacteristic
414C2×C13#328411yescharacteristic
415C2×C13#328911yescharacteristic
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8C2×D4×C1311yescharacteristic
421C2×Q8C2×D4×C1311yescharacteristic
422C2×Q8C2×D4×C1311yescharacteristic
423C2×D4C2×D4×C1311yescharacteristic
424C22×C4—21no—
425C22×C4—41no—
426Q16—22no—
427Q16—42no—
428Q16—42no—
429Q16—81no—
430Q16—81no—
431Q16—81no—
432SD16—22no—
433M16—42no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8C2×D4×C1311yescharacteristic
440C2×C8C2×D4×C1311yescharacteristic
441C2×C8C2×D4×C1311yescharacteristic
442C2×C8C2×D4×C1311yescharacteristic
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—41no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4C2×D4×C1311yescharacteristic
464C4⋊C4C2×D4×C1311yescharacteristic
465C4⋊C4C2×D4×C1311yescharacteristic
466C4⋊C4C2×D4×C1311yescharacteristic
467C22⋊C4—21no—
468C22⋊C4—41no—
469C22⋊C4—41no—
470C22⋊C4—41no—
471C42—21no—
472C42—21no—
473C42—21no—
474C42—41no—
475C42—41no—
476C42—41no—
477C42C24×C1311yescharacteristic
478C13#1988111yescharacteristic, direct product factor, Sylow
479C23—21no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—41no—
486Q8—41no—
487Q8—41no—
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—81no—
492Q8C13×#13712yes—
493D4—21no—
494D4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—161no—
509C2×C4C22×D4×C1311yescharacteristic
510C2×C4C22×D4×C1311yescharacteristic
511C2×C4C13×H(5,𝔽2)11yescharacteristic
512C8—21no—
513C8—21no—
514C8—21no—
515C8—41no—
516C8—41no—
517C8—41no—
518C8—41no—
519C8—41no—
520C8C13×#13512yes—
521C22—41no—
522C22—41no—
523C22—41no—
524C22D42×C1311yescharacteristic
525C4—22no—
526C4—21no—
527C4—41no—
528C4—41no—
529C4—41no—
530C4—41no—
531C4—41no—
532C4—41no—
533C4—81no—
534C4—81no—
535C4—81no—
536C4—81no—
537C4C2×C13×#13511yescharacteristic
538C4C2×C13×#13711yescharacteristic
539C4C13×#57711yescharacteristic
540C4C13×#57811yescharacteristic
541C2—81no—
542C2C13×#327011yescharacteristic
543C2C13×#328411yescharacteristic
544C2C13×#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×#3395C2semidirect
5. C13×#1716C2semidirect
7. C13×#1680C2semidirect
8. C13×#1672C2semidirect
9. C13×#1672C2semidirect
10. C13×#1653C2semidirect
13. C13×#1636C2semidirect
15. C13×#1579C2semidirect
144. #19881C13direct (N × H)
207. #3395C2×C13semidirect
211. #1716C2×C13semidirect
213. #1680C2×C13semidirect
214. #1672C2×C13semidirect
215. #1672C2×C13semidirect
216. #1653C2×C13semidirect
219. #1636C2×C13semidirect
221. #1579C2×C13semidirect
478. C13#19881direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#33952
C13×#33812
C13×#33642
C13×#33562
C13×#17162
C13×#16892
C13×#16802
C13×#16722
C13×#16532
C13×#16522
C13×#16442
C13×#16362
C13×#15832
C13×#15792
#1988113