Finite Group Databasebeta

← C13×#19790 #15706129

Subgroups — C13×#19790 #15706129

Order 3328.

626 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3381C211yesmaximal, characteristic, complemented
2C13×#3372C211yesmaximal, characteristic, complemented
3C13×#3295C211yesmaximal, characteristic
4C13×#3295C211yesmaximal, characteristic
5C13×#1720C211yesmaximal, characteristic, complemented
6C13×#1698C211yesmaximal, characteristic, complemented
7C13×#1683C211yesmaximal, characteristic, complemented
8C13×#1678C211yesmaximal, characteristic, complemented
9C13×#1671C211yesmaximal, characteristic, complemented
10C13×#1639C211yesmaximal, characteristic
11C13×#1632C211yesmaximal, characteristic, complemented
12C13×#1632C211yesmaximal, characteristic, complemented
13C13×#1626C211yesmaximal, characteristic, complemented
14C13×#1582C211yesmaximal, characteristic, complemented
15C13×SD16⋊C8C211yesmaximal, characteristic, complemented
16C13×#557C2211yescharacteristic, complemented
17C13×#554C2211yescharacteristic
18C13×#554C2211yescharacteristic
19D42×C13C2211yescharacteristic
20C13×#499—21no—
21C13×#498C2211yescharacteristic, complemented
22C13×#494C2211yescharacteristic, complemented
23C13×#491—21no—
24C13×#487C2211yescharacteristic, complemented
25C13×#486C2211yescharacteristic
26C13×#486C2211yescharacteristic
27C13×#486C2211yescharacteristic
28C13×#481—21no—
29C13×#481—21no—
30C13×#479—21no—
31C13×#479—21no—
32C13×#478—21no—
33C13×#477C2211yescharacteristic, complemented
34C13×#477C2211yescharacteristic, complemented
35C13×#476C2211yescharacteristic
36C13×#476C2211yescharacteristic
37C13×#474C2211yescharacteristic
38C13×#465—21no—
39C13×#465—21no—
40C13×#461—21no—
41C13×#461C2211yescharacteristic
42C13×#460C2211yescharacteristic
43C13×#460C2211yescharacteristic
44C13×#450—21no—
45C13×#450—21no—
46C13×#446C2211yescharacteristic, complemented
47C8×Q8×C13C2211yescharacteristic, complemented
48C13×#440—21no—
49C4×C13×SD16—21no—
50C4×C13×SD16C2211yescharacteristic
51C4×C13×SD16C2211yescharacteristic
52C8×D4×C13C2211yescharacteristic
53C8×D4×C13C2211yescharacteristic
54C2×C13×#102—21no—
55C2×C13×#102—21no—
56C13×#335C2211yescharacteristic, complemented
57C13×#334C2211yescharacteristic, complemented
58C13×#333C2211yescharacteristic, complemented
59C13×#333C2211yescharacteristic, complemented
60C13×#332C2211yescharacteristic, complemented
61C13×#331C2211yescharacteristic
62C13×Q8⋊C8C2211yescharacteristic, complemented
63C13×Q8⋊C8C2211yescharacteristic, complemented
64C13×D4⋊C8C2211yescharacteristic
65C13×D4⋊C8C2211yescharacteristic
66C13×#322C2211yescharacteristic, complemented
67C22×D4×C13—21no—
68C22×D4×C13—21no—
69C2×C13×Q16—41no—
70C2×C13×SD16—21no—
71C2×C13×SD16—21no—
72C2×C13×SD16—21no—
73C2×C13×SD16D411yescharacteristic
74C2×C13×SD16D411yescharacteristic
75C22×C8×C13—21no—
76C22×C8×C13—21no—
77C13×C4⋊Q8—21no—
78C13×C4⋊Q8C2311yescharacteristic
79C13×C4⋊Q8C2311yescharacteristic
80C13×C4⋊Q8C2311yescharacteristic
81C13×#127C2311yescharacteristic
82C13×#125—21no—
83C13×#125—21no—
84C13×#125—21no—
85C13×#125—41no—
86C13×C22⋊Q8—21no—
87C13×C22⋊Q8—21no—
88C13×C22⋊Q8—41no—
89C13×C22⋊Q8—41no—
90C13×#121—21no—
91C13×#121—21no—
92C13×#120—41no—
93C4×Q8×C13—21no—
94C4×Q8×C13—21no—
95C4×Q8×C13C2311yescharacteristic
96C4×Q8×C13C2311yescharacteristic
97C4×D4×C13—21no—
98C4×D4×C13—21no—
99C4×D4×C13C2311yescharacteristic
100C4×D4×C13C2311yescharacteristic
101C2×C13×C4⋊C4—21no—
102C2×C13×C4⋊C4—21no—
103C13×#107—21no—
104C13×#107—21no—
105C13×#107—21no—
106C13×#106—21no—
107C13×#106—21no—
108C13×#106—21no—
109C13×#106—21no—
110C13×#106D411yescharacteristic
111C13×#106D411yescharacteristic
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×#103D411yescharacteristic
124C13×#103D411yescharacteristic
125C13×#102—21no—
126C13×#102—21no—
127C13×#102—21no—
128C13×#102—21no—
129C13×#102—21no—
130C13×#102—21no—
131C13×#102—21no—
132C13×#102—21no—
133C13×#102—21no—
134C13×#102—41no—
135C13×#102D411yescharacteristic
136C13×#102D411yescharacteristic
137C13×C22⋊C8—21no—
138C13×C22⋊C8—21no—
139C13×#97—21no—
140C4×C8×C13—21no—
141C4×C8×C13C2311yescharacteristic
142C4×C8×C13C2311yescharacteristic
143C4×C8×C13C2311yescharacteristic
144#19790C1311yesmaximal, characteristic, direct product factor, Sylow
145C24×C13—41no—
146C2×Q8×C13—21no—
147C2×Q8×C13—21no—
148C2×Q8×C13—21no—
149C2×Q8×C13C2×D411yescharacteristic
150C2×Q8×C13C2×D411yescharacteristic
151C2×D4×C13—21no—
152C2×D4×C13—21no—
153C2×D4×C13—21no—
154C2×D4×C13—41no—
155C2×D4×C13—41no—
156C2×D4×C13—42no—
157C2×D4×C13—42no—
158C2×D4×C13—81no—
159C2×D4×C13—81no—
160C2×D4×C13C2×D411yescharacteristic
161C2×D4×C13C2×D411yescharacteristic
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—41no—
165C22×C4×C13—41no—
166C13×Q16—82no—
167C13×SD16—22no—
168C13×SD16—22no—
169C13×SD16—42no—
170C13×SD16—81no—
171C13×SD16—81no—
172C2×C8×C13—21no—
173C2×C8×C13—21no—
174C2×C8×C13—21no—
175C2×C8×C13—21no—
176C2×C8×C13—21no—
177C2×C8×C13—81no—
178C2×C8×C13—81no—
179C2×C8×C13C2×D411yescharacteristic
180C2×C8×C13C2×D411yescharacteristic
181C2×C8×C13C2×D411yescharacteristic
182C2×C8×C13C2×D411yescharacteristic
183C13×C4⋊C4—21no—
184C13×C4⋊C4—21no—
185C13×C4⋊C4—21no—
186C13×C4⋊C4—21no—
187C13×C4⋊C4—21no—
188C13×C4⋊C4—21no—
189C13×C4⋊C4—21no—
190C13×C4⋊C4—21no—
191C13×C4⋊C4—41no—
192C13×C4⋊C4—41no—
193C13×C4⋊C4—41no—
194C13×C4⋊C4—41no—
195C13×C4⋊C4—41no—
196C13×C4⋊C4—41no—
197C13×C4⋊C4—41no—
198C13×C4⋊C4C2×D411yescharacteristic
199C13×C4⋊C4C2×D411yescharacteristic
200C13×C4⋊C4C2×D411yescharacteristic
201C13×C4⋊C4C2×D411yescharacteristic
202C13×C22⋊C4—21no—
203C13×C22⋊C4—21no—
204C13×C22⋊C4—41no—
205C13×C22⋊C4—41no—
206C13×C22⋊C4—41no—
207C42×C13—21no—
208C42×C13—21no—
209C42×C13—41no—
210C42×C13C2411yescharacteristic
211#3381C2×C1311yescharacteristic, complemented
212#3372C2×C1311yescharacteristic, complemented
213#3295C2×C1311yescharacteristic
214#3295C2×C1311yescharacteristic
215#1720C2×C1311yescharacteristic, complemented
216#1698C2×C1311yescharacteristic, complemented
217#1683C2×C1311yescharacteristic, complemented
218#1678C2×C1311yescharacteristic, complemented
219#1671C2×C1311yescharacteristic, complemented
220#1639C2×C1311yescharacteristic
221#1632C2×C1311yescharacteristic, complemented
222#1632C2×C1311yescharacteristic, complemented
223#1626C2×C1311yescharacteristic, complemented
224#1582C2×C1311yescharacteristic, complemented
225SD16⋊C8C2×C1311yescharacteristic, complemented
226C23×C13—21no—
227C23×C13—21no—
228C23×C13—41no—
229C23×C13—82no—
230C23×C13—82no—
231C23×C13—161no—
232Q8×C13—21no—
233Q8×C13—21no—
234Q8×C13—21no—
235Q8×C13—21no—
236Q8×C13—41no—
237Q8×C13—41no—
238Q8×C13—81no—
239Q8×C13—81no—
240D4×C13—21no—
241D4×C13—21no—
242D4×C13—41no—
243D4×C13—41no—
244D4×C13—41no—
245D4×C13—41no—
246D4×C13—81no—
247D4×C13—82no—
248D4×C13—82no—
249D4×C13#13512yes—
250D4×C13#13712yes—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—161no—
265C2×C4×C13—161no—
266C2×C4×C13C22×D411yescharacteristic
267C2×C4×C13C22×D411yescharacteristic
268C2×C4×C13H(5,𝔽2)11yescharacteristic
269C8×C13—21no—
270C8×C13—21no—
271C8×C13—21no—
272C8×C13—21no—
273C8×C13—41no—
274C8×C13—41no—
275C8×C13—41no—
276C8×C13—41no—
277C8×C13—41no—
278#557C22×C1311yescharacteristic, complemented
279#554C22×C1311yescharacteristic
280#554C22×C1311yescharacteristic
281D42C22×C1311yescharacteristic
282#499—21no—
283#498C22×C1311yescharacteristic, complemented
284#494C22×C1311yescharacteristic, complemented
285#491—21no—
286#487C22×C1311yescharacteristic, complemented
287#486C22×C1311yescharacteristic
288#486C22×C1311yescharacteristic
289#486C22×C1311yescharacteristic
290#481—21no—
291#481—21no—
292#479—21no—
293#479—21no—
294#478—21no—
295#477C22×C1311yescharacteristic, complemented
296#477C22×C1311yescharacteristic, complemented
297#476C22×C1311yescharacteristic
298#476C22×C1311yescharacteristic
299#474C22×C1311yescharacteristic
300#465—21no—
301#465—21no—
302#461—21no—
303#461C22×C1311yescharacteristic
304#460C22×C1311yescharacteristic
305#460C22×C1311yescharacteristic
306#450—21no—
307#450—21no—
308#446C22×C1311yescharacteristic, complemented
309C8×Q8C22×C1311yescharacteristic, complemented
310#440—21no—
311C4×SD16—21no—
312C4×SD16C22×C1311yescharacteristic
313C4×SD16C22×C1311yescharacteristic
314C8×D4C22×C1311yescharacteristic
315C8×D4C22×C1311yescharacteristic
316C2×#102—21no—
317C2×#102—21no—
318#335C22×C1311yescharacteristic, complemented
319#334C22×C1311yescharacteristic, complemented
320#333C22×C1311yescharacteristic, complemented
321#333C22×C1311yescharacteristic, complemented
322#332C22×C1311yescharacteristic, complemented
323#331C22×C1311yescharacteristic
324Q8⋊C8C22×C1311yescharacteristic, complemented
325Q8⋊C8C22×C1311yescharacteristic, complemented
326D4⋊C8C22×C1311yescharacteristic
327D4⋊C8C22×C1311yescharacteristic
328#322C22×C1311yescharacteristic, complemented
329C22×C13—22no—
330C22×C13—22no—
331C22×C13—41no—
332C22×C13—41no—
333C22×C13—41no—
334C22×C13—41no—
335C22×C13—81no—
336C22×C13—81no—
337C22×C13—81no—
338C22×C13—164no—
339C22×C13D4211yescharacteristic
340C4×C13—21no—
341C4×C13—41no—
342C4×C13—41no—
343C4×C13—41no—
344C4×C13—41no—
345C4×C13—41no—
346C4×C13—41no—
347C4×C13—81no—
348C4×C13—81no—
349C4×C13—81no—
350C4×C13C2×#13511yescharacteristic
351C4×C13C2×#13711yescharacteristic
352C4×C13#57711yescharacteristic
353C4×C13#57711yescharacteristic
354C22×D4—21no—
355C22×D4—21no—
356C2×Q16—41no—
357C2×SD16—21no—
358C2×SD16—21no—
359C2×SD16—21no—
360C2×SD16D4×C1311yescharacteristic
361C2×SD16D4×C1311yescharacteristic
362C22×C8—21no—
363C22×C8—21no—
364C4⋊Q8—21no—
365C4⋊Q8C23×C1311yescharacteristic
366C4⋊Q8C23×C1311yescharacteristic
367C4⋊Q8C23×C1311yescharacteristic
368#127C23×C1311yescharacteristic
369#125—21no—
370#125—21no—
371#125—21no—
372#125—41no—
373C22⋊Q8—21no—
374C22⋊Q8—21no—
375C22⋊Q8—41no—
376C22⋊Q8—41no—
377#121—21no—
378#121—21no—
379#120—41no—
380C4×Q8—21no—
381C4×Q8—21no—
382C4×Q8C23×C1311yescharacteristic
383C4×Q8C23×C1311yescharacteristic
384C4×D4—21no—
385C4×D4—21no—
386C4×D4C23×C1311yescharacteristic
387C4×D4C23×C1311yescharacteristic
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390#107—21no—
391#107—21no—
392#107—21no—
393#106—21no—
394#106—21no—
395#106—21no—
396#106—21no—
397#106D4×C1311yescharacteristic
398#106D4×C1311yescharacteristic
399C4⋊C8—21no—
400C4⋊C8—21no—
401C4⋊C8C23×C1311yescharacteristic
402C4⋊C8C23×C1311yescharacteristic
403C4⋊C8C23×C1311yescharacteristic
404C4⋊C8C23×C1311yescharacteristic
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103D4×C1311yescharacteristic
411#103D4×C1311yescharacteristic
412#102—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102—41no—
422#102D4×C1311yescharacteristic
423#102D4×C1311yescharacteristic
424C22⋊C8—21no—
425C22⋊C8—21no—
426#97—21no—
427C4×C8—21no—
428C4×C8C23×C1311yescharacteristic
429C4×C8C23×C1311yescharacteristic
430C4×C8C23×C1311yescharacteristic
431C2×C13—42no—
432C2×C13—42no—
433C2×C13—161no—
434C2×C13#326611yescharacteristic
435C2×C13#328211yescharacteristic
436C2×C13#328811yescharacteristic
437C24—41no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8C2×D4×C1311yescharacteristic
442C2×Q8C2×D4×C1311yescharacteristic
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4—81no—
451C2×D4—81no—
452C2×D4C2×D4×C1311yescharacteristic
453C2×D4C2×D4×C1311yescharacteristic
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—41no—
457C22×C4—41no—
458Q16—82no—
459SD16—22no—
460SD16—22no—
461SD16—42no—
462SD16—81no—
463SD16—81no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—81no—
470C2×C8—81no—
471C2×C8C2×D4×C1311yescharacteristic
472C2×C8C2×D4×C1311yescharacteristic
473C2×C8C2×D4×C1311yescharacteristic
474C2×C8C2×D4×C1311yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4C2×D4×C1311yescharacteristic
491C4⋊C4C2×D4×C1311yescharacteristic
492C4⋊C4C2×D4×C1311yescharacteristic
493C4⋊C4C2×D4×C1311yescharacteristic
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C42—21no—
500C42—21no—
501C42—41no—
502C42C24×C1311yescharacteristic
503C13#1979011yescharacteristic, direct product factor, Sylow
504C23—21no—
505C23—21no—
506C23—41no—
507C23—82no—
508C23—82no—
509C23—161no—
510Q8—21no—
511Q8—21no—
512Q8—21no—
513Q8—21no—
514Q8—41no—
515Q8—41no—
516Q8—81no—
517Q8—81no—
518D4—21no—
519D4—21no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—81no—
525D4—82no—
526D4—82no—
527D4C13×#13512yes—
528D4C13×#13712yes—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—161no—
543C2×C4—161no—
544C2×C4C22×D4×C1311yescharacteristic
545C2×C4C22×D4×C1311yescharacteristic
546C2×C4C13×H(5,𝔽2)11yescharacteristic
547C8—21no—
548C8—21no—
549C8—21no—
550C8—21no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C22—22no—
557C22—22no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—164no—
566C22D42×C1311yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4C2×C13×#13511yescharacteristic
578C4C2×C13×#13711yescharacteristic
579C4C13×#57711yescharacteristic
580C4C13×#57711yescharacteristic
581C2—42no—
582C2—42no—
583C2—161no—
584C2C13×#326611yescharacteristic
585C2C13×#328211yescharacteristic
586C2C13×#328811yescharacteristic
subgroupG/H
center, socleC22×C13D42
commutator, Frattini, cosocleC42C24×C13
prime radicalD42×C13C22
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×#3381C2semidirect
2. C13×#3372C2semidirect
5. C13×#1720C2semidirect
6. C13×#1698C2semidirect
7. C13×#1683C2semidirect
8. C13×#1678C2semidirect
9. C13×#1671C2semidirect
11. C13×#1632C2semidirect
12. C13×#1632C2semidirect
13. C13×#1626C2semidirect
14. C13×#1582C2semidirect
15. C13×SD16⋊C8C2semidirect
16. C13×#557C22semidirect
21. C13×#498C22semidirect
22. C13×#494C22semidirect
24. C13×#487C22semidirect
33. C13×#477C22semidirect
34. C13×#477C22semidirect
46. C13×#446C22semidirect
47. C8×Q8×C13C22semidirect
56. C13×#335C22semidirect
57. C13×#334C22semidirect
58. C13×#333C22semidirect
59. C13×#333C22semidirect
60. C13×#332C22semidirect
62. C13×Q8⋊C8C22semidirect
63. C13×Q8⋊C8C22semidirect
66. C13×#322C22semidirect
144. #19790C13direct (N × H)
211. #3381C2×C13semidirect
212. #3372C2×C13semidirect
215. #1720C2×C13semidirect
216. #1698C2×C13semidirect
217. #1683C2×C13semidirect
218. #1678C2×C13semidirect
219. #1671C2×C13semidirect
221. #1632C2×C13semidirect
222. #1632C2×C13semidirect
223. #1626C2×C13semidirect
224. #1582C2×C13semidirect
225. SD16⋊C8C2×C13semidirect
278. #557C22×C13semidirect
283. #498C22×C13semidirect
284. #494C22×C13semidirect
286. #487C22×C13semidirect
295. #477C22×C13semidirect
296. #477C22×C13semidirect
308. #446C22×C13semidirect
309. C8×Q8C22×C13semidirect
318. #335C22×C13semidirect
319. #334C22×C13semidirect
320. #333C22×C13semidirect
321. #333C22×C13semidirect
322. #332C22×C13semidirect
324. Q8⋊C8C22×C13semidirect
325. Q8⋊C8C22×C13semidirect
328. #322C22×C13semidirect
503. C13#19790direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#33812
C13×#33722
C13×#32952
C13×#17202
C13×#16982
C13×#16832
C13×#16782
C13×#16712
C13×#16392
C13×#16322
C13×#16262
C13×#15822
C13×SD16⋊C82
#1979013