Finite Group Databasebeta

← C13×#10399 #15696738

Subgroups — C13×#10399 #15696738

Order 3328.

694 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×#2626C211yesmaximal, characteristic
2C13×#1872C211yesmaximal, characteristic, complemented
3C13×#1852C211yesmaximal, characteristic, complemented
4C2×C13×#328C211yesmaximal, characteristic, complemented
5C2×C13×#323C211yesmaximal, characteristic
6C13×#1439C211yesmaximal, characteristic
7C13×#1294C211yesmaximal, characteristic, complemented
8C2×C13×C22⋊Q8C2211yescharacteristic
9C22×C13×C4⋊C4C2211yescharacteristic
10C22×C13×C22⋊C4—21no—
11C22×C13×C22⋊C4C2211yescharacteristic
12C2×C13×#107—21no—
13C2×C13×#103—21no—
14C2×C13×C22⋊C8C2211yescharacteristic
15C2×C13×C22⋊C8C2211yescharacteristic
16C13×#399—21no—
17C13×#396—21no—
18C13×#396—21no—
19C13×#393—21no—
20C13×#385—21no—
21C13×#380C2211yescharacteristic
22C13×#379—21no—
23C2×C13×#95—21no—
24C2×C13×#95C2211yescharacteristic
25C13×#340—21no—
26C13×#340—21no—
27C13×#328—22no—
28C13×#323—22no—
29C25×C13D411yescharacteristic
30C22×Q8×C13D411yescharacteristic
31C23×C4×C13—21no—
32C23×C4×C13—21no—
33C23×C4×C13D411yescharacteristic
34C23×C4×C13C2311yescharacteristic
35C22×C8×C13—21no—
36C22×C8×C13—21no—
37C13×C22⋊Q8—21no—
38C13×C22⋊Q8—21no—
39C13×C22⋊Q8—21no—
40C13×C22⋊Q8—21no—
41C2×C13×C4⋊C4—21no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4—42no—
47C2×C13×C4⋊C4D411yescharacteristic
48C2×C13×C4⋊C4D411yescharacteristic
49C2×C13×C4⋊C4D411yescharacteristic
50C2×C13×C22⋊C4—21no—
51C2×C13×C22⋊C4—21no—
52C2×C13×C22⋊C4—21no—
53C2×C13×C22⋊C4—21no—
54C2×C13×C22⋊C4—21no—
55C2×C13×C22⋊C4—21no—
56C2×C13×C22⋊C4—21no—
57C2×C13×C22⋊C4—21no—
58C2×C13×C22⋊C4—21no—
59C2×C13×C22⋊C4—21no—
60C2×C13×C22⋊C4—21no—
61C2×C13×C22⋊C4—21no—
62C2×C13×C22⋊C4—42no—
63C2×C13×C22⋊C4—42no—
64C2×C13×C22⋊C4—42no—
65C13×#107—42no—
66C13×#103—42no—
67C13×C22⋊C8—21no—
68C13×C22⋊C8—21no—
69C13×C22⋊C8—21no—
70C13×C22⋊C8D412yes—
71C13×#95—21no—
72C13×#95—21no—
73C13×#95—21no—
74C13×#95—21no—
75C13×#95—21no—
76C13×#95—42no—
77#10399C1311yesmaximal, characteristic, direct product factor, Sylow
78C24×C13—21no—
79C24×C13—21no—
80C24×C13—21no—
81C24×C13—21no—
82C24×C13—21no—
83C24×C13—21no—
84C24×C13—41no—
85C24×C13—41no—
86C24×C13—41no—
87C24×C13—41no—
88C24×C13Q1612yes—
89C24×C13C2×D411yescharacteristic
90C2×Q8×C13—21no—
91C2×Q8×C13—21no—
92C2×Q8×C13—41no—
93C2×Q8×C13—41no—
94C22×C4×C13—22no—
95C22×C4×C13—22no—
96C22×C4×C13—21no—
97C22×C4×C13—21no—
98C22×C4×C13—21no—
99C22×C4×C13—21no—
100C22×C4×C13—21no—
101C22×C4×C13—21no—
102C22×C4×C13—21no—
103C22×C4×C13—41no—
104C22×C4×C13—41no—
105C22×C4×C13—41no—
106C22×C4×C13—41no—
107C22×C4×C13—41no—
108C22×C4×C13—41no—
109C22×C4×C13—41no—
110C22×C4×C13—41no—
111C22×C4×C13—41no—
112C22×C4×C13—41no—
113C22×C4×C13—41no—
114C22×C4×C13—41no—
115C22×C4×C13—41no—
116C22×C4×C13—41no—
117C22×C4×C13—41no—
118C22×C4×C13—41no—
119C22×C4×C13C2×D411yescharacteristic
120C22×C4×C13C2×D411yescharacteristic
121C22×C4×C13C2×D411yescharacteristic
122C22×C4×C13#4111yescharacteristic
123C22×C4×C13#4111yescharacteristic
124C22×C4×C13#4111yescharacteristic
125C2×C8×C13—22no—
126C2×C8×C13—41no—
127C2×C8×C13—41no—
128C2×C8×C13—41no—
129C2×C8×C13—41no—
130C2×C8×C13—41no—
131C13×C4⋊C4—22no—
132C13×C4⋊C4—22no—
133C13×C4⋊C4—21no—
134C13×C4⋊C4—21no—
135C13×C4⋊C4—41no—
136C13×C4⋊C4—41no—
137C13×C4⋊C4—41no—
138C13×C4⋊C4—41no—
139C13×C4⋊C4—41no—
140C13×C4⋊C4—41no—
141C13×C4⋊C4—81no—
142C13×C4⋊C4—81no—
143C13×C22⋊C4—48no—
144C13×C22⋊C4—41no—
145C13×C22⋊C4—41no—
146C13×C22⋊C4—41no—
147C13×C22⋊C4—41no—
148C13×C22⋊C4—41no—
149C13×C22⋊C4—41no—
150C13×C22⋊C4—41no—
151C13×C22⋊C4—41no—
152C13×C22⋊C4—81no—
153C13×C22⋊C4—81no—
154C13×C22⋊C4—81no—
155C13×C22⋊C4—81no—
156#2626C2×C1311yescharacteristic
157#1872C2×C1311yescharacteristic, complemented
158#1852C2×C1311yescharacteristic, complemented
159C2×#328C2×C1311yescharacteristic, complemented
160C2×#323C2×C1311yescharacteristic
161#1439C2×C1311yescharacteristic
162#1294C2×C1311yescharacteristic, complemented
163C23×C13—21no—
164C23×C13—21no—
165C23×C13—21no—
166C23×C13—21no—
167C23×C13—22no—
168C23×C13—22no—
169C23×C13—22no—
170C23×C13—42no—
171C23×C13—42no—
172C23×C13—42no—
173C23×C13—42no—
174C23×C13—42no—
175C23×C13—42no—
176C23×C13—41no—
177C23×C13—41no—
178C23×C13—41no—
179C23×C13—41no—
180C23×C13—41no—
181C23×C13—41no—
182C23×C13—41no—
183C23×C13—41no—
184C23×C13—81no—
185C23×C13—81no—
186C23×C13—81no—
187C23×C13—81no—
188C23×C13—81no—
189C23×C13—81no—
190C23×C13#12011yescharacteristic
191C23×C13#12111yescharacteristic
192C23×C13#12311yescharacteristic
193C23×C13C2×Q1611yescharacteristic
194C23×C13#13511yescharacteristic
195C23×C13AGL(1,ℤ/8)11yescharacteristic
196C23×C13#13711yescharacteristic
197Q8×C13—42no—
198Q8×C13—81no—
199C2×C4×C13—21no—
200C2×C4×C13—21no—
201C2×C4×C13—21no—
202C2×C4×C13—21no—
203C2×C4×C13—41no—
204C2×C4×C13—41no—
205C2×C4×C13—41no—
206C2×C4×C13—41no—
207C2×C4×C13—42no—
208C2×C4×C13—42no—
209C2×C4×C13—42no—
210C2×C4×C13—42no—
211C2×C4×C13—42no—
212C2×C4×C13—42no—
213C2×C4×C13—41no—
214C2×C4×C13—41no—
215C2×C4×C13—41no—
216C2×C4×C13—41no—
217C2×C4×C13—41no—
218C2×C4×C13—41no—
219C2×C4×C13—41no—
220C2×C4×C13—41no—
221C2×C4×C13—41no—
222C2×C4×C13—41no—
223C2×C4×C13—41no—
224C2×C4×C13—41no—
225C2×C4×C13—41no—
226C2×C4×C13—42no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13—81no—
230C2×C4×C13—81no—
231C2×C4×C13—81no—
232C2×C4×C13—81no—
233C2×C4×C13—81no—
234C2×C4×C13—81no—
235C2×C4×C13—81no—
236C2×C4×C13—81no—
237C2×C4×C13—81no—
238C2×C4×C13#12111yescharacteristic
239C2×C4×C13#12111yescharacteristic
240C2×C4×C13#12311yescharacteristic
241C2×C4×C13#12411yescharacteristic
242C8×C13—42no—
243C8×C13—81no—
244C2×C22⋊Q8C22×C1311yescharacteristic
245C22×C4⋊C4C22×C1311yescharacteristic
246C22×C22⋊C4—21no—
247C22×C22⋊C4C22×C1311yescharacteristic
248C2×#107—21no—
249C2×#103—21no—
250C2×C22⋊C8C22×C1311yescharacteristic
251C2×C22⋊C8C22×C1311yescharacteristic
252#399—21no—
253#396—21no—
254#396—21no—
255#393—21no—
256#385—21no—
257#380C22×C1311yescharacteristic
258#379—21no—
259C2×#95—21no—
260C2×#95C22×C1311yescharacteristic
261#340—21no—
262#340—21no—
263#328—22no—
264#323—22no—
265C22×C13—21no—
266C22×C13—21no—
267C22×C13—21no—
268C22×C13—21no—
269C22×C13—21no—
270C22×C13—21no—
271C22×C13—21no—
272C22×C13—21no—
273C22×C13—21no—
274C22×C13—21no—
275C22×C13—21no—
276C22×C13—21no—
277C22×C13—44no—
278C22×C13—42no—
279C22×C13—42no—
280C22×C13—42no—
281C22×C13—82no—
282C22×C13—82no—
283C22×C13—82no—
284C22×C13—81no—
285C22×C13—81no—
286C22×C13—81no—
287C22×C13—81no—
288C22×C13#39411yescharacteristic
289C22×C13#44911yescharacteristic
290C22×C13#45111yescharacteristic
291C22×C13#45311yescharacteristic
292C22×C13#45511yescharacteristic
293C22×C13B(4,𝔽2)11yescharacteristic
294C22×C13#45811yescharacteristic
295C22×C13#46711yescharacteristic
296C22×C13#46811yescharacteristic
297C22×C13#48411yescharacteristic
298C22×C13#48511yescharacteristic
299C4×C13—21no—
300C4×C13—21no—
301C4×C13—21no—
302C4×C13—21no—
303C4×C13—82no—
304C4×C13—81no—
305C4×C13—82no—
306C4×C13—81no—
307C4×C13—81no—
308C4×C13—81no—
309C4×C13—81no—
310C25D4×C1311yescharacteristic
311C22×Q8D4×C1311yescharacteristic
312C23×C4—21no—
313C23×C4—21no—
314C23×C4D4×C1311yescharacteristic
315C23×C4C23×C1311yescharacteristic
316C22×C8—21no—
317C22×C8—21no—
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4D4×C1311yescharacteristic
329C2×C4⋊C4D4×C1311yescharacteristic
330C2×C4⋊C4D4×C1311yescharacteristic
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346#107—42no—
347#103—42no—
348C22⋊C8—21no—
349C22⋊C8—21no—
350C22⋊C8—21no—
351C22⋊C8D4×C1312yes—
352#95—21no—
353#95—21no—
354#95—21no—
355#95—21no—
356#95—21no—
357#95—42no—
358C2×C13—21no—
359C2×C13—21no—
360C2×C13—21no—
361C2×C13—21no—
362C2×C13—82no—
363C2×C13#160011yescharacteristic
364C2×C13#160211yescharacteristic
365C2×C13#161211yescharacteristic
366C2×C13#161411yescharacteristic
367C2×C13#203611yescharacteristic
368C2×C13#203711yescharacteristic
369C2×C13#204411yescharacteristic
370C24—21no—
371C24—21no—
372C24—21no—
373C24—21no—
374C24—21no—
375C24—21no—
376C24—41no—
377C24—41no—
378C24—41no—
379C24—41no—
380C24C13×Q1612yes—
381C24C2×D4×C1311yescharacteristic
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—41no—
385C2×Q8—41no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—41no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4C2×D4×C1311yescharacteristic
412C22×C4C2×D4×C1311yescharacteristic
413C22×C4C2×D4×C1311yescharacteristic
414C22×C4C13×#4111yescharacteristic
415C22×C4C13×#4111yescharacteristic
416C22×C4C13×#4111yescharacteristic
417C2×C8—22no—
418C2×C8—41no—
419C2×C8—41no—
420C2×C8—41no—
421C2×C8—41no—
422C2×C8—41no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4—41no—
430C4⋊C4—41no—
431C4⋊C4—41no—
432C4⋊C4—41no—
433C4⋊C4—81no—
434C4⋊C4—81no—
435C22⋊C4—48no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—41no—
444C22⋊C4—81no—
445C22⋊C4—81no—
446C22⋊C4—81no—
447C22⋊C4—81no—
448C13#1039911yescharacteristic, direct product factor, Sylow
449C23—21no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23—42no—
461C23—42no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—81no—
471C23—81no—
472C23—81no—
473C23—81no—
474C23—81no—
475C23—81no—
476C23C13×#12011yescharacteristic
477C23C13×#12111yescharacteristic
478C23C13×#12311yescharacteristic
479C23C2×C13×Q1611yescharacteristic
480C23C13×#13511yescharacteristic
481C23C13×AGL(1,ℤ/8)11yescharacteristic
482C23C13×#13711yescharacteristic
483Q8—42no—
484Q8—81no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—81no—
516C2×C4—81no—
517C2×C4—81no—
518C2×C4—81no—
519C2×C4—81no—
520C2×C4—81no—
521C2×C4—81no—
522C2×C4—81no—
523C2×C4—81no—
524C2×C4C13×#12111yescharacteristic
525C2×C4C13×#12111yescharacteristic
526C2×C4C13×#12311yescharacteristic
527C2×C4C13×#12411yescharacteristic
528C8—42no—
529C8—81no—
530C22—21no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—44no—
543C22—42no—
544C22—42no—
545C22—42no—
546C22—82no—
547C22—82no—
548C22—82no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22C13×#39411yescharacteristic
554C22C13×#44911yescharacteristic
555C22C13×#45111yescharacteristic
556C22C13×#45311yescharacteristic
557C22C13×#45511yescharacteristic
558C22C13×B(4,𝔽2)11yescharacteristic
559C22C13×#45811yescharacteristic
560C22C13×#46711yescharacteristic
561C22C13×#46811yescharacteristic
562C22C13×#48411yescharacteristic
563C22C13×#48511yescharacteristic
564C4—21no—
565C4—21no—
566C4—21no—
567C4—21no—
568C4—82no—
569C4—81no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4—82no—
574C4—81no—
575C2—21no—
576C2—21no—
577C2—21no—
578C2—21no—
579C2—82no—
580C2C13×#160011yescharacteristic
581C2C13×#160211yescharacteristic
582C2C13×#161211yescharacteristic
583C2C13×#161411yescharacteristic
584C2C13×#203611yescharacteristic
585C2C13×#203711yescharacteristic
586C2C13×#204411yescharacteristic
subgroupG/H
center, socleC23×C13#120
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC25×C13D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#1872C2semidirect
3. C13×#1852C2semidirect
4. C2×C13×#328C2semidirect
7. C13×#1294C2semidirect
77. #10399C13direct (N × H)
157. #1872C2×C13semidirect
158. #1852C2×C13semidirect
159. C2×#328C2×C13semidirect
162. #1294C2×C13semidirect
448. C13#10399direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26262
C13×#18722
C13×#18522
C2×C13×#3282
C2×C13×#3232
C13×#14392
C13×#12942
#1039913