Finite Group Databasebeta

← C13×#10404 #15696743

Subgroups — C13×#10404 #15696743

Order 3328.

602 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2639C211yesmaximal, characteristic
2C13×#1874C211yesmaximal, characteristic
3C13×#1872C211yesmaximal, characteristic, complemented
4C2×C13×#328C211yesmaximal, characteristic, complemented
5C2×C13×#327C211yesmaximal, characteristic
6C13×#1442C211yesmaximal, characteristic, complemented
7C13×#1280C211yesmaximal, characteristic, complemented
8C2×C13×C22⋊Q8C2211yescharacteristic
9C2×C13×#121C2211yescharacteristic
10C22×C13×C4⋊C4C2211yescharacteristic
11C2×C13×#103—21no—
12C2×C13×#102—21no—
13C2×C13×C22⋊C8C2211yescharacteristic
14C2×C13×C22⋊C8C2211yescharacteristic
15C13×#400—21no—
16C13×#397—21no—
17C13×#394—21no—
18C13×#393—21no—
19C13×#386—21no—
20C13×#386—21no—
21C2×C13×#95—21no—
22C2×C13×#95—21no—
23C2×C13×#95C2211yescharacteristic
24C2×C13×#95C2211yescharacteristic
25C13×#340—21no—
26C13×#340—21no—
27C13×#328—22no—
28C13×#327—22no—
29C22×Q8×C13D411yescharacteristic
30C22×D4×C13—21no—
31C22×D4×C13D411yescharacteristic
32C23×C4×C13—21no—
33C23×C4×C13—21no—
34C23×C4×C13D411yescharacteristic
35C23×C4×C13D411yescharacteristic
36C23×C4×C13C2311yescharacteristic
37C22×C8×C13—21no—
38C22×C8×C13—21no—
39C13×C22⋊Q8—21no—
40C13×C22⋊Q8—21no—
41C13×C22⋊Q8—21no—
42C13×C22⋊Q8—21no—
43C13×#121—21no—
44C13×#121—21no—
45C13×#121—21no—
46C13×#121—21no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—42no—
51C2×C13×C4⋊C4D411yescharacteristic
52C2×C13×C4⋊C4D411yescharacteristic
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—
59C13×#103—42no—
60C13×#102—42no—
61C13×C22⋊C8—21no—
62C13×C22⋊C8—21no—
63C13×C22⋊C8—21no—
64C13×C22⋊C8—21no—
65C13×#95—21no—
66C13×#95—21no—
67C13×#95—21no—
68C13×#95—21no—
69C13×#95—21no—
70C13×#95—21no—
71C13×#95—21no—
72C13×#95—42no—
73C13×#95—42no—
74C13×#95D412yes—
75#10404C1311yesmaximal, characteristic, direct product factor, Sylow
76C24×C13—21no—
77C24×C13C2×D411yescharacteristic
78C2×Q8×C13—21no—
79C2×Q8×C13—21no—
80C2×Q8×C13—41no—
81C2×Q8×C13—41no—
82C2×D4×C13—21no—
83C2×D4×C13—21no—
84C2×D4×C13—41no—
85C2×D4×C13—41no—
86C2×D4×C13—41no—
87C2×D4×C13—41no—
88C2×D4×C13—41no—
89C2×D4×C13—41no—
90C2×D4×C13—41no—
91C2×D4×C13—41no—
92C22×C4×C13—22no—
93C22×C4×C13—21no—
94C22×C4×C13—21no—
95C22×C4×C13—21no—
96C22×C4×C13—21no—
97C22×C4×C13—21no—
98C22×C4×C13—22no—
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×C13—41no—
120C22×C4×C13—41no—
121C22×C4×C13C2×D411yescharacteristic
122C22×C4×C13C2×D411yescharacteristic
123C22×C4×C13C2×D411yescharacteristic
124C22×C4×C13#4111yescharacteristic
125C22×C4×C13#4111yescharacteristic
126C22×C4×C13#4111yescharacteristic
127C2×C8×C13—41no—
128C2×C8×C13—41no—
129C2×C8×C13—41no—
130C2×C8×C13—41no—
131C2×C8×C13—41no—
132C2×C8×C13—41no—
133C13×C4⋊C4—22no—
134C13×C4⋊C4—22no—
135C13×C4⋊C4—21no—
136C13×C4⋊C4—21no—
137C13×C4⋊C4—21no—
138C13×C4⋊C4—21no—
139C13×C4⋊C4—41no—
140C13×C4⋊C4—41no—
141C13×C4⋊C4—41no—
142C13×C4⋊C4—41no—
143C13×C22⋊C4—41no—
144C13×C22⋊C4—41no—
145C13×C22⋊C4—41no—
146C13×C22⋊C4—41no—
147C13×C22⋊C4—81no—
148C13×C22⋊C4—81no—
149C13×C22⋊C4—81no—
150C13×C22⋊C4—81no—
151#2639C2×C1311yescharacteristic
152#1874C2×C1311yescharacteristic
153#1872C2×C1311yescharacteristic, complemented
154C2×#328C2×C1311yescharacteristic, complemented
155C2×#327C2×C1311yescharacteristic
156#1442C2×C1311yescharacteristic, complemented
157#1280C2×C1311yescharacteristic, complemented
158C23×C13—21no—
159C23×C13—21no—
160C23×C13—21no—
161C23×C13—21no—
162C23×C13—41no—
163C23×C13—41no—
164C23×C13—41no—
165C23×C13—41no—
166C23×C13—41no—
167C23×C13—41no—
168C23×C13—41no—
169C23×C13#12011yescharacteristic
170C23×C13#12111yescharacteristic
171C23×C13#12411yescharacteristic
172C23×C13#13511yescharacteristic
173C23×C13#13511yescharacteristic
174C23×C13AGL(1,ℤ/8)11yescharacteristic
175C23×C13#13711yescharacteristic
176Q8×C13—42no—
177Q8×C13—81no—
178D4×C13—42no—
179D4×C13—81no—
180D4×C13—81no—
181D4×C13—81no—
182D4×C13—81no—
183D4×C13—81no—
184C2×C4×C13—21no—
185C2×C4×C13—21no—
186C2×C4×C13—21no—
187C2×C4×C13—21no—
188C2×C4×C13—41no—
189C2×C4×C13—41no—
190C2×C4×C13—41no—
191C2×C4×C13—41no—
192C2×C4×C13—42no—
193C2×C4×C13—42no—
194C2×C4×C13—42no—
195C2×C4×C13—42no—
196C2×C4×C13—42no—
197C2×C4×C13—42no—
198C2×C4×C13—41no—
199C2×C4×C13—41no—
200C2×C4×C13—41no—
201C2×C4×C13—41no—
202C2×C4×C13—41no—
203C2×C4×C13—41no—
204C2×C4×C13—41no—
205C2×C4×C13—41no—
206C2×C4×C13—41no—
207C2×C4×C13—41no—
208C2×C4×C13—41no—
209C2×C4×C13—41no—
210C2×C4×C13—41no—
211C2×C4×C13—42no—
212C2×C4×C13—41no—
213C2×C4×C13—41no—
214C2×C4×C13—42no—
215C2×C4×C13—81no—
216C2×C4×C13—81no—
217C2×C4×C13—81no—
218C2×C4×C13—81no—
219C2×C4×C13—81no—
220C2×C4×C13—81no—
221C2×C4×C13—81no—
222C2×C4×C13—81no—
223C2×C4×C13—81no—
224C2×C4×C13—81no—
225C2×C4×C13#12111yescharacteristic
226C2×C4×C13#12111yescharacteristic
227C2×C4×C13#12311yescharacteristic
228C2×C4×C13#12311yescharacteristic
229C8×C13—81no—
230C8×C13—81no—
231C2×C22⋊Q8C22×C1311yescharacteristic
232C2×#121C22×C1311yescharacteristic
233C22×C4⋊C4C22×C1311yescharacteristic
234C2×#103—21no—
235C2×#102—21no—
236C2×C22⋊C8C22×C1311yescharacteristic
237C2×C22⋊C8C22×C1311yescharacteristic
238#400—21no—
239#397—21no—
240#394—21no—
241#393—21no—
242#386—21no—
243#386—21no—
244C2×#95—21no—
245C2×#95—21no—
246C2×#95C22×C1311yescharacteristic
247C2×#95C22×C1311yescharacteristic
248#340—21no—
249#340—21no—
250#328—22no—
251#327—22no—
252C22×C13—21no—
253C22×C13—21no—
254C22×C13—21no—
255C22×C13—21no—
256C22×C13—21no—
257C22×C13—21no—
258C22×C13—21no—
259C22×C13—21no—
260C22×C13—21no—
261C22×C13—21no—
262C22×C13—21no—
263C22×C13—21no—
264C22×C13—81no—
265C22×C13—81no—
266C22×C13—81no—
267C22×C13—81no—
268C22×C13—81no—
269C22×C13—81no—
270C22×C13—81no—
271C22×C13#39411yescharacteristic
272C22×C13#44911yescharacteristic
273C22×C13#45211yescharacteristic
274C22×C13#45411yescharacteristic
275C22×C13#45511yescharacteristic
276C22×C13B(4,𝔽2)11yescharacteristic
277C22×C13#45811yescharacteristic
278C22×C13#46311yescharacteristic
279C22×C13#46411yescharacteristic
280C22×C13#48811yescharacteristic
281C22×C13#48911yescharacteristic
282C4×C13—21no—
283C4×C13—21no—
284C4×C13—21no—
285C4×C13—21no—
286C4×C13—82no—
287C4×C13—82no—
288C4×C13—81no—
289C4×C13—81no—
290C4×C13—81no—
291C4×C13—81no—
292C4×C13—81no—
293C22×Q8D4×C1311yescharacteristic
294C22×D4—21no—
295C22×D4D4×C1311yescharacteristic
296C23×C4—21no—
297C23×C4—21no—
298C23×C4D4×C1311yescharacteristic
299C23×C4D4×C1311yescharacteristic
300C23×C4C23×C1311yescharacteristic
301C22×C8—21no—
302C22×C8—21no—
303C22⋊Q8—21no—
304C22⋊Q8—21no—
305C22⋊Q8—21no—
306C22⋊Q8—21no—
307#121—21no—
308#121—21no—
309#121—21no—
310#121—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4D4×C1311yescharacteristic
316C2×C4⋊C4D4×C1311yescharacteristic
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323#103—42no—
324#102—42no—
325C22⋊C8—21no—
326C22⋊C8—21no—
327C22⋊C8—21no—
328C22⋊C8—21no—
329#95—21no—
330#95—21no—
331#95—21no—
332#95—21no—
333#95—21no—
334#95—21no—
335#95—21no—
336#95—42no—
337#95—42no—
338#95D4×C1312yes—
339C2×C13—21no—
340C2×C13—21no—
341C2×C13—21no—
342C2×C13—21no—
343C2×C13—161no—
344C2×C13#159711yescharacteristic
345C2×C13#160611yescharacteristic
346C2×C13#161211yescharacteristic
347C2×C13#161511yescharacteristic
348C2×C13#204011yescharacteristic
349C2×C13#204211yescharacteristic
350C2×C13#204411yescharacteristic
351C24—21no—
352C24C2×D4×C1311yescharacteristic
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—41no—
356C2×Q8—41no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—41no—
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—41no—
367C22×C4—22no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4C2×D4×C1311yescharacteristic
397C22×C4C2×D4×C1311yescharacteristic
398C22×C4C2×D4×C1311yescharacteristic
399C22×C4C13×#4111yescharacteristic
400C22×C4C13×#4111yescharacteristic
401C22×C4C13×#4111yescharacteristic
402C2×C8—41no—
403C2×C8—41no—
404C2×C8—41no—
405C2×C8—41no—
406C2×C8—41no—
407C2×C8—41no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—41no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4—41no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—41no—
421C22⋊C4—41no—
422C22⋊C4—81no—
423C22⋊C4—81no—
424C22⋊C4—81no—
425C22⋊C4—81no—
426C13#1040411yescharacteristic, direct product factor, Sylow
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23C13×#12011yescharacteristic
439C23C13×#12111yescharacteristic
440C23C13×#12411yescharacteristic
441C23C13×#13511yescharacteristic
442C23C13×#13511yescharacteristic
443C23C13×AGL(1,ℤ/8)11yescharacteristic
444C23C13×#13711yescharacteristic
445Q8—42no—
446Q8—81no—
447D4—42no—
448D4—81no—
449D4—81no—
450D4—81no—
451D4—81no—
452D4—81no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—42no—
484C2×C4—81no—
485C2×C4—81no—
486C2×C4—81no—
487C2×C4—81no—
488C2×C4—81no—
489C2×C4—81no—
490C2×C4—81no—
491C2×C4—81no—
492C2×C4—81no—
493C2×C4—81no—
494C2×C4C13×#12111yescharacteristic
495C2×C4C13×#12111yescharacteristic
496C2×C4C13×#12311yescharacteristic
497C2×C4C13×#12311yescharacteristic
498C8—81no—
499C8—81no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—81no—
513C22—81no—
514C22—81no—
515C22—81no—
516C22—81no—
517C22—81no—
518C22—81no—
519C22C13×#39411yescharacteristic
520C22C13×#44911yescharacteristic
521C22C13×#45211yescharacteristic
522C22C13×#45411yescharacteristic
523C22C13×#45511yescharacteristic
524C22C13×B(4,𝔽2)11yescharacteristic
525C22C13×#45811yescharacteristic
526C22C13×#46311yescharacteristic
527C22C13×#46411yescharacteristic
528C22C13×#48811yescharacteristic
529C22C13×#48911yescharacteristic
530C4—21no—
531C4—21no—
532C4—21no—
533C4—21no—
534C4—82no—
535C4—81no—
536C4—81no—
537C4—81no—
538C4—82no—
539C4—81no—
540C4—81no—
541C2—21no—
542C2—21no—
543C2—21no—
544C2—21no—
545C2—161no—
546C2C13×#159711yescharacteristic
547C2C13×#160611yescharacteristic
548C2C13×#161211yescharacteristic
549C2C13×#161511yescharacteristic
550C2C13×#204011yescharacteristic
551C2C13×#204211yescharacteristic
552C2C13×#204411yescharacteristic
subgroupG/H
center, socleC23×C13#120
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC2×C13×#121C22
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
3. C13×#1872C2semidirect
4. C2×C13×#328C2semidirect
6. C13×#1442C2semidirect
7. C13×#1280C2semidirect
75. #10404C13direct (N × H)
153. #1872C2×C13semidirect
154. C2×#328C2×C13semidirect
156. #1442C2×C13semidirect
157. #1280C2×C13semidirect
426. C13#10404direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26392
C13×#18742
C13×#18722
C2×C13×#3282
C2×C13×#3272
C13×#14422
C13×#12802
#1040413