Finite Group Databasebeta

← C13×#10340 #15696679

Subgroups — C13×#10340 #15696679

Order 3328.

900 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2659C211yesmaximal, characteristic, complemented
2C13×#1786C212yesmaximal
3C13×#1438C211yesmaximal, characteristic
4C13×#1294C212yesmaximal, complemented
5C13×#1280C211yesmaximal, characteristic, complemented
6C23×D4×C13C2211yescharacteristic
7C2×C13×C22⋊Q8—21no—
8C22×C13×C22⋊C4—21no—
9C22×C13×C22⋊C4—21no—
10C2×C13×#102—22no—
11C2×C13×#102—22no—
12C2×C13×C22⋊C8C2212yes—
13C13×#398—22no—
14C13×#395—22no—
15C13×#380—21no—
16C13×#380C2212yes—
17C2×C13×#95C2211yescharacteristic
18C2×C13×#95C2211yescharacteristic
19C25×C13—21no—
20C22×Q8×C13—21no—
21C22×D4×C13—22no—
22C22×D4×C13—22no—
23C22×D4×C13—21no—
24C22×D4×C13—42no—
25C22×D4×C13—42no—
26C22×D4×C13Q812yescomplemented
27C23×C4×C13—21no—
28C23×C4×C13D411yescharacteristic
29C23×C4×C13D411yescharacteristic
30C23×C4×C13C2311yescharacteristic
31C22×C8×C13—22no—
32C13×C22⋊Q8—42no—
33C13×C22⋊Q8—42no—
34C2×C13×C4⋊C4—22no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4D412yes—
39C2×C13×C4⋊C4D412yes—
40C2×C13×C22⋊C4—22no—
41C2×C13×C22⋊C4—42no—
42C2×C13×C22⋊C4—42no—
43C2×C13×C22⋊C4—42no—
44C2×C13×C22⋊C4—42no—
45C2×C13×C22⋊C4—42no—
46C2×C13×C22⋊C4—42no—
47C13×#102—44no—
48C13×#102—44no—
49C13×C22⋊C8—22no—
50C13×C22⋊C8—22no—
51C13×#95—22no—
52C13×#95—22no—
53C13×#95—22no—
54C13×#95—22no—
55#10340C1311yesmaximal, characteristic, direct product factor, Sylow
56C24×C13—22no—
57C24×C13—22no—
58C24×C13—22no—
59C24×C13—41no—
60C24×C13—41no—
61C24×C13—41no—
62C24×C13—41no—
63C24×C13—41no—
64C24×C13—41no—
65C24×C13—41no—
66C24×C13—41no—
67C24×C13—41no—
68C24×C13—41no—
69C24×C13—41no—
70C24×C13—41no—
71C24×C13C2×D411yescharacteristic
72C2×Q8×C13—42no—
73C2×Q8×C13—81no—
74C2×Q8×C13—81no—
75C2×D4×C13—24no—
76C2×D4×C13—24no—
77C2×D4×C13—24no—
78C2×D4×C13—42no—
79C2×D4×C13—42no—
80C2×D4×C13—44no—
81C2×D4×C13—48no—
82C2×D4×C13—44no—
83C2×D4×C13—42no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—22no—
89C22×C4×C13—22no—
90C22×C4×C13—22no—
91C22×C4×C13—41no—
92C22×C4×C13—41no—
93C22×C4×C13—41no—
94C22×C4×C13—41no—
95C22×C4×C13—41no—
96C22×C4×C13—41no—
97C22×C4×C13—41no—
98C22×C4×C13—41no—
99C22×C4×C13—41no—
100C22×C4×C13—41no—
101C22×C4×C13—41no—
102C22×C4×C13—41no—
103C22×C4×C13D812yes—
104C22×C4×C13SD1612yes—
105C22×C4×C13C2×D412yes—
106C22×C4×C13C2×Q811yescharacteristic
107C22×C4×C13#4112yes—
108C22×C4×C13#4111yescharacteristic
109C2×C8×C13—42no—
110C2×C8×C13—42no—
111C2×C8×C13—42no—
112C13×C4⋊C4—42no—
113C13×C4⋊C4—42no—
114C13×C4⋊C4—42no—
115C13×C4⋊C4—44no—
116C13×C4⋊C4—81no—
117C13×C4⋊C4—81no—
118C13×C22⋊C4—48no—
119C13×C22⋊C4—48no—
120C13×C22⋊C4—42no—
121C13×C22⋊C4—42no—
122#2659C2×C1311yescharacteristic, complemented
123#1786C2×C1312yes—
124#1438C2×C1311yescharacteristic
125#1294C2×C1312yescomplemented
126#1280C2×C1311yescharacteristic, complemented
127C23×C13—21no—
128C23×C13—21no—
129C23×C13—21no—
130C23×C13—21no—
131C23×C13—24no—
132C23×C13—42no—
133C23×C13—42no—
134C23×C13—42no—
135C23×C13—42no—
136C23×C13—42no—
137C23×C13—42no—
138C23×C13—42no—
139C23×C13—42no—
140C23×C13—42no—
141C23×C13—42no—
142C23×C13—42no—
143C23×C13—42no—
144C23×C13—42no—
145C23×C13—42no—
146C23×C13—42no—
147C23×C13—42no—
148C23×C13—42no—
149C23×C13—42no—
150C23×C13—81no—
151C23×C13—81no—
152C23×C13—81no—
153C23×C13—81no—
154C23×C13—81no—
155C23×C13—81no—
156C23×C13—81no—
157C23×C13—81no—
158C23×C13—81no—
159C23×C13—81no—
160C23×C13—81no—
161C23×C13—81no—
162C23×C13—81no—
163C23×C13—81no—
164C23×C13—81no—
165C23×C13—81no—
166C23×C13#12011yescharacteristic
167C23×C13C22⋊Q811yescharacteristic
168C23×C13#12411yescharacteristic
169C23×C13C2×D811yescharacteristic
170C23×C13C2×SD1611yescharacteristic
171C23×C13AGL(1,ℤ/8)11yescharacteristic
172C23×C13#13711yescharacteristic
173Q8×C13—84no—
174D4×C13—28no—
175D4×C13—44no—
176D4×C13—44no—
177D4×C13—44no—
178C2×C4×C13—22no—
179C2×C4×C13—22no—
180C2×C4×C13—22no—
181C2×C4×C13—22no—
182C2×C4×C13—41no—
183C2×C4×C13—41no—
184C2×C4×C13—42no—
185C2×C4×C13—41no—
186C2×C4×C13—41no—
187C2×C4×C13—41no—
188C2×C4×C13—41no—
189C2×C4×C13—42no—
190C2×C4×C13—42no—
191C2×C4×C13—42no—
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—42no—
199C2×C4×C13—42no—
200C2×C4×C13—81no—
201C2×C4×C13—81no—
202C2×C4×C13—81no—
203C2×C4×C13—81no—
204C2×C4×C13—81no—
205C2×C4×C13—81no—
206C2×C4×C13C22⋊Q812yes—
207C2×C4×C13#12412yes—
208C8×C13—82no—
209C23×D4C22×C1311yescharacteristic
210C2×C22⋊Q8—21no—
211C22×C22⋊C4—21no—
212C22×C22⋊C4—21no—
213C2×#102—22no—
214C2×#102—22no—
215C2×C22⋊C8C22×C1312yes—
216#398—22no—
217#395—22no—
218#380—21no—
219#380C22×C1312yes—
220C2×#95C22×C1311yescharacteristic
221C2×#95C22×C1311yescharacteristic
222C22×C13—21no—
223C22×C13—21no—
224C22×C13—21no—
225C22×C13—21no—
226C22×C13—21no—
227C22×C13—21no—
228C22×C13—21no—
229C22×C13—21no—
230C22×C13—21no—
231C22×C13—21no—
232C22×C13—21no—
233C22×C13—21no—
234C22×C13—44no—
235C22×C13—44no—
236C22×C13—44no—
237C22×C13—82no—
238C22×C13—82no—
239C22×C13—82no—
240C22×C13—82no—
241C22×C13—82no—
242C22×C13—82no—
243C22×C13—82no—
244C22×C13—82no—
245C22×C13—82no—
246C22×C13—82no—
247C22×C13—82no—
248C22×C13—82no—
249C22×C13#39311yescharacteristic
250C22×C13#44711yescharacteristic
251C22×C13#44811yescharacteristic
252C22×C13#45311yescharacteristic
253C22×C13#45411yescharacteristic
254C22×C13B(4,𝔽2)11yescharacteristic
255C22×C13B(4,𝔽2)11yescharacteristic
256C22×C13#47411yescharacteristic
257C22×C13#47611yescharacteristic
258C22×C13#48611yescharacteristic
259C22×C13#48911yescharacteristic
260C4×C13—22no—
261C4×C13—22no—
262C4×C13—42no—
263C4×C13—42no—
264C4×C13—82no—
265C4×C13—82no—
266C4×C13—82no—
267C25—21no—
268C22×Q8—21no—
269C22×D4—22no—
270C22×D4—22no—
271C22×D4—21no—
272C22×D4—42no—
273C22×D4—42no—
274C22×D4Q8×C1312yescomplemented
275C23×C4—21no—
276C23×C4D4×C1311yescharacteristic
277C23×C4D4×C1311yescharacteristic
278C23×C4C23×C1311yescharacteristic
279C22×C8—22no—
280C22⋊Q8—42no—
281C22⋊Q8—42no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4D4×C1312yes—
287C2×C4⋊C4D4×C1312yes—
288C2×C22⋊C4—22no—
289C2×C22⋊C4—42no—
290C2×C22⋊C4—42no—
291C2×C22⋊C4—42no—
292C2×C22⋊C4—42no—
293C2×C22⋊C4—42no—
294C2×C22⋊C4—42no—
295#102—44no—
296#102—44no—
297C22⋊C8—22no—
298C22⋊C8—22no—
299#95—22no—
300#95—22no—
301#95—22no—
302#95—22no—
303C2×C13—21no—
304C2×C13—21no—
305C2×C13—21no—
306C2×C13—21no—
307C2×C13—84no—
308C2×C13#159511yescharacteristic
309C2×C13#159611yescharacteristic
310C2×C13#159811yescharacteristic
311C2×C13#159911yescharacteristic
312C2×C13#202311yescharacteristic
313C2×C13#202711yescharacteristic
314C2×C13#202911yescharacteristic
315C24—22no—
316C24—22no—
317C24—22no—
318C24—41no—
319C24—41no—
320C24—41no—
321C24—41no—
322C24—41no—
323C24—41no—
324C24—41no—
325C24—41no—
326C24—41no—
327C24—41no—
328C24—41no—
329C24—41no—
330C24C2×D4×C1311yescharacteristic
331C2×Q8—42no—
332C2×Q8—81no—
333C2×Q8—81no—
334C2×D4—24no—
335C2×D4—24no—
336C2×D4—24no—
337C2×D4—42no—
338C2×D4—42no—
339C2×D4—44no—
340C2×D4—48no—
341C2×D4—44no—
342C2×D4—42no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4C13×D812yes—
363C22×C4C13×SD1612yes—
364C22×C4C2×D4×C1312yes—
365C22×C4C2×Q8×C1311yescharacteristic
366C22×C4C13×#4112yes—
367C22×C4C13×#4111yescharacteristic
368C2×C8—42no—
369C2×C8—42no—
370C2×C8—42no—
371C4⋊C4—42no—
372C4⋊C4—42no—
373C4⋊C4—42no—
374C4⋊C4—44no—
375C4⋊C4—81no—
376C4⋊C4—81no—
377C22⋊C4—48no—
378C22⋊C4—48no—
379C22⋊C4—42no—
380C22⋊C4—42no—
381C13#1034011yescharacteristic, direct product factor, Sylow
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—24no—
387C23—42no—
388C23—42no—
389C23—42no—
390C23—42no—
391C23—42no—
392C23—42no—
393C23—42no—
394C23—42no—
395C23—42no—
396C23—42no—
397C23—42no—
398C23—42no—
399C23—42no—
400C23—42no—
401C23—42no—
402C23—42no—
403C23—42no—
404C23—42no—
405C23—81no—
406C23—81no—
407C23—81no—
408C23—81no—
409C23—81no—
410C23—81no—
411C23—81no—
412C23—81no—
413C23—81no—
414C23—81no—
415C23—81no—
416C23—81no—
417C23—81no—
418C23—81no—
419C23—81no—
420C23—81no—
421C23C13×#12011yescharacteristic
422C23C13×C22⋊Q811yescharacteristic
423C23C13×#12411yescharacteristic
424C23C2×C13×D811yescharacteristic
425C23C2×C13×SD1611yescharacteristic
426C23C13×AGL(1,ℤ/8)11yescharacteristic
427C23C13×#13711yescharacteristic
428Q8—84no—
429D4—28no—
430D4—44no—
431D4—44no—
432D4—44no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—81no—
456C2×C4—81no—
457C2×C4—81no—
458C2×C4—81no—
459C2×C4—81no—
460C2×C4—81no—
461C2×C4C13×C22⋊Q812yes—
462C2×C4C13×#12412yes—
463C8—82no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—44no—
477C22—44no—
478C22—44no—
479C22—82no—
480C22—82no—
481C22—82no—
482C22—82no—
483C22—82no—
484C22—82no—
485C22—82no—
486C22—82no—
487C22—82no—
488C22—82no—
489C22—82no—
490C22—82no—
491C22C13×#39311yescharacteristic
492C22C13×#44711yescharacteristic
493C22C13×#44811yescharacteristic
494C22C13×#45311yescharacteristic
495C22C13×#45411yescharacteristic
496C22C13×B(4,𝔽2)11yescharacteristic
497C22C13×B(4,𝔽2)11yescharacteristic
498C22C13×#47411yescharacteristic
499C22C13×#47611yescharacteristic
500C22C13×#48611yescharacteristic
501C22C13×#48911yescharacteristic
502C4—22no—
503C4—22no—
504C4—42no—
505C4—42no—
506C4—82no—
507C4—82no—
508C4—82no—
509C2—21no—
510C2—21no—
511C2—21no—
512C2—21no—
513C2—84no—
514C2C13×#159511yescharacteristic
515C2C13×#159611yescharacteristic
516C2C13×#159811yescharacteristic
517C2C13×#159911yescharacteristic
518C2C13×#202311yescharacteristic
519C2C13×#202711yescharacteristic
520C2C13×#202911yescharacteristic
subgroupG/H
center, socleC23×C13#120
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC23×D4×C13C22
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
1. C13×#2659C2semidirect
4. C13×#1294C2semidirect
5. C13×#1280C2semidirect
26. C22×D4×C13Q8semidirect
55. #10340C13direct (N × H)
122. #2659C2×C13semidirect
125. #1294C2×C13semidirect
126. #1280C2×C13semidirect
274. C22×D4Q8×C13semidirect
381. C13#10340direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26592
C13×#17862
C13×#14382
C13×#12942
C13×#12802
#1034013