Finite Group Databasebeta

← C13×#13424 #15699763

Subgroups — C13×#13424 #15699763

Order 3328.

612 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2684C211yesmaximal, characteristic
2C2×C13×#354C211yesmaximal, characteristic, complemented
3C2×C13×AΣL(1,𝔽16)C211yesmaximal, characteristic
4C13×#1889C211yesmaximal, characteristic
5C13×#1885C211yesmaximal, characteristic, complemented
6C13×#1867C211yesmaximal, characteristic, complemented
7C13×#1390C211yesmaximal, characteristic, complemented
8C2×C13×#124C2211yescharacteristic
9C2×C13×#120C2211yescharacteristic
10C13×#518C2211yescharacteristic
11C13×#419—21no—
12C2×C13×#100C2211yescharacteristic
13C2×C13×#99C2211yescharacteristic
14C2×C13×#99C2211yescharacteristic
15C13×#397—21no—
16C13×#394—21no—
17C13×#393—21no—
18C13×#388—21no—
19C13×#386—21no—
20C13×#386C2211yescharacteristic
21C13×#385—21no—
22C13×#379—21no—
23C13×#379—21no—
24C13×#354—22no—
25C13×AΣL(1,𝔽16)—22no—
26C13×#342—21no—
27C13×#342—21no—
28C13×#339—21no—
29C25×C13D411yescharacteristic
30C22×Q8×C13D411yescharacteristic
31C22×D4×C13—21no—
32C22×D4×C13C2311yescharacteristic
33C23×C4×C13D411yescharacteristic
34C2×C13×M16—21no—
35C13×#124—21no—
36C13×#124—21no—
37C13×#124—21no—
38C13×#124—21no—
39C13×#120—21no—
40C13×#120—21no—
41C13×#120—21no—
42C13×#120—21no—
43C4×D4×C13—41no—
44C4×D4×C13—41no—
45C13×#117—21no—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4—41no—
48C2×C13×C22⋊C4—21no—
49C2×C13×C22⋊C4—21no—
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—41no—
61C2×C13×C22⋊C4—41no—
62C2×C13×C22⋊C4D411yescharacteristic
63C2×C13×C22⋊C4D411yescharacteristic
64C2×C42×C13D411yescharacteristic
65C13×#103—41no—
66C13×#103—41no—
67C13×#100—21no—
68C13×#100—21no—
69C13×#99—21no—
70C13×#99—21no—
71C13×#99—21no—
72C13×#99D412yes—
73C13×#95—21no—
74C13×#95—21no—
75C13×#95—21no—
76C13×#95—21no—
77C13×#95—41no—
78#13424C1311yesmaximal, characteristic, direct product factor, Sylow
79C24×C13—21no—
80C24×C13—21no—
81C24×C13—21no—
82C24×C13—41no—
83C24×C13—41no—
84C24×C13—42no—
85C24×C13—81no—
86C24×C13C2×D411yescharacteristic
87C24×C13C2×D411yescharacteristic
88C2×Q8×C13—21no—
89C2×Q8×C13—21no—
90C2×Q8×C13—41no—
91C2×Q8×C13—41no—
92C2×D4×C13—41no—
93C2×D4×C13—41no—
94C2×D4×C13—42no—
95C2×D4×C13—41no—
96C2×D4×C13—41no—
97C2×D4×C13—81no—
98C2×D4×C13C2×D411yescharacteristic
99C2×D4×C13#4111yescharacteristic
100C2×D4×C13#4111yescharacteristic
101C2×D4×C13#4111yescharacteristic
102C22×C4×C13—21no—
103C22×C4×C13—21no—
104C22×C4×C13—21no—
105C22×C4×C13—21no—
106C22×C4×C13—21no—
107C22×C4×C13—21no—
108C22×C4×C13—21no—
109C22×C4×C13—21no—
110C22×C4×C13—21no—
111C22×C4×C13—41no—
112C22×C4×C13—41no—
113C22×C4×C13—41no—
114C22×C4×C13—81no—
115C22×C4×C13C2×D411yescharacteristic
116C13×M16—41no—
117C13×M16—41no—
118C2×C8×C13—41no—
119C13×C4⋊C4—21no—
120C13×C4⋊C4—21no—
121C13×C4⋊C4—81no—
122C13×C4⋊C4—82no—
123C13×C22⋊C4—22no—
124C13×C22⋊C4—21no—
125C13×C22⋊C4—21no—
126C13×C22⋊C4—41no—
127C13×C22⋊C4—42no—
128C13×C22⋊C4—41no—
129C13×C22⋊C4—41no—
130C13×C22⋊C4—41no—
131C13×C22⋊C4—41no—
132C13×C22⋊C4—41no—
133C13×C22⋊C4—41no—
134C13×C22⋊C4—41no—
135C13×C22⋊C4—41no—
136C13×C22⋊C4—41no—
137C13×C22⋊C4—41no—
138C13×C22⋊C4—41no—
139C13×C22⋊C4—41no—
140C13×C22⋊C4—81no—
141C13×C22⋊C4—81no—
142C13×C22⋊C4—81no—
143C13×C22⋊C4—81no—
144C13×C22⋊C4—82no—
145C13×C22⋊C4—82no—
146C42×C13—21no—
147C42×C13—21no—
148C42×C13—41no—
149#2684C2×C1311yescharacteristic
150C2×#354C2×C1311yescharacteristic, complemented
151C2×AΣL(1,𝔽16)C2×C1311yescharacteristic
152#1889C2×C1311yescharacteristic
153#1885C2×C1311yescharacteristic, complemented
154#1867C2×C1311yescharacteristic, complemented
155#1390C2×C1311yescharacteristic, complemented
156C23×C13—21no—
157C23×C13—21no—
158C23×C13—21no—
159C23×C13—21no—
160C23×C13—22no—
161C23×C13—41no—
162C23×C13—41no—
163C23×C13—41no—
164C23×C13—41no—
165C23×C13—41no—
166C23×C13—41no—
167C23×C13—41no—
168C23×C13—42no—
169C23×C13—42no—
170C23×C13—42no—
171C23×C13—41no—
172C23×C13—41no—
173C23×C13—41no—
174C23×C13—81no—
175C23×C13—82no—
176C23×C13—81no—
177C23×C13—84no—
178C23×C13—82no—
179C23×C13—81no—
180C23×C13#12011yescharacteristic
181C23×C13#12111yescharacteristic
182C23×C13#12111yescharacteristic
183C23×C13#12311yescharacteristic
184C23×C13#12411yescharacteristic
185Q8×C13—42no—
186Q8×C13—81no—
187D4×C13—41no—
188D4×C13—41no—
189D4×C13—41no—
190D4×C13—41no—
191D4×C13—82no—
192D4×C13—82no—
193C2×C4×C13—21no—
194C2×C4×C13—21no—
195C2×C4×C13—42no—
196C2×C4×C13—41no—
197C2×C4×C13—41no—
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—42no—
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—41no—
212C2×C4×C13—41no—
213C2×C4×C13—41no—
214C2×C4×C13—81no—
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#12111yescharacteristic
225C2×C4×C13#12311yescharacteristic
226C8×C13—81no—
227C2×#124C22×C1311yescharacteristic
228C2×#120C22×C1311yescharacteristic
229#518C22×C1311yescharacteristic
230#419—21no—
231C2×#100C22×C1311yescharacteristic
232C2×#99C22×C1311yescharacteristic
233C2×#99C22×C1311yescharacteristic
234#397—21no—
235#394—21no—
236#393—21no—
237#388—21no—
238#386—21no—
239#386C22×C1311yescharacteristic
240#385—21no—
241#379—21no—
242#379—21no—
243#354—22no—
244AΣL(1,𝔽16)—22no—
245#342—21no—
246#342—21no—
247#339—21no—
248C22×C13—21no—
249C22×C13—21no—
250C22×C13—21no—
251C22×C13—21no—
252C22×C13—21no—
253C22×C13—21no—
254C22×C13—41no—
255C22×C13—41no—
256C22×C13—41no—
257C22×C13—41no—
258C22×C13—42no—
259C22×C13—42no—
260C22×C13—41no—
261C22×C13—41no—
262C22×C13—41no—
263C22×C13—41no—
264C22×C13—44no—
265C22×C13—42no—
266C22×C13—81no—
267C22×C13—81no—
268C22×C13—81no—
269C22×C13—81no—
270C22×C13—82no—
271C22×C13—82no—
272C22×C13—82no—
273C22×C13—81no—
274C22×C13—81no—
275C22×C13#39411yescharacteristic
276C22×C13B(4,𝔽2)11yescharacteristic
277C22×C13#45811yescharacteristic
278C4×C13—21no—
279C4×C13—21no—
280C4×C13—81no—
281C4×C13—81no—
282C4×C13—81no—
283C4×C13—82no—
284C4×C13—81no—
285C4×C13—81no—
286C4×C13—81no—
287C4×C13—81no—
288C4×C13—161no—
289C25D4×C1311yescharacteristic
290C22×Q8D4×C1311yescharacteristic
291C22×D4—21no—
292C22×D4C23×C1311yescharacteristic
293C23×C4D4×C1311yescharacteristic
294C2×M16—21no—
295#124—21no—
296#124—21no—
297#124—21no—
298#124—21no—
299#120—21no—
300#120—21no—
301#120—21no—
302#120—21no—
303C4×D4—41no—
304C4×D4—41no—
305#117—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—41no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—41no—
321C2×C22⋊C4—41no—
322C2×C22⋊C4D4×C1311yescharacteristic
323C2×C22⋊C4D4×C1311yescharacteristic
324C2×C42D4×C1311yescharacteristic
325#103—41no—
326#103—41no—
327#100—21no—
328#100—21no—
329#99—21no—
330#99—21no—
331#99—21no—
332#99D4×C1312yes—
333#95—21no—
334#95—21no—
335#95—21no—
336#95—21no—
337#95—41no—
338C2×C13—21no—
339C2×C13—21no—
340C2×C13—41no—
341C2×C13—41no—
342C2×C13—41no—
343C2×C13—41no—
344C2×C13—82no—
345C2×C13#204411yescharacteristic
346C2×C13#219711yescharacteristic
347C2×C13#219911yescharacteristic
348C24—21no—
349C24—21no—
350C24—21no—
351C24—41no—
352C24—41no—
353C24—42no—
354C24—81no—
355C24C2×D4×C1311yescharacteristic
356C24C2×D4×C1311yescharacteristic
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—41no—
360C2×Q8—41no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—42no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—81no—
367C2×D4C2×D4×C1311yescharacteristic
368C2×D4C13×#4111yescharacteristic
369C2×D4C13×#4111yescharacteristic
370C2×D4C13×#4111yescharacteristic
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—81no—
384C22×C4C2×D4×C1311yescharacteristic
385M16—41no—
386M16—41no—
387C2×C8—41no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—81no—
391C4⋊C4—82no—
392C22⋊C4—22no—
393C22⋊C4—21no—
394C22⋊C4—21no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—42no—
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—81no—
410C22⋊C4—81no—
411C22⋊C4—81no—
412C22⋊C4—81no—
413C22⋊C4—82no—
414C22⋊C4—82no—
415C42—21no—
416C42—21no—
417C42—41no—
418C13#1342411yescharacteristic, direct product factor, Sylow
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—22no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—42no—
432C23—42no—
433C23—42no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—81no—
438C23—82no—
439C23—81no—
440C23—82no—
441C23—84no—
442C23—81no—
443C23C13×#12011yescharacteristic
444C23C13×#12111yescharacteristic
445C23C13×#12111yescharacteristic
446C23C13×#12311yescharacteristic
447C23C13×#12411yescharacteristic
448Q8—42no—
449Q8—81no—
450D4—41no—
451D4—41no—
452D4—41no—
453D4—41no—
454D4—82no—
455D4—82no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—42no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
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—81no—
478C2×C4—81no—
479C2×C4—81no—
480C2×C4—81no—
481C2×C4—81no—
482C2×C4—81no—
483C2×C4—81no—
484C2×C4—81no—
485C2×C4—81no—
486C2×C4—81no—
487C2×C4C13×#12111yescharacteristic
488C2×C4C13×#12311yescharacteristic
489C8—81no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—42no—
501C22—42no—
502C22—41no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—44no—
507C22—42no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—82no—
513C22—82no—
514C22—82no—
515C22—81no—
516C22—81no—
517C22C13×#39411yescharacteristic
518C22C13×B(4,𝔽2)11yescharacteristic
519C22C13×#45811yescharacteristic
520C4—21no—
521C4—21no—
522C4—81no—
523C4—81no—
524C4—81no—
525C4—82no—
526C4—81no—
527C4—81no—
528C4—81no—
529C4—81no—
530C4—161no—
531C2—21no—
532C2—21no—
533C2—41no—
534C2—41no—
535C2—41no—
536C2—41no—
537C2—82no—
538C2C13×#204411yescharacteristic
539C2C13×#219711yescharacteristic
540C2C13×#219911yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C13
prime radicalC2×C13×#120C22
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C13 ◁ C22×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#354C2semidirect
5. C13×#1885C2semidirect
6. C13×#1867C2semidirect
7. C13×#1390C2semidirect
78. #13424C13direct (N × H)
150. C2×#354C2×C13semidirect
153. #1885C2×C13semidirect
154. #1867C2×C13semidirect
155. #1390C2×C13semidirect
418. C13#13424direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26842
C2×C13×#3542
C2×C13×AΣL(1,𝔽16)2
C13×#18892
C13×#18852
C13×#18672
C13×#13902
#1342413