Finite Group Databasebeta

← C13×#13376 #15699715

Subgroups — C13×#13376 #15699715

Order 3328.

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

normal subgroups only

This group has 640 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×#2748C211yesmaximal, characteristic, complemented
2C13×#1792C211yesmaximal, characteristic
3C13×#1790C211yesmaximal, characteristic
4C13×#1790C211yesmaximal, characteristic
5C13×#1393C211yesmaximal, characteristic, complemented
6C13×#1390C211yesmaximal, characteristic, complemented
7C13×#1390C211yesmaximal, characteristic, complemented
8C2×C13×H(5,𝔽2)C2211yescharacteristic
9C2×C13×#104—21no—
10C13×#417—21no—
11C2×C13×#100C2211yescharacteristic
12C2×C13×#99—21no—
13C2×C13×#99—21no—
14C2×C13×#99C2211yescharacteristic
15C2×C13×#99C2211yescharacteristic
16C13×#399—21no—
17C13×#398—21no—
18C13×#396—21no—
19C13×#390C2211yescharacteristic
20C13×#387—21no—
21C13×#386—21no—
22C13×#386—21no—
23C13×#386C2211yescharacteristic
24C13×#386C2211yescharacteristic
25C13×#385—21no—
26C13×#380—21no—
27C13×H(5,𝔽2)—21no—
28C13×H(5,𝔽2)—21no—
29C13×H(5,𝔽2)—21no—
30C13×H(5,𝔽2)—42no—
31C13×H(5,𝔽2)Q812yes—
32C2×C13×#41—21no—
33C2×C13×#41—41no—
34C22×D4×C13—21no—
35C22×D4×C13—21no—
36C22×D4×C13—41no—
37C22×D4×C13C2311yescharacteristic
38C23×C4×C13D411yescharacteristic
39C23×C4×C13D411yescharacteristic
40C2×C13×M16—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⋊C4D411yescharacteristic
47C2×C13×C22⋊C4—21no—
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—41no—
54C2×C13×C22⋊C4—41no—
55C2×C13×C22⋊C4D411yescharacteristic
56C2×C13×C22⋊C4D411yescharacteristic
57C2×C42×C13D411yescharacteristic
58C13×#104—42no—
59C13×#103—41no—
60C13×#102—41no—
61C13×#100—21no—
62C13×#100—21no—
63C13×#99—21no—
64C13×#99—21no—
65C13×#99—21no—
66C13×#99—21no—
67C13×#99—42no—
68C13×#99—42no—
69C13×#95—21no—
70C13×#95—21no—
71C13×#95—21no—
72C13×#95—21no—
73C13×#95—21no—
74C13×#95—41no—
75C13×#95—41no—
76#13376C1311yesmaximal, characteristic, direct product factor, Sylow
77C24×C13—21no—
78C24×C13—21no—
79C24×C13C2×D411yescharacteristic
80C24×C13C2×D411yescharacteristic
81C13×#41—22no—
82C13×#41—22no—
83C13×#41—42no—
84C13×#41—41no—
85C13×#41—42no—
86C13×#41—42no—
87C13×#41—42no—
88C13×#41—41no—
89C2×Q8×C13—21no—
90C2×D4×C13—21no—
91C2×D4×C13—22no—
92C2×D4×C13—22no—
93C2×D4×C13—22no—
94C2×D4×C13—22no—
95C2×D4×C13—41no—
96C2×D4×C13—41no—
97C2×D4×C13—42no—
98C2×D4×C13—42no—
99C2×D4×C13—41no—
100C2×D4×C13—41no—
101C2×D4×C13—41no—
102C2×D4×C13—41no—
103C2×D4×C13—42no—
104C2×D4×C13—42no—
105C2×D4×C13—41no—
106C2×D4×C13—41no—
107C2×D4×C13—41no—
108C2×D4×C13C2×Q811yescharacteristic
109C2×D4×C13#4111yescharacteristic
110C2×D4×C13#4111yescharacteristic
111C2×D4×C13#4111yescharacteristic
112C22×C4×C13—21no—
113C22×C4×C13—21no—
114C22×C4×C13—21no—
115C22×C4×C13—21no—
116C22×C4×C13—21no—
117C22×C4×C13—21no—
118C22×C4×C13—21no—
119C22×C4×C13—21no—
120C22×C4×C13—41no—
121C22×C4×C13—42no—
122C22×C4×C13—41no—
123C22×C4×C13—41no—
124C22×C4×C13—41no—
125C22×C4×C13—41no—
126C22×C4×C13—81no—
127C22×C4×C13C2×D411yescharacteristic
128C13×M16—41no—
129C13×M16—41no—
130C2×C8×C13—41no—
131C13×C4⋊C4—41no—
132C13×C4⋊C4—42no—
133C13×C4⋊C4—81no—
134C13×C4⋊C4—81no—
135C13×C4⋊C4—81no—
136C13×C4⋊C4—81no—
137C13×C22⋊C4—42no—
138C13×C22⋊C4—41no—
139C13×C22⋊C4—41no—
140C13×C22⋊C4—41no—
141C13×C22⋊C4—41no—
142C13×C22⋊C4—41no—
143C13×C22⋊C4—41no—
144C13×C22⋊C4—81no—
145C13×C22⋊C4—81no—
146C13×C22⋊C4—81no—
147C13×C22⋊C4—82no—
148C13×C22⋊C4—82no—
149C42×C13—41no—
150#2748C2×C1311yescharacteristic, complemented
151#1792C2×C1311yescharacteristic
152#1790C2×C1311yescharacteristic
153#1790C2×C1311yescharacteristic
154#1393C2×C1311yescharacteristic, complemented
155#1390C2×C1311yescharacteristic, complemented
156#1390C2×C1311yescharacteristic, complemented
157C23×C13—21no—
158C23×C13—21no—
159C23×C13—21no—
160C23×C13—21no—
161C23×C13—22no—
162C23×C13—22no—
163C23×C13—41no—
164C23×C13—41no—
165C23×C13—41no—
166C23×C13—41no—
167C23×C13—41no—
168C23×C13—41no—
169C23×C13—41no—
170C23×C13—81no—
171C23×C13—81no—
172C23×C13—81no—
173C23×C13—81no—
174C23×C13#12011yescharacteristic
175C23×C13C22⋊Q811yescharacteristic
176C23×C13C22⋊Q811yescharacteristic
177C23×C13#12411yescharacteristic
178C23×C13#12411yescharacteristic
179Q8×C13—22no—
180Q8×C13—41no—
181D4×C13—22no—
182D4×C13—41no—
183D4×C13—41no—
184D4×C13—41no—
185D4×C13—41no—
186D4×C13—41no—
187D4×C13—42no—
188D4×C13—42no—
189D4×C13—42no—
190D4×C13—42no—
191D4×C13—42no—
192D4×C13—42no—
193C2×C4×C13—21no—
194C2×C4×C13—21no—
195C2×C4×C13—22no—
196C2×C4×C13—22no—
197C2×C4×C13—22no—
198C2×C4×C13—42no—
199C2×C4×C13—42no—
200C2×C4×C13—41no—
201C2×C4×C13—41no—
202C2×C4×C13—41no—
203C2×C4×C13—41no—
204C2×C4×C13—41no—
205C2×C4×C13—42no—
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—41no—
215C2×C4×C13—41no—
216C2×C4×C13—42no—
217C2×C4×C13—41no—
218C2×C4×C13—41no—
219C2×C4×C13—41no—
220C2×C4×C13—41no—
221C2×C4×C13—41no—
222C2×C4×C13—81no—
223C2×C4×C13—81no—
224C2×C4×C13—81no—
225C2×C4×C13—81no—
226C2×C4×C13—81no—
227C2×C4×C13—81no—
228C2×C4×C13—81no—
229C2×C4×C13—81no—
230C2×C4×C13C22⋊Q811yescharacteristic
231C2×C4×C13#12411yescharacteristic
232C8×C13—81no—
233C2×H(5,𝔽2)C22×C1311yescharacteristic
234C2×#104—21no—
235#417—21no—
236C2×#100C22×C1311yescharacteristic
237C2×#99—21no—
238C2×#99—21no—
239C2×#99C22×C1311yescharacteristic
240C2×#99C22×C1311yescharacteristic
241#399—21no—
242#398—21no—
243#396—21no—
244#390C22×C1311yescharacteristic
245#387—21no—
246#386—21no—
247#386—21no—
248#386C22×C1311yescharacteristic
249#386C22×C1311yescharacteristic
250#385—21no—
251#380—21no—
252C22×C13—21no—
253C22×C13—21no—
254C22×C13—21no—
255C22×C13—21no—
256C22×C13—21no—
257C22×C13—21no—
258C22×C13—41no—
259C22×C13—41no—
260C22×C13—41no—
261C22×C13—41no—
262C22×C13—41no—
263C22×C13—41no—
264C22×C13—41no—
265C22×C13—41no—
266C22×C13—42no—
267C22×C13—81no—
268C22×C13—81no—
269C22×C13—82no—
270C22×C13—82no—
271C22×C13—81no—
272C22×C13—81no—
273C22×C13—161no—
274C22×C13—161no—
275C22×C13#39311yescharacteristic
276C22×C13B(4,𝔽2)11yescharacteristic
277C22×C13B(4,𝔽2)11yescharacteristic
278C4×C13—21no—
279C4×C13—21no—
280C4×C13—42no—
281C4×C13—42no—
282C4×C13—81no—
283C4×C13—81no—
284C4×C13—81no—
285C4×C13—81no—
286C4×C13—81no—
287C4×C13—161no—
288C4×C13—161no—
289H(5,𝔽2)—21no—
290H(5,𝔽2)—21no—
291H(5,𝔽2)—21no—
292H(5,𝔽2)—42no—
293H(5,𝔽2)Q8×C1312yes—
294C2×#41—21no—
295C2×#41—41no—
296C22×D4—21no—
297C22×D4—21no—
298C22×D4—41no—
299C22×D4C23×C1311yescharacteristic
300C23×C4D4×C1311yescharacteristic
301C23×C4D4×C1311yescharacteristic
302C2×M16—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4D4×C1311yescharacteristic
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—41no—
316C2×C22⋊C4—41no—
317C2×C22⋊C4D4×C1311yescharacteristic
318C2×C22⋊C4D4×C1311yescharacteristic
319C2×C42D4×C1311yescharacteristic
320#104—42no—
321#103—41no—
322#102—41no—
323#100—21no—
324#100—21no—
325#99—21no—
326#99—21no—
327#99—21no—
328#99—21no—
329#99—42no—
330#99—42no—
331#95—21no—
332#95—21no—
333#95—21no—
334#95—21no—
335#95—21no—
336#95—41no—
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#202911yescharacteristic
346C2×C13#219711yescharacteristic
347C2×C13#220011yescharacteristic
348C24—21no—
349C24—21no—
350C24C2×D4×C1311yescharacteristic
351C24C2×D4×C1311yescharacteristic
352#41—22no—
353#41—22no—
354#41—42no—
355#41—41no—
356#41—42no—
357#41—42no—
358#41—42no—
359#41—41no—
360C2×Q8—21no—
361C2×D4—21no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—42no—
369C2×D4—42no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—42no—
375C2×D4—42no—
376C2×D4—41no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4C2×Q8×C1311yescharacteristic
380C2×D4C13×#4111yescharacteristic
381C2×D4C13×#4111yescharacteristic
382C2×D4C13×#4111yescharacteristic
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—41no—
392C22×C4—42no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—81no—
398C22×C4C2×D4×C1311yescharacteristic
399M16—41no—
400M16—41no—
401C2×C8—41no—
402C4⋊C4—41no—
403C4⋊C4—42no—
404C4⋊C4—81no—
405C4⋊C4—81no—
406C4⋊C4—81no—
407C4⋊C4—81no—
408C22⋊C4—42no—
409C22⋊C4—41no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—81no—
416C22⋊C4—81no—
417C22⋊C4—81no—
418C22⋊C4—82no—
419C22⋊C4—82no—
420C42—41no—
421C13#1337611yescharacteristic, direct product factor, Sylow
422C23—21no—
423C23—21no—
424C23—21no—
425C23—21no—
426C23—22no—
427C23—22no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—81no—
436C23—81no—
437C23—81no—
438C23—81no—
439C23C13×#12011yescharacteristic
440C23C13×C22⋊Q811yescharacteristic
441C23C13×C22⋊Q811yescharacteristic
442C23C13×#12411yescharacteristic
443C23C13×#12411yescharacteristic
444Q8—22no—
445Q8—41no—
446D4—22no—
447D4—41no—
448D4—41no—
449D4—41no—
450D4—41no—
451D4—41no—
452D4—42no—
453D4—42no—
454D4—42no—
455D4—42no—
456D4—42no—
457D4—42no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—42no—
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—41no—
481C2×C4—42no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—81no—
488C2×C4—81no—
489C2×C4—81no—
490C2×C4—81no—
491C2×C4—81no—
492C2×C4—81no—
493C2×C4—81no—
494C2×C4—81no—
495C2×C4C13×C22⋊Q811yescharacteristic
496C2×C4C13×#12411yescharacteristic
497C8—81no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—41no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—42no—
513C22—81no—
514C22—81no—
515C22—82no—
516C22—82no—
517C22—81no—
518C22—81no—
519C22—161no—
520C22—161no—
521C22C13×#39311yescharacteristic
522C22C13×B(4,𝔽2)11yescharacteristic
523C22C13×B(4,𝔽2)11yescharacteristic
524C4—21no—
525C4—21no—
526C4—42no—
527C4—42no—
528C4—81no—
529C4—81no—
530C4—81no—
531C4—81no—
532C4—81no—
533C4—161no—
534C4—161no—
535C2—21no—
536C2—21no—
537C2—41no—
538C2—41no—
539C2—41no—
540C2—41no—
541C2—82no—
542C2C13×#202911yescharacteristic
543C2C13×#219711yescharacteristic
544C2C13×#220011yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C13
prime radicalC2×C13×H(5,𝔽2)C22
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
1. C13×#2748C2semidirect
5. C13×#1393C2semidirect
6. C13×#1390C2semidirect
7. C13×#1390C2semidirect
76. #13376C13direct (N × H)
150. #2748C2×C13semidirect
154. #1393C2×C13semidirect
155. #1390C2×C13semidirect
156. #1390C2×C13semidirect
421. C13#13376direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#27482
C13×#17922
C13×#17902
C13×#13932
C13×#13902
#1337613