Finite Group Databasebeta

← C13×#13422 #15699761

Subgroups — C13×#13422 #15699761

Order 3328.

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

normal subgroups only

This group has 734 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×#2669C211yesmaximal, characteristic
2C2×C13×#353C211yesmaximal, characteristic, complemented
3C2×C13×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
4C13×#1889C211yesmaximal, characteristic, complemented
5C13×#1887C211yesmaximal, characteristic, complemented
6C13×#1867C211yesmaximal, characteristic, complemented
7C13×#1390C211yesmaximal, characteristic, complemented
8C2×C13×#127C2211yescharacteristic
9C2×C13×#121—21no—
10C2×C13×#120—21no—
11C2×C13×#120C2211yescharacteristic
12C13×#518C2211yescharacteristic
13C13×#418—21no—
14C2×C13×#100C2211yescharacteristic
15C2×C13×#99C2211yescharacteristic
16C2×C13×#99C2211yescharacteristic
17C13×#394—21no—
18C13×#392—21no—
19C13×#392—21no—
20C13×#388—21no—
21C13×#386C2211yescharacteristic
22C13×#385—21no—
23C13×#379—21no—
24C13×#353—22no—
25C13×AΣL(1,𝔽16)—22no—
26C13×#342—21no—
27C13×#342—21no—
28C13×#339—21no—
29C25×C13D411yescharacteristic
30C22×D4×C13—21no—
31C22×D4×C13—21no—
32C22×D4×C13—21no—
33C22×D4×C13—21no—
34C22×D4×C13—21no—
35C22×D4×C13D411yescharacteristic
36C22×D4×C13C2311yescharacteristic
37C23×C4×C13D411yescharacteristic
38C2×C13×M16—21no—
39C13×#127—21no—
40C13×#127—21no—
41C13×#127—21no—
42C13×#127—21no—
43C13×#121—44no—
44C13×#120—21no—
45C13×#120—21no—
46C13×#120—21no—
47C13×#120—21no—
48C13×#120—44no—
49C4×D4×C13—41no—
50C4×D4×C13—41no—
51C13×#117—21no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—41no—
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—21no—
63C2×C13×C22⋊C4—21no—
64C2×C13×C22⋊C4—41no—
65C2×C13×C22⋊C4—41no—
66C2×C13×C22⋊C4D411yescharacteristic
67C2×C13×C22⋊C4D411yescharacteristic
68C2×C42×C13D411yescharacteristic
69C13×#102—41no—
70C13×#102—41no—
71C13×#100—21no—
72C13×#100—21no—
73C13×#99—21no—
74C13×#99—21no—
75C13×#99—21no—
76C13×#99D412yescomplemented
77C13×#95—21no—
78C13×#95—21no—
79C13×#95—41no—
80#13422C1311yesmaximal, characteristic, direct product factor, Sylow
81C24×C13—21no—
82C24×C13—21no—
83C24×C13—21no—
84C24×C13—21no—
85C24×C13—41no—
86C24×C13—42no—
87C24×C13—41no—
88C24×C13—81no—
89C24×C13C2×D411yescharacteristic
90C24×C13C2×D411yescharacteristic
91C2×D4×C13—21no—
92C2×D4×C13—21no—
93C2×D4×C13—41no—
94C2×D4×C13—41no—
95C2×D4×C13—41no—
96C2×D4×C13—41no—
97C2×D4×C13—42no—
98C2×D4×C13—42no—
99C2×D4×C13—42no—
100C2×D4×C13—42no—
101C2×D4×C13—42no—
102C2×D4×C13—42no—
103C2×D4×C13—41no—
104C2×D4×C13—41no—
105C2×D4×C13—41no—
106C2×D4×C13—41no—
107C2×D4×C13—41no—
108C2×D4×C13—41no—
109C2×D4×C13—81no—
110C2×D4×C13—81no—
111C2×D4×C13—81no—
112C2×D4×C13—81no—
113C2×D4×C13—81no—
114C2×D4×C13—81no—
115C2×D4×C13C2×D411yescharacteristic
116C2×D4×C13#4111yescharacteristic
117C2×D4×C13#4111yescharacteristic
118C2×D4×C13#4111yescharacteristic
119C22×C4×C13—21no—
120C22×C4×C13—21no—
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—42no—
128C22×C4×C13—41no—
129C22×C4×C13—41no—
130C22×C4×C13—41no—
131C22×C4×C13C2×D411yescharacteristic
132C13×M16—41no—
133C13×M16—41no—
134C2×C8×C13—41no—
135C13×C4⋊C4—21no—
136C13×C4⋊C4—21no—
137C13×C4⋊C4—42no—
138C13×C4⋊C4—82no—
139C13×C22⋊C4—24no—
140C13×C22⋊C4—22no—
141C13×C22⋊C4—21no—
142C13×C22⋊C4—21no—
143C13×C22⋊C4—42no—
144C13×C22⋊C4—42no—
145C13×C22⋊C4—42no—
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—41no—
153C13×C22⋊C4—41no—
154C13×C22⋊C4—41no—
155C13×C22⋊C4—81no—
156C13×C22⋊C4—82no—
157C13×C22⋊C4—82no—
158C42×C13—21no—
159C42×C13—21no—
160C42×C13—41no—
161#2669C2×C1311yescharacteristic
162C2×#353C2×C1311yescharacteristic, complemented
163C2×AΣL(1,𝔽16)C2×C1311yescharacteristic, complemented
164#1889C2×C1311yescharacteristic, complemented
165#1887C2×C1311yescharacteristic, complemented
166#1867C2×C1311yescharacteristic, complemented
167#1390C2×C1311yescharacteristic, complemented
168C23×C13—21no—
169C23×C13—21no—
170C23×C13—21no—
171C23×C13—21no—
172C23×C13—22no—
173C23×C13—41no—
174C23×C13—41no—
175C23×C13—41no—
176C23×C13—41no—
177C23×C13—41no—
178C23×C13—41no—
179C23×C13—41no—
180C23×C13—42no—
181C23×C13—41no—
182C23×C13—41no—
183C23×C13—41no—
184C23×C13—41no—
185C23×C13—42no—
186C23×C13—42no—
187C23×C13—41no—
188C23×C13—41no—
189C23×C13—41no—
190C23×C13—41no—
191C23×C13—41no—
192C23×C13—41no—
193C23×C13—81no—
194C23×C13—82no—
195C23×C13—81no—
196C23×C13—84no—
197C23×C13—82no—
198C23×C13—81no—
199C23×C13#12011yescharacteristic
200C23×C13#12111yescharacteristic
201C23×C13#12111yescharacteristic
202C23×C13#12311yescharacteristic
203C23×C13#12411yescharacteristic
204D4×C13—41no—
205D4×C13—41no—
206D4×C13—41no—
207D4×C13—41no—
208D4×C13—42no—
209D4×C13—81no—
210D4×C13—82no—
211D4×C13—82no—
212D4×C13—82no—
213D4×C13—82no—
214D4×C13—84no—
215D4×C13—82no—
216D4×C13—82no—
217D4×C13—84no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—22no—
221C2×C4×C13—22no—
222C2×C4×C13—41no—
223C2×C4×C13—41no—
224C2×C4×C13—41no—
225C2×C4×C13—41no—
226C2×C4×C13—42no—
227C2×C4×C13—42no—
228C2×C4×C13—41no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—81no—
237C2×C4×C13—81no—
238C2×C4×C13—81no—
239C2×C4×C13—81no—
240C2×C4×C13—81no—
241C2×C4×C13—81no—
242C2×C4×C13—81no—
243C2×C4×C13—81no—
244C2×C4×C13—81no—
245C2×C4×C13—81no—
246C2×C4×C13#12111yescharacteristic
247C2×C4×C13#12311yescharacteristic
248C8×C13—81no—
249C2×#127C22×C1311yescharacteristic
250C2×#121—21no—
251C2×#120—21no—
252C2×#120C22×C1311yescharacteristic
253#518C22×C1311yescharacteristic
254#418—21no—
255C2×#100C22×C1311yescharacteristic
256C2×#99C22×C1311yescharacteristic
257C2×#99C22×C1311yescharacteristic
258#394—21no—
259#392—21no—
260#392—21no—
261#388—21no—
262#386C22×C1311yescharacteristic
263#385—21no—
264#379—21no—
265#353—22no—
266AΣL(1,𝔽16)—22no—
267#342—21no—
268#342—21no—
269#339—21no—
270C22×C13—21no—
271C22×C13—21no—
272C22×C13—21no—
273C22×C13—21no—
274C22×C13—21no—
275C22×C13—21no—
276C22×C13—41no—
277C22×C13—41no—
278C22×C13—41no—
279C22×C13—41no—
280C22×C13—42no—
281C22×C13—42no—
282C22×C13—41no—
283C22×C13—41no—
284C22×C13—41no—
285C22×C13—41no—
286C22×C13—44no—
287C22×C13—42no—
288C22×C13—81no—
289C22×C13—81no—
290C22×C13—81no—
291C22×C13—81no—
292C22×C13—81no—
293C22×C13—81no—
294C22×C13—81no—
295C22×C13—81no—
296C22×C13—82no—
297C22×C13—82no—
298C22×C13—82no—
299C22×C13—81no—
300C22×C13—81no—
301C22×C13—81no—
302C22×C13—81no—
303C22×C13—81no—
304C22×C13#39411yescharacteristic
305C22×C13B(4,𝔽2)11yescharacteristic
306C22×C13#45811yescharacteristic
307C4×C13—21no—
308C4×C13—21no—
309C4×C13—42no—
310C4×C13—42no—
311C4×C13—81no—
312C4×C13—81no—
313C4×C13—82no—
314C4×C13—81no—
315C4×C13—81no—
316C4×C13—161no—
317C25D4×C1311yescharacteristic
318C22×D4—21no—
319C22×D4—21no—
320C22×D4—21no—
321C22×D4—21no—
322C22×D4—21no—
323C22×D4D4×C1311yescharacteristic
324C22×D4C23×C1311yescharacteristic
325C23×C4D4×C1311yescharacteristic
326C2×M16—21no—
327#127—21no—
328#127—21no—
329#127—21no—
330#127—21no—
331#121—44no—
332#120—21no—
333#120—21no—
334#120—21no—
335#120—21no—
336#120—44no—
337C4×D4—41no—
338C4×D4—41no—
339#117—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—41no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—41no—
353C2×C22⋊C4—41no—
354C2×C22⋊C4D4×C1311yescharacteristic
355C2×C22⋊C4D4×C1311yescharacteristic
356C2×C42D4×C1311yescharacteristic
357#102—41no—
358#102—41no—
359#100—21no—
360#100—21no—
361#99—21no—
362#99—21no—
363#99—21no—
364#99D4×C1312yescomplemented
365#95—21no—
366#95—21no—
367#95—41no—
368C2×C13—21no—
369C2×C13—21no—
370C2×C13—41no—
371C2×C13—41no—
372C2×C13—41no—
373C2×C13—41no—
374C2×C13—82no—
375C2×C13—161no—
376C2×C13#204411yescharacteristic
377C2×C13#219611yescharacteristic
378C2×C13#220011yescharacteristic
379C24—21no—
380C24—21no—
381C24—21no—
382C24—21no—
383C24—41no—
384C24—42no—
385C24—41no—
386C24—81no—
387C24C2×D4×C1311yescharacteristic
388C24C2×D4×C1311yescharacteristic
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—41no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—42no—
396C2×D4—42no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4—42no—
400C2×D4—42no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—81no—
408C2×D4—81no—
409C2×D4—81no—
410C2×D4—81no—
411C2×D4—81no—
412C2×D4—81no—
413C2×D4C2×D4×C1311yescharacteristic
414C2×D4C13×#4111yescharacteristic
415C2×D4C13×#4111yescharacteristic
416C2×D4C13×#4111yescharacteristic
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—42no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4C2×D4×C1311yescharacteristic
430M16—41no—
431M16—41no—
432C2×C8—41no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—42no—
436C4⋊C4—82no—
437C22⋊C4—24no—
438C22⋊C4—22no—
439C22⋊C4—21no—
440C22⋊C4—21no—
441C22⋊C4—42no—
442C22⋊C4—42no—
443C22⋊C4—42no—
444C22⋊C4—41no—
445C22⋊C4—41no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C22⋊C4—41no—
449C22⋊C4—41no—
450C22⋊C4—41no—
451C22⋊C4—41no—
452C22⋊C4—41no—
453C22⋊C4—81no—
454C22⋊C4—82no—
455C22⋊C4—82no—
456C42—21no—
457C42—21no—
458C42—41no—
459C13#1342211yescharacteristic, direct product factor, Sylow
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—22no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—42no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—42no—
478C23—42no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23—81no—
486C23—82no—
487C23—81no—
488C23—82no—
489C23—84no—
490C23—81no—
491C23C13×#12011yescharacteristic
492C23C13×#12111yescharacteristic
493C23C13×#12111yescharacteristic
494C23C13×#12311yescharacteristic
495C23C13×#12411yescharacteristic
496D4—41no—
497D4—41no—
498D4—41no—
499D4—41no—
500D4—42no—
501D4—81no—
502D4—82no—
503D4—82no—
504D4—82no—
505D4—82no—
506D4—84no—
507D4—82no—
508D4—82no—
509D4—84no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—81no—
529C2×C4—81no—
530C2×C4—81no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—81no—
534C2×C4—81no—
535C2×C4—81no—
536C2×C4—81no—
537C2×C4—81no—
538C2×C4C13×#12111yescharacteristic
539C2×C4C13×#12311yescharacteristic
540C8—81no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—42no—
552C22—42no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—44no—
558C22—42no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—82no—
568C22—82no—
569C22—82no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22C13×#39411yescharacteristic
576C22C13×B(4,𝔽2)11yescharacteristic
577C22C13×#45811yescharacteristic
578C4—21no—
579C4—21no—
580C4—42no—
581C4—42no—
582C4—81no—
583C4—81no—
584C4—82no—
585C4—81no—
586C4—81no—
587C4—161no—
588C2—21no—
589C2—21no—
590C2—41no—
591C2—41no—
592C2—41no—
593C2—41no—
594C2—82no—
595C2—161no—
596C2C13×#204411yescharacteristic
597C2C13×#219611yescharacteristic
598C2C13×#220011yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C13
prime radicalC13×#2669C2
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×#353C2semidirect
3. C2×C13×AΣL(1,𝔽16)C2semidirect
4. C13×#1889C2semidirect
5. C13×#1887C2semidirect
6. C13×#1867C2semidirect
7. C13×#1390C2semidirect
76. C13×#99D4semidirect
80. #13422C13direct (N × H)
162. C2×#353C2×C13semidirect
163. C2×AΣL(1,𝔽16)C2×C13semidirect
164. #1889C2×C13semidirect
165. #1887C2×C13semidirect
166. #1867C2×C13semidirect
167. #1390C2×C13semidirect
364. #99D4×C13semidirect
459. C13#13422direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26692
C2×C13×#3532
C2×C13×AΣL(1,𝔽16)2
C13×#18892
C13×#18872
C13×#18672
C13×#13902
#1342213