Finite Group Databasebeta

← C13×#13358 #15699697

Subgroups — C13×#13358 #15699697

Order 3328.

722 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 722 conjugacy classes of subgroups — too many to draw. Only its 98 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
1C2×C13×#456C211yesmaximal, characteristic, complemented
2C2×C13×#454C211yesmaximal, characteristic
3C13×#2731C211yesmaximal, characteristic, complemented
4C2×C13×#356C211yesmaximal, characteristic, complemented
5C2×C13×#355C211yesmaximal, characteristic, complemented
6C13×#1793C211yesmaximal, characteristic, complemented
7C13×#1394C211yesmaximal, characteristic, complemented
8C2×C13×2−1+4C2211yescharacteristic
9C2×C13×#137—21no—
10C2×C13×AGL(1,ℤ/8)—21no—
11C2×C13×C4⋊Q8C2211yescharacteristic
12C2×C13×#124C2211yescharacteristic
13C13×#456—22no—
14C13×#456—22no—
15C13×#454—22no—
16C13×#454—22no—
17C2×C13×#104—21no—
18C2×C13×#104—21no—
19C2×C13×#104—21no—
20C13×#417—21no—
21C2×C13×#101C2211yescharacteristic
22C2×C13×#101C2211yescharacteristic
23C2×C13×#101C2211yescharacteristic
24C13×#396—21no—
25C13×#394—21no—
26C13×#393—21no—
27C13×#391C2211yescharacteristic
28C13×#388—21no—
29C13×#388—21no—
30C13×#387—21no—
31C13×#356—22no—
32C13×#355—22no—
33C13×2−1+4—21no—
34C13×2−1+4—21no—
35C13×2−1+4—21no—
36C13×2−1+4—42no—
37C13×2−1+4D412yes—
38C2×C13×#41—21no—
39C2×C13×#41—21no—
40C2×C13×#41—21no—
41C2×C13×#41—41no—
42C22×Q8×C13—41no—
43C22×Q8×C13D411yescharacteristic
44C22×Q8×C13C2311yescharacteristic
45C22×D4×C13D411yescharacteristic
46C13×#137—24no—
47C13×#137—42no—
48C13×AGL(1,ℤ/8)—24no—
49C13×AGL(1,ℤ/8)—42no—
50C2×C13×Q16—41no—
51C2×C13×SD16—41no—
52C2×C13×SD16—41no—
53C2×C13×D8—41no—
54C2×C13×M16—21no—
55C2×C13×M16—21no—
56C2×C13×M16—21no—
57C13×C4⋊Q8—21no—
58C13×C4⋊Q8—21no—
59C13×C4⋊Q8—21no—
60C13×C4⋊Q8—21no—
61C13×#124—21no—
62C13×#124—21no—
63C13×#124—21no—
64C13×#124—21no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4D411yescharacteristic
69C2×C13×C22⋊C4—21no—
70C2×C13×C22⋊C4—21no—
71C2×C13×C22⋊C4—21no—
72C2×C13×C22⋊C4—21no—
73C2×C13×C22⋊C4—21no—
74C2×C13×C22⋊C4—21no—
75C2×C42×C13D411yescharacteristic
76C2×C42×C13D411yescharacteristic
77C2×C42×C13D411yescharacteristic
78C13×#104—24no—
79C13×#104—24no—
80C13×#104—42no—
81C13×#103—41no—
82C13×#102—41no—
83C13×#101—21no—
84C13×#101—21no—
85C13×#101—21no—
86C13×#101—21no—
87C13×#101D412yes—
88C13×#101D412yes—
89C13×#95—21no—
90C13×#95—21no—
91C13×#95—21no—
92C13×#95—21no—
93C13×#95—21no—
94#13358C1311yesmaximal, characteristic, direct product factor, Sylow
95C24×C13—21no—
96C13×#41—22no—
97C13×#41—22no—
98C13×#41—22no—
99C13×#41—22no—
100C13×#41—22no—
101C13×#41—22no—
102C13×#41—41no—
103C13×#41—41no—
104C13×#41—41no—
105C13×#41—42no—
106C13×#41—42no—
107C13×#41—42no—
108C13×#41—42no—
109C13×#41—41no—
110C13×#41—41no—
111C13×#41—41no—
112C2×Q8×C13—21no—
113C2×Q8×C13—21no—
114C2×Q8×C13—21no—
115C2×Q8×C13—21no—
116C2×Q8×C13—21no—
117C2×Q8×C13—41no—
118C2×Q8×C13—41no—
119C2×Q8×C13—41no—
120C2×Q8×C13—41no—
121C2×Q8×C13—42no—
122C2×Q8×C13—42no—
123C2×Q8×C13—42no—
124C2×Q8×C13—42no—
125C2×Q8×C13C2×D411yescharacteristic
126C2×Q8×C13C2×D411yescharacteristic
127C2×Q8×C13C2×D411yescharacteristic
128C2×Q8×C13#4111yescharacteristic
129C2×D4×C13—21no—
130C2×D4×C13—21no—
131C2×D4×C13—21no—
132C2×D4×C13—21no—
133C2×D4×C13—21no—
134C2×D4×C13—41no—
135C2×D4×C13—41no—
136C2×D4×C13—41no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—41no—
143C22×C4×C13—41no—
144C22×C4×C13—41no—
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C13×Q16—44no—
149C13×SD16—44no—
150C13×SD16—44no—
151C13×D8—44no—
152C13×M16—22no—
153C13×M16—22no—
154C13×M16—41no—
155C13×M16—41no—
156C13×M16—41no—
157C13×M16—41no—
158C2×C8×C13—41no—
159C2×C8×C13—41no—
160C2×C8×C13—41no—
161C13×C4⋊C4—41no—
162C13×C4⋊C4—42no—
163C13×C4⋊C4—41no—
164C13×C4⋊C4—41no—
165C13×C4⋊C4—41no—
166C13×C4⋊C4—41no—
167C13×C22⋊C4—42no—
168C13×C22⋊C4—42no—
169C13×C22⋊C4—41no—
170C13×C22⋊C4—41no—
171C13×C22⋊C4—41no—
172C13×C22⋊C4—41no—
173C13×C22⋊C4—81no—
174C13×C22⋊C4—81no—
175C42×C13—21no—
176C42×C13—21no—
177C42×C13—21no—
178C42×C13—21no—
179C42×C13—41no—
180C2×#456C2×C1311yescharacteristic, complemented
181C2×#454C2×C1311yescharacteristic
182#2731C2×C1311yescharacteristic, complemented
183C2×#356C2×C1311yescharacteristic, complemented
184C2×#355C2×C1311yescharacteristic, complemented
185#1793C2×C1311yescharacteristic, complemented
186#1394C2×C1311yescharacteristic, complemented
187C23×C13—41no—
188C23×C13—41no—
189C23×C13—41no—
190C23×C13—41no—
191C23×C13—41no—
192C23×C13—41no—
193C23×C13—41no—
194C23×C13—41no—
195C23×C13#12011yescharacteristic
196Q8×C13—22no—
197Q8×C13—22no—
198Q8×C13—22no—
199Q8×C13—41no—
200Q8×C13—41no—
201Q8×C13—41no—
202Q8×C13—41no—
203Q8×C13—41no—
204Q8×C13—41no—
205Q8×C13—41no—
206Q8×C13—42no—
207Q8×C13—81no—
208D4×C13—22no—
209D4×C13—22no—
210D4×C13—22no—
211D4×C13—41no—
212D4×C13—41no—
213D4×C13—41no—
214D4×C13—42no—
215D4×C13—42no—
216D4×C13—42no—
217D4×C13—81no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—22no—
225C2×C4×C13—42no—
226C2×C4×C13—42no—
227C2×C4×C13—42no—
228C2×C4×C13—42no—
229C2×C4×C13—42no—
230C2×C4×C13—42no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13#12011yescharacteristic
247C2×C4×C13#12011yescharacteristic
248C2×C4×C13#12111yescharacteristic
249C2×C4×C13#12111yescharacteristic
250C2×C4×C13#12111yescharacteristic
251C2×C4×C13#12711yescharacteristic
252C8×C13—42no—
253C8×C13—42no—
254C8×C13—81no—
255C2×2−1+4C22×C1311yescharacteristic
256C2×#137—21no—
257C2×AGL(1,ℤ/8)—21no—
258C2×C4⋊Q8C22×C1311yescharacteristic
259C2×#124C22×C1311yescharacteristic
260#456—22no—
261#456—22no—
262#454—22no—
263#454—22no—
264C2×#104—21no—
265C2×#104—21no—
266C2×#104—21no—
267#417—21no—
268C2×#101C22×C1311yescharacteristic
269C2×#101C22×C1311yescharacteristic
270C2×#101C22×C1311yescharacteristic
271#396—21no—
272#394—21no—
273#393—21no—
274#391C22×C1311yescharacteristic
275#388—21no—
276#388—21no—
277#387—21no—
278#356—22no—
279#355—22no—
280C22×C13—21no—
281C22×C13—21no—
282C22×C13—42no—
283C22×C13—81no—
284C22×C13—81no—
285C22×C13—81no—
286C22×C13—81no—
287C22×C13—81no—
288C22×C13—81no—
289C22×C13—81no—
290C22×C13—81no—
291C22×C13—81no—
292C22×C13#39211yescharacteristic
293C22×C13B(4,𝔽2)11yescharacteristic
294C22×C13B(4,𝔽2)11yescharacteristic
295C4×C13—21no—
296C4×C13—21no—
297C4×C13—21no—
298C4×C13—21no—
299C4×C13—21no—
300C4×C13—21no—
301C4×C13—42no—
302C4×C13—42no—
303C4×C13—81no—
304C4×C13—81no—
305C4×C13—81no—
306C4×C13—81no—
3072−1+4—21no—
3082−1+4—21no—
3092−1+4—21no—
3102−1+4—42no—
3112−1+4D4×C1312yes—
312C2×#41—21no—
313C2×#41—21no—
314C2×#41—21no—
315C2×#41—41no—
316C22×Q8—41no—
317C22×Q8D4×C1311yescharacteristic
318C22×Q8C23×C1311yescharacteristic
319C22×D4D4×C1311yescharacteristic
320#137—24no—
321#137—42no—
322AGL(1,ℤ/8)—24no—
323AGL(1,ℤ/8)—42no—
324C2×Q16—41no—
325C2×SD16—41no—
326C2×SD16—41no—
327C2×D8—41no—
328C2×M16—21no—
329C2×M16—21no—
330C2×M16—21no—
331C4⋊Q8—21no—
332C4⋊Q8—21no—
333C4⋊Q8—21no—
334C4⋊Q8—21no—
335#124—21no—
336#124—21no—
337#124—21no—
338#124—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4D4×C1311yescharacteristic
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×C42D4×C1311yescharacteristic
350C2×C42D4×C1311yescharacteristic
351C2×C42D4×C1311yescharacteristic
352#104—24no—
353#104—24no—
354#104—42no—
355#103—41no—
356#102—41no—
357#101—21no—
358#101—21no—
359#101—21no—
360#101—21no—
361#101D4×C1312yes—
362#101D4×C1312yes—
363#95—21no—
364#95—21no—
365#95—21no—
366#95—21no—
367#95—21no—
368C2×C13—21no—
369C2×C13—21no—
370C2×C13—82no—
371C2×C13—161no—
372C2×C13#202111yescharacteristic
373C2×C13#220311yescharacteristic
374C2×C13#220411yescharacteristic
375C24—21no—
376#41—22no—
377#41—22no—
378#41—22no—
379#41—22no—
380#41—22no—
381#41—22no—
382#41—41no—
383#41—41no—
384#41—41no—
385#41—42no—
386#41—42no—
387#41—42no—
388#41—42no—
389#41—41no—
390#41—41no—
391#41—41no—
392C2×Q8—21no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8—41no—
398C2×Q8—41no—
399C2×Q8—41no—
400C2×Q8—41no—
401C2×Q8—42no—
402C2×Q8—42no—
403C2×Q8—42no—
404C2×Q8—42no—
405C2×Q8C2×D4×C1311yescharacteristic
406C2×Q8C2×D4×C1311yescharacteristic
407C2×Q8C2×D4×C1311yescharacteristic
408C2×Q8C13×#4111yescharacteristic
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—41no—
415C2×D4—41no—
416C2×D4—41no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4C2×D4×C1311yescharacteristic
426C22×C4C2×D4×C1311yescharacteristic
427C22×C4C2×D4×C1311yescharacteristic
428Q16—44no—
429SD16—44no—
430SD16—44no—
431D8—44no—
432M16—22no—
433M16—22no—
434M16—41no—
435M16—41no—
436M16—41no—
437M16—41no—
438C2×C8—41no—
439C2×C8—41no—
440C2×C8—41no—
441C4⋊C4—41no—
442C4⋊C4—42no—
443C4⋊C4—41no—
444C4⋊C4—41no—
445C4⋊C4—41no—
446C4⋊C4—41no—
447C22⋊C4—42no—
448C22⋊C4—42no—
449C22⋊C4—41no—
450C22⋊C4—41no—
451C22⋊C4—41no—
452C22⋊C4—41no—
453C22⋊C4—81no—
454C22⋊C4—81no—
455C42—21no—
456C42—21no—
457C42—21no—
458C42—21no—
459C42—41no—
460C13#1335811yescharacteristic, direct product factor, Sylow
461C23—41no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23C13×#12011yescharacteristic
470Q8—22no—
471Q8—22no—
472Q8—22no—
473Q8—41no—
474Q8—41no—
475Q8—41no—
476Q8—41no—
477Q8—41no—
478Q8—41no—
479Q8—41no—
480Q8—42no—
481Q8—81no—
482D4—22no—
483D4—22no—
484D4—22no—
485D4—41no—
486D4—41no—
487D4—41no—
488D4—42no—
489D4—42no—
490D4—42no—
491D4—81no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4C13×#12011yescharacteristic
521C2×C4C13×#12011yescharacteristic
522C2×C4C13×#12111yescharacteristic
523C2×C4C13×#12111yescharacteristic
524C2×C4C13×#12111yescharacteristic
525C2×C4C13×#12711yescharacteristic
526C8—42no—
527C8—42no—
528C8—81no—
529C22—21no—
530C22—21no—
531C22—42no—
532C22—81no—
533C22—81no—
534C22—81no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22—81no—
541C22C13×#39211yescharacteristic
542C22C13×B(4,𝔽2)11yescharacteristic
543C22C13×B(4,𝔽2)11yescharacteristic
544C4—21no—
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—21no—
550C4—42no—
551C4—42no—
552C4—81no—
553C4—81no—
554C4—81no—
555C4—81no—
556C2—21no—
557C2—21no—
558C2—82no—
559C2—161no—
560C2C13×#202111yescharacteristic
561C2C13×#220311yescharacteristic
562C2C13×#220411yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC22×Q8C23×C13
prime radicalC2×C13×#454C2
LCSG ▷ C22×Q8 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C13 ◁ C22×Q8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C13×#456C2semidirect
3. C13×#2731C2semidirect
4. C2×C13×#356C2semidirect
5. C2×C13×#355C2semidirect
6. C13×#1793C2semidirect
7. C13×#1394C2semidirect
94. #13358C13direct (N × H)
180. C2×#456C2×C13semidirect
182. #2731C2×C13semidirect
183. C2×#356C2×C13semidirect
184. C2×#355C2×C13semidirect
185. #1793C2×C13semidirect
186. #1394C2×C13semidirect
460. C13#13358direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#4562
C2×C13×#4542
C13×#27312
C2×C13×#3562
C2×C13×#3552
C13×#17932
C13×#13942
#1335813