Finite Group Databasebeta

← C13×#9938 #15696277

Subgroups — C13×#9938 #15696277

Order 3328.

1008 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 102 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×#3006C211yesmaximal, characteristic, complemented
2C13×#2539C211yesmaximal, characteristic, complemented
3C13×#2404C211yesmaximal, characteristic, complemented
4C13×#1789C211yesmaximal, characteristic, complemented
5C13×#1510C211yesmaximal, characteristic, complemented
6C13×#1462C211yesmaximal, characteristic, complemented
7C13×#1284C211yesmaximal, characteristic, complemented
8C22×C13×#41C2211yescharacteristic
9C2×C13×AGL(1,ℤ/8)—21no—
10C2×C13×#123—21no—
11C2×C13×#121C2211yescharacteristic
12C2×C13×#120—21no—
13C2×C13×#120—21no—
14C22×C13×C22⋊C4C2211yescharacteristic
15C13×#449—22no—
16C13×#448—21no—
17C13×#447—21no—
18C2×C13×#104—22no—
19C13×#417—21no—
20C13×#407C2211yescharacteristic
21C13×#407C2211yescharacteristic
22C13×#399—21no—
23C13×#393—21no—
24C13×#392—21no—
25C13×#392—21no—
26C13×#390—22no—
27C13×#386—21no—
28C13×#386—22no—
29C13×#381C2211yescharacteristic
30C4×C13×C22⋊C4C2211yescharacteristic
31C13×#327—22no—
32C13×#323—22no—
33C25×C13D411yescharacteristic
34C2×C13×#41—21no—
35C2×C13×#41—21no—
36C2×C13×#41—21no—
37C2×C13×#41—21no—
38C2×C13×#41—44no—
39C22×Q8×C13D411yescharacteristic, complemented
40C22×D4×C13—21no—
41C22×D4×C13—21no—
42C22×D4×C13—22no—
43C22×D4×C13—22no—
44C22×D4×C13D411yescharacteristic, complemented
45C22×D4×C13D411yescharacteristic, complemented
46C23×C4×C13—21no—
47C23×C4×C13D411yescharacteristic
48C23×C4×C13C2311yescharacteristic
49C13×AGL(1,ℤ/8)—44no—
50C2×C13×SD16—22no—
51C2×C13×D8—22no—
52C2×C13×M16—21no—
53C2×C13×M16—21no—
54C13×#123—44no—
55C13×#121—21no—
56C13×#121—21no—
57C13×#121—21no—
58C13×#121—21no—
59C13×#120—44no—
60C13×#120—44no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4D411yescharacteristic, complemented
63C2×C13×C22⋊C4—21no—
64C2×C13×C22⋊C4—22no—
65C2×C13×C22⋊C4—22no—
66C2×C13×C22⋊C4—22no—
67C2×C13×C22⋊C4—21no—
68C2×C13×C22⋊C4—21no—
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×C13×C22⋊C4—22no—
76C2×C42×C13D412yescomplemented
77C13×#104—44no—
78C13×#103—22no—
79C13×#102—22no—
80C13×C22⋊C8—21no—
81C13×C22⋊C8—21no—
82C13×C22⋊C8—21no—
83C13×C22⋊C8D412yescomplemented
84C13×#95—22no—
85C13×#95—21no—
86C13×#95—21no—
87C13×#95D412yescomplemented
88#9938C1311yesmaximal, characteristic, direct product factor, Sylow
89C24×C13—21no—
90C24×C13—21no—
91C24×C13—21no—
92C24×C13—21no—
93C24×C13—21no—
94C24×C13—42no—
95C24×C13—42no—
96C24×C13—42no—
97C24×C13C2×D411yescharacteristic
98C13×#41—24no—
99C13×#41—24no—
100C13×#41—42no—
101C13×#41—42no—
102C13×#41—42no—
103C13×#41—42no—
104C13×#41—42no—
105C13×#41—42no—
106C2×Q8×C13—21no—
107C2×Q8×C13—21no—
108C2×Q8×C13—42no—
109C2×D4×C13—24no—
110C2×D4×C13—21no—
111C2×D4×C13—21no—
112C2×D4×C13—21no—
113C2×D4×C13—21no—
114C2×D4×C13—42no—
115C2×D4×C13—44no—
116C2×D4×C13—42no—
117C2×D4×C13—42no—
118C2×D4×C13—41no—
119C2×D4×C13—41no—
120C2×D4×C13—42no—
121C2×D4×C13—44no—
122C2×D4×C13—42no—
123C2×D4×C13—44no—
124C2×D4×C13—44no—
125C2×D4×C13—41no—
126C2×D4×C13—41no—
127C2×D4×C13—82no—
128C2×D4×C13—82no—
129C22×C4×C13—21no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—42no—
137C22×C4×C13—42no—
138C22×C4×C13—42no—
139C22×C4×C13—41no—
140C22×C4×C13—41no—
141C22×C4×C13—42no—
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13#4111yescharacteristic
148C13×SD16—44no—
149C13×D8—44no—
150C13×M16—42no—
151C13×M16—42no—
152C2×C8×C13—22no—
153C2×C8×C13—41no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—44no—
157C13×C22⋊C4—24no—
158C13×C22⋊C4—44no—
159C13×C22⋊C4—44no—
160C13×C22⋊C4—44no—
161C13×C22⋊C4—42no—
162C13×C22⋊C4—41no—
163C13×C22⋊C4—41no—
164C13×C22⋊C4—41no—
165C13×C22⋊C4—41no—
166C13×C22⋊C4—41no—
167C13×C22⋊C4—41no—
168C13×C22⋊C4—82no—
169C42×C13—42no—
170#3006C2×C1311yescharacteristic, complemented
171#2539C2×C1311yescharacteristic, complemented
172#2404C2×C1311yescharacteristic, complemented
173#1789C2×C1311yescharacteristic, complemented
174#1510C2×C1311yescharacteristic, complemented
175#1462C2×C1311yescharacteristic, complemented
176#1284C2×C1311yescharacteristic, complemented
177C23×C13—22no—
178C23×C13—22no—
179C23×C13—22no—
180C23×C13—22no—
181C23×C13—22no—
182C23×C13—22no—
183C23×C13—41no—
184C23×C13—42no—
185C23×C13—42no—
186C23×C13—41no—
187C23×C13—42no—
188C23×C13—41no—
189C23×C13—41no—
190C23×C13—41no—
191C23×C13—41no—
192C23×C13—41no—
193C23×C13—42no—
194C23×C13—41no—
195C23×C13—41no—
196C23×C13—42no—
197C23×C13—42no—
198C23×C13—42no—
199C23×C13—41no—
200C23×C13—42no—
201C23×C13—81no—
202C23×C13—81no—
203C23×C13—88no—
204C23×C13#12011yescharacteristic
205C23×C13#12011yescharacteristic
206C23×C13#12111yescharacteristic
207Q8×C13—22no—
208Q8×C13—22no—
209Q8×C13—41no—
210Q8×C13—41no—
211D4×C13—22no—
212D4×C13—22no—
213D4×C13—41no—
214D4×C13—41no—
215D4×C13—42no—
216D4×C13—44no—
217D4×C13—44no—
218D4×C13—81no—
219D4×C13—88no—
220D4×C13—82no—
221D4×C13—88no—
222D4×C13—82no—
223C2×C4×C13—22no—
224C2×C4×C13—22no—
225C2×C4×C13—24no—
226C2×C4×C13—22no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—44no—
232C2×C4×C13—44no—
233C2×C4×C13—41no—
234C2×C4×C13—42no—
235C2×C4×C13—41no—
236C2×C4×C13—42no—
237C2×C4×C13—42no—
238C2×C4×C13—41no—
239C2×C4×C13—42no—
240C2×C4×C13—41no—
241C2×C4×C13—42no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—42no—
245C2×C4×C13—42no—
246C2×C4×C13—81no—
247C2×C4×C13#12011yescharacteristic
248C2×C4×C13#12111yescharacteristic
249C2×C4×C13#12111yescharacteristic
250C2×C4×C13#12711yescharacteristic
251C8×C13—42no—
252C8×C13—81no—
253C22×#41C22×C1311yescharacteristic
254C2×AGL(1,ℤ/8)—21no—
255C2×#123—21no—
256C2×#121C22×C1311yescharacteristic
257C2×#120—21no—
258C2×#120—21no—
259C22×C22⋊C4C22×C1311yescharacteristic
260#449—22no—
261#448—21no—
262#447—21no—
263C2×#104—22no—
264#417—21no—
265#407C22×C1311yescharacteristic
266#407C22×C1311yescharacteristic
267#399—21no—
268#393—21no—
269#392—21no—
270#392—21no—
271#390—22no—
272#386—21no—
273#386—22no—
274#381C22×C1311yescharacteristic
275C4×C22⋊C4C22×C1311yescharacteristic
276#327—22no—
277#323—22no—
278C22×C13—21no—
279C22×C13—21no—
280C22×C13—21no—
281C22×C13—21no—
282C22×C13—21no—
283C22×C13—21no—
284C22×C13—21no—
285C22×C13—44no—
286C22×C13—44no—
287C22×C13—44no—
288C22×C13—44no—
289C22×C13—42no—
290C22×C13—42no—
291C22×C13—82no—
292C22×C13—82no—
293C22×C13—82no—
294C22×C13—82no—
295C22×C13—82no—
296C22×C13—82no—
297C22×C13—82no—
298C22×C13—81no—
299C22×C13—81no—
300C22×C13—81no—
301C22×C13—81no—
302C22×C13—81no—
303C22×C13—81no—
304C22×C13—81no—
305C22×C13#39211yescharacteristic
306C22×C13#45312yes—
307C22×C13B(4,𝔽2)12yes—
308C4×C13—21no—
309C4×C13—21no—
310C4×C13—21no—
311C4×C13—21no—
312C4×C13—44no—
313C4×C13—42no—
314C4×C13—82no—
315C4×C13—81no—
316C4×C13—81no—
317C25D4×C1311yescharacteristic
318C2×#41—21no—
319C2×#41—21no—
320C2×#41—21no—
321C2×#41—21no—
322C2×#41—44no—
323C22×Q8D4×C1311yescharacteristic, complemented
324C22×D4—21no—
325C22×D4—21no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4D4×C1311yescharacteristic, complemented
329C22×D4D4×C1311yescharacteristic, complemented
330C23×C4—21no—
331C23×C4D4×C1311yescharacteristic
332C23×C4C23×C1311yescharacteristic
333AGL(1,ℤ/8)—44no—
334C2×SD16—22no—
335C2×D8—22no—
336C2×M16—21no—
337C2×M16—21no—
338#123—44no—
339#121—21no—
340#121—21no—
341#121—21no—
342#121—21no—
343#120—44no—
344#120—44no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4D4×C1311yescharacteristic, complemented
347C2×C22⋊C4—21no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—22no—
360C2×C42D4×C1312yescomplemented
361#104—44no—
362#103—22no—
363#102—22no—
364C22⋊C8—21no—
365C22⋊C8—21no—
366C22⋊C8—21no—
367C22⋊C8D4×C1312yescomplemented
368#95—22no—
369#95—21no—
370#95—21no—
371#95D4×C1312yescomplemented
372C2×C13—22no—
373C2×C13—22no—
374C2×C13—41no—
375C2×C13—82no—
376C2×C13—82no—
377C2×C13—161no—
378C2×C13#200211yescharacteristic
379C2×C13#201011yescharacteristic
380C2×C13#202111yescharacteristic
381C24—21no—
382C24—21no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—42no—
387C24—42no—
388C24—42no—
389C24C2×D4×C1311yescharacteristic
390#41—24no—
391#41—24no—
392#41—42no—
393#41—42no—
394#41—42no—
395#41—42no—
396#41—42no—
397#41—42no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—42no—
401C2×D4—24no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—42no—
407C2×D4—44no—
408C2×D4—42no—
409C2×D4—42no—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4—42no—
413C2×D4—44no—
414C2×D4—42no—
415C2×D4—44no—
416C2×D4—44no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—82no—
420C2×D4—82no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—42no—
434C22×C4C2×D4×C1311yescharacteristic
435C22×C4C2×D4×C1311yescharacteristic
436C22×C4C2×D4×C1311yescharacteristic
437C22×C4C2×D4×C1311yescharacteristic
438C22×C4C2×D4×C1311yescharacteristic
439C22×C4C13×#4111yescharacteristic
440SD16—44no—
441D8—44no—
442M16—42no—
443M16—42no—
444C2×C8—22no—
445C2×C8—41no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—44no—
449C22⋊C4—24no—
450C22⋊C4—44no—
451C22⋊C4—44no—
452C22⋊C4—44no—
453C22⋊C4—42no—
454C22⋊C4—41no—
455C22⋊C4—41no—
456C22⋊C4—41no—
457C22⋊C4—41no—
458C22⋊C4—41no—
459C22⋊C4—41no—
460C22⋊C4—82no—
461C42—42no—
462C13#993811yescharacteristic, direct product factor, Sylow
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—22no—
469C23—41no—
470C23—42no—
471C23—42no—
472C23—41no—
473C23—42no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—42no—
480C23—41no—
481C23—41no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—41no—
486C23—42no—
487C23—81no—
488C23—81no—
489C23—88no—
490C23C13×#12011yescharacteristic
491C23C13×#12011yescharacteristic
492C23C13×#12111yescharacteristic
493Q8—22no—
494Q8—22no—
495Q8—41no—
496Q8—41no—
497D4—22no—
498D4—22no—
499D4—41no—
500D4—41no—
501D4—42no—
502D4—44no—
503D4—44no—
504D4—81no—
505D4—88no—
506D4—82no—
507D4—88no—
508D4—82no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—44no—
518C2×C4—44no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—81no—
533C2×C4C13×#12011yescharacteristic
534C2×C4C13×#12111yescharacteristic
535C2×C4C13×#12111yescharacteristic
536C2×C4C13×#12711yescharacteristic
537C8—42no—
538C8—81no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—44no—
547C22—44no—
548C22—44no—
549C22—44no—
550C22—42no—
551C22—42no—
552C22—82no—
553C22—82no—
554C22—82no—
555C22—82no—
556C22—82no—
557C22—82no—
558C22—82no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22C13×#39211yescharacteristic
567C22C13×#45312yes—
568C22C13×B(4,𝔽2)12yes—
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—44no—
574C4—42no—
575C4—82no—
576C4—81no—
577C4—81no—
578C2—22no—
579C2—22no—
580C2—41no—
581C2—82no—
582C2—82no—
583C2—161no—
584C2C13×#200211yescharacteristic
585C2C13×#201011yescharacteristic
586C2C13×#202111yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC23×C4C23×C13
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3006C2semidirect
2. C13×#2539C2semidirect
3. C13×#2404C2semidirect
4. C13×#1789C2semidirect
5. C13×#1510C2semidirect
6. C13×#1462C2semidirect
7. C13×#1284C2semidirect
39. C22×Q8×C13D4semidirect
44. C22×D4×C13D4semidirect
45. C22×D4×C13D4semidirect
62. C2×C13×C4⋊C4D4semidirect
76. C2×C42×C13D4semidirect
83. C13×C22⋊C8D4semidirect
87. C13×#95D4semidirect
88. #9938C13direct (N × H)
170. #3006C2×C13semidirect
171. #2539C2×C13semidirect
172. #2404C2×C13semidirect
173. #1789C2×C13semidirect
174. #1510C2×C13semidirect
175. #1462C2×C13semidirect
176. #1284C2×C13semidirect
323. C22×Q8D4×C13semidirect
328. C22×D4D4×C13semidirect
329. C22×D4D4×C13semidirect
346. C2×C4⋊C4D4×C13semidirect
360. C2×C42D4×C13semidirect
367. C22⋊C8D4×C13semidirect
371. #95D4×C13semidirect
462. C13#9938direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#30062
C13×#25392
C13×#24042
C13×#17892
C13×#15102
C13×#14622
C13×#12842
#993813