Finite Group Databasebeta

← C13×#9939 #15696278

Subgroups — C13×#9939 #15696278

Order 3328.

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

normal subgroups only

This group has 824 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
2C13×#2591C211yesmaximal, characteristic, complemented
3C13×#2406C211yesmaximal, characteristic, complemented
4C13×#1789C211yesmaximal, characteristic, complemented
5C13×#1510C211yesmaximal, characteristic, complemented
6C13×#1463C211yesmaximal, characteristic, complemented
7C13×#1284C211yesmaximal, characteristic, complemented
8C22×C13×#41C2211yescharacteristic
9C2×C13×AGL(1,ℤ/8)—21no—
10C2×C13×#123—21no—
11C2×C13×#121C2211yescharacteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C13×#449—22no—
14C13×#448—21no—
15C13×#447—21no—
16C2×C13×#104—22no—
17C13×#417—21no—
18C13×#407C2211yescharacteristic
19C13×#407C2211yescharacteristic
20C13×#400—21no—
21C13×#395—21no—
22C13×#394—21no—
23C13×#394—21no—
24C13×#388—22no—
25C13×#386—21no—
26C13×#386—21no—
27C13×#386—21no—
28C13×#385—22no—
29C13×#381C2211yescharacteristic
30C4×C13×C22⋊C4C2211yescharacteristic
31C13×#327—22no—
32C13×#324—22no—
33C2×C13×#41—21no—
34C2×C13×#41—21no—
35C2×C13×#41—21no—
36C2×C13×#41—21no—
37C2×C13×#41—44no—
38C22×Q8×C13D411yescharacteristic
39C22×D4×C13—21no—
40C22×D4×C13—21no—
41C22×D4×C13D411yescharacteristic
42C22×D4×C13D411yescharacteristic
43C23×C4×C13—21no—
44C23×C4×C13D411yescharacteristic
45C23×C4×C13D411yescharacteristic
46C23×C4×C13C2311yescharacteristic
47C13×AGL(1,ℤ/8)—44no—
48C2×C13×SD16—22no—
49C2×C13×D8—22no—
50C2×C13×M16—21no—
51C2×C13×M16—21no—
52C13×#123—44no—
53C13×#121—21no—
54C13×#121—21no—
55C13×#121—21no—
56C13×#121—21no—
57C2×C13×C4⋊C4—22no—
58C2×C13×C4⋊C4—21no—
59C2×C13×C4⋊C4—21no—
60C2×C13×C4⋊C4—21no—
61C2×C13×C4⋊C4—21no—
62C2×C13×C4⋊C4—21no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4D411yescharacteristic
65C2×C13×C22⋊C4—22no—
66C2×C13×C22⋊C4—22no—
67C2×C13×C22⋊C4—22no—
68C2×C13×C22⋊C4—21no—
69C2×C13×C22⋊C4—21no—
70C2×C13×C22⋊C4—21no—
71C2×C13×C22⋊C4—22no—
72C2×C42×C13D412yes—
73C13×#104—44no—
74C13×#103—22no—
75C13×#102—22no—
76C13×C22⋊C8—21no—
77C13×C22⋊C8—21no—
78C13×C22⋊C8—21no—
79C13×C22⋊C8D412yes—
80C13×#95—22no—
81C13×#95—22no—
82C13×#95—22no—
83C13×#95—21no—
84C13×#95—21no—
85C13×#95D412yes—
86#9939C1311yesmaximal, characteristic, direct product factor, Sylow
87C24×C13—21no—
88C24×C13—21no—
89C24×C13C2×D411yescharacteristic
90C13×#41—24no—
91C13×#41—24no—
92C13×#41—42no—
93C13×#41—42no—
94C13×#41—42no—
95C13×#41—42no—
96C13×#41—42no—
97C13×#41—42no—
98C2×Q8×C13—21no—
99C2×Q8×C13—21no—
100C2×Q8×C13—42no—
101C2×D4×C13—24no—
102C2×D4×C13—21no—
103C2×D4×C13—21no—
104C2×D4×C13—21no—
105C2×D4×C13—21no—
106C2×D4×C13—42no—
107C2×D4×C13—42no—
108C2×D4×C13—42no—
109C2×D4×C13—41no—
110C2×D4×C13—41no—
111C2×D4×C13—44no—
112C2×D4×C13—41no—
113C2×D4×C13—41no—
114C22×C4×C13—21no—
115C22×C4×C13—21no—
116C22×C4×C13—21no—
117C22×C4×C13—21no—
118C22×C4×C13—21no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—42no—
125C22×C4×C13—42no—
126C22×C4×C13—42no—
127C22×C4×C13—42no—
128C22×C4×C13—41no—
129C22×C4×C13—41no—
130C22×C4×C13—42no—
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13#4111yescharacteristic
137C13×SD16—44no—
138C13×D8—44no—
139C13×M16—42no—
140C13×M16—42no—
141C2×C8×C13—22no—
142C2×C8×C13—41no—
143C13×C4⋊C4—21no—
144C13×C4⋊C4—21no—
145C13×C4⋊C4—44no—
146C13×C4⋊C4—41no—
147C13×C4⋊C4—41no—
148C13×C4⋊C4—41no—
149C13×C4⋊C4—41no—
150C13×C22⋊C4—44no—
151C13×C22⋊C4—44no—
152C13×C22⋊C4—42no—
153C13×C22⋊C4—42no—
154C13×C22⋊C4—44no—
155C13×C22⋊C4—41no—
156C13×C22⋊C4—41no—
157C13×C22⋊C4—82no—
158C42×C13—42no—
159#3006C2×C1311yescharacteristic
160#2591C2×C1311yescharacteristic, complemented
161#2406C2×C1311yescharacteristic, complemented
162#1789C2×C1311yescharacteristic, complemented
163#1510C2×C1311yescharacteristic, complemented
164#1463C2×C1311yescharacteristic, complemented
165#1284C2×C1311yescharacteristic, complemented
166C23×C13—22no—
167C23×C13—22no—
168C23×C13—22no—
169C23×C13—41no—
170C23×C13—42no—
171C23×C13—41no—
172C23×C13—42no—
173C23×C13—42no—
174C23×C13—41no—
175C23×C13—42no—
176C23×C13—41no—
177C23×C13—42no—
178C23×C13#12011yescharacteristic
179C23×C13#12011yescharacteristic
180C23×C13#12111yescharacteristic
181Q8×C13—22no—
182Q8×C13—22no—
183Q8×C13—41no—
184Q8×C13—41no—
185D4×C13—22no—
186D4×C13—22no—
187D4×C13—41no—
188D4×C13—41no—
189D4×C13—42no—
190D4×C13—44no—
191D4×C13—44no—
192D4×C13—81no—
193D4×C13—82no—
194D4×C13—82no—
195C2×C4×C13—22no—
196C2×C4×C13—22no—
197C2×C4×C13—22no—
198C2×C4×C13—22no—
199C2×C4×C13—22no—
200C2×C4×C13—22no—
201C2×C4×C13—41no—
202C2×C4×C13—41no—
203C2×C4×C13—41no—
204C2×C4×C13—41no—
205C2×C4×C13—44no—
206C2×C4×C13—44no—
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—42no—
214C2×C4×C13—42no—
215C2×C4×C13—42no—
216C2×C4×C13—42no—
217C2×C4×C13—42no—
218C2×C4×C13—42no—
219C2×C4×C13—41no—
220C2×C4×C13—41no—
221C2×C4×C13—42no—
222C2×C4×C13—42no—
223C2×C4×C13—42no—
224C2×C4×C13—81no—
225C2×C4×C13#12011yescharacteristic
226C2×C4×C13#12111yescharacteristic
227C2×C4×C13#12111yescharacteristic
228C2×C4×C13#12711yescharacteristic
229C8×C13—42no—
230C8×C13—81no—
231C22×#41C22×C1311yescharacteristic
232C2×AGL(1,ℤ/8)—21no—
233C2×#123—21no—
234C2×#121C22×C1311yescharacteristic
235C22×C4⋊C4C22×C1311yescharacteristic
236#449—22no—
237#448—21no—
238#447—21no—
239C2×#104—22no—
240#417—21no—
241#407C22×C1311yescharacteristic
242#407C22×C1311yescharacteristic
243#400—21no—
244#395—21no—
245#394—21no—
246#394—21no—
247#388—22no—
248#386—21no—
249#386—21no—
250#386—21no—
251#385—22no—
252#381C22×C1311yescharacteristic
253C4×C22⋊C4C22×C1311yescharacteristic
254#327—22no—
255#324—22no—
256C22×C13—21no—
257C22×C13—21no—
258C22×C13—21no—
259C22×C13—21no—
260C22×C13—21no—
261C22×C13—21no—
262C22×C13—21no—
263C22×C13—44no—
264C22×C13—44no—
265C22×C13—42no—
266C22×C13—82no—
267C22×C13—84no—
268C22×C13—81no—
269C22×C13—81no—
270C22×C13—81no—
271C22×C13—81no—
272C22×C13—81no—
273C22×C13#39211yescharacteristic
274C22×C13#45412yes—
275C22×C13B(4,𝔽2)12yes—
276C4×C13—21no—
277C4×C13—21no—
278C4×C13—21no—
279C4×C13—21no—
280C4×C13—42no—
281C4×C13—42no—
282C4×C13—82no—
283C4×C13—82no—
284C4×C13—81no—
285C4×C13—81no—
286C2×#41—21no—
287C2×#41—21no—
288C2×#41—21no—
289C2×#41—21no—
290C2×#41—44no—
291C22×Q8D4×C1311yescharacteristic
292C22×D4—21no—
293C22×D4—21no—
294C22×D4D4×C1311yescharacteristic
295C22×D4D4×C1311yescharacteristic
296C23×C4—21no—
297C23×C4D4×C1311yescharacteristic
298C23×C4D4×C1311yescharacteristic
299C23×C4C23×C1311yescharacteristic
300AGL(1,ℤ/8)—44no—
301C2×SD16—22no—
302C2×D8—22no—
303C2×M16—21no—
304C2×M16—21no—
305#123—44no—
306#121—21no—
307#121—21no—
308#121—21no—
309#121—21no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4D4×C1311yescharacteristic
318C2×C22⋊C4—22no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—22no—
325C2×C42D4×C1312yes—
326#104—44no—
327#103—22no—
328#102—22no—
329C22⋊C8—21no—
330C22⋊C8—21no—
331C22⋊C8—21no—
332C22⋊C8D4×C1312yes—
333#95—22no—
334#95—22no—
335#95—22no—
336#95—21no—
337#95—21no—
338#95D4×C1312yes—
339C2×C13—22no—
340C2×C13—22no—
341C2×C13—41no—
342C2×C13—82no—
343C2×C13—161no—
344C2×C13#200311yescharacteristic
345C2×C13#201011yescharacteristic
346C2×C13#202111yescharacteristic
347C24—21no—
348C24—21no—
349C24C2×D4×C1311yescharacteristic
350#41—24no—
351#41—24no—
352#41—42no—
353#41—42no—
354#41—42no—
355#41—42no—
356#41—42no—
357#41—42no—
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8—42no—
361C2×D4—24no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—42no—
367C2×D4—42no—
368C2×D4—42no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—44no—
372C2×D4—41no—
373C2×D4—41no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4—42no—
387C22×C4—42no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—42no—
391C22×C4C2×D4×C1311yescharacteristic
392C22×C4C2×D4×C1311yescharacteristic
393C22×C4C2×D4×C1311yescharacteristic
394C22×C4C2×D4×C1311yescharacteristic
395C22×C4C2×D4×C1311yescharacteristic
396C22×C4C13×#4111yescharacteristic
397SD16—44no—
398D8—44no—
399M16—42no—
400M16—42no—
401C2×C8—22no—
402C2×C8—41no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—44no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C22⋊C4—44no—
411C22⋊C4—44no—
412C22⋊C4—42no—
413C22⋊C4—44no—
414C22⋊C4—42no—
415C22⋊C4—41no—
416C22⋊C4—41no—
417C22⋊C4—82no—
418C42—42no—
419C13#993911yescharacteristic, direct product factor, Sylow
420C23—22no—
421C23—22no—
422C23—22no—
423C23—41no—
424C23—42no—
425C23—41no—
426C23—42no—
427C23—42no—
428C23—41no—
429C23—42no—
430C23—41no—
431C23—42no—
432C23C13×#12011yescharacteristic
433C23C13×#12011yescharacteristic
434C23C13×#12111yescharacteristic
435Q8—22no—
436Q8—22no—
437Q8—41no—
438Q8—41no—
439D4—22no—
440D4—22no—
441D4—41no—
442D4—41no—
443D4—42no—
444D4—44no—
445D4—44no—
446D4—81no—
447D4—82no—
448D4—82no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—44no—
460C2×C4—44no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—81no—
479C2×C4C13×#12011yescharacteristic
480C2×C4C13×#12111yescharacteristic
481C2×C4C13×#12111yescharacteristic
482C2×C4C13×#12711yescharacteristic
483C8—42no—
484C8—81no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—44no—
493C22—44no—
494C22—42no—
495C22—82no—
496C22—84no—
497C22—81no—
498C22—81no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22C13×#39211yescharacteristic
503C22C13×#45412yes—
504C22C13×B(4,𝔽2)12yes—
505C4—21no—
506C4—21no—
507C4—21no—
508C4—21no—
509C4—42no—
510C4—42no—
511C4—82no—
512C4—82no—
513C4—81no—
514C4—81no—
515C2—22no—
516C2—22no—
517C2—41no—
518C2—82no—
519C2—161no—
520C2C13×#200311yescharacteristic
521C2C13×#201011yescharacteristic
522C2C13×#202111yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC13×#3006C2
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
2. C13×#2591C2semidirect
3. C13×#2406C2semidirect
4. C13×#1789C2semidirect
5. C13×#1510C2semidirect
6. C13×#1463C2semidirect
7. C13×#1284C2semidirect
86. #9939C13direct (N × H)
160. #2591C2×C13semidirect
161. #2406C2×C13semidirect
162. #1789C2×C13semidirect
163. #1510C2×C13semidirect
164. #1463C2×C13semidirect
165. #1284C2×C13semidirect
419. C13#9939direct (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×#25912
C13×#24062
C13×#17892
C13×#15102
C13×#14632
C13×#12842
#993913