Finite Group Databasebeta

← C13×#32696 #15719035

Subgroups — C13×#32696 #15719035

Order 3328.

552 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2102C211yesmaximal, characteristic, complemented
2C13×#2082C211yesmaximal, characteristic, complemented
3C13×#2082C211yesmaximal, characteristic, complemented
4C13×#2069C211yesmaximal, characteristic, complemented
5C13×#2049C211yesmaximal, characteristic, complemented
6C13×#2004C211yesmaximal, characteristic
7C13×#1967C211yesmaximal, characteristic, complemented
8C13×#1932C211yesmaximal, characteristic, complemented
9C13×#1914C211yesmaximal, characteristic
10C13×#1911C211yesmaximal, characteristic
11C13×#1902C211yesmaximal, characteristic, complemented
12C13×#1885C211yesmaximal, characteristic, complemented
13C13×#1861C211yesmaximal, characteristic, complemented
14C13×#1841C211yesmaximal, characteristic, complemented
15C13×#1829C211yesmaximal, characteristic, complemented
16C2×C13×#137C2211yescharacteristic
17C13×#568C2211yescharacteristic
18C13×#535C2211yescharacteristic
19C2×C13×#124C2211yescharacteristic
20C13×#518C2211yescharacteristic
21C13×#430C2211yescharacteristic
22C13×#430C2211yescharacteristic
23C13×#430C2211yescharacteristic
24C13×#423C2211yescharacteristic
25C13×#421C2211yescharacteristic
26C13×#421C2211yescharacteristic
27C2×C13×#104C2211yescharacteristic
28C13×#419C2211yescharacteristic
29C13×#419C2211yescharacteristic
30C13×#419C2211yescharacteristic
31C13×#413C2211yescharacteristic
32C2×C13×#101C2211yescharacteristic
33C2×C13×#101C2211yescharacteristic
34C2×C13×#100C2211yescharacteristic
35C2×C13×#100C2211yescharacteristic
36C2×C13×#100C2211yescharacteristic
37C2×C13×#100C2211yescharacteristic
38C4×C13×M16C2211yescharacteristic
39C13×#344C2211yescharacteristic
40C13×#344C2211yescharacteristic
41C13×#344C2211yescharacteristic
42C13×#344C2211yescharacteristic
43C13×#344C2211yescharacteristic
44C13×#344C2211yescharacteristic
45C13×#339C2211yescharacteristic
46C13×#339C2211yescharacteristic
47C13×#339C2211yescharacteristic
48C13×#338C2211yescharacteristic
49C13×H(3,ℤ/4)C2211yescharacteristic
50C13×H(3,ℤ/4)C2211yescharacteristic
51C2×C13×#41C2311yescharacteristic
52C22×Q8×C13C2311yescharacteristic
53C22×D4×C13C2311yescharacteristic
54C13×#137—41no—
55C13×#137—41no—
56C2×C13×Q16—21no—
57C2×C13×SD16—21no—
58C13×#131—41no—
59C13×#131—41no—
60C2×C13×M16—41no—
61C2×C13×M16C2311yescharacteristic
62C2×C13×M16C2311yescharacteristic
63C2×C13×M16C2311yescharacteristic
64C2×C13×M16C2311yescharacteristic
65C2×C13×M16C2311yescharacteristic
66C2×C13×M16C2311yescharacteristic
67C2×C13×M16C2311yescharacteristic
68C2×C13×M16C2311yescharacteristic
69C13×#127—21no—
70C13×#124—21no—
71C13×#124—21no—
72C13×#124—21no—
73C13×#124—41no—
74C13×#121—41no—
75C13×#120—22no—
76C4×D4×C13—41no—
77C4×D4×C13—41no—
78C13×#117C2311yescharacteristic
79C13×#117C2311yescharacteristic
80C13×#117C2311yescharacteristic
81C2×C13×C22⋊C4—22no—
82C2×C13×C22⋊C4—22no—
83C2×C42×C13C2311yescharacteristic
84C13×#108—41no—
85C13×#108—41no—
86C13×#108—41no—
87C13×C4⋊C8—41no—
88C13×#104—21no—
89C13×#104—21no—
90C13×#104—41no—
91C13×#104—41no—
92C13×#103—41no—
93C13×#103—41no—
94C13×#103—41no—
95C13×#101—21no—
96C13×#101—41no—
97C13×#101—41no—
98C13×#100—21no—
99C13×#100—41no—
100C13×#100—41no—
101C13×#100—41no—
102C13×#100—41no—
103C13×#97—21no—
104C4×C8×C13—21no—
105#32696C1311yesmaximal, characteristic, direct product factor, Sylow
106C24×C13#4112yes—
107C13×#41—21no—
108C13×#41—21no—
109C13×#41—21no—
110C13×#41—21no—
111C2×Q8×C13—21no—
112C2×Q8×C13—21no—
113C2×Q8×C13—21no—
114C2×Q8×C13—21no—
115C2×Q8×C13—21no—
116C2×Q8×C13—21no—
117C2×Q8×C13#4111yescharacteristic
118C2×D4×C13—21no—
119C2×D4×C13—21no—
120C2×D4×C13—21no—
121C2×D4×C13—21no—
122C2×D4×C13—21no—
123C2×D4×C13—21no—
124C2×D4×C13—21no—
125C2×D4×C13—42no—
126C2×D4×C13#4111yescharacteristic
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—42no—
131C22×C4×C13C2411yescharacteristic
132C13×Q16—42no—
133C13×SD16—42no—
134C13×M16—21no—
135C13×M16—21no—
136C13×M16—21no—
137C13×M16—21no—
138C13×M16—21no—
139C13×M16—21no—
140C13×M16—21no—
141C13×M16—21no—
142C13×M16—21no—
143C13×M16—21no—
144C13×M16—21no—
145C13×M16—21no—
146C13×M16—21no—
147C13×M16—21no—
148C13×M16—21no—
149C13×M16—21no—
150C13×M16—42no—
151C2×C8×C13—21no—
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C2×C8×C13—21no—
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13—42no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C22⋊C4—21no—
164C13×C22⋊C4—21no—
165C13×C22⋊C4—21no—
166C13×C22⋊C4—42no—
167C13×C22⋊C4—42no—
168C13×C22⋊C4—42no—
169C13×C22⋊C4—42no—
170C42×C13—21no—
171C42×C13—21no—
172C42×C13—21no—
173C42×C13—21no—
174C42×C13#4111yescharacteristic
175C42×C13#4111yescharacteristic
176#2102C2×C1311yescharacteristic, complemented
177#2082C2×C1311yescharacteristic, complemented
178#2082C2×C1311yescharacteristic, complemented
179#2069C2×C1311yescharacteristic, complemented
180#2049C2×C1311yescharacteristic, complemented
181#2004C2×C1311yescharacteristic
182#1967C2×C1311yescharacteristic, complemented
183#1932C2×C1311yescharacteristic, complemented
184#1914C2×C1311yescharacteristic
185#1911C2×C1311yescharacteristic
186#1902C2×C1311yescharacteristic, complemented
187#1885C2×C1311yescharacteristic, complemented
188#1861C2×C1311yescharacteristic, complemented
189#1841C2×C1311yescharacteristic, complemented
190#1829C2×C1311yescharacteristic, complemented
191C23×C13—22no—
192C23×C13—22no—
193C23×C13—22no—
194C23×C13—21no—
195C23×C13—82no—
196C23×C13C2×#4111yescharacteristic
197Q8×C13—21no—
198Q8×C13—21no—
199Q8×C13—41no—
200Q8×C13—41no—
201Q8×C13—41no—
202Q8×C13—41no—
203D4×C13—21no—
204D4×C13—21no—
205D4×C13—41no—
206D4×C13—41no—
207D4×C13—41no—
208D4×C13—41no—
209D4×C13—41no—
210D4×C13—41no—
211D4×C13—162no—
212C2×C4×C13—21no—
213C2×C4×C13—21no—
214C2×C4×C13—21no—
215C2×C4×C13—41no—
216C2×C4×C13—41no—
217C2×C4×C13—41no—
218C2×C4×C13—41no—
219C2×C4×C13—41no—
220C2×C4×C13—41no—
221C2×C4×C13—41no—
222C2×C4×C13—41no—
223C2×C4×C13—81no—
224C2×C4×C13—162no—
225C2×C4×C13C2×#4111yescharacteristic
226C2×C4×C13C2×#4111yescharacteristic
227C2×C4×C13H(5,𝔽2)11yescharacteristic
228C2×C4×C13H(5,𝔽2)11yescharacteristic
229C2×C4×C13H(5,𝔽2)11yescharacteristic
230C2×C4×C13H(5,𝔽2)11yescharacteristic
231C8×C13—41no—
232C8×C13—41no—
233C8×C13—41no—
234C8×C13—41no—
235C8×C13—41no—
236C8×C13—41no—
237C8×C13—41no—
238C8×C13—41no—
239C2×#137C22×C1311yescharacteristic
240#568C22×C1311yescharacteristic
241#535C22×C1311yescharacteristic
242C2×#124C22×C1311yescharacteristic
243#518C22×C1311yescharacteristic
244#430C22×C1311yescharacteristic
245#430C22×C1311yescharacteristic
246#430C22×C1311yescharacteristic
247#423C22×C1311yescharacteristic
248#421C22×C1311yescharacteristic
249#421C22×C1311yescharacteristic
250C2×#104C22×C1311yescharacteristic
251#419C22×C1311yescharacteristic
252#419C22×C1311yescharacteristic
253#419C22×C1311yescharacteristic
254#413C22×C1311yescharacteristic
255C2×#101C22×C1311yescharacteristic
256C2×#101C22×C1311yescharacteristic
257C2×#100C22×C1311yescharacteristic
258C2×#100C22×C1311yescharacteristic
259C2×#100C22×C1311yescharacteristic
260C2×#100C22×C1311yescharacteristic
261C4×M16C22×C1311yescharacteristic
262#344C22×C1311yescharacteristic
263#344C22×C1311yescharacteristic
264#344C22×C1311yescharacteristic
265#344C22×C1311yescharacteristic
266#344C22×C1311yescharacteristic
267#344C22×C1311yescharacteristic
268#339C22×C1311yescharacteristic
269#339C22×C1311yescharacteristic
270#339C22×C1311yescharacteristic
271#338C22×C1311yescharacteristic
272H(3,ℤ/4)C22×C1311yescharacteristic
273H(3,ℤ/4)C22×C1311yescharacteristic
274C22×C13—41no—
275C22×C13—41no—
276C22×C13—42no—
277C22×C13—82no—
278C22×C13—81no—
279C22×C13—82no—
280C22×C13—82no—
281C22×C13#53811yescharacteristic
282C22×C13#55111yescharacteristic
283C22×C13#55111yescharacteristic
284C4×C13—41no—
285C4×C13—41no—
286C4×C13—41no—
287C4×C13—81no—
288C4×C13—81no—
289C4×C13—81no—
290C4×C13—81no—
291C4×C13#53811yescharacteristic
292C4×C13#54011yescharacteristic
293C4×C13#55311yescharacteristic
294C4×C13#56011yescharacteristic
295C2×#41C23×C1311yescharacteristic
296C22×Q8C23×C1311yescharacteristic
297C22×D4C23×C1311yescharacteristic
298#137—41no—
299#137—41no—
300C2×Q16—21no—
301C2×SD16—21no—
302#131—41no—
303#131—41no—
304C2×M16—41no—
305C2×M16C23×C1311yescharacteristic
306C2×M16C23×C1311yescharacteristic
307C2×M16C23×C1311yescharacteristic
308C2×M16C23×C1311yescharacteristic
309C2×M16C23×C1311yescharacteristic
310C2×M16C23×C1311yescharacteristic
311C2×M16C23×C1311yescharacteristic
312C2×M16C23×C1311yescharacteristic
313#127—21no—
314#124—21no—
315#124—21no—
316#124—21no—
317#124—41no—
318#121—41no—
319#120—22no—
320C4×D4—41no—
321C4×D4—41no—
322#117C23×C1311yescharacteristic
323#117C23×C1311yescharacteristic
324#117C23×C1311yescharacteristic
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C42C23×C1311yescharacteristic
328#108—41no—
329#108—41no—
330#108—41no—
331C4⋊C8—41no—
332#104—21no—
333#104—21no—
334#104—41no—
335#104—41no—
336#103—41no—
337#103—41no—
338#103—41no—
339#101—21no—
340#101—41no—
341#101—41no—
342#100—21no—
343#100—41no—
344#100—41no—
345#100—41no—
346#100—41no—
347#97—21no—
348C4×C8—21no—
349C2×C13—21no—
350C2×C13—21no—
351C2×C13—21no—
352C2×C13—81no—
353C2×C13—82no—
354C2×C13#274911yescharacteristic
355C24C13×#4112yes—
356#41—21no—
357#41—21no—
358#41—21no—
359#41—21no—
360C2×Q8—21no—
361C2×Q8—21no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×Q8—21no—
366C2×Q8C13×#4111yescharacteristic
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4—42no—
375C2×D4C13×#4111yescharacteristic
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—42no—
380C22×C4C24×C1311yescharacteristic
381Q16—42no—
382SD16—42no—
383M16—21no—
384M16—21no—
385M16—21no—
386M16—21no—
387M16—21no—
388M16—21no—
389M16—21no—
390M16—21no—
391M16—21no—
392M16—21no—
393M16—21no—
394M16—21no—
395M16—21no—
396M16—21no—
397M16—21no—
398M16—21no—
399M16—42no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8—21no—
405C2×C8—21no—
406C2×C8—21no—
407C2×C8—21no—
408C2×C8—42no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C22⋊C4—21no—
413C22⋊C4—21no—
414C22⋊C4—21no—
415C22⋊C4—42no—
416C22⋊C4—42no—
417C22⋊C4—42no—
418C22⋊C4—42no—
419C42—21no—
420C42—21no—
421C42—21no—
422C42—21no—
423C42C13×#4111yescharacteristic
424C42C13×#4111yescharacteristic
425C13#3269611yescharacteristic, direct product factor, Sylow
426C23—22no—
427C23—22no—
428C23—22no—
429C23—21no—
430C23—82no—
431C23C2×C13×#4111yescharacteristic
432Q8—21no—
433Q8—21no—
434Q8—41no—
435Q8—41no—
436Q8—41no—
437Q8—41no—
438D4—21no—
439D4—21no—
440D4—41no—
441D4—41no—
442D4—41no—
443D4—41no—
444D4—41no—
445D4—41no—
446D4—162no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—81no—
459C2×C4—162no—
460C2×C4C2×C13×#4111yescharacteristic
461C2×C4C2×C13×#4111yescharacteristic
462C2×C4C13×H(5,𝔽2)11yescharacteristic
463C2×C4C13×H(5,𝔽2)11yescharacteristic
464C2×C4C13×H(5,𝔽2)11yescharacteristic
465C2×C4C13×H(5,𝔽2)11yescharacteristic
466C8—41no—
467C8—41no—
468C8—41no—
469C8—41no—
470C8—41no—
471C8—41no—
472C8—41no—
473C8—41no—
474C22—41no—
475C22—41no—
476C22—42no—
477C22—82no—
478C22—81no—
479C22—82no—
480C22—82no—
481C22C13×#53811yescharacteristic
482C22C13×#55111yescharacteristic
483C22C13×#55111yescharacteristic
484C4—41no—
485C4—41no—
486C4—41no—
487C4—81no—
488C4—81no—
489C4—81no—
490C4—81no—
491C4C13×#53811yescharacteristic
492C4C13×#54011yescharacteristic
493C4C13×#55311yescharacteristic
494C4C13×#56011yescharacteristic
495C2—21no—
496C2—21no—
497C2—21no—
498C2—82no—
499C2—81no—
500C2C13×#274911yescharacteristic
subgroupG/H
center, socleC2×C13#2749
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#535C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2102C2semidirect
2. C13×#2082C2semidirect
3. C13×#2082C2semidirect
4. C13×#2069C2semidirect
5. C13×#2049C2semidirect
7. C13×#1967C2semidirect
8. C13×#1932C2semidirect
11. C13×#1902C2semidirect
12. C13×#1885C2semidirect
13. C13×#1861C2semidirect
14. C13×#1841C2semidirect
15. C13×#1829C2semidirect
105. #32696C13direct (N × H)
176. #2102C2×C13semidirect
177. #2082C2×C13semidirect
178. #2082C2×C13semidirect
179. #2069C2×C13semidirect
180. #2049C2×C13semidirect
182. #1967C2×C13semidirect
183. #1932C2×C13semidirect
186. #1902C2×C13semidirect
187. #1885C2×C13semidirect
188. #1861C2×C13semidirect
189. #1841C2×C13semidirect
190. #1829C2×C13semidirect
425. C13#32696direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#21022
C13×#20822
C13×#20692
C13×#20492
C13×#20042
C13×#19672
C13×#19322
C13×#19142
C13×#19112
C13×#19022
C13×#18852
C13×#18612
C13×#18412
C13×#18292
#3269613