Finite Group Databasebeta

← C13×#32697 #15719036

Subgroups — C13×#32697 #15719036

Order 3328.

528 conjugacy classes of subgroups.

The subgroup lattice has 488 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×#2070C211yesmaximal, characteristic, complemented
5C13×#2049C211yesmaximal, characteristic
6C13×#2005C211yesmaximal, characteristic
7C13×#1966C211yesmaximal, characteristic, complemented
8C13×#1932C211yesmaximal, characteristic
9C13×#1915C211yesmaximal, characteristic
10C13×#1912C211yesmaximal, characteristic
11C13×#1902C211yesmaximal, characteristic
12C13×#1886C211yesmaximal, characteristic, complemented
13C13×#1861C211yesmaximal, characteristic
14C13×#1841C211yesmaximal, characteristic, complemented
15C13×#1830C211yesmaximal, characteristic, complemented
16C2×C13×#137C2211yescharacteristic
17C13×#568C2211yescharacteristic
18C13×#536C2211yescharacteristic
19C2×C13×C4⋊Q8C2211yescharacteristic
20C13×#519C2211yescharacteristic
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×#101C2211yescharacteristic
35C2×C13×#101C2211yescharacteristic
36C2×C13×#101C2211yescharacteristic
37C2×C13×#101C2211yescharacteristic
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×Q8×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×C4⋊Q8—21no—
70C13×C4⋊Q8—21no—
71C13×C4⋊Q8—21no—
72C13×C4⋊Q8—41no—
73C13×#124—21no—
74C13×#123—22no—
75C13×C22⋊Q8—41no—
76C4×Q8×C13—41no—
77C4×Q8×C13—41no—
78C13×#117—22no—
79C13×#117C2311yescharacteristic
80C13×#117C2311yescharacteristic
81C13×#117C2311yescharacteristic
82C2×C13×C4⋊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×#101—41no—
99C13×#101—41no—
100C13×#101—41no—
101C13×#101—41no—
102C13×#100—21no—
103C13×#97—21no—
104C4×C8×C13—21no—
105#32697C1311yesmaximal, characteristic, direct product factor, Sylow
106C13×#41—21no—
107C13×#41—21no—
108C13×#41—21no—
109C13×#41—21no—
110C2×Q8×C13—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—21no—
118C2×Q8×C13—21no—
119C2×Q8×C13—21no—
120C2×Q8×C13—21no—
121C2×Q8×C13—21no—
122C2×Q8×C13#4111yescharacteristic
123C2×D4×C13—21no—
124C2×D4×C13#4111yescharacteristic
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13#4112yes—
129C22×C4×C13C2411yescharacteristic
130C13×Q16—42no—
131C13×SD16—42no—
132C13×M16—21no—
133C13×M16—21no—
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—42no—
149C2×C8×C13—21no—
150C2×C8×C13—21no—
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—42no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—42no—
162C13×C4⋊C4—42no—
163C13×C4⋊C4—42no—
164C13×C4⋊C4—42no—
165C13×C22⋊C4—21no—
166C13×C22⋊C4—21no—
167C13×C22⋊C4—21no—
168C13×C22⋊C4—42no—
169C42×C13—21no—
170C42×C13—21no—
171C42×C13—21no—
172C42×C13—21no—
173C42×C13—42no—
174C42×C13#4111yescharacteristic
175C42×C13#4111yescharacteristic
176#2102C2×C1311yescharacteristic, complemented
177#2082C2×C1311yescharacteristic, complemented
178#2082C2×C1311yescharacteristic, complemented
179#2070C2×C1311yescharacteristic, complemented
180#2049C2×C1311yescharacteristic
181#2005C2×C1311yescharacteristic
182#1966C2×C1311yescharacteristic, complemented
183#1932C2×C1311yescharacteristic
184#1915C2×C1311yescharacteristic
185#1912C2×C1311yescharacteristic
186#1902C2×C1311yescharacteristic
187#1886C2×C1311yescharacteristic, complemented
188#1861C2×C1311yescharacteristic
189#1841C2×C1311yescharacteristic, complemented
190#1830C2×C1311yescharacteristic, complemented
191C23×C13—21no—
192C23×C13C2×#4111yescharacteristic
193Q8×C13—21no—
194Q8×C13—21no—
195Q8×C13—41no—
196Q8×C13—41no—
197Q8×C13—41no—
198Q8×C13—41no—
199Q8×C13—41no—
200Q8×C13—41no—
201Q8×C13—41no—
202Q8×C13—41no—
203D4×C13—21no—
204D4×C13—21no—
205D4×C13—41no—
206D4×C13—41no—
207C2×C4×C13—21no—
208C2×C4×C13—22no—
209C2×C4×C13—21no—
210C2×C4×C13—22no—
211C2×C4×C13—21no—
212C2×C4×C13—22no—
213C2×C4×C13—42no—
214C2×C4×C13—41no—
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×C13C2×#4111yescharacteristic
223C2×C4×C13C2×#4111yescharacteristic
224C2×C4×C13H(5,𝔽2)11yescharacteristic
225C2×C4×C13H(5,𝔽2)11yescharacteristic
226C2×C4×C13H(5,𝔽2)11yescharacteristic
227C2×C4×C13H(5,𝔽2)11yescharacteristic
228C8×C13—41no—
229C8×C13—41no—
230C8×C13—41no—
231C8×C13—41no—
232C8×C13—41no—
233C8×C13—41no—
234C8×C13—41no—
235C8×C13—41no—
236C2×#137C22×C1311yescharacteristic
237#568C22×C1311yescharacteristic
238#536C22×C1311yescharacteristic
239C2×C4⋊Q8C22×C1311yescharacteristic
240#519C22×C1311yescharacteristic
241#430C22×C1311yescharacteristic
242#430C22×C1311yescharacteristic
243#430C22×C1311yescharacteristic
244#423C22×C1311yescharacteristic
245#421C22×C1311yescharacteristic
246#421C22×C1311yescharacteristic
247C2×#104C22×C1311yescharacteristic
248#419C22×C1311yescharacteristic
249#419C22×C1311yescharacteristic
250#419C22×C1311yescharacteristic
251#413C22×C1311yescharacteristic
252C2×#101C22×C1311yescharacteristic
253C2×#101C22×C1311yescharacteristic
254C2×#101C22×C1311yescharacteristic
255C2×#101C22×C1311yescharacteristic
256C2×#101C22×C1311yescharacteristic
257C2×#101C22×C1311yescharacteristic
258C4×M16C22×C1311yescharacteristic
259#344C22×C1311yescharacteristic
260#344C22×C1311yescharacteristic
261#344C22×C1311yescharacteristic
262#344C22×C1311yescharacteristic
263#344C22×C1311yescharacteristic
264#344C22×C1311yescharacteristic
265#339C22×C1311yescharacteristic
266#339C22×C1311yescharacteristic
267#339C22×C1311yescharacteristic
268#338C22×C1311yescharacteristic
269H(3,ℤ/4)C22×C1311yescharacteristic
270H(3,ℤ/4)C22×C1311yescharacteristic
271C22×C13—41no—
272C22×C13—41no—
273C22×C13—81no—
274C22×C13#53811yescharacteristic
275C22×C13#55111yescharacteristic
276C22×C13#55111yescharacteristic
277C4×C13—22no—
278C4×C13—41no—
279C4×C13—42no—
280C4×C13—41no—
281C4×C13—81no—
282C4×C13—81no—
283C4×C13—81no—
284C4×C13—81no—
285C4×C13#53811yescharacteristic
286C4×C13#54011yescharacteristic
287C4×C13#55311yescharacteristic
288C4×C13#56011yescharacteristic
289C2×#41C23×C1311yescharacteristic
290C22×Q8C23×C1311yescharacteristic
291C22×Q8C23×C1311yescharacteristic
292#137—41no—
293#137—41no—
294C2×Q16—21no—
295C2×SD16—21no—
296#131—41no—
297#131—41no—
298C2×M16—41no—
299C2×M16C23×C1311yescharacteristic
300C2×M16C23×C1311yescharacteristic
301C2×M16C23×C1311yescharacteristic
302C2×M16C23×C1311yescharacteristic
303C2×M16C23×C1311yescharacteristic
304C2×M16C23×C1311yescharacteristic
305C2×M16C23×C1311yescharacteristic
306C2×M16C23×C1311yescharacteristic
307C4⋊Q8—21no—
308C4⋊Q8—21no—
309C4⋊Q8—21no—
310C4⋊Q8—41no—
311#124—21no—
312#123—22no—
313C22⋊Q8—41no—
314C4×Q8—41no—
315C4×Q8—41no—
316#117—22no—
317#117C23×C1311yescharacteristic
318#117C23×C1311yescharacteristic
319#117C23×C1311yescharacteristic
320C2×C4⋊C4—22no—
321C2×C42C23×C1311yescharacteristic
322#108—41no—
323#108—41no—
324#108—41no—
325C4⋊C8—41no—
326#104—21no—
327#104—21no—
328#104—41no—
329#104—41no—
330#103—41no—
331#103—41no—
332#103—41no—
333#101—21no—
334#101—41no—
335#101—41no—
336#101—41no—
337#101—41no—
338#101—41no—
339#101—41no—
340#100—21no—
341#97—21no—
342C4×C8—21no—
343C2×C13—21no—
344C2×C13—21no—
345C2×C13—21no—
346C2×C13—81no—
347C2×C13#274911yescharacteristic
348#41—21no—
349#41—21no—
350#41—21no—
351#41—21no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8—21no—
361C2×Q8—21no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8C13×#4111yescharacteristic
365C2×D4—21no—
366C2×D4C13×#4111yescharacteristic
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4C13×#4112yes—
371C22×C4C24×C1311yescharacteristic
372Q16—42no—
373SD16—42no—
374M16—21no—
375M16—21no—
376M16—21no—
377M16—21no—
378M16—21no—
379M16—21no—
380M16—21no—
381M16—21no—
382M16—21no—
383M16—21no—
384M16—21no—
385M16—21no—
386M16—21no—
387M16—21no—
388M16—21no—
389M16—21no—
390M16—42no—
391C2×C8—21no—
392C2×C8—21no—
393C2×C8—21no—
394C2×C8—21no—
395C2×C8—21no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8—42no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—42no—
404C4⋊C4—42no—
405C4⋊C4—42no—
406C4⋊C4—42no—
407C22⋊C4—21no—
408C22⋊C4—21no—
409C22⋊C4—21no—
410C22⋊C4—42no—
411C42—21no—
412C42—21no—
413C42—21no—
414C42—21no—
415C42—42no—
416C42C13×#4111yescharacteristic
417C42C13×#4111yescharacteristic
418C13#3269711yescharacteristic, direct product factor, Sylow
419C23—21no—
420C23C2×C13×#4111yescharacteristic
421Q8—21no—
422Q8—21no—
423Q8—41no—
424Q8—41no—
425Q8—41no—
426Q8—41no—
427Q8—41no—
428Q8—41no—
429Q8—41no—
430Q8—41no—
431D4—21no—
432D4—21no—
433D4—41no—
434D4—41no—
435C2×C4—21no—
436C2×C4—22no—
437C2×C4—21no—
438C2×C4—22no—
439C2×C4—21no—
440C2×C4—22no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4C2×C13×#4111yescharacteristic
451C2×C4C2×C13×#4111yescharacteristic
452C2×C4C13×H(5,𝔽2)11yescharacteristic
453C2×C4C13×H(5,𝔽2)11yescharacteristic
454C2×C4C13×H(5,𝔽2)11yescharacteristic
455C2×C4C13×H(5,𝔽2)11yescharacteristic
456C8—41no—
457C8—41no—
458C8—41no—
459C8—41no—
460C8—41no—
461C8—41no—
462C8—41no—
463C8—41no—
464C22—41no—
465C22—41no—
466C22—81no—
467C22C13×#53811yescharacteristic
468C22C13×#55111yescharacteristic
469C22C13×#55111yescharacteristic
470C4—22no—
471C4—41no—
472C4—42no—
473C4—41no—
474C4—81no—
475C4—81no—
476C4—81no—
477C4—81no—
478C4C13×#53811yescharacteristic
479C4C13×#54011yescharacteristic
480C4C13×#55311yescharacteristic
481C4C13×#56011yescharacteristic
482C2—21no—
483C2—21no—
484C2—21no—
485C2—81no—
486C2C13×#274911yescharacteristic
subgroupG/H
center, socleC2×C13#2749
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC2×C13×#41C23
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×#2070C2semidirect
7. C13×#1966C2semidirect
12. C13×#1886C2semidirect
14. C13×#1841C2semidirect
15. C13×#1830C2semidirect
105. #32697C13direct (N × H)
176. #2102C2×C13semidirect
177. #2082C2×C13semidirect
178. #2082C2×C13semidirect
179. #2070C2×C13semidirect
182. #1966C2×C13semidirect
187. #1886C2×C13semidirect
189. #1841C2×C13semidirect
190. #1830C2×C13semidirect
418. C13#32697direct (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×#20702
C13×#20492
C13×#20052
C13×#19662
C13×#19322
C13×#19152
C13×#19122
C13×#19022
C13×#18862
C13×#18612
C13×#18412
C13×#18302
#3269713