Finite Group Databasebeta

← C13×#32871 #15719210

Subgroups — C13×#32871 #15719210

Order 3328.

492 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2103C211yesmaximal, characteristic, complemented
2C13×#2103C211yesmaximal, characteristic, complemented
3C13×#2098C211yesmaximal, characteristic, complemented
4C13×#2082C211yesmaximal, characteristic, complemented
5C13×#2081C211yesmaximal, characteristic, complemented
6C13×#2070C211yesmaximal, characteristic, complemented
7C13×#2069C211yesmaximal, characteristic, complemented
8C13×#2049C211yesmaximal, characteristic, complemented
9C13×#2048C211yesmaximal, characteristic
10C13×#2046C211yesmaximal, characteristic, complemented
11C13×#2046C211yesmaximal, characteristic, complemented
12C13×#2019C211yesmaximal, characteristic
13C13×#1903C211yesmaximal, characteristic
14C13×#1902C211yesmaximal, characteristic, complemented
15C13×#1858C211yesmaximal, characteristic, complemented
16C2×C13×#137C2211yescharacteristic
17C2×C13×AGL(1,ℤ/8)C2211yescharacteristic
18C22×C13×SD16C2211yescharacteristic
19C13×#568C2211yescharacteristic
20C13×#430C2211yescharacteristic
21C13×#430C2211yescharacteristic
22C13×#430C2211yescharacteristic
23C13×#430C2211yescharacteristic
24C13×#430C2211yescharacteristic
25C13×#424C2211yescharacteristic
26C13×#424C2211yescharacteristic
27C13×#421C2211yescharacteristic
28C13×#421C2211yescharacteristic
29C13×#419C2211yescharacteristic
30C13×#419C2211yescharacteristic
31C13×#418C2211yescharacteristic
32C13×#418C2211yescharacteristic
33C13×#413C2211yescharacteristic
34C2×C13×#101C2211yescharacteristic
35C2×C13×#101C2211yescharacteristic
36C2×C13×#101C2211yescharacteristic
37C2×C13×#100C2211yescharacteristic
38C2×C13×#100C2211yescharacteristic
39C2×C13×#100C2211yescharacteristic
40C13×#408C2211yescharacteristic
41C13×#344C2211yescharacteristic
42C13×#344C2211yescharacteristic
43C13×#344C2211yescharacteristic
44C13×#344C2211yescharacteristic
45C13×#341C2211yescharacteristic
46C13×#341C2211yescharacteristic
47C13×#341C2211yescharacteristic
48C13×#338C2211yescharacteristic
49C13×#338C2211yescharacteristic
50C13×H(3,ℤ/4)C2211yescharacteristic
51C2×C13×#41C2311yescharacteristic
52C22×Q8×C13C2311yescharacteristic
53C22×D4×C13C2311yescharacteristic
54C13×#137—41no—
55C13×#137—41no—
56C13×AGL(1,ℤ/8)—41no—
57C13×AGL(1,ℤ/8)—41no—
58C2×C13×Q16—21no—
59C2×C13×SD16—21no—
60C2×C13×SD16—21no—
61C2×C13×SD16—41no—
62C2×C13×SD16—41no—
63C2×C13×SD16—41no—
64C2×C13×D8—21no—
65C13×#131—41no—
66C13×#131—41no—
67C2×C13×M16—41no—
68C2×C13×M16C2311yescharacteristic
69C2×C13×M16C2311yescharacteristic
70C2×C13×M16C2311yescharacteristic
71C2×C13×M16C2311yescharacteristic
72C2×C13×M16C2311yescharacteristic
73C2×C13×M16C2311yescharacteristic
74C2×C13×M16C2311yescharacteristic
75C2×C13×M16C2311yescharacteristic
76C2×C13×M16C2311yescharacteristic
77C22×C8×C13C2311yescharacteristic
78C13×#117C2311yescharacteristic
79C13×#117C2311yescharacteristic
80C13×#108—41no—
81C13×#108—41no—
82C13×#108—41no—
83C13×#108—41no—
84C13×#108—41no—
85C13×C4⋊C8—41no—
86C13×C4⋊C8—41no—
87C13×#104—41no—
88C13×#104—41no—
89C13×#103—41no—
90C13×#103—41no—
91C13×#102—41no—
92C13×#102—41no—
93C13×#101—21no—
94C13×#101—41no—
95C13×#101—41no—
96C13×#101—41no—
97C13×#100—21no—
98C13×#100—41no—
99C13×#100—41no—
100C13×#100—41no—
101C13×C22⋊C8—41no—
102#32871C1311yesmaximal, characteristic, direct product factor, Sylow
103C24×C13—21no—
104C13×#41—21no—
105C13×#41—21no—
106C13×#41—21no—
107C13×#41—21no—
108C2×Q8×C13—21no—
109C2×Q8×C13—21no—
110C2×Q8×C13—21no—
111C2×Q8×C13—21no—
112C2×Q8×C13—21no—
113C2×Q8×C13—21no—
114C2×Q8×C13#4111yescharacteristic
115C2×D4×C13—21no—
116C2×D4×C13—21no—
117C2×D4×C13—21no—
118C2×D4×C13—21no—
119C2×D4×C13—21no—
120C2×D4×C13—21no—
121C2×D4×C13—21no—
122C2×D4×C13#4111yescharacteristic
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13C2411yescharacteristic
126C13×Q16—42no—
127C13×SD16—42no—
128C13×SD16—42no—
129C13×SD16—44no—
130C13×D8—42no—
131C13×M16—21no—
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—21no—
149C13×M16—42no—
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—21no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—42no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C22⋊C4—21no—
166C13×C22⋊C4—21no—
167C42×C13—21no—
168C42×C13—21no—
169#2103C2×C1311yescharacteristic, complemented
170#2103C2×C1311yescharacteristic, complemented
171#2098C2×C1311yescharacteristic, complemented
172#2082C2×C1311yescharacteristic, complemented
173#2081C2×C1311yescharacteristic, complemented
174#2070C2×C1311yescharacteristic, complemented
175#2069C2×C1311yescharacteristic, complemented
176#2049C2×C1311yescharacteristic, complemented
177#2048C2×C1311yescharacteristic
178#2046C2×C1311yescharacteristic, complemented
179#2046C2×C1311yescharacteristic, complemented
180#2019C2×C1311yescharacteristic
181#1903C2×C1311yescharacteristic
182#1902C2×C1311yescharacteristic, complemented
183#1858C2×C1311yescharacteristic, complemented
184C23×C13—21no—
185C23×C13—41no—
186C23×C13—41no—
187C23×C13—41no—
188C23×C13—161no—
189C23×C132−1+411yescharacteristic
190Q8×C13—21no—
191Q8×C13—21no—
192Q8×C13—41no—
193Q8×C13—41no—
194Q8×C13—41no—
195Q8×C13—41no—
196D4×C13—21no—
197D4×C13—21no—
198D4×C13—41no—
199D4×C13—41no—
200D4×C13—41no—
201D4×C13—41no—
202D4×C13—41no—
203D4×C13—41no—
204C2×C4×C13—21no—
205C2×C4×C13—41no—
206C2×C4×C13—41no—
207C2×C4×C13—41no—
208C2×C4×C13—41no—
209C2×C4×C13—41no—
210C2×C4×C13—41no—
211C2×C4×C13—41no—
212C2×C4×C13C2×#4111yescharacteristic
213C2×C4×C13H(5,𝔽2)11yescharacteristic
214C2×C4×C13H(5,𝔽2)11yescharacteristic
215C2×C4×C13H(5,𝔽2)11yescharacteristic
216C2×C4×C13H(5,𝔽2)11yescharacteristic
217C2×C4×C13H(5,𝔽2)11yescharacteristic
218C8×C13—41no—
219C8×C13—41no—
220C8×C13—41no—
221C8×C13—41no—
222C8×C13—41no—
223C8×C13—41no—
224C8×C13—41no—
225C8×C13—41no—
226C8×C13—41no—
227C8×C13—41no—
228C2×#137C22×C1311yescharacteristic
229C2×AGL(1,ℤ/8)C22×C1311yescharacteristic
230C22×SD16C22×C1311yescharacteristic
231#568C22×C1311yescharacteristic
232#430C22×C1311yescharacteristic
233#430C22×C1311yescharacteristic
234#430C22×C1311yescharacteristic
235#430C22×C1311yescharacteristic
236#430C22×C1311yescharacteristic
237#424C22×C1311yescharacteristic
238#424C22×C1311yescharacteristic
239#421C22×C1311yescharacteristic
240#421C22×C1311yescharacteristic
241#419C22×C1311yescharacteristic
242#419C22×C1311yescharacteristic
243#418C22×C1311yescharacteristic
244#418C22×C1311yescharacteristic
245#413C22×C1311yescharacteristic
246C2×#101C22×C1311yescharacteristic
247C2×#101C22×C1311yescharacteristic
248C2×#101C22×C1311yescharacteristic
249C2×#100C22×C1311yescharacteristic
250C2×#100C22×C1311yescharacteristic
251C2×#100C22×C1311yescharacteristic
252#408C22×C1311yescharacteristic
253#344C22×C1311yescharacteristic
254#344C22×C1311yescharacteristic
255#344C22×C1311yescharacteristic
256#344C22×C1311yescharacteristic
257#341C22×C1311yescharacteristic
258#341C22×C1311yescharacteristic
259#341C22×C1311yescharacteristic
260#338C22×C1311yescharacteristic
261#338C22×C1311yescharacteristic
262H(3,ℤ/4)C22×C1311yescharacteristic
263C22×C13—41no—
264C22×C13—41no—
265C22×C13—81no—
266C22×C13—81no—
267C22×C13—161no—
268C22×C13—161no—
269C22×C13—161no—
270C22×C13#53911yescharacteristic
271C22×C13#56211yescharacteristic
272C22×C13#56211yescharacteristic
273C4×C13—41no—
274C4×C13—81no—
275C4×C13—81no—
276C4×C13—81no—
277C4×C13#53811yescharacteristic
278C4×C13#53811yescharacteristic
279C4×C13#56011yescharacteristic
280C4×C13#56011yescharacteristic
281C2×#41C23×C1311yescharacteristic
282C22×Q8C23×C1311yescharacteristic
283C22×D4C23×C1311yescharacteristic
284#137—41no—
285#137—41no—
286AGL(1,ℤ/8)—41no—
287AGL(1,ℤ/8)—41no—
288C2×Q16—21no—
289C2×SD16—21no—
290C2×SD16—21no—
291C2×SD16—41no—
292C2×SD16—41no—
293C2×SD16—41no—
294C2×D8—21no—
295#131—41no—
296#131—41no—
297C2×M16—41no—
298C2×M16C23×C1311yescharacteristic
299C2×M16C23×C1311yescharacteristic
300C2×M16C23×C1311yescharacteristic
301C2×M16C23×C1311yescharacteristic
302C2×M16C23×C1311yescharacteristic
303C2×M16C23×C1311yescharacteristic
304C2×M16C23×C1311yescharacteristic
305C2×M16C23×C1311yescharacteristic
306C2×M16C23×C1311yescharacteristic
307C22×C8C23×C1311yescharacteristic
308#117C23×C1311yescharacteristic
309#117C23×C1311yescharacteristic
310#108—41no—
311#108—41no—
312#108—41no—
313#108—41no—
314#108—41no—
315C4⋊C8—41no—
316C4⋊C8—41no—
317#104—41no—
318#104—41no—
319#103—41no—
320#103—41no—
321#102—41no—
322#102—41no—
323#101—21no—
324#101—41no—
325#101—41no—
326#101—41no—
327#100—21no—
328#100—41no—
329#100—41no—
330#100—41no—
331C22⋊C8—41no—
332C2×C13—21no—
333C2×C13—21no—
334C2×C13—21no—
335C2×C13—81no—
336C2×C13—161no—
337C2×C13#282611yescharacteristic
338C24—21no—
339#41—21no—
340#41—21no—
341#41—21no—
342#41—21no—
343C2×Q8—21no—
344C2×Q8—21no—
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8C13×#4111yescharacteristic
350C2×D4—21no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4C13×#4111yescharacteristic
358C22×C4—21no—
359C22×C4—21no—
360C22×C4C24×C1311yescharacteristic
361Q16—42no—
362SD16—42no—
363SD16—42no—
364SD16—44no—
365D8—42no—
366M16—21no—
367M16—21no—
368M16—21no—
369M16—21no—
370M16—21no—
371M16—21no—
372M16—21no—
373M16—21no—
374M16—21no—
375M16—21no—
376M16—21no—
377M16—21no—
378M16—21no—
379M16—21no—
380M16—21no—
381M16—21no—
382M16—21no—
383M16—21no—
384M16—42no—
385C2×C8—21no—
386C2×C8—21no—
387C2×C8—21no—
388C2×C8—21no—
389C2×C8—21no—
390C2×C8—21no—
391C2×C8—21no—
392C2×C8—21no—
393C2×C8—21no—
394C2×C8—21no—
395C2×C8—21no—
396C2×C8—21no—
397C2×C8—42no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C22⋊C4—21no—
401C22⋊C4—21no—
402C42—21no—
403C42—21no—
404C13#3287111yescharacteristic, direct product factor, Sylow
405C23—21no—
406C23—41no—
407C23—41no—
408C23—41no—
409C23—161no—
410C23C13×2−1+411yescharacteristic
411Q8—21no—
412Q8—21no—
413Q8—41no—
414Q8—41no—
415Q8—41no—
416Q8—41no—
417D4—21no—
418D4—21no—
419D4—41no—
420D4—41no—
421D4—41no—
422D4—41no—
423D4—41no—
424D4—41no—
425C2×C4—21no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4C2×C13×#4111yescharacteristic
434C2×C4C13×H(5,𝔽2)11yescharacteristic
435C2×C4C13×H(5,𝔽2)11yescharacteristic
436C2×C4C13×H(5,𝔽2)11yescharacteristic
437C2×C4C13×H(5,𝔽2)11yescharacteristic
438C2×C4C13×H(5,𝔽2)11yescharacteristic
439C8—41no—
440C8—41no—
441C8—41no—
442C8—41no—
443C8—41no—
444C8—41no—
445C8—41no—
446C8—41no—
447C8—41no—
448C8—41no—
449C22—41no—
450C22—41no—
451C22—81no—
452C22—81no—
453C22—161no—
454C22—161no—
455C22—161no—
456C22C13×#53911yescharacteristic
457C22C13×#56211yescharacteristic
458C22C13×#56211yescharacteristic
459C4—41no—
460C4—81no—
461C4—81no—
462C4—81no—
463C4C13×#53811yescharacteristic
464C4C13×#53811yescharacteristic
465C4C13×#56011yescharacteristic
466C4C13×#56011yescharacteristic
467C2—21no—
468C2—21no—
469C2—21no—
470C2—81no—
471C2—161no—
472C2C13×#282611yescharacteristic
subgroupG/H
center, socleC2×C13#2826
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC2×C13×AGL(1,ℤ/8)C22
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×#2103C2semidirect
2. C13×#2103C2semidirect
3. C13×#2098C2semidirect
4. C13×#2082C2semidirect
5. C13×#2081C2semidirect
6. C13×#2070C2semidirect
7. C13×#2069C2semidirect
8. C13×#2049C2semidirect
10. C13×#2046C2semidirect
11. C13×#2046C2semidirect
14. C13×#1902C2semidirect
15. C13×#1858C2semidirect
102. #32871C13direct (N × H)
169. #2103C2×C13semidirect
170. #2103C2×C13semidirect
171. #2098C2×C13semidirect
172. #2082C2×C13semidirect
173. #2081C2×C13semidirect
174. #2070C2×C13semidirect
175. #2069C2×C13semidirect
176. #2049C2×C13semidirect
178. #2046C2×C13semidirect
179. #2046C2×C13semidirect
182. #1902C2×C13semidirect
183. #1858C2×C13semidirect
404. C13#32871direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#21032
C13×#20982
C13×#20822
C13×#20812
C13×#20702
C13×#20692
C13×#20492
C13×#20482
C13×#20462
C13×#20192
C13×#19032
C13×#19022
C13×#18582
#3287113