Finite Group Databasebeta

← C13×#33791 #15720130

Subgroups — C13×#33791 #15720130

Order 3328.

574 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3175C211yesmaximal, characteristic, complemented
2C13×#3156C211yesmaximal, characteristic, complemented
3C13×#2251C211yesmaximal, characteristic, complemented
4C13×#2249C211yesmaximal, characteristic, complemented
5C13×#2243C211yesmaximal, characteristic, complemented
6C13×#2241C211yesmaximal, characteristic, complemented
7C13×#2211C211yesmaximal, characteristic, complemented
8C13×#2210C211yesmaximal, characteristic, complemented
9C13×#2209C211yesmaximal, characteristic, complemented
10C13×#2208C211yesmaximal, characteristic, complemented
11C13×#2189C211yesmaximal, characteristic, complemented
12C13×#2188C211yesmaximal, characteristic, complemented
13C13×#2186C211yesmaximal, characteristic
14C13×#2185C211yesmaximal, characteristic, complemented
15C13×#2164C211yesmaximal, characteristic, complemented
16C2×C13×#137—21no—
17C2×C13×#135C2211yescharacteristic
18C22×C13×Q16C2211yescharacteristic
19C13×#542—21no—
20C13×#536—21no—
21C2×C13×Q32C2211yescharacteristic
22C2×C13×Q32C2211yescharacteristic
23C2×C13×Q32C2211yescharacteristic
24C2×C13×SD32C2211yescharacteristic
25C2×C13×SD32C2211yescharacteristic
26C2×C13×SD32C2211yescharacteristic
27C2×C13×SD32C2211yescharacteristic
28C2×C13×D16C2211yescharacteristic
29C13×#500C2211yescharacteristic
30C13×#497—21no—
31C13×#497—21no—
32C13×#495C2211yescharacteristic
33C13×#495C2211yescharacteristic
34C13×#495C2211yescharacteristic
35C13×#494C2211yescharacteristic
36C13×#494C2211yescharacteristic
37C13×#489—21no—
38C13×#468—21no—
39C13×#467C2211yescharacteristic
40C13×#466C2211yescharacteristic
41C13×#440—21no—
42C4×C13×Q16C2211yescharacteristic
43C4×C13×D8C2211yescharacteristic
44C13×#405C2211yescharacteristic
45C13×C4⋊C16C2211yescharacteristic
46C13×C4⋊C16C2211yescharacteristic
47C13×#358C2211yescharacteristic
48C13×#358C2211yescharacteristic
49C13×#358C2211yescharacteristic
50C13×#358C2211yescharacteristic
51C13×#358C2211yescharacteristic
52C13×#358C2211yescharacteristic
53C13×#357C2211yescharacteristic
54C13×#357C2211yescharacteristic
55C13×C22⋊C16C2211yescharacteristic
56C13×C22⋊C16C2211yescharacteristic
57C13×#346C2211yescharacteristic
58C4×C13×C16C2211yescharacteristic
59C2×C13×#41—21no—
60C22×Q8×C13—21no—
61C13×#137—44no—
62C13×#135—41no—
63C13×#135—41no—
64C2×C13×Q16—21no—
65C2×C13×Q16—21no—
66C2×C13×Q16—21no—
67C2×C13×Q16—41no—
68C2×C13×Q16—41no—
69C2×C13×Q16C2311yescharacteristic
70C2×C13×Q16C2311yescharacteristic
71C2×C13×Q16C2311yescharacteristic
72C2×C13×Q16C2311yescharacteristic
73C2×C13×SD16—21no—
74C2×C13×SD16—21no—
75C2×C13×SD16—21no—
76C2×C13×SD16—21no—
77C2×C13×D8C2311yescharacteristic
78C2×C13×D8C2311yescharacteristic
79C2×C13×M16D411yescharacteristic
80C22×C8×C13C2311yescharacteristic
81C13×C4⋊Q8—21no—
82C13×C4⋊Q8—21no—
83C13×C4⋊Q8—21no—
84C13×#126—41no—
85C13×#124—21no—
86C13×#124—21no—
87C13×#124—21no—
88C13×#124—41no—
89C13×#123—41no—
90C13×#123—41no—
91C13×#123—41no—
92C13×C22⋊Q8—21no—
93C13×C22⋊Q8—41no—
94C13×C22⋊Q8—41no—
95C13×C22⋊Q8—41no—
96C13×#121—21no—
97C4×Q8×C13—21no—
98C4×D4×C13—21no—
99C13×#117D411yescharacteristic
100C13×Q32—41no—
101C13×Q32—41no—
102C13×Q32—41no—
103C13×SD32—41no—
104C13×SD32—41no—
105C13×SD32—41no—
106C13×SD32—41no—
107C13×D16—41no—
108C2×C13×C16C2311yescharacteristic
109C2×C13×C16C2311yescharacteristic
110C2×C13×C16C2311yescharacteristic
111C2×C13×C16C2311yescharacteristic
112C13×#107—21no—
113C13×#107C2311yescharacteristic
114C13×#107C2311yescharacteristic
115C13×#103—21no—
116C13×#103—21no—
117C13×#102—21no—
118C13×#102—21no—
119C13×#97D411yescharacteristic
120C13×#97D411yescharacteristic
121C4×C8×C13C2311yescharacteristic
122C4×C8×C13C2311yescharacteristic
123#33791C1311yesmaximal, characteristic, direct product factor, Sylow
124C13×#41—42no—
125C13×#41—42no—
126C2×Q8×C13—21no—
127C2×Q8×C13—21no—
128C2×Q8×C13—21no—
129C2×Q8×C13—21no—
130C2×Q8×C13—42no—
131C2×Q8×C13—42no—
132C2×Q8×C13—41no—
133C2×Q8×C13—41no—
134C2×D4×C13—21no—
135C2×D4×C13—21no—
136C2×D4×C13—41no—
137C2×D4×C13—41no—
138C22×C4×C13—41no—
139C22×C4×C13—41no—
140C22×C4×C13—41no—
141C22×C4×C13C2×D411yescharacteristic
142C13×Q16—21no—
143C13×Q16—21no—
144C13×Q16—21no—
145C13×Q16—21no—
146C13×Q16—21no—
147C13×Q16—21no—
148C13×Q16—21no—
149C13×Q16—21no—
150C13×Q16—42no—
151C13×Q16—42no—
152C13×Q16—42no—
153C13×SD16—42no—
154C13×SD16—42no—
155C13×SD16—42no—
156C13×SD16—42no—
157C13×D8—21no—
158C13×D8—21no—
159C13×D8—21no—
160C13×D8—21no—
161C13×M16—22no—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
164C2×C8×C13C2×D411yescharacteristic
165C2×C8×C13C2×D411yescharacteristic
166C2×C8×C13C2×D411yescharacteristic
167C2×C8×C13C2411yescharacteristic
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—41no—
171C13×C4⋊C4—41no—
172C13×C4⋊C4—41no—
173C13×C4⋊C4—41no—
174C13×C4⋊C4—41no—
175C13×C4⋊C4—41no—
176C13×C4⋊C4—41no—
177C13×C4⋊C4D811yescharacteristic
178C13×C4⋊C4D811yescharacteristic
179C13×C22⋊C4—41no—
180C13×C22⋊C4—41no—
181C13×C22⋊C4—41no—
182C13×C22⋊C4—41no—
183C13×C22⋊C4—41no—
184C13×C22⋊C4—41no—
185C13×C22⋊C4—41no—
186C13×C22⋊C4—41no—
187C13×C22⋊C4—41no—
188C13×C22⋊C4D811yescharacteristic
189C13×C22⋊C4D811yescharacteristic
190C42×C13—41no—
191C42×C13C2×D411yescharacteristic
192C42×C13C2×D411yescharacteristic
193C13×C16—21no—
194C13×C16—21no—
195C13×C16—21no—
196C13×C16—21no—
197#3175C2×C1311yescharacteristic, complemented
198#3156C2×C1311yescharacteristic, complemented
199#2251C2×C1311yescharacteristic, complemented
200#2249C2×C1311yescharacteristic, complemented
201#2243C2×C1311yescharacteristic, complemented
202#2241C2×C1311yescharacteristic, complemented
203#2211C2×C1311yescharacteristic, complemented
204#2210C2×C1311yescharacteristic, complemented
205#2209C2×C1311yescharacteristic, complemented
206#2208C2×C1311yescharacteristic, complemented
207#2189C2×C1311yescharacteristic, complemented
208#2188C2×C1311yescharacteristic, complemented
209#2186C2×C1311yescharacteristic
210#2185C2×C1311yescharacteristic, complemented
211#2164C2×C1311yescharacteristic, complemented
212C23×C13—41no—
213C23×C13—41no—
214C23×C13C2×D811yescharacteristic
215Q8×C13—41no—
216Q8×C13—41no—
217Q8×C13—41no—
218Q8×C13—41no—
219Q8×C13—41no—
220Q8×C13—41no—
221Q8×C13—41no—
222Q8×C13—41no—
223Q8×C13—82no—
224Q8×C13—161no—
225D4×C13—41no—
226D4×C13—41no—
227D4×C13—41no—
228D4×C13—41no—
229D4×C13—82no—
230D4×C13—161no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—82no—
240C2×C4×C13—82no—
241C2×C4×C13—161no—
242C2×C4×C13C2×D811yescharacteristic
243C2×C4×C13C2×D811yescharacteristic
244C2×C4×C13C2×D811yescharacteristic
245C2×C4×C13C2×D811yescharacteristic
246C2×C4×C13C2×D811yescharacteristic
247C2×C4×C13C22×D411yescharacteristic
248C8×C13—21no—
249C8×C13—21no—
250C8×C13AGL(1,ℤ/8)12yes—
251C8×C13H(5,𝔽2)11yescharacteristic
252C8×C13H(5,𝔽2)11yescharacteristic
253C2×#137—21no—
254C2×#135C22×C1311yescharacteristic
255C22×Q16C22×C1311yescharacteristic
256#542—21no—
257#536—21no—
258C2×Q32C22×C1311yescharacteristic
259C2×Q32C22×C1311yescharacteristic
260C2×Q32C22×C1311yescharacteristic
261C2×SD32C22×C1311yescharacteristic
262C2×SD32C22×C1311yescharacteristic
263C2×SD32C22×C1311yescharacteristic
264C2×SD32C22×C1311yescharacteristic
265C2×D16C22×C1311yescharacteristic
266#500C22×C1311yescharacteristic
267#497—21no—
268#497—21no—
269#495C22×C1311yescharacteristic
270#495C22×C1311yescharacteristic
271#495C22×C1311yescharacteristic
272#494C22×C1311yescharacteristic
273#494C22×C1311yescharacteristic
274#489—21no—
275#468—21no—
276#467C22×C1311yescharacteristic
277#466C22×C1311yescharacteristic
278#440—21no—
279C4×Q16C22×C1311yescharacteristic
280C4×D8C22×C1311yescharacteristic
281#405C22×C1311yescharacteristic
282C4⋊C16C22×C1311yescharacteristic
283C4⋊C16C22×C1311yescharacteristic
284#358C22×C1311yescharacteristic
285#358C22×C1311yescharacteristic
286#358C22×C1311yescharacteristic
287#358C22×C1311yescharacteristic
288#358C22×C1311yescharacteristic
289#358C22×C1311yescharacteristic
290#357C22×C1311yescharacteristic
291#357C22×C1311yescharacteristic
292C22⋊C16C22×C1311yescharacteristic
293C22⋊C16C22×C1311yescharacteristic
294#346C22×C1311yescharacteristic
295C4×C16C22×C1311yescharacteristic
296C22×C13—21no—
297C22×C13—21no—
298C22×C13—21no—
299C22×C13—81no—
300C22×C13—81no—
301C22×C13—81no—
302C22×C13—81no—
303C22×C13—81no—
304C22×C13—81no—
305C22×C13C22×D811yescharacteristic
306C4×C13—21no—
307C4×C13—21no—
308C4×C13—21no—
309C4×C13—21no—
310C4×C13—21no—
311C4×C13—81no—
312C4×C13—81no—
313C4×C13—81no—
314C4×C13—81no—
315C4×C13—81no—
316C4×C13—81no—
317C4×C13#53511yescharacteristic
318C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
319C2×#41—21no—
320C22×Q8—21no—
321#137—44no—
322#135—41no—
323#135—41no—
324C2×Q16—21no—
325C2×Q16—21no—
326C2×Q16—21no—
327C2×Q16—41no—
328C2×Q16—41no—
329C2×Q16C23×C1311yescharacteristic
330C2×Q16C23×C1311yescharacteristic
331C2×Q16C23×C1311yescharacteristic
332C2×Q16C23×C1311yescharacteristic
333C2×SD16—21no—
334C2×SD16—21no—
335C2×SD16—21no—
336C2×SD16—21no—
337C2×D8C23×C1311yescharacteristic
338C2×D8C23×C1311yescharacteristic
339C2×M16D4×C1311yescharacteristic
340C22×C8C23×C1311yescharacteristic
341C4⋊Q8—21no—
342C4⋊Q8—21no—
343C4⋊Q8—21no—
344#126—41no—
345#124—21no—
346#124—21no—
347#124—21no—
348#124—41no—
349#123—41no—
350#123—41no—
351#123—41no—
352C22⋊Q8—21no—
353C22⋊Q8—41no—
354C22⋊Q8—41no—
355C22⋊Q8—41no—
356#121—21no—
357C4×Q8—21no—
358C4×D4—21no—
359#117D4×C1311yescharacteristic
360Q32—41no—
361Q32—41no—
362Q32—41no—
363SD32—41no—
364SD32—41no—
365SD32—41no—
366SD32—41no—
367D16—41no—
368C2×C16C23×C1311yescharacteristic
369C2×C16C23×C1311yescharacteristic
370C2×C16C23×C1311yescharacteristic
371C2×C16C23×C1311yescharacteristic
372#107—21no—
373#107C23×C1311yescharacteristic
374#107C23×C1311yescharacteristic
375#103—21no—
376#103—21no—
377#102—21no—
378#102—21no—
379#97D4×C1311yescharacteristic
380#97D4×C1311yescharacteristic
381C4×C8C23×C1311yescharacteristic
382C4×C8C23×C1311yescharacteristic
383C2×C13—41no—
384C2×C13—161no—
385C2×C13—161no—
386C2×C13#320511yescharacteristic
387C2×C13#341611yescharacteristic
388C2×C13#341711yescharacteristic
389#41—42no—
390#41—42no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8—42no—
396C2×Q8—42no—
397C2×Q8—41no—
398C2×Q8—41no—
399C2×D4—21no—
400C2×D4—21no—
401C2×D4—41no—
402C2×D4—41no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4—41no—
406C22×C4C2×D4×C1311yescharacteristic
407Q16—21no—
408Q16—21no—
409Q16—21no—
410Q16—21no—
411Q16—21no—
412Q16—21no—
413Q16—21no—
414Q16—21no—
415Q16—42no—
416Q16—42no—
417Q16—42no—
418SD16—42no—
419SD16—42no—
420SD16—42no—
421SD16—42no—
422D8—21no—
423D8—21no—
424D8—21no—
425D8—21no—
426M16—22no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8C2×D4×C1311yescharacteristic
430C2×C8C2×D4×C1311yescharacteristic
431C2×C8C2×D4×C1311yescharacteristic
432C2×C8C24×C1311yescharacteristic
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—41no—
436C4⋊C4—41no—
437C4⋊C4—41no—
438C4⋊C4—41no—
439C4⋊C4—41no—
440C4⋊C4—41no—
441C4⋊C4—41no—
442C4⋊C4C13×D811yescharacteristic
443C4⋊C4C13×D811yescharacteristic
444C22⋊C4—41no—
445C22⋊C4—41no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C22⋊C4—41no—
449C22⋊C4—41no—
450C22⋊C4—41no—
451C22⋊C4—41no—
452C22⋊C4—41no—
453C22⋊C4C13×D811yescharacteristic
454C22⋊C4C13×D811yescharacteristic
455C42—41no—
456C42C2×D4×C1311yescharacteristic
457C42C2×D4×C1311yescharacteristic
458C16—21no—
459C16—21no—
460C16—21no—
461C16—21no—
462C13#3379111yescharacteristic, direct product factor, Sylow
463C23—41no—
464C23—41no—
465C23C2×C13×D811yescharacteristic
466Q8—41no—
467Q8—41no—
468Q8—41no—
469Q8—41no—
470Q8—41no—
471Q8—41no—
472Q8—41no—
473Q8—41no—
474Q8—82no—
475Q8—161no—
476D4—41no—
477D4—41no—
478D4—41no—
479D4—41no—
480D4—82no—
481D4—161no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—82no—
491C2×C4—82no—
492C2×C4—161no—
493C2×C4C2×C13×D811yescharacteristic
494C2×C4C2×C13×D811yescharacteristic
495C2×C4C2×C13×D811yescharacteristic
496C2×C4C2×C13×D811yescharacteristic
497C2×C4C2×C13×D811yescharacteristic
498C2×C4C22×D4×C1311yescharacteristic
499C8—21no—
500C8—21no—
501C8C13×AGL(1,ℤ/8)12yes—
502C8C13×H(5,𝔽2)11yescharacteristic
503C8C13×H(5,𝔽2)11yescharacteristic
504C22—21no—
505C22—21no—
506C22—21no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22C22×C13×D811yescharacteristic
514C4—21no—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—21no—
519C4—81no—
520C4—81no—
521C4—81no—
522C4—81no—
523C4—81no—
524C4—81no—
525C4C13×#53511yescharacteristic
526C4C2×C13×AGL(1,ℤ/8)11yescharacteristic
527C2—41no—
528C2—161no—
529C2—161no—
530C2C13×#320511yescharacteristic
531C2C13×#341611yescharacteristic
532C2C13×#341711yescharacteristic
subgroupG/H
center, socleC22×C13C22×D8
commutator, Frattini, cosocleC2×C8C24×C13
prime radicalC13×#2186C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C13×#117 ◁ C13×#405 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3175C2semidirect
2. C13×#3156C2semidirect
3. C13×#2251C2semidirect
4. C13×#2249C2semidirect
5. C13×#2243C2semidirect
6. C13×#2241C2semidirect
7. C13×#2211C2semidirect
8. C13×#2210C2semidirect
9. C13×#2209C2semidirect
10. C13×#2208C2semidirect
11. C13×#2189C2semidirect
12. C13×#2188C2semidirect
14. C13×#2185C2semidirect
15. C13×#2164C2semidirect
123. #33791C13direct (N × H)
197. #3175C2×C13semidirect
198. #3156C2×C13semidirect
199. #2251C2×C13semidirect
200. #2249C2×C13semidirect
201. #2243C2×C13semidirect
202. #2241C2×C13semidirect
203. #2211C2×C13semidirect
204. #2210C2×C13semidirect
205. #2209C2×C13semidirect
206. #2208C2×C13semidirect
207. #2189C2×C13semidirect
208. #2188C2×C13semidirect
210. #2185C2×C13semidirect
211. #2164C2×C13semidirect
462. C13#33791direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31752
C13×#31562
C13×#22512
C13×#22492
C13×#22432
C13×#22412
C13×#22112
C13×#22102
C13×#22092
C13×#22082
C13×#21892
C13×#21882
C13×#21862
C13×#21852
C13×#21642
#3379113