Finite Group Databasebeta

← C13×#33767 #15720106

Subgroups — C13×#33767 #15720106

Order 3328.

564 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3061C211yesmaximal, characteristic
2C13×#3059C211yesmaximal, characteristic, complemented
3C13×#2237C211yesmaximal, characteristic, complemented
4C13×#2236C211yesmaximal, characteristic, complemented
5C13×#2235C211yesmaximal, characteristic, complemented
6C13×#2234C211yesmaximal, characteristic, complemented
7C13×#2220C211yesmaximal, characteristic, complemented
8C13×#2219C211yesmaximal, characteristic, complemented
9C13×#2217C211yesmaximal, characteristic, complemented
10C13×#2216C211yesmaximal, characteristic, complemented
11C13×#2189C211yesmaximal, characteristic, complemented
12C13×#2189C211yesmaximal, characteristic, complemented
13C13×#2188C211yesmaximal, characteristic, complemented
14C13×#2185C211yesmaximal, characteristic, complemented
15C13×#2113C211yesmaximal, characteristic, complemented
16C2×C13×#135C2211yescharacteristic
17C22×C13×Q16C2211yescharacteristic
18C2×C13×#131C2211yescharacteristic
19C13×#537—21no—
20C13×#536—21no—
21C2×C13×Q32C2211yescharacteristic
22C2×C13×Q32C2211yescharacteristic
23C2×C13×SD32C2211yescharacteristic
24C2×C13×SD32C2211yescharacteristic
25C2×C13×M32C2211yescharacteristic
26C22×C13×C16C2211yescharacteristic
27C13×#470—21no—
28C13×#470—21no—
29C13×#468—21no—
30C13×#468—21no—
31C13×#467C2211yescharacteristic
32C13×#467C2211yescharacteristic
33C13×#467C2211yescharacteristic
34C13×#467C2211yescharacteristic
35C13×#467C2211yescharacteristic
36C13×#467C2211yescharacteristic
37C13×#466C2211yescharacteristic
38C13×#466C2211yescharacteristic
39C13×#427C2211yescharacteristic
40C2×C13×#107C2211yescharacteristic
41C13×#419—21no—
42C13×#417—21no—
43C13×#367C2211yescharacteristic
44C13×#367C2211yescharacteristic
45C13×#366C2211yescharacteristic
46C13×#366C2211yescharacteristic
47C13×#358C2211yescharacteristic
48C13×#358C2211yescharacteristic
49C13×#358C2211yescharacteristic
50C13×#358C2211yescharacteristic
51C13×#358C2211yescharacteristic
52C13×#358C2211yescharacteristic
53C13×#357C2211yescharacteristic
54C13×#357C2211yescharacteristic
55C13×C22⋊C16C2211yescharacteristic
56C13×C22⋊C16C2211yescharacteristic
57C13×C22⋊C16C2211yescharacteristic
58C13×C22⋊C16C2211yescharacteristic
59C2×C13×#41—21no—
60C2×C13×#41D411yescharacteristic
61C22×Q8×C13—21no—
62C13×#135—41no—
63C13×#135—41no—
64C2×C13×Q16—21no—
65C2×C13×Q16—41no—
66C2×C13×Q16—41no—
67C2×C13×Q16C2311yescharacteristic
68C2×C13×Q16C2311yescharacteristic
69C2×C13×Q16C2311yescharacteristic
70C2×C13×SD16—21no—
71C2×C13×D8C2311yescharacteristic
72C13×#131—41no—
73C13×#131—41no—
74C2×C13×M16D411yescharacteristic
75C2×C13×M16D411yescharacteristic
76C2×C13×M16D411yescharacteristic
77C22×C8×C13C2311yescharacteristic
78C22×C8×C13C2311yescharacteristic
79C22×C8×C13C2311yescharacteristic
80C13×C4⋊Q8—41no—
81C13×#124—41no—
82C13×#123—41no—
83C13×#123—41no—
84C13×C22⋊Q8—21no—
85C13×C22⋊Q8—21no—
86C13×C22⋊Q8—21no—
87C13×C22⋊Q8—21no—
88C13×C22⋊Q8—21no—
89C13×C22⋊Q8—21no—
90C13×C22⋊Q8—41no—
91C13×#121—21no—
92C13×#121—21no—
93C13×#121—41no—
94C13×#121—41no—
95C13×#121—41no—
96C13×#117—21no—
97C2×C13×C4⋊C4—21no—
98C13×Q32—41no—
99C13×Q32—41no—
100C13×SD32—41no—
101C13×SD32—41no—
102C13×M32—41no—
103C2×C13×C16—41no—
104C2×C13×C16C2311yescharacteristic
105C2×C13×C16C2311yescharacteristic
106C2×C13×C16C2311yescharacteristic
107C2×C13×C16C2311yescharacteristic
108C13×#107—21no—
109C13×#107C2311yescharacteristic
110C13×#107C2311yescharacteristic
111C13×#107C2311yescharacteristic
112C13×#107C2311yescharacteristic
113C13×#106—21no—
114C13×#103—21no—
115C13×#103—21no—
116C13×#103—21no—
117C13×#103—21no—
118C13×#103—21no—
119C13×#103—21no—
120C13×#102—21no—
121C13×#102—21no—
122#33767C1311yesmaximal, characteristic, direct product factor, Sylow
123C13×#41—41no—
124C13×#41—41no—
125C13×#41—42no—
126C13×#41—42no—
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×C13D811yescharacteristic
134C2×D4×C13—21no—
135C2×D4×C13—41no—
136C2×D4×C13—41no—
137C2×D4×C13—41no—
138C2×D4×C13D811yescharacteristic
139C2×D4×C13D811yescharacteristic
140C2×D4×C13D811yescharacteristic
141C22×C4×C13—41no—
142C22×C4×C13—41no—
143C22×C4×C13—41no—
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C13×Q16—21no—
148C13×Q16—21no—
149C13×Q16—21no—
150C13×Q16—21no—
151C13×Q16—21no—
152C13×Q16—21no—
153C13×Q16—42no—
154C13×SD16—42no—
155C13×D8—21no—
156C13×D8—21no—
157C13×M16—41no—
158C13×M16—41no—
159C13×M16—41no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13C2×D411yescharacteristic
167C2×C8×C13C2×D411yescharacteristic
168C2×C8×C13C2×D411yescharacteristic
169C2×C8×C13C2411yescharacteristic
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—41no—
175C13×C4⋊C4—41no—
176C13×C4⋊C4—41no—
177C13×C4⋊C4—41no—
178C13×C4⋊C4—41no—
179C13×C4⋊C4—41no—
180C13×C4⋊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⋊C4—41no—
189C13×C22⋊C4—41no—
190C42×C13—41no—
191C13×C16—21no—
192C13×C16—21no—
193C13×C16—21no—
194C13×C16—21no—
195#3061C2×C1311yescharacteristic
196#3059C2×C1311yescharacteristic, complemented
197#2237C2×C1311yescharacteristic, complemented
198#2236C2×C1311yescharacteristic, complemented
199#2235C2×C1311yescharacteristic, complemented
200#2234C2×C1311yescharacteristic, complemented
201#2220C2×C1311yescharacteristic, complemented
202#2219C2×C1311yescharacteristic, complemented
203#2217C2×C1311yescharacteristic, complemented
204#2216C2×C1311yescharacteristic, complemented
205#2189C2×C1311yescharacteristic, complemented
206#2189C2×C1311yescharacteristic, complemented
207#2188C2×C1311yescharacteristic, complemented
208#2185C2×C1311yescharacteristic, complemented
209#2113C2×C1311yescharacteristic, complemented
210C23×C13—41no—
211C23×C13C2×D811yescharacteristic
212C23×C13C2×D811yescharacteristic
213C23×C13C2×D811yescharacteristic
214Q8×C13—41no—
215Q8×C13—41no—
216Q8×C13—41no—
217Q8×C13—41no—
218Q8×C13—41no—
219Q8×C13—41no—
220Q8×C13—41no—
221Q8×C13—82no—
222D4×C13—41no—
223D4×C13—41no—
224D4×C13—41no—
225D4×C13—41no—
226D4×C13—41no—
227D4×C13—82no—
228D4×C13—161no—
229D4×C13—161no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—82no—
244C2×C4×C13—82no—
245C2×C4×C13—161no—
246C2×C4×C13C2×D811yescharacteristic
247C2×C4×C13C2×D811yescharacteristic
248C2×C4×C13C2×D811yescharacteristic
249C2×C4×C13C22×D411yescharacteristic
250C8×C13—21no—
251C8×C13—21no—
252C8×C13—21no—
253C8×C13H(5,𝔽2)11yescharacteristic
254C8×C13H(5,𝔽2)11yescharacteristic
255C2×#135C22×C1311yescharacteristic
256C22×Q16C22×C1311yescharacteristic
257C2×#131C22×C1311yescharacteristic
258#537—21no—
259#536—21no—
260C2×Q32C22×C1311yescharacteristic
261C2×Q32C22×C1311yescharacteristic
262C2×SD32C22×C1311yescharacteristic
263C2×SD32C22×C1311yescharacteristic
264C2×M32C22×C1311yescharacteristic
265C22×C16C22×C1311yescharacteristic
266#470—21no—
267#470—21no—
268#468—21no—
269#468—21no—
270#467C22×C1311yescharacteristic
271#467C22×C1311yescharacteristic
272#467C22×C1311yescharacteristic
273#467C22×C1311yescharacteristic
274#467C22×C1311yescharacteristic
275#467C22×C1311yescharacteristic
276#466C22×C1311yescharacteristic
277#466C22×C1311yescharacteristic
278#427C22×C1311yescharacteristic
279C2×#107C22×C1311yescharacteristic
280#419—21no—
281#417—21no—
282#367C22×C1311yescharacteristic
283#367C22×C1311yescharacteristic
284#366C22×C1311yescharacteristic
285#366C22×C1311yescharacteristic
286#358C22×C1311yescharacteristic
287#358C22×C1311yescharacteristic
288#358C22×C1311yescharacteristic
289#358C22×C1311yescharacteristic
290#358C22×C1311yescharacteristic
291#358C22×C1311yescharacteristic
292#357C22×C1311yescharacteristic
293#357C22×C1311yescharacteristic
294C22⋊C16C22×C1311yescharacteristic
295C22⋊C16C22×C1311yescharacteristic
296C22⋊C16C22×C1311yescharacteristic
297C22⋊C16C22×C1311yescharacteristic
298C22×C13—21no—
299C22×C13—21no—
300C22×C13—21no—
301C22×C13—21no—
302C22×C13—21no—
303C22×C13—21no—
304C22×C13—21no—
305C22×C13—21no—
306C22×C13—21no—
307C22×C13—81no—
308C22×C13—81no—
309C22×C13—81no—
310C22×C13C22×D811yescharacteristic
311C4×C13—21no—
312C4×C13—21no—
313C4×C13—21no—
314C4×C13—81no—
315C4×C13—81no—
316C4×C13—81no—
317C4×C13—81no—
318C4×C13—81no—
319C4×C13—81no—
320C4×C13—81no—
321C4×C13#53411yescharacteristic
322C4×C13#57511yescharacteristic
323C2×#41—21no—
324C2×#41D4×C1311yescharacteristic
325C22×Q8—21no—
326#135—41no—
327#135—41no—
328C2×Q16—21no—
329C2×Q16—41no—
330C2×Q16—41no—
331C2×Q16C23×C1311yescharacteristic
332C2×Q16C23×C1311yescharacteristic
333C2×Q16C23×C1311yescharacteristic
334C2×SD16—21no—
335C2×D8C23×C1311yescharacteristic
336#131—41no—
337#131—41no—
338C2×M16D4×C1311yescharacteristic
339C2×M16D4×C1311yescharacteristic
340C2×M16D4×C1311yescharacteristic
341C22×C8C23×C1311yescharacteristic
342C22×C8C23×C1311yescharacteristic
343C22×C8C23×C1311yescharacteristic
344C4⋊Q8—41no—
345#124—41no—
346#123—41no—
347#123—41no—
348C22⋊Q8—21no—
349C22⋊Q8—21no—
350C22⋊Q8—21no—
351C22⋊Q8—21no—
352C22⋊Q8—21no—
353C22⋊Q8—21no—
354C22⋊Q8—41no—
355#121—21no—
356#121—21no—
357#121—41no—
358#121—41no—
359#121—41no—
360#117—21no—
361C2×C4⋊C4—21no—
362Q32—41no—
363Q32—41no—
364SD32—41no—
365SD32—41no—
366M32—41no—
367C2×C16—41no—
368C2×C16C23×C1311yescharacteristic
369C2×C16C23×C1311yescharacteristic
370C2×C16C23×C1311yescharacteristic
371C2×C16C23×C1311yescharacteristic
372#107—21no—
373#107C23×C1311yescharacteristic
374#107C23×C1311yescharacteristic
375#107C23×C1311yescharacteristic
376#107C23×C1311yescharacteristic
377#106—21no—
378#103—21no—
379#103—21no—
380#103—21no—
381#103—21no—
382#103—21no—
383#103—21no—
384#102—21no—
385#102—21no—
386C2×C13—41no—
387C2×C13—41no—
388C2×C13—41no—
389C2×C13—161no—
390C2×C13#318611yescharacteristic
391C2×C13#341611yescharacteristic
392C2×C13#341711yescharacteristic
393#41—41no—
394#41—41no—
395#41—42no—
396#41—42no—
397C2×Q8—21no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—42no—
401C2×Q8—42no—
402C2×Q8—41no—
403C2×Q8C13×D811yescharacteristic
404C2×D4—21no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4C13×D811yescharacteristic
409C2×D4C13×D811yescharacteristic
410C2×D4C13×D811yescharacteristic
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4C2×D4×C1311yescharacteristic
415C22×C4C2×D4×C1311yescharacteristic
416C22×C4C2×D4×C1311yescharacteristic
417Q16—21no—
418Q16—21no—
419Q16—21no—
420Q16—21no—
421Q16—21no—
422Q16—21no—
423Q16—42no—
424SD16—42no—
425D8—21no—
426D8—21no—
427M16—41no—
428M16—41no—
429M16—41no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8C2×D4×C1311yescharacteristic
437C2×C8C2×D4×C1311yescharacteristic
438C2×C8C2×D4×C1311yescharacteristic
439C2×C8C24×C1311yescharacteristic
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—41no—
445C4⋊C4—41no—
446C4⋊C4—41no—
447C4⋊C4—41no—
448C4⋊C4—41no—
449C4⋊C4—41no—
450C4⋊C4—41no—
451C22⋊C4—41no—
452C22⋊C4—41no—
453C22⋊C4—41no—
454C22⋊C4—41no—
455C22⋊C4—41no—
456C22⋊C4—41no—
457C22⋊C4—41no—
458C22⋊C4—41no—
459C22⋊C4—41no—
460C42—41no—
461C16—21no—
462C16—21no—
463C16—21no—
464C16—21no—
465C13#3376711yescharacteristic, direct product factor, Sylow
466C23—41no—
467C23C2×C13×D811yescharacteristic
468C23C2×C13×D811yescharacteristic
469C23C2×C13×D811yescharacteristic
470Q8—41no—
471Q8—41no—
472Q8—41no—
473Q8—41no—
474Q8—41no—
475Q8—41no—
476Q8—41no—
477Q8—82no—
478D4—41no—
479D4—41no—
480D4—41no—
481D4—41no—
482D4—41no—
483D4—82no—
484D4—161no—
485D4—161no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—82no—
500C2×C4—82no—
501C2×C4—161no—
502C2×C4C2×C13×D811yescharacteristic
503C2×C4C2×C13×D811yescharacteristic
504C2×C4C2×C13×D811yescharacteristic
505C2×C4C22×D4×C1311yescharacteristic
506C8—21no—
507C8—21no—
508C8—21no—
509C8C13×H(5,𝔽2)11yescharacteristic
510C8C13×H(5,𝔽2)11yescharacteristic
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—81no—
521C22—81no—
522C22—81no—
523C22C22×C13×D811yescharacteristic
524C4—21no—
525C4—21no—
526C4—21no—
527C4—81no—
528C4—81no—
529C4—81no—
530C4—81no—
531C4—81no—
532C4—81no—
533C4—81no—
534C4C13×#53411yescharacteristic
535C4C13×#57511yescharacteristic
536C2—41no—
537C2—41no—
538C2—41no—
539C2—161no—
540C2C13×#318611yescharacteristic
541C2C13×#341611yescharacteristic
542C2C13×#341711yescharacteristic
subgroupG/H
center, socleC22×C13C22×D8
commutator, Frattini, cosocleC2×C8C24×C13
prime radicalC13×#3061C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C13×#41 ◁ C2×C13×#131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#3059C2semidirect
3. C13×#2237C2semidirect
4. C13×#2236C2semidirect
5. C13×#2235C2semidirect
6. C13×#2234C2semidirect
7. C13×#2220C2semidirect
8. C13×#2219C2semidirect
9. C13×#2217C2semidirect
10. C13×#2216C2semidirect
11. C13×#2189C2semidirect
12. C13×#2189C2semidirect
13. C13×#2188C2semidirect
14. C13×#2185C2semidirect
15. C13×#2113C2semidirect
122. #33767C13direct (N × H)
196. #3059C2×C13semidirect
197. #2237C2×C13semidirect
198. #2236C2×C13semidirect
199. #2235C2×C13semidirect
200. #2234C2×C13semidirect
201. #2220C2×C13semidirect
202. #2219C2×C13semidirect
203. #2217C2×C13semidirect
204. #2216C2×C13semidirect
205. #2189C2×C13semidirect
206. #2189C2×C13semidirect
207. #2188C2×C13semidirect
208. #2185C2×C13semidirect
209. #2113C2×C13semidirect
465. C13#33767direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#30612
C13×#30592
C13×#22372
C13×#22362
C13×#22352
C13×#22342
C13×#22202
C13×#22192
C13×#22172
C13×#22162
C13×#21892
C13×#21882
C13×#21852
C13×#21132
#3376713