Finite Group Databasebeta

← C13×#33873 #15720212

Subgroups — C13×#33873 #15720212

Order 3328.

602 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3334C211yesmaximal, characteristic, complemented
2C13×#3280C211yesmaximal, characteristic, complemented
3C13×#2243C211yesmaximal, characteristic, complemented
4C13×#2235C211yesmaximal, characteristic, complemented
5C13×#2233C211yesmaximal, characteristic, complemented
6C13×#2226C211yesmaximal, characteristic, complemented
7C13×#2218C211yesmaximal, characteristic, complemented
8C13×#2217C211yesmaximal, characteristic, complemented
9C13×#2210C211yesmaximal, characteristic, complemented
10C13×#2186C211yesmaximal, characteristic, complemented
11C13×#2184C211yesmaximal, characteristic, complemented
12C13×#2177C211yesmaximal, characteristic, complemented
13C13×#2168C211yesmaximal, characteristic, complemented
14C13×#2139C211yesmaximal, characteristic, complemented
15C2×C13×#357C211yesmaximal, characteristic, complemented
16C2×C13×#135C2211yescharacteristic
17C22×C13×D8C2211yescharacteristic
18C13×#547—21no—
19C13×#546—21no—
20C2×C13×SD32C2211yescharacteristic, complemented
21C2×C13×D16C2211yescharacteristic
22C2×C13×D16C2211yescharacteristic
23C2×C13×M32C2211yescharacteristic, complemented
24C22×C13×C16C2211yescharacteristic
25C13×#500C2211yescharacteristic, complemented
26C13×#495C2211yescharacteristic
27C13×#480—21no—
28C13×#480—21no—
29C13×#474—21no—
30C13×#467C2211yescharacteristic
31C13×#466C2211yescharacteristic
32C13×#466C2211yescharacteristic
33C13×#466C2211yescharacteristic, complemented
34C13×#463—21no—
35C13×#450—21no—
36C13×#449—21no—
37C4×C13×D8C2211yescharacteristic
38C4×C13×D8C2211yescharacteristic, complemented
39C8×D4×C13C2211yescharacteristic
40C2×C13×#107C2211yescharacteristic
41C2×C13×#107C2211yescharacteristic, complemented
42C13×#367C2211yescharacteristic, complemented
43C13×#367C2211yescharacteristic, complemented
44C13×#367C2211yescharacteristic, complemented
45C13×C4⋊C16C2211yescharacteristic, complemented
46C13×#358C2211yescharacteristic, complemented
47C13×#358C2211yescharacteristic, complemented
48C13×#358C2211yescharacteristic, complemented
49C13×#357C2211yescharacteristic
50C13×#357C2211yescharacteristic
51C13×#357C2211yescharacteristic
52C13×#357C2211yescharacteristic
53C13×#357C2211yescharacteristic
54C13×#357C2211yescharacteristic
55C13×#357C2211yescharacteristic, complemented
56C13×C22⋊C16C2211yescharacteristic
57C13×C22⋊C16C2211yescharacteristic, complemented
58C13×#346C2211yescharacteristic, complemented
59C2×C13×#41—21no—
60C2×C13×#41—41no—
61C22×D4×C13—21no—
62C13×#135—22no—
63C13×#135—41no—
64C2×C13×Q16C2311yescharacteristic
65C2×C13×SD16—21no—
66C2×C13×SD16—21no—
67C2×C13×D8—22no—
68C2×C13×D8—21no—
69C2×C13×D8—41no—
70C2×C13×D8C2311yescharacteristic
71C2×C13×D8C2311yescharacteristic
72C2×C13×D8C2311yescharacteristic
73C22×C8×C13C2311yescharacteristic
74C22×C8×C13C2311yescharacteristic
75C13×C4⋊Q8—21no—
76C13×#124—21no—
77C13×#123—41no—
78C13×#123—41no—
79C13×#123—41no—
80C13×C22⋊Q8—21no—
81C13×C22⋊Q8—41no—
82C13×#121—21no—
83C13×#121—21no—
84C13×#121—21no—
85C13×#121—41no—
86C13×#120—41no—
87C4×D4×C13—21no—
88C4×D4×C13—21no—
89C4×D4×C13D411yescharacteristic
90C2×C13×C4⋊C4—21no—
91C2×C13×C4⋊C4—21no—
92C2×C13×C22⋊C4—41no—
93C13×SD32—41no—
94C13×D16—22no—
95C13×D16—41no—
96C13×M32—41no—
97C2×C13×C16—41no—
98C2×C13×C16C2311yescharacteristic
99C2×C13×C16C2311yescharacteristic
100C2×C13×C16C2311yescharacteristic
101C2×C13×C16C2311yescharacteristic
102C13×#107—21no—
103C13×#107—21no—
104C13×#107—21no—
105C13×#107C2311yescharacteristic
106C13×#107C2311yescharacteristic
107C13×#107C2311yescharacteristic
108C13×#107C2311yescharacteristic
109C13×C4⋊C8D411yescharacteristic
110C13×#103—21no—
111C13×#102—21no—
112C13×#102—21no—
113C13×#102—21no—
114C13×#102—21no—
115C13×#102—21no—
116C13×C22⋊C8D411yescharacteristic
117C13×C22⋊C8D411yescharacteristic
118C4×C8×C13C2311yescharacteristic
119#33873C1311yesmaximal, characteristic, direct product factor, Sylow
120C24×C13—41no—
121C13×#41—42no—
122C13×#41—81no—
123C13×#41—84no—
124C2×Q8×C13—21no—
125C2×Q8×C13—41no—
126C2×D4×C13—21no—
127C2×D4×C13—21no—
128C2×D4×C13—21no—
129C2×D4×C13—42no—
130C2×D4×C13—41no—
131C2×D4×C13—41no—
132C2×D4×C13—41no—
133C2×D4×C13—41no—
134C2×D4×C13—41no—
135C2×D4×C13—81no—
136C2×D4×C13D811yescharacteristic
137C22×C4×C13—41no—
138C22×C4×C13—41no—
139C22×C4×C13—41no—
140C22×C4×C13—41no—
141C22×C4×C13—41no—
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C13×Q16—21no—
145C13×Q16—21no—
146C13×SD16—42no—
147C13×SD16—81no—
148C13×D8—21no—
149C13×D8—21no—
150C13×D8—21no—
151C13×D8—21no—
152C13×D8—21no—
153C13×D8—42no—
154C13×D8#4112yescomplemented
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13C2×D411yescharacteristic
160C2×C8×C13C2×D411yescharacteristic
161C2×C8×C13C2×D411yescharacteristic
162C2×C8×C13C2411yescharacteristic
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—41no—
168C13×C4⋊C4—41no—
169C13×C4⋊C4—41no—
170C13×C4⋊C4—41no—
171C13×C4⋊C4D811yescharacteristic
172C13×C22⋊C4—41no—
173C13×C22⋊C4—41no—
174C13×C22⋊C4—41no—
175C13×C22⋊C4—41no—
176C13×C22⋊C4—41no—
177C13×C22⋊C4—41no—
178C13×C22⋊C4—41no—
179C13×C22⋊C4—41no—
180C13×C22⋊C4D811yescharacteristic
181C13×C22⋊C4D811yescharacteristic
182C42×C13C2×D411yescharacteristic
183C13×C16—21no—
184C13×C16—21no—
185C13×C16—21no—
186C13×C16—21no—
187#3334C2×C1311yescharacteristic, complemented
188#3280C2×C1311yescharacteristic, complemented
189#2243C2×C1311yescharacteristic, complemented
190#2235C2×C1311yescharacteristic, complemented
191#2233C2×C1311yescharacteristic, complemented
192#2226C2×C1311yescharacteristic, complemented
193#2218C2×C1311yescharacteristic, complemented
194#2217C2×C1311yescharacteristic, complemented
195#2210C2×C1311yescharacteristic, complemented
196#2186C2×C1311yescharacteristic, complemented
197#2184C2×C1311yescharacteristic, complemented
198#2177C2×C1311yescharacteristic, complemented
199#2168C2×C1311yescharacteristic, complemented
200#2139C2×C1311yescharacteristic, complemented
201C2×#357C2×C1311yescharacteristic, complemented
202C23×C13—41no—
203C23×C13—41no—
204C23×C13—41no—
205C23×C13—82no—
206C23×C13—82no—
207C23×C13—161no—
208C23×C13C2×D811yescharacteristic
209C23×C13C2×D811yescharacteristic
210Q8×C13—41no—
211Q8×C13—41no—
212Q8×C13—82no—
213D4×C13—22no—
214D4×C13—22no—
215D4×C13—41no—
216D4×C13—41no—
217D4×C13—41no—
218D4×C13—41no—
219D4×C13—41no—
220D4×C13—82no—
221D4×C13—82no—
222D4×C13—82no—
223D4×C13—82no—
224D4×C13—161no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—82no—
235C2×C4×C13—82no—
236C2×C4×C13—82no—
237C2×C4×C13—82no—
238C2×C4×C13—161no—
239C2×C4×C13C2×D811yescharacteristic
240C2×C4×C13C2×D811yescharacteristic
241C2×C4×C13C2×D811yescharacteristic
242C2×C4×C13C2×D811yescharacteristic
243C2×C4×C13C22×D411yescharacteristic
244C8×C13—21no—
245C8×C13—21no—
246C8×C13—21no—
247C8×C13C2×#4111yescharacteristic
248C8×C13H(5,𝔽2)11yescharacteristic
249C2×#135C22×C1311yescharacteristic
250C22×D8C22×C1311yescharacteristic
251#547—21no—
252#546—21no—
253C2×SD32C22×C1311yescharacteristic, complemented
254C2×D16C22×C1311yescharacteristic
255C2×D16C22×C1311yescharacteristic
256C2×M32C22×C1311yescharacteristic, complemented
257C22×C16C22×C1311yescharacteristic
258#500C22×C1311yescharacteristic, complemented
259#495C22×C1311yescharacteristic
260#480—21no—
261#480—21no—
262#474—21no—
263#467C22×C1311yescharacteristic
264#466C22×C1311yescharacteristic
265#466C22×C1311yescharacteristic
266#466C22×C1311yescharacteristic, complemented
267#463—21no—
268#450—21no—
269#449—21no—
270C4×D8C22×C1311yescharacteristic
271C4×D8C22×C1311yescharacteristic, complemented
272C8×D4C22×C1311yescharacteristic
273C2×#107C22×C1311yescharacteristic
274C2×#107C22×C1311yescharacteristic, complemented
275#367C22×C1311yescharacteristic, complemented
276#367C22×C1311yescharacteristic, complemented
277#367C22×C1311yescharacteristic, complemented
278C4⋊C16C22×C1311yescharacteristic, complemented
279#358C22×C1311yescharacteristic, complemented
280#358C22×C1311yescharacteristic, complemented
281#358C22×C1311yescharacteristic, complemented
282#357C22×C1311yescharacteristic
283#357C22×C1311yescharacteristic
284#357C22×C1311yescharacteristic
285#357C22×C1311yescharacteristic
286#357C22×C1311yescharacteristic
287#357C22×C1311yescharacteristic
288#357C22×C1311yescharacteristic, complemented
289C22⋊C16C22×C1311yescharacteristic
290C22⋊C16C22×C1311yescharacteristic, complemented
291#346C22×C1311yescharacteristic, complemented
292C22×C13—21no—
293C22×C13—21no—
294C22×C13—21no—
295C22×C13—21no—
296C22×C13—21no—
297C22×C13—42no—
298C22×C13—81no—
299C22×C13—81no—
300C22×C13—81no—
301C22×C13—81no—
302C22×C13—81no—
303C22×C13—81no—
304C22×C13—81no—
305C22×C13—81no—
306C22×C13—164no—
307C22×C13#50912yes—
308C22×C13C22×D811yescharacteristic
309C4×C13—21no—
310C4×C13—21no—
311C4×C13—21no—
312C4×C13—21no—
313C4×C13—81no—
314C4×C13—81no—
315C4×C13—81no—
316C4×C13—81no—
317C4×C13—81no—
318C4×C13#54611yescharacteristic
319C4×C13#57711yescharacteristic
320C2×#41—21no—
321C2×#41—41no—
322C22×D4—21no—
323#135—22no—
324#135—41no—
325C2×Q16C23×C1311yescharacteristic
326C2×SD16—21no—
327C2×SD16—21no—
328C2×D8—22no—
329C2×D8—21no—
330C2×D8—41no—
331C2×D8C23×C1311yescharacteristic
332C2×D8C23×C1311yescharacteristic
333C2×D8C23×C1311yescharacteristic
334C22×C8C23×C1311yescharacteristic
335C22×C8C23×C1311yescharacteristic
336C4⋊Q8—21no—
337#124—21no—
338#123—41no—
339#123—41no—
340#123—41no—
341C22⋊Q8—21no—
342C22⋊Q8—41no—
343#121—21no—
344#121—21no—
345#121—21no—
346#121—41no—
347#120—41no—
348C4×D4—21no—
349C4×D4—21no—
350C4×D4D4×C1311yescharacteristic
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C22⋊C4—41no—
354SD32—41no—
355D16—22no—
356D16—41no—
357M32—41no—
358C2×C16—41no—
359C2×C16C23×C1311yescharacteristic
360C2×C16C23×C1311yescharacteristic
361C2×C16C23×C1311yescharacteristic
362C2×C16C23×C1311yescharacteristic
363#107—21no—
364#107—21no—
365#107—21no—
366#107C23×C1311yescharacteristic
367#107C23×C1311yescharacteristic
368#107C23×C1311yescharacteristic
369#107C23×C1311yescharacteristic
370C4⋊C8D4×C1311yescharacteristic
371#103—21no—
372#102—21no—
373#102—21no—
374#102—21no—
375#102—21no—
376#102—21no—
377C22⋊C8D4×C1311yescharacteristic
378C22⋊C8D4×C1311yescharacteristic
379C4×C8C23×C1311yescharacteristic
380C2×C13—22no—
381C2×C13—41no—
382C2×C13—82no—
383C2×C13—161no—
384C2×C13—161no—
385C2×C13#329411yescharacteristic
386C2×C13C2×#50911yescharacteristic
387C2×C13#341611yescharacteristic
388C24—41no—
389#41—42no—
390#41—81no—
391#41—84no—
392C2×Q8—21no—
393C2×Q8—41no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—42no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—81no—
404C2×D4C13×D811yescharacteristic
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4C2×D4×C1311yescharacteristic
411C22×C4C2×D4×C1311yescharacteristic
412Q16—21no—
413Q16—21no—
414SD16—42no—
415SD16—81no—
416D8—21no—
417D8—21no—
418D8—21no—
419D8—21no—
420D8—21no—
421D8—42no—
422D8C13×#4112yescomplemented
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8C2×D4×C1311yescharacteristic
428C2×C8C2×D4×C1311yescharacteristic
429C2×C8C2×D4×C1311yescharacteristic
430C2×C8C24×C1311yescharacteristic
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—41no—
436C4⋊C4—41no—
437C4⋊C4—41no—
438C4⋊C4—41no—
439C4⋊C4C13×D811yescharacteristic
440C22⋊C4—41no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—41no—
444C22⋊C4—41no—
445C22⋊C4—41no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C22⋊C4C13×D811yescharacteristic
449C22⋊C4C13×D811yescharacteristic
450C42C2×D4×C1311yescharacteristic
451C16—21no—
452C16—21no—
453C16—21no—
454C16—21no—
455C13#3387311yescharacteristic, direct product factor, Sylow
456C23—41no—
457C23—41no—
458C23—41no—
459C23—82no—
460C23—82no—
461C23—161no—
462C23C2×C13×D811yescharacteristic
463C23C2×C13×D811yescharacteristic
464Q8—41no—
465Q8—41no—
466Q8—82no—
467D4—22no—
468D4—22no—
469D4—41no—
470D4—41no—
471D4—41no—
472D4—41no—
473D4—41no—
474D4—82no—
475D4—82no—
476D4—82no—
477D4—82no—
478D4—161no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—82no—
489C2×C4—82no—
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×C4C22×D4×C1311yescharacteristic
498C8—21no—
499C8—21no—
500C8—21no—
501C8C2×C13×#4111yescharacteristic
502C8C13×H(5,𝔽2)11yescharacteristic
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—42no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22—81no—
514C22—81no—
515C22—81no—
516C22—81no—
517C22—164no—
518C22C13×#50912yes—
519C22C22×C13×D811yescharacteristic
520C4—21no—
521C4—21no—
522C4—21no—
523C4—21no—
524C4—81no—
525C4—81no—
526C4—81no—
527C4—81no—
528C4—81no—
529C4C13×#54611yescharacteristic
530C4C13×#57711yescharacteristic
531C2—22no—
532C2—41no—
533C2—82no—
534C2—161no—
535C2—161no—
536C2C13×#329411yescharacteristic
537C2C2×C13×#50911yescharacteristic
538C2C13×#341611yescharacteristic
subgroupG/H
center, socleC22×C13C22×D8
commutator, Frattini, cosocleC2×C8C24×C13
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C4×D4×C13 ◁ C8×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3334C2semidirect
2. C13×#3280C2semidirect
3. C13×#2243C2semidirect
4. C13×#2235C2semidirect
5. C13×#2233C2semidirect
6. C13×#2226C2semidirect
7. C13×#2218C2semidirect
8. C13×#2217C2semidirect
9. C13×#2210C2semidirect
10. C13×#2186C2semidirect
11. C13×#2184C2semidirect
12. C13×#2177C2semidirect
13. C13×#2168C2semidirect
14. C13×#2139C2semidirect
15. C2×C13×#357C2semidirect
20. C2×C13×SD32C22semidirect
23. C2×C13×M32C22semidirect
25. C13×#500C22semidirect
33. C13×#466C22semidirect
38. C4×C13×D8C22semidirect
41. C2×C13×#107C22semidirect
42. C13×#367C22semidirect
43. C13×#367C22semidirect
44. C13×#367C22semidirect
45. C13×C4⋊C16C22semidirect
46. C13×#358C22semidirect
47. C13×#358C22semidirect
48. C13×#358C22semidirect
55. C13×#357C22semidirect
57. C13×C22⋊C16C22semidirect
58. C13×#346C22semidirect
119. #33873C13direct (N × H)
154. C13×D8#41semidirect
187. #3334C2×C13semidirect
188. #3280C2×C13semidirect
189. #2243C2×C13semidirect
190. #2235C2×C13semidirect
191. #2233C2×C13semidirect
192. #2226C2×C13semidirect
193. #2218C2×C13semidirect
194. #2217C2×C13semidirect
195. #2210C2×C13semidirect
196. #2186C2×C13semidirect
197. #2184C2×C13semidirect
198. #2177C2×C13semidirect
199. #2168C2×C13semidirect
200. #2139C2×C13semidirect
201. C2×#357C2×C13semidirect
253. C2×SD32C22×C13semidirect
256. C2×M32C22×C13semidirect
258. #500C22×C13semidirect
266. #466C22×C13semidirect
271. C4×D8C22×C13semidirect
274. C2×#107C22×C13semidirect
275. #367C22×C13semidirect
276. #367C22×C13semidirect
277. #367C22×C13semidirect
278. C4⋊C16C22×C13semidirect
279. #358C22×C13semidirect
280. #358C22×C13semidirect
281. #358C22×C13semidirect
288. #357C22×C13semidirect
290. C22⋊C16C22×C13semidirect
291. #346C22×C13semidirect
422. D8C13×#41semidirect
455. C13#33873direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#33342
C13×#32802
C13×#22432
C13×#22352
C13×#22332
C13×#22262
C13×#22182
C13×#22172
C13×#22102
C13×#21862
C13×#21842
C13×#21772
C13×#21682
C13×#21392
C2×C13×#3572
#3387313