Finite Group Databasebeta

← C13×#33886 #15720225

Subgroups — C13×#33886 #15720225

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×#3341C211yesmaximal, characteristic, complemented
2C13×#3280C211yesmaximal, characteristic, complemented
3C13×#2243C211yesmaximal, characteristic, complemented
4C13×#2237C211yesmaximal, characteristic, complemented
5C13×#2234C211yesmaximal, characteristic, complemented
6C13×#2224C211yesmaximal, characteristic, complemented
7C13×#2220C211yesmaximal, characteristic, complemented
8C13×#2215C211yesmaximal, characteristic, complemented
9C13×#2210C211yesmaximal, characteristic, complemented
10C13×#2186C211yesmaximal, characteristic, complemented
11C13×#2184C211yesmaximal, characteristic, complemented
12C13×#2177C211yesmaximal, characteristic, complemented
13C13×#2168C211yesmaximal, characteristic, complemented
14C13×#2140C211yesmaximal, characteristic, complemented
15C13×#2138C211yesmaximal, characteristic, complemented
16C2×C13×#135C2211yescharacteristic
17C22×C13×D8C2211yescharacteristic
18C13×#555—21no—
19C13×#546—21no—
20C2×C13×SD32C2211yescharacteristic, complemented
21C2×C13×D16C2211yescharacteristic
22C2×C13×D16C2211yescharacteristic
23C2×C13×M32C2211yescharacteristic
24C22×C13×C16C2211yescharacteristic, complemented
25C13×#500C2211yescharacteristic, complemented
26C13×#495C2211yescharacteristic
27C13×#482—21no—
28C13×#482—21no—
29C13×#476—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
40C13×#427C2211yescharacteristic
41C13×#427C2211yescharacteristic, complemented
42C13×#367C2211yescharacteristic, complemented
43C13×#366C2211yescharacteristic, complemented
44C13×#366C2211yescharacteristic, 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—
60C22×D4×C13—21no—
61C13×#135—22no—
62C13×#135—41no—
63C2×C13×Q16C2311yescharacteristic
64C2×C13×SD16—21no—
65C2×C13×SD16—21no—
66C2×C13×D8—22no—
67C2×C13×D8—21no—
68C2×C13×D8—41no—
69C2×C13×D8C2311yescharacteristic
70C2×C13×D8C2311yescharacteristic
71C2×C13×D8C2311yescharacteristic
72C22×C8×C13C2311yescharacteristic
73C22×C8×C13C2311yescharacteristic
74C13×C4⋊Q8—21no—
75C13×#124—21no—
76C13×#124—41no—
77C13×#124—41no—
78C13×#123—41no—
79C13×C22⋊Q8—21no—
80C13×#121—21no—
81C13×#121—21no—
82C13×#121—21no—
83C13×#121—41no—
84C13×#121—41no—
85C13×#120—41no—
86C4×D4×C13—21no—
87C4×D4×C13—21no—
88C4×D4×C13D411yescharacteristic
89C13×#117—21no—
90C13×#117—21no—
91C13×#117—41no—
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×#107C2311yescharacteristic
104C13×#107C2311yescharacteristic
105C13×#107C2311yescharacteristic
106C13×#107C2311yescharacteristic
107C13×#106—21no—
108C13×#106—21no—
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#33886C1311yesmaximal, characteristic, direct product factor, Sylow
120C24×C13—41no—
121C13×#41—42no—
122C13×#41—81no—
123C2×Q8×C13—21no—
124C2×Q8×C13—41no—
125C2×D4×C13—21no—
126C2×D4×C13—21no—
127C2×D4×C13—21no—
128C2×D4×C13—42no—
129C2×D4×C13—41no—
130C2×D4×C13—41no—
131C2×D4×C13—41no—
132C2×D4×C13—41no—
133C2×D4×C13—41no—
134C2×D4×C13—81no—
135C2×D4×C13D811yescharacteristic
136C22×C4×C13—41no—
137C22×C4×C13—41no—
138C22×C4×C13—41no—
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C13×Q16—21no—
142C13×Q16—21no—
143C13×SD16—42no—
144C13×SD16—81no—
145C13×D8—21no—
146C13×D8—21no—
147C13×D8—21no—
148C13×D8—21no—
149C13×D8—21no—
150C13×D8—42no—
151C13×D8#4112yes—
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C2×C8×C13—21no—
155C2×C8×C13—21no—
156C2×C8×C13C2×D411yescharacteristic
157C2×C8×C13C2×D411yescharacteristic
158C2×C8×C13C2×D411yescharacteristic
159C2×C8×C13C2411yescharacteristic
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—41no—
165C13×C4⋊C4—41no—
166C13×C4⋊C4D811yescharacteristic
167C13×C22⋊C4—41no—
168C13×C22⋊C4—41no—
169C13×C22⋊C4—41no—
170C13×C22⋊C4—41no—
171C13×C22⋊C4—41no—
172C13×C22⋊C4—41no—
173C13×C22⋊C4—41no—
174C13×C22⋊C4—41no—
175C13×C22⋊C4—41no—
176C13×C22⋊C4—41no—
177C13×C22⋊C4D811yescharacteristic
178C13×C22⋊C4D811yescharacteristic
179C42×C13—41no—
180C42×C13—41no—
181C42×C13C2×D411yescharacteristic
182C13×C16—21no—
183C13×C16—21no—
184C13×C16—21no—
185C13×C16—21no—
186#3341C2×C1311yescharacteristic, complemented
187#3280C2×C1311yescharacteristic, complemented
188#2243C2×C1311yescharacteristic, complemented
189#2237C2×C1311yescharacteristic, complemented
190#2234C2×C1311yescharacteristic, complemented
191#2224C2×C1311yescharacteristic, complemented
192#2220C2×C1311yescharacteristic, complemented
193#2215C2×C1311yescharacteristic, complemented
194#2210C2×C1311yescharacteristic, complemented
195#2186C2×C1311yescharacteristic, complemented
196#2184C2×C1311yescharacteristic, complemented
197#2177C2×C1311yescharacteristic, complemented
198#2168C2×C1311yescharacteristic, complemented
199#2140C2×C1311yescharacteristic, complemented
200#2138C2×C1311yescharacteristic, complemented
201C23×C13—41no—
202C23×C13—41no—
203C23×C13—41no—
204C23×C13—82no—
205C23×C13—82no—
206C23×C13—161no—
207C23×C13C2×D811yescharacteristic
208C23×C13C2×D811yescharacteristic
209Q8×C13—41no—
210Q8×C13—41no—
211Q8×C13—161no—
212D4×C13—22no—
213D4×C13—41no—
214D4×C13—41no—
215D4×C13—41no—
216D4×C13—41no—
217D4×C13—41no—
218D4×C13—41no—
219D4×C13—82no—
220D4×C13—82no—
221D4×C13—161no—
222D4×C13—161no—
223D4×C13—161no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—41no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13—82no—
234C2×C4×C13—82no—
235C2×C4×C13—161no—
236C2×C4×C13C2×D811yescharacteristic
237C2×C4×C13C2×D811yescharacteristic
238C2×C4×C13C2×D811yescharacteristic
239C2×C4×C13C2×D811yescharacteristic
240C2×C4×C13C22×D411yescharacteristic
241C8×C13—21no—
242C8×C13—21no—
243C8×C13—21no—
244C8×C13C2×#4111yescharacteristic
245C8×C13H(5,𝔽2)11yescharacteristic
246C2×#135C22×C1311yescharacteristic
247C22×D8C22×C1311yescharacteristic
248#555—21no—
249#546—21no—
250C2×SD32C22×C1311yescharacteristic, complemented
251C2×D16C22×C1311yescharacteristic
252C2×D16C22×C1311yescharacteristic
253C2×M32C22×C1311yescharacteristic
254C22×C16C22×C1311yescharacteristic, complemented
255#500C22×C1311yescharacteristic, complemented
256#495C22×C1311yescharacteristic
257#482—21no—
258#482—21no—
259#476—21no—
260#467C22×C1311yescharacteristic
261#466C22×C1311yescharacteristic
262#466C22×C1311yescharacteristic
263#466C22×C1311yescharacteristic, complemented
264#463—21no—
265#450—21no—
266#449—21no—
267C4×D8C22×C1311yescharacteristic
268C4×D8C22×C1311yescharacteristic, complemented
269C8×D4C22×C1311yescharacteristic
270#427C22×C1311yescharacteristic
271#427C22×C1311yescharacteristic, complemented
272#367C22×C1311yescharacteristic, complemented
273#366C22×C1311yescharacteristic, complemented
274#366C22×C1311yescharacteristic, complemented
275C4⋊C16C22×C1311yescharacteristic, complemented
276#358C22×C1311yescharacteristic, complemented
277#358C22×C1311yescharacteristic, complemented
278#358C22×C1311yescharacteristic, complemented
279#357C22×C1311yescharacteristic
280#357C22×C1311yescharacteristic
281#357C22×C1311yescharacteristic
282#357C22×C1311yescharacteristic
283#357C22×C1311yescharacteristic
284#357C22×C1311yescharacteristic
285#357C22×C1311yescharacteristic, complemented
286C22⋊C16C22×C1311yescharacteristic
287C22⋊C16C22×C1311yescharacteristic, complemented
288#346C22×C1311yescharacteristic, complemented
289C22×C13—21no—
290C22×C13—21no—
291C22×C13—21no—
292C22×C13—21no—
293C22×C13—21no—
294C22×C13—21no—
295C22×C13—42no—
296C22×C13—81no—
297C22×C13—81no—
298C22×C13—81no—
299C22×C13—81no—
300C22×C13—81no—
301C22×C13—81no—
302C22×C13—81no—
303C22×C13—81no—
304C22×C13—164no—
305C22×C13C22×D811yescharacteristic
306C4×C13—21no—
307C4×C13—21no—
308C4×C13—21no—
309C4×C13—21no—
310C4×C13—81no—
311C4×C13—81no—
312C4×C13—81no—
313C4×C13—81no—
314C4×C13—81no—
315C4×C13#54611yescharacteristic
316C4×C13#57711yescharacteristic
317C2×#41—21no—
318C22×D4—21no—
319#135—22no—
320#135—41no—
321C2×Q16C23×C1311yescharacteristic
322C2×SD16—21no—
323C2×SD16—21no—
324C2×D8—22no—
325C2×D8—21no—
326C2×D8—41no—
327C2×D8C23×C1311yescharacteristic
328C2×D8C23×C1311yescharacteristic
329C2×D8C23×C1311yescharacteristic
330C22×C8C23×C1311yescharacteristic
331C22×C8C23×C1311yescharacteristic
332C4⋊Q8—21no—
333#124—21no—
334#124—41no—
335#124—41no—
336#123—41no—
337C22⋊Q8—21no—
338#121—21no—
339#121—21no—
340#121—21no—
341#121—41no—
342#121—41no—
343#120—41no—
344C4×D4—21no—
345C4×D4—21no—
346C4×D4D4×C1311yescharacteristic
347#117—21no—
348#117—21no—
349#117—41no—
350C2×C22⋊C4—41no—
351SD32—41no—
352D16—22no—
353D16—41no—
354M32—41no—
355C2×C16—41no—
356C2×C16C23×C1311yescharacteristic
357C2×C16C23×C1311yescharacteristic
358C2×C16C23×C1311yescharacteristic
359C2×C16C23×C1311yescharacteristic
360#107—21no—
361#107C23×C1311yescharacteristic
362#107C23×C1311yescharacteristic
363#107C23×C1311yescharacteristic
364#107C23×C1311yescharacteristic
365#106—21no—
366#106—21no—
367C4⋊C8D4×C1311yescharacteristic
368#103—21no—
369#102—21no—
370#102—21no—
371#102—21no—
372#102—21no—
373#102—21no—
374C22⋊C8D4×C1311yescharacteristic
375C22⋊C8D4×C1311yescharacteristic
376C4×C8C23×C1311yescharacteristic
377C2×C13—41no—
378C2×C13—41no—
379C2×C13—82no—
380C2×C13—161no—
381C2×C13—161no—
382C2×C13#329411yescharacteristic
383C2×C13#341411yescharacteristic
384C2×C13#341511yescharacteristic
385C24—41no—
386#41—42no—
387#41—81no—
388C2×Q8—21no—
389C2×Q8—41no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—42no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—81no—
400C2×D4C13×D811yescharacteristic
401C22×C4—41no—
402C22×C4—41no—
403C22×C4—41no—
404C22×C4C2×D4×C1311yescharacteristic
405C22×C4C2×D4×C1311yescharacteristic
406Q16—21no—
407Q16—21no—
408SD16—42no—
409SD16—81no—
410D8—21no—
411D8—21no—
412D8—21no—
413D8—21no—
414D8—21no—
415D8—42no—
416D8C13×#4112yes—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8C2×D4×C1311yescharacteristic
422C2×C8C2×D4×C1311yescharacteristic
423C2×C8C2×D4×C1311yescharacteristic
424C2×C8C24×C1311yescharacteristic
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—41no—
430C4⋊C4—41no—
431C4⋊C4C13×D811yescharacteristic
432C22⋊C4—41no—
433C22⋊C4—41no—
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C22⋊C4—41no—
442C22⋊C4C13×D811yescharacteristic
443C22⋊C4C13×D811yescharacteristic
444C42—41no—
445C42—41no—
446C42C2×D4×C1311yescharacteristic
447C16—21no—
448C16—21no—
449C16—21no—
450C16—21no—
451C13#3388611yescharacteristic, direct product factor, Sylow
452C23—41no—
453C23—41no—
454C23—41no—
455C23—82no—
456C23—82no—
457C23—161no—
458C23C2×C13×D811yescharacteristic
459C23C2×C13×D811yescharacteristic
460Q8—41no—
461Q8—41no—
462Q8—161no—
463D4—22no—
464D4—41no—
465D4—41no—
466D4—41no—
467D4—41no—
468D4—41no—
469D4—41no—
470D4—82no—
471D4—82no—
472D4—161no—
473D4—161no—
474D4—161no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—82no—
485C2×C4—82no—
486C2×C4—161no—
487C2×C4C2×C13×D811yescharacteristic
488C2×C4C2×C13×D811yescharacteristic
489C2×C4C2×C13×D811yescharacteristic
490C2×C4C2×C13×D811yescharacteristic
491C2×C4C22×D4×C1311yescharacteristic
492C8—21no—
493C8—21no—
494C8—21no—
495C8C2×C13×#4111yescharacteristic
496C8C13×H(5,𝔽2)11yescharacteristic
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—42no—
504C22—81no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—164no—
513C22C22×C13×D811yescharacteristic
514C4—21no—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—81no—
519C4—81no—
520C4—81no—
521C4—81no—
522C4—81no—
523C4C13×#54611yescharacteristic
524C4C13×#57711yescharacteristic
525C2—41no—
526C2—41no—
527C2—82no—
528C2—161no—
529C2—161no—
530C2C13×#329411yescharacteristic
531C2C13×#341411yescharacteristic
532C2C13×#341511yescharacteristic
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×#3341C2semidirect
2. C13×#3280C2semidirect
3. C13×#2243C2semidirect
4. C13×#2237C2semidirect
5. C13×#2234C2semidirect
6. C13×#2224C2semidirect
7. C13×#2220C2semidirect
8. C13×#2215C2semidirect
9. C13×#2210C2semidirect
10. C13×#2186C2semidirect
11. C13×#2184C2semidirect
12. C13×#2177C2semidirect
13. C13×#2168C2semidirect
14. C13×#2140C2semidirect
15. C13×#2138C2semidirect
20. C2×C13×SD32C22semidirect
24. C22×C13×C16C22semidirect
25. C13×#500C22semidirect
33. C13×#466C22semidirect
38. C4×C13×D8C22semidirect
41. C13×#427C22semidirect
42. C13×#367C22semidirect
43. C13×#366C22semidirect
44. C13×#366C22semidirect
45. C13×C4⋊C16C22semidirect
46. C13×#358C22semidirect
47. C13×#358C22semidirect
48. C13×#358C22semidirect
55. C13×#357C22semidirect
57. C13×C22⋊C16C22semidirect
58. C13×#346C22semidirect
119. #33886C13direct (N × H)
186. #3341C2×C13semidirect
187. #3280C2×C13semidirect
188. #2243C2×C13semidirect
189. #2237C2×C13semidirect
190. #2234C2×C13semidirect
191. #2224C2×C13semidirect
192. #2220C2×C13semidirect
193. #2215C2×C13semidirect
194. #2210C2×C13semidirect
195. #2186C2×C13semidirect
196. #2184C2×C13semidirect
197. #2177C2×C13semidirect
198. #2168C2×C13semidirect
199. #2140C2×C13semidirect
200. #2138C2×C13semidirect
250. C2×SD32C22×C13semidirect
254. C22×C16C22×C13semidirect
255. #500C22×C13semidirect
263. #466C22×C13semidirect
268. C4×D8C22×C13semidirect
271. #427C22×C13semidirect
272. #367C22×C13semidirect
273. #366C22×C13semidirect
274. #366C22×C13semidirect
275. C4⋊C16C22×C13semidirect
276. #358C22×C13semidirect
277. #358C22×C13semidirect
278. #358C22×C13semidirect
285. #357C22×C13semidirect
287. C22⋊C16C22×C13semidirect
288. #346C22×C13semidirect
451. C13#33886direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#33412
C13×#32802
C13×#22432
C13×#22372
C13×#22342
C13×#22242
C13×#22202
C13×#22152
C13×#22102
C13×#21862
C13×#21842
C13×#21772
C13×#21682
C13×#21402
C13×#21382
#3388613