Finite Group Databasebeta

← C13×#33877 #15720216

Subgroups — C13×#33877 #15720216

Order 3328.

610 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3336C211yesmaximal, characteristic, complemented
2D4×C13×D8C211yesmaximal, characteristic
3C13×#2244C211yesmaximal, characteristic, complemented
4C13×#2234C211yesmaximal, characteristic, complemented
5C13×#2232C211yesmaximal, characteristic, complemented
6C13×#2228C211yesmaximal, characteristic, complemented
7C13×#2220C211yesmaximal, characteristic, complemented
8C13×#2217C211yesmaximal, characteristic, complemented
9C13×#2207C211yesmaximal, characteristic, complemented
10C13×#2187C211yesmaximal, characteristic, complemented
11C13×#2187C211yesmaximal, characteristic, complemented
12C13×#2175C211yesmaximal, characteristic, complemented
13C13×#2168C211yesmaximal, characteristic, complemented
14C13×#2140C211yesmaximal, characteristic, complemented
15C2×C13×#357C211yesmaximal, characteristic, complemented
16C22×C13×D8C2211yescharacteristic
17C22×C13×D8C2211yescharacteristic
18C13×#552—21no—
19D42×C13—21no—
20C2×C13×SD32C2211yescharacteristic
21C2×C13×SD32C2211yescharacteristic, complemented
22C2×C13×SD32C2211yescharacteristic, complemented
23C2×C13×M32C2211yescharacteristic, complemented
24C22×C13×C16C2211yescharacteristic, complemented
25C13×#499C2211yescharacteristic, complemented
26C13×#493C2211yescharacteristic
27C13×#485—21no—
28C13×#483—21no—
29C13×#479—21no—
30C13×#467C2211yescharacteristic, complemented
31C13×#467C2211yescharacteristic, complemented
32C13×#466C2211yescharacteristic
33C13×#466C2211yescharacteristic
34C13×#459—21no—
35C13×#447—21no—
36C13×#447—21no—
37C4×C13×Q16C2211yescharacteristic, complemented
38C4×C13×D8C2211yescharacteristic
39C8×D4×C13C2211yescharacteristic
40C13×#427C2211yescharacteristic, complemented
41C2×C13×#107C2211yescharacteristic, complemented
42C13×#367C2211yescharacteristic, complemented
43C13×#366C2211yescharacteristic, complemented
44C13×#366C2211yescharacteristic, complemented
45C13×C4⋊C16C2211yescharacteristic, complemented
46C13×#358C2211yescharacteristic, complemented
47C13×#357C2211yescharacteristic
48C13×#357C2211yescharacteristic
49C13×#357C2211yescharacteristic
50C13×#357C2211yescharacteristic, complemented
51C13×#357C2211yescharacteristic, complemented
52C13×#357C2211yescharacteristic, complemented
53C13×#357C2211yescharacteristic, complemented
54C13×#357C2211yescharacteristic, complemented
55C13×#357C2211yescharacteristic, complemented
56C13×C22⋊C16C2211yescharacteristic, complemented
57C13×C22⋊C16C2211yescharacteristic, complemented
58C13×#346C2211yescharacteristic, complemented
59C22×D4×C13—21no—
60C22×D4×C13—21no—
61C22×D4×C13—41no—
62C2×C13×Q16C2311yescharacteristic
63C2×C13×D8—22no—
64C2×C13×D8—22no—
65C2×C13×D8—21no—
66C2×C13×D8—21no—
67C2×C13×D8—21no—
68C2×C13×D8—41no—
69C2×C13×D8—41no—
70C2×C13×D8C2311yescharacteristic
71C2×C13×D8C2311yescharacteristic
72C2×C13×D8C2311yescharacteristic
73C22×C8×C13C2311yescharacteristic
74C22×C8×C13C2311yescharacteristic
75C13×#127—21no—
76C13×#126—41no—
77C13×#125—21no—
78C13×#125—41no—
79C13×#123—41no—
80C13×C22⋊Q8—21no—
81C13×C22⋊Q8—21no—
82C13×#121—21no—
83C13×#121—21no—
84C13×#121—41no—
85C13×#120—41no—
86C13×#120—41no—
87C4×Q8×C13—21no—
88C4×D4×C13—21no—
89C4×D4×C13D411yescharacteristic
90C13×#117—21no—
91C13×#117—41no—
92C2×C13×C4⋊C4—21no—
93C13×SD32—22no—
94C13×SD32—41no—
95C13×SD32—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×#103—21no—
112C13×#103—21no—
113C13×#102—21no—
114C13×#102—21no—
115C13×#102—21no—
116C13×C22⋊C8D411yescharacteristic
117C13×C22⋊C8D411yescharacteristic
118C4×C8×C13C2311yescharacteristic
119#33877C1311yesmaximal, characteristic, direct product factor, Sylow
120C24×C13—41no—
121C24×C13—41no—
122C2×Q8×C13—21no—
123C2×D4×C13—21no—
124C2×D4×C13—21no—
125C2×D4×C13—21no—
126C2×D4×C13—42no—
127C2×D4×C13—42no—
128C2×D4×C13—41no—
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×C13—81no—
136C2×D4×C13—84no—
137C2×D4×C13D811yescharacteristic
138C22×C4×C13—41no—
139C22×C4×C13—41no—
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C13×Q16—21no—
143C13×Q16—21no—
144C13×D8—21no—
145C13×D8—21no—
146C13×D8—21no—
147C13×D8—21no—
148C13×D8—21no—
149C13×D8—42no—
150C13×D8—42no—
151C13×D8—81no—
152C13×D8#4112yes—
153C2×C8×C13—21no—
154C2×C8×C13—21no—
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13C2×D411yescharacteristic
158C2×C8×C13C2×D411yescharacteristic
159C2×C8×C13C2×D411yescharacteristic
160C2×C8×C13C2411yescharacteristic
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—41no—
166C13×C4⋊C4—41no—
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⋊C4D811yescharacteristic
179C13×C22⋊C4D811yescharacteristic
180C42×C13—41no—
181C42×C13—41no—
182C42×C13C2×D411yescharacteristic
183C13×C16—21no—
184C13×C16—21no—
185C13×C16—21no—
186C13×C16—21no—
187#3336C2×C1311yescharacteristic, complemented
188D4×D8C2×C1311yescharacteristic
189#2244C2×C1311yescharacteristic, complemented
190#2234C2×C1311yescharacteristic, complemented
191#2232C2×C1311yescharacteristic, complemented
192#2228C2×C1311yescharacteristic, complemented
193#2220C2×C1311yescharacteristic, complemented
194#2217C2×C1311yescharacteristic, complemented
195#2207C2×C1311yescharacteristic, complemented
196#2187C2×C1311yescharacteristic, complemented
197#2187C2×C1311yescharacteristic, complemented
198#2175C2×C1311yescharacteristic, complemented
199#2168C2×C1311yescharacteristic, complemented
200#2140C2×C1311yescharacteristic, complemented
201C2×#357C2×C1311yescharacteristic, complemented
202C23×C13—41no—
203C23×C13—41no—
204C23×C13—41no—
205C23×C13—82no—
206C23×C13—82no—
207C23×C13—82no—
208C23×C13—82no—
209C23×C13—161no—
210C23×C13—161no—
211C23×C13C2×D811yescharacteristic
212C23×C13C2×D811yescharacteristic
213Q8×C13—41no—
214Q8×C13—41no—
215D4×C13—22no—
216D4×C13—22no—
217D4×C13—41no—
218D4×C13—41no—
219D4×C13—41no—
220D4×C13—41no—
221D4×C13—41no—
222D4×C13—82no—
223D4×C13—82no—
224D4×C13—82no—
225D4×C13—82no—
226D4×C13—82no—
227D4×C13—161no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—82no—
238C2×C4×C13—82no—
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
249C22×D8C22×C1311yescharacteristic
250C22×D8C22×C1311yescharacteristic
251#552—21no—
252D42—21no—
253C2×SD32C22×C1311yescharacteristic
254C2×SD32C22×C1311yescharacteristic, complemented
255C2×SD32C22×C1311yescharacteristic, complemented
256C2×M32C22×C1311yescharacteristic, complemented
257C22×C16C22×C1311yescharacteristic, complemented
258#499C22×C1311yescharacteristic, complemented
259#493C22×C1311yescharacteristic
260#485—21no—
261#483—21no—
262#479—21no—
263#467C22×C1311yescharacteristic, complemented
264#467C22×C1311yescharacteristic, complemented
265#466C22×C1311yescharacteristic
266#466C22×C1311yescharacteristic
267#459—21no—
268#447—21no—
269#447—21no—
270C4×Q16C22×C1311yescharacteristic, complemented
271C4×D8C22×C1311yescharacteristic
272C8×D4C22×C1311yescharacteristic
273#427C22×C1311yescharacteristic, complemented
274C2×#107C22×C1311yescharacteristic, complemented
275#367C22×C1311yescharacteristic, complemented
276#366C22×C1311yescharacteristic, complemented
277#366C22×C1311yescharacteristic, complemented
278C4⋊C16C22×C1311yescharacteristic, complemented
279#358C22×C1311yescharacteristic, complemented
280#357C22×C1311yescharacteristic
281#357C22×C1311yescharacteristic
282#357C22×C1311yescharacteristic
283#357C22×C1311yescharacteristic, complemented
284#357C22×C1311yescharacteristic, complemented
285#357C22×C1311yescharacteristic, complemented
286#357C22×C1311yescharacteristic, complemented
287#357C22×C1311yescharacteristic, complemented
288#357C22×C1311yescharacteristic, complemented
289C22⋊C16C22×C1311yescharacteristic, complemented
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—164no—
308C22×C13#50912yes—
309C22×C13C22×D811yescharacteristic
310C4×C13—21no—
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#54611yescharacteristic
320C4×C13#57711yescharacteristic
321C22×D4—21no—
322C22×D4—21no—
323C22×D4—41no—
324C2×Q16C23×C1311yescharacteristic
325C2×D8—22no—
326C2×D8—22no—
327C2×D8—21no—
328C2×D8—21no—
329C2×D8—21no—
330C2×D8—41no—
331C2×D8—41no—
332C2×D8C23×C1311yescharacteristic
333C2×D8C23×C1311yescharacteristic
334C2×D8C23×C1311yescharacteristic
335C22×C8C23×C1311yescharacteristic
336C22×C8C23×C1311yescharacteristic
337#127—21no—
338#126—41no—
339#125—21no—
340#125—41no—
341#123—41no—
342C22⋊Q8—21no—
343C22⋊Q8—21no—
344#121—21no—
345#121—21no—
346#121—41no—
347#120—41no—
348#120—41no—
349C4×Q8—21no—
350C4×D4—21no—
351C4×D4D4×C1311yescharacteristic
352#117—21no—
353#117—41no—
354C2×C4⋊C4—21no—
355SD32—22no—
356SD32—41no—
357SD32—41no—
358M32—41no—
359C2×C16—41no—
360C2×C16C23×C1311yescharacteristic
361C2×C16C23×C1311yescharacteristic
362C2×C16C23×C1311yescharacteristic
363C2×C16C23×C1311yescharacteristic
364#107—21no—
365#107C23×C1311yescharacteristic
366#107C23×C1311yescharacteristic
367#107C23×C1311yescharacteristic
368#107C23×C1311yescharacteristic
369#106—21no—
370#106—21no—
371C4⋊C8D4×C1311yescharacteristic
372#103—21no—
373#103—21no—
374#103—21no—
375#102—21no—
376#102—21no—
377#102—21no—
378C22⋊C8D4×C1311yescharacteristic
379C22⋊C8D4×C1311yescharacteristic
380C4×C8C23×C1311yescharacteristic
381C2×C13—22no—
382C2×C13—41no—
383C2×C13—82no—
384C2×C13—161no—
385C2×C13—161no—
386C2×C13#329411yescharacteristic
387C2×C13C2×#50911yescharacteristic
388C2×C13#341611yescharacteristic
389C24—41no—
390C24—41no—
391C2×Q8—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—42no—
396C2×D4—42no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—81no—
404C2×D4—81no—
405C2×D4—84no—
406C2×D4C13×D811yescharacteristic
407C22×C4—41no—
408C22×C4—41no—
409C22×C4C2×D4×C1311yescharacteristic
410C22×C4C2×D4×C1311yescharacteristic
411Q16—21no—
412Q16—21no—
413D8—21no—
414D8—21no—
415D8—21no—
416D8—21no—
417D8—21no—
418D8—42no—
419D8—42no—
420D8—81no—
421D8C13×#4112yes—
422C2×C8—21no—
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8C2×D4×C1311yescharacteristic
427C2×C8C2×D4×C1311yescharacteristic
428C2×C8C2×D4×C1311yescharacteristic
429C2×C8C24×C1311yescharacteristic
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—41no—
435C4⋊C4—41no—
436C4⋊C4—41no—
437C4⋊C4—41no—
438C4⋊C4—41no—
439C4⋊C4—41no—
440C4⋊C4C13×D811yescharacteristic
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—41no—
444C22⋊C4—41no—
445C22⋊C4—41no—
446C22⋊C4—41no—
447C22⋊C4C13×D811yescharacteristic
448C22⋊C4C13×D811yescharacteristic
449C42—41no—
450C42—41no—
451C42C2×D4×C1311yescharacteristic
452C16—21no—
453C16—21no—
454C16—21no—
455C16—21no—
456C13#3387711yescharacteristic, direct product factor, Sylow
457C23—41no—
458C23—41no—
459C23—41no—
460C23—82no—
461C23—82no—
462C23—82no—
463C23—82no—
464C23—161no—
465C23—161no—
466C23C2×C13×D811yescharacteristic
467C23C2×C13×D811yescharacteristic
468Q8—41no—
469Q8—41no—
470D4—22no—
471D4—22no—
472D4—41no—
473D4—41no—
474D4—41no—
475D4—41no—
476D4—41no—
477D4—82no—
478D4—82no—
479D4—82no—
480D4—82no—
481D4—82no—
482D4—161no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—82no—
493C2×C4—82no—
494C2×C4C2×C13×D811yescharacteristic
495C2×C4C2×C13×D811yescharacteristic
496C2×C4C2×C13×D811yescharacteristic
497C2×C4C2×C13×D811yescharacteristic
498C2×C4C22×D4×C1311yescharacteristic
499C8—21no—
500C8—21no—
501C8—21no—
502C8C2×C13×#4111yescharacteristic
503C8C13×H(5,𝔽2)11yescharacteristic
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—42no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22—81no—
514C22—81no—
515C22—81no—
516C22—81no—
517C22—81no—
518C22—164no—
519C22—164no—
520C22C13×#50912yes—
521C22C22×C13×D811yescharacteristic
522C4—21no—
523C4—21no—
524C4—21no—
525C4—21no—
526C4—81no—
527C4—81no—
528C4—81no—
529C4—81no—
530C4—81no—
531C4C13×#54611yescharacteristic
532C4C13×#57711yescharacteristic
533C2—22no—
534C2—41no—
535C2—82no—
536C2—161no—
537C2—161no—
538C2C13×#329411yescharacteristic
539C2C2×C13×#50911yescharacteristic
540C2C13×#341611yescharacteristic
subgroupG/H
center, socleC22×C13C22×D8
commutator, Frattini, cosocleC2×C8C24×C13
prime radicalD4×C13×D8C2
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×#3336C2semidirect
3. C13×#2244C2semidirect
4. C13×#2234C2semidirect
5. C13×#2232C2semidirect
6. C13×#2228C2semidirect
7. C13×#2220C2semidirect
8. C13×#2217C2semidirect
9. C13×#2207C2semidirect
10. C13×#2187C2semidirect
11. C13×#2187C2semidirect
12. C13×#2175C2semidirect
13. C13×#2168C2semidirect
14. C13×#2140C2semidirect
15. C2×C13×#357C2semidirect
21. C2×C13×SD32C22semidirect
22. C2×C13×SD32C22semidirect
23. C2×C13×M32C22semidirect
24. C22×C13×C16C22semidirect
25. C13×#499C22semidirect
30. C13×#467C22semidirect
31. C13×#467C22semidirect
37. C4×C13×Q16C22semidirect
40. C13×#427C22semidirect
41. C2×C13×#107C22semidirect
42. C13×#367C22semidirect
43. C13×#366C22semidirect
44. C13×#366C22semidirect
45. C13×C4⋊C16C22semidirect
46. C13×#358C22semidirect
50. C13×#357C22semidirect
51. C13×#357C22semidirect
52. C13×#357C22semidirect
53. C13×#357C22semidirect
54. C13×#357C22semidirect
55. C13×#357C22semidirect
56. C13×C22⋊C16C22semidirect
57. C13×C22⋊C16C22semidirect
58. C13×#346C22semidirect
119. #33877C13direct (N × H)
187. #3336C2×C13semidirect
189. #2244C2×C13semidirect
190. #2234C2×C13semidirect
191. #2232C2×C13semidirect
192. #2228C2×C13semidirect
193. #2220C2×C13semidirect
194. #2217C2×C13semidirect
195. #2207C2×C13semidirect
196. #2187C2×C13semidirect
197. #2187C2×C13semidirect
198. #2175C2×C13semidirect
199. #2168C2×C13semidirect
200. #2140C2×C13semidirect
201. C2×#357C2×C13semidirect
254. C2×SD32C22×C13semidirect
255. C2×SD32C22×C13semidirect
256. C2×M32C22×C13semidirect
257. C22×C16C22×C13semidirect
258. #499C22×C13semidirect
263. #467C22×C13semidirect
264. #467C22×C13semidirect
270. C4×Q16C22×C13semidirect
273. #427C22×C13semidirect
274. C2×#107C22×C13semidirect
275. #367C22×C13semidirect
276. #366C22×C13semidirect
277. #366C22×C13semidirect
278. C4⋊C16C22×C13semidirect
279. #358C22×C13semidirect
283. #357C22×C13semidirect
284. #357C22×C13semidirect
285. #357C22×C13semidirect
286. #357C22×C13semidirect
287. #357C22×C13semidirect
288. #357C22×C13semidirect
289. C22⋊C16C22×C13semidirect
290. C22⋊C16C22×C13semidirect
291. #346C22×C13semidirect
456. C13#33877direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#33362
D4×C13×D82
C13×#22442
C13×#22342
C13×#22322
C13×#22282
C13×#22202
C13×#22172
C13×#22072
C13×#21872
C13×#21752
C13×#21682
C13×#21402
C2×C13×#3572
#3387713