Finite Group Databasebeta

← C13×#13100 #15699439

Subgroups — C13×#13100 #15699439

Order 3328.

672 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3009C211yesmaximal, characteristic
2C13×#2883C211yesmaximal, characteristic
3C13×#2129C211yesmaximal, characteristic, complemented
4C13×#2123C211yesmaximal, characteristic, complemented
5C13×#1795C211yesmaximal, characteristic
6C13×#1395C211yesmaximal, characteristic, complemented
7C13×#1391C211yesmaximal, characteristic, complemented
8C2×C13×H(5,𝔽2)C2211yescharacteristic
9C2×C13×#137C411yescharacteristic, complemented
10C22×C13×SD16C411yescharacteristic, complemented
11C13×#536C2211yescharacteristic
12C13×#518—21no—
13C13×#452—21no—
14C13×#452—21no—
15C13×#450—21no—
16C13×#450—21no—
17C13×#421—21no—
18C13×#418—21no—
19C13×#418C411yescharacteristic, complemented
20C13×#416C411yescharacteristic, complemented
21C13×#413C2211yescharacteristic
22C13×#410—21no—
23C13×#410C2211yescharacteristic
24C13×#410C2211yescharacteristic
25C13×#410C2211yescharacteristic
26C2×C13×#99—22no—
27C2×C13×#99—22no—
28C13×#408C2211yescharacteristic
29C13×#354—22no—
30C13×#352—22no—
31C13×H(5,𝔽2)—42no—
32C13×H(5,𝔽2)—42no—
33C2×C13×#41—21no—
34C2×C13×#41C2×C411yescharacteristic
35C2×C13×#41D411yescharacteristic
36C2×C13×#41D411yescharacteristic
37C2×C13×#41C2311yescharacteristic
38C22×Q8×C13C2×C411yescharacteristic, complemented
39C22×D4×C13—21no—
40C22×D4×C13—21no—
41C22×D4×C13—21no—
42C22×D4×C13C2×C411yescharacteristic
43C22×D4×C13D411yescharacteristic
44C22×D4×C13D411yescharacteristic
45C13×#137—42no—
46C2×C13×Q16—21no—
47C2×C13×SD16—21no—
48C2×C13×SD16—21no—
49C2×C13×SD16—21no—
50C2×C13×SD16—42no—
51C2×C13×M16—21no—
52C2×C13×M16C2×C411yescharacteristic, complemented
53C22×C8×C13C2×C411yescharacteristic, complemented
54C13×C4⋊Q8—21no—
55C13×#124—21no—
56C13×#123—21no—
57C13×#123—21no—
58C13×C22⋊Q8—21no—
59C13×C22⋊Q8—21no—
60C4×D4×C13—42no—
61C4×D4×C13—42no—
62C13×#117—21no—
63C13×#117—21no—
64C13×#117—21no—
65C13×#117C2×C411yescharacteristic, complemented
66C2×C13×C22⋊C4—24no—
67C13×#104—42no—
68C13×#103—21no—
69C13×#102—21no—
70C13×#102—21no—
71C13×#102—21no—
72C13×#102—42no—
73C13×#101—21no—
74C13×#100—21no—
75C13×#99—24no—
76C13×#99—21no—
77C13×#99—21no—
78C13×#99—21no—
79C13×#99—21no—
80C13×#99D412yes—
81C13×#99D412yes—
82C13×C22⋊C8—21no—
83C13×C22⋊C8—21no—
84#13100C1311yesmaximal, characteristic, direct product factor, Sylow
85C24×C13—21no—
86C24×C13—21no—
87C24×C13—21no—
88C13×#41—22no—
89C13×#41—22no—
90C13×#41—41no—
91C13×#41—41no—
92C13×#41—41no—
93C13×#41—41no—
94C13×#41—41no—
95C13×#41—41no—
96C13×#41—44no—
97C2×Q8×C13—21no—
98C2×Q8×C13—21no—
99C2×Q8×C13—41no—
100C2×Q8×C13—41no—
101C2×Q8×C13C22⋊C411yescharacteristic
102C2×Q8×C13#4111yescharacteristic
103C2×D4×C13—22no—
104C2×D4×C13—22no—
105C2×D4×C13—22no—
106C2×D4×C13—22no—
107C2×D4×C13—21no—
108C2×D4×C13—21no—
109C2×D4×C13—21no—
110C2×D4×C13—21no—
111C2×D4×C13—21no—
112C2×D4×C13—21no—
113C2×D4×C13—41no—
114C2×D4×C13—41no—
115C2×D4×C13—44no—
116C2×D4×C13—44no—
117C2×D4×C13—44no—
118C2×D4×C13C22⋊C411yescharacteristic
119C2×D4×C13C22⋊C411yescharacteristic
120C2×D4×C13C22⋊C411yescharacteristic
121C2×D4×C13C2×D411yescharacteristic
122C2×D4×C13C2×D411yescharacteristic
123C2×D4×C13#4111yescharacteristic
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—44no—
129C22×C4×C13C22×C411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C13×Q16—42no—
133C13×SD16—42no—
134C13×SD16—42no—
135C13×SD16—42no—
136C13×M16—41no—
137C13×M16—41no—
138C13×M16—41no—
139C2×C8×C13—21no—
140C2×C8×C13—21no—
141C2×C8×C13—41no—
142C2×C8×C13—41no—
143C13×C4⋊C4—21no—
144C13×C4⋊C4—41no—
145C13×C4⋊C4—41no—
146C13×C4⋊C4—41no—
147C13×C4⋊C4—41no—
148C13×C4⋊C4—41no—
149C13×C22⋊C4—21no—
150C13×C22⋊C4—22no—
151C13×C22⋊C4—22no—
152C13×C22⋊C4—44no—
153C13×C22⋊C4—41no—
154C13×C22⋊C4—41no—
155C13×C22⋊C4—41no—
156C42×C13—21no—
157C42×C13—41no—
158C42×C13—41no—
159C42×C13—41no—
160#3009C2×C1311yescharacteristic
161#2883C2×C1311yescharacteristic
162#2129C2×C1311yescharacteristic, complemented
163#2123C2×C1311yescharacteristic, complemented
164#1795C2×C1311yescharacteristic
165#1395C2×C1311yescharacteristic, complemented
166#1391C2×C1311yescharacteristic, complemented
167C23×C13—24no—
168C23×C13—21no—
169C23×C13—21no—
170C23×C13—21no—
171C23×C13—42no—
172C23×C13—42no—
173C23×C13—161no—
174C23×C13—161no—
175C23×C13—161no—
176C23×C13C4×D411yescharacteristic
177C23×C13#12011yescharacteristic
178C23×C13#12111yescharacteristic
179Q8×C13—21no—
180Q8×C13—21no—
181Q8×C13—41no—
182Q8×C13—41no—
183Q8×C13—41no—
184Q8×C13—81no—
185D4×C13—24no—
186D4×C13—21no—
187D4×C13—21no—
188D4×C13—21no—
189D4×C13—21no—
190D4×C13—41no—
191D4×C13—41no—
192D4×C13—41no—
193D4×C13—42no—
194D4×C13—42no—
195D4×C13—42no—
196D4×C13—42no—
197D4×C13—42no—
198D4×C13#9912yes—
199D4×C13#9912yes—
200C2×C4×C13—21no—
201C2×C4×C13—21no—
202C2×C4×C13—21no—
203C2×C4×C13—21no—
204C2×C4×C13—21no—
205C2×C4×C13—21no—
206C2×C4×C13—21no—
207C2×C4×C13—42no—
208C2×C4×C13—42no—
209C2×C4×C13—42no—
210C2×C4×C13—42no—
211C2×C4×C13—42no—
212C2×C4×C13—41no—
213C2×C4×C13—41no—
214C2×C4×C13—81no—
215C2×C4×C13—81no—
216C2×C4×C13—164no—
217C2×C4×C13C2×C22⋊C411yescharacteristic
218C2×C4×C13C4×D411yescharacteristic
219C2×C4×C13#12111yescharacteristic
220C2×C4×C13#12311yescharacteristic
221C8×C13—41no—
222C8×C13—41no—
223C8×C13—81no—
224C2×H(5,𝔽2)C22×C1311yescharacteristic
225C2×#137C4×C1311yescharacteristic, complemented
226C22×SD16C4×C1311yescharacteristic, complemented
227#536C22×C1311yescharacteristic
228#518—21no—
229#452—21no—
230#452—21no—
231#450—21no—
232#450—21no—
233#421—21no—
234#418—21no—
235#418C4×C1311yescharacteristic, complemented
236#416C4×C1311yescharacteristic, complemented
237#413C22×C1311yescharacteristic
238#410—21no—
239#410C22×C1311yescharacteristic
240#410C22×C1311yescharacteristic
241#410C22×C1311yescharacteristic
242C2×#99—22no—
243C2×#99—22no—
244#408C22×C1311yescharacteristic
245#354—22no—
246#352—22no—
247C22×C13—21no—
248C22×C13—21no—
249C22×C13—21no—
250C22×C13—22no—
251C22×C13—22no—
252C22×C13—41no—
253C22×C13—41no—
254C22×C13—41no—
255C22×C13—41no—
256C22×C13—81no—
257C22×C13—81no—
258C22×C13—81no—
259C22×C13—84no—
260C22×C13—162no—
261C22×C13—162no—
262C22×C13#38611yescharacteristic
263C4×C13—21no—
264C4×C13—21no—
265C4×C13—21no—
266C4×C13—41no—
267C4×C13—81no—
268C4×C13—82no—
269C4×C13—82no—
270C4×C13—81no—
271C4×C13—161no—
272C4×C13C2×#9911yescharacteristic
273C4×C13C2×#9911yescharacteristic
274H(5,𝔽2)—42no—
275H(5,𝔽2)—42no—
276C2×#41—21no—
277C2×#41C2×C4×C1311yescharacteristic
278C2×#41D4×C1311yescharacteristic
279C2×#41D4×C1311yescharacteristic
280C2×#41C23×C1311yescharacteristic
281C22×Q8C2×C4×C1311yescharacteristic, complemented
282C22×D4—21no—
283C22×D4—21no—
284C22×D4—21no—
285C22×D4C2×C4×C1311yescharacteristic
286C22×D4D4×C1311yescharacteristic
287C22×D4D4×C1311yescharacteristic
288#137—42no—
289C2×Q16—21no—
290C2×SD16—21no—
291C2×SD16—21no—
292C2×SD16—21no—
293C2×SD16—42no—
294C2×M16—21no—
295C2×M16C2×C4×C1311yescharacteristic, complemented
296C22×C8C2×C4×C1311yescharacteristic, complemented
297C4⋊Q8—21no—
298#124—21no—
299#123—21no—
300#123—21no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303C4×D4—42no—
304C4×D4—42no—
305#117—21no—
306#117—21no—
307#117—21no—
308#117C2×C4×C1311yescharacteristic, complemented
309C2×C22⋊C4—24no—
310#104—42no—
311#103—21no—
312#102—21no—
313#102—21no—
314#102—21no—
315#102—42no—
316#101—21no—
317#100—21no—
318#99—24no—
319#99—21no—
320#99—21no—
321#99—21no—
322#99—21no—
323#99D4×C1312yes—
324#99D4×C1312yes—
325C22⋊C8—21no—
326C22⋊C8—21no—
327C2×C13—21no—
328C2×C13—41no—
329C2×C13—41no—
330C2×C13—41no—
331C2×C13—42no—
332C2×C13—42no—
333C2×C13—81no—
334C2×C13#189811yescharacteristic
335C24—21no—
336C24—21no—
337C24—21no—
338#41—22no—
339#41—22no—
340#41—41no—
341#41—41no—
342#41—41no—
343#41—41no—
344#41—41no—
345#41—41no—
346#41—44no—
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8—41no—
350C2×Q8—41no—
351C2×Q8C13×C22⋊C411yescharacteristic
352C2×Q8C13×#4111yescharacteristic
353C2×D4—22no—
354C2×D4—22no—
355C2×D4—22no—
356C2×D4—22no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—44no—
366C2×D4—44no—
367C2×D4—44no—
368C2×D4C13×C22⋊C411yescharacteristic
369C2×D4C13×C22⋊C411yescharacteristic
370C2×D4C13×C22⋊C411yescharacteristic
371C2×D4C2×D4×C1311yescharacteristic
372C2×D4C2×D4×C1311yescharacteristic
373C2×D4C13×#4111yescharacteristic
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—44no—
379C22×C4C22×C4×C1311yescharacteristic
380C22×C4C2×D4×C1311yescharacteristic
381C22×C4C2×D4×C1311yescharacteristic
382Q16—42no—
383SD16—42no—
384SD16—42no—
385SD16—42no—
386M16—41no—
387M16—41no—
388M16—41no—
389C2×C8—21no—
390C2×C8—21no—
391C2×C8—41no—
392C2×C8—41no—
393C4⋊C4—21no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C4⋊C4—41no—
398C4⋊C4—41no—
399C22⋊C4—21no—
400C22⋊C4—22no—
401C22⋊C4—22no—
402C22⋊C4—44no—
403C22⋊C4—41no—
404C22⋊C4—41no—
405C22⋊C4—41no—
406C42—21no—
407C42—41no—
408C42—41no—
409C42—41no—
410C13#1310011yescharacteristic, direct product factor, Sylow
411C23—24no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—42no—
416C23—42no—
417C23—161no—
418C23—161no—
419C23—161no—
420C23C4×D4×C1311yescharacteristic
421C23C13×#12011yescharacteristic
422C23C13×#12111yescharacteristic
423Q8—21no—
424Q8—21no—
425Q8—41no—
426Q8—41no—
427Q8—41no—
428Q8—81no—
429D4—24no—
430D4—21no—
431D4—21no—
432D4—21no—
433D4—21no—
434D4—41no—
435D4—41no—
436D4—41no—
437D4—42no—
438D4—42no—
439D4—42no—
440D4—42no—
441D4—42no—
442D4C13×#9912yes—
443D4C13×#9912yes—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—81no—
459C2×C4—81no—
460C2×C4—164no—
461C2×C4C2×C13×C22⋊C411yescharacteristic
462C2×C4C4×D4×C1311yescharacteristic
463C2×C4C13×#12111yescharacteristic
464C2×C4C13×#12311yescharacteristic
465C8—41no—
466C8—41no—
467C8—81no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—22no—
472C22—22no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—41no—
477C22—81no—
478C22—81no—
479C22—81no—
480C22—84no—
481C22—162no—
482C22—162no—
483C22C13×#38611yescharacteristic
484C4—21no—
485C4—21no—
486C4—21no—
487C4—41no—
488C4—81no—
489C4—82no—
490C4—82no—
491C4—81no—
492C4—161no—
493C4C2×C13×#9911yescharacteristic
494C4C2×C13×#9911yescharacteristic
495C2—21no—
496C2—41no—
497C2—41no—
498C2—41no—
499C2—42no—
500C2—42no—
501C2—81no—
502C2C13×#189811yescharacteristic
subgroupG/H
center, socleC2×C13#1898
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×#41C23×C13
prime radicalC2×C13×H(5,𝔽2)C22
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C13×H(5,𝔽2) ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#2129C2semidirect
4. C13×#2123C2semidirect
6. C13×#1395C2semidirect
7. C13×#1391C2semidirect
9. C2×C13×#137C4semidirect
10. C22×C13×SD16C4semidirect
19. C13×#418C4semidirect
20. C13×#416C4semidirect
38. C22×Q8×C13C2×C4semidirect
52. C2×C13×M16C2×C4semidirect
53. C22×C8×C13C2×C4semidirect
65. C13×#117C2×C4semidirect
84. #13100C13direct (N × H)
162. #2129C2×C13semidirect
163. #2123C2×C13semidirect
165. #1395C2×C13semidirect
166. #1391C2×C13semidirect
225. C2×#137C4×C13semidirect
226. C22×SD16C4×C13semidirect
235. #418C4×C13semidirect
236. #416C4×C13semidirect
281. C22×Q8C2×C4×C13semidirect
295. C2×M16C2×C4×C13semidirect
296. C22×C8C2×C4×C13semidirect
308. #117C2×C4×C13semidirect
410. C13#13100direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#30092
C13×#28832
C13×#21292
C13×#21232
C13×#17952
C13×#13952
C13×#13912
#1310013