Finite Group Databasebeta

← C13×#13099 #15699438

Subgroups — C13×#13099 #15699438

Order 3328.

666 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3008C211yesmaximal, characteristic
2C13×#2888C211yesmaximal, characteristic, complemented
3C13×#2134C211yesmaximal, characteristic, complemented
4C13×#2122C211yesmaximal, characteristic, complemented
5C13×#1795C211yesmaximal, characteristic, complemented
6C13×#1395C211yesmaximal, characteristic, complemented
7C13×#1392C211yesmaximal, characteristic, complemented
8C2×C13×H(5,𝔽2)C2211yescharacteristic
9C2×C13×AGL(1,ℤ/8)C411yescharacteristic, complemented
10C22×C13×D8C411yescharacteristic, complemented
11C13×#568—21no—
12C13×#535C2211yescharacteristic
13C13×#449—21no—
14C13×#449—21no—
15C13×#447—21no—
16C13×#447—21no—
17C13×#421—21no—
18C13×#418—21no—
19C13×#418C411yescharacteristic, complemented
20C13×#416C411yescharacteristic, complemented
21C13×#413—22no—
22C13×#413C2211yescharacteristic
23C13×#413C2211yescharacteristic
24C13×#413C2211yescharacteristic
25C2×C13×#100—21no—
26C2×C13×#100—22no—
27C13×#410C2211yescharacteristic
28C13×#408C2211yescharacteristic
29C13×#355—22no—
30C13×AΣL(1,𝔽16)—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×D4×C13—21no—
39C22×D4×C13—21no—
40C22×D4×C13—21no—
41C22×D4×C13C2×C411yescharacteristic
42C22×D4×C13C2×C411yescharacteristic
43C22×D4×C13D411yescharacteristic
44C22×D4×C13D411yescharacteristic
45C13×AGL(1,ℤ/8)—42no—
46C2×C13×SD16—21no—
47C2×C13×D8—21no—
48C2×C13×D8—21no—
49C2×C13×D8—21no—
50C2×C13×D8—42no—
51C13×#131—42no—
52C13×#131—42no—
53C2×C13×M16—24no—
54C2×C13×M16—21no—
55C2×C13×M16—21no—
56C2×C13×M16—21no—
57C2×C13×M16C2×C411yescharacteristic
58C22×C8×C13C2×C411yescharacteristic
59C13×#127—21no—
60C13×#124—21no—
61C13×#121—21no—
62C13×#121—21no—
63C13×#120—21no—
64C13×#120—21no—
65C13×#117—21no—
66C13×#117C2×C411yescharacteristic
67C13×#104—42no—
68C13×#103—21no—
69C13×#102—21no—
70C13×#102—21no—
71C13×#102—21no—
72C13×#102—42no—
73C13×#101—21no—
74C13×#101—21no—
75C13×#101D412yes—
76C13×#100—24no—
77C13×#100—21no—
78C13×#100—21no—
79C13×#100D412yes—
80C13×#99—21no—
81C13×#99—21no—
82C13×C22⋊C8—21no—
83C13×C22⋊C8—21no—
84#13099C1311yesmaximal, characteristic, direct product factor, Sylow
85C24×C13—21no—
86C24×C13—21no—
87C24×C13—21no—
88C24×C13—21no—
89C13×#41—22no—
90C13×#41—22no—
91C13×#41—22no—
92C13×#41—22no—
93C13×#41—41no—
94C13×#41—41no—
95C13×#41—41no—
96C13×#41—41no—
97C13×#41—44no—
98C2×Q8×C13C22⋊C411yescharacteristic
99C2×Q8×C13C2×D411yescharacteristic
100C2×D4×C13—21no—
101C2×D4×C13—22no—
102C2×D4×C13—22no—
103C2×D4×C13—21no—
104C2×D4×C13—21no—
105C2×D4×C13—21no—
106C2×D4×C13—21no—
107C2×D4×C13—21no—
108C2×D4×C13—21no—
109C2×D4×C13—21no—
110C2×D4×C13—41no—
111C2×D4×C13—41no—
112C2×D4×C13—41no—
113C2×D4×C13—41no—
114C2×D4×C13—44no—
115C2×D4×C13—41no—
116C2×D4×C13—41no—
117C2×D4×C13—44no—
118C2×D4×C13—44no—
119C2×D4×C13—41no—
120C2×D4×C13—41no—
121C2×D4×C13C22⋊C411yescharacteristic
122C2×D4×C13C22⋊C411yescharacteristic
123C2×D4×C13C22⋊C411yescharacteristic
124C2×D4×C13C2×D411yescharacteristic
125C2×D4×C13#4111yescharacteristic
126C2×D4×C13#4111yescharacteristic
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13C22×C411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C13×SD16—42no—
134C13×D8—42no—
135C13×D8—42no—
136C13×D8—42no—
137C13×M16—22no—
138C13×M16—22no—
139C13×M16—44no—
140C13×M16—41no—
141C13×M16—41no—
142C13×M16—41no—
143C13×M16—41no—
144C13×M16—41no—
145C2×C8×C13—21no—
146C2×C8×C13—21no—
147C2×C8×C13—44no—
148C2×C8×C13—41no—
149C2×C8×C13—41no—
150C2×C8×C13—41no—
151C2×C8×C13—41no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—41no—
154C13×C22⋊C4—21no—
155C13×C22⋊C4—41no—
156C13×C22⋊C4—41no—
157C13×C22⋊C4—41no—
158C42×C13—21no—
159C42×C13—41no—
160#3008C2×C1311yescharacteristic
161#2888C2×C1311yescharacteristic, complemented
162#2134C2×C1311yescharacteristic, complemented
163#2122C2×C1311yescharacteristic, complemented
164#1795C2×C1311yescharacteristic, complemented
165#1395C2×C1311yescharacteristic, complemented
166#1392C2×C1311yescharacteristic, complemented
167C23×C13—21no—
168C23×C13—21no—
169C23×C13—21no—
170C23×C13—42no—
171C23×C13—42no—
172C23×C13—42no—
173C23×C13—41no—
174C23×C13—81no—
175C23×C13—161no—
176C23×C13—161no—
177C23×C13—161no—
178C23×C13—161no—
179C23×C13C4×D411yescharacteristic
180C23×C13#12111yescharacteristic
181C23×C13#12311yescharacteristic
182Q8×C13—21no—
183Q8×C13—41no—
184Q8×C13#9912yes—
185D4×C13—24no—
186D4×C13—21no—
187D4×C13—21no—
188D4×C13—21no—
189D4×C13—21no—
190D4×C13—21no—
191D4×C13—41no—
192D4×C13—41no—
193D4×C13—41no—
194D4×C13—42no—
195D4×C13—42no—
196D4×C13—42no—
197D4×C13—42no—
198D4×C13—42no—
199D4×C13—41no—
200D4×C13—41no—
201D4×C13—81no—
202D4×C13—161no—
203D4×C13—161no—
204D4×C13#9912yes—
205C2×C4×C13—24no—
206C2×C4×C13—21no—
207C2×C4×C13—21no—
208C2×C4×C13—21no—
209C2×C4×C13—21no—
210C2×C4×C13—21no—
211C2×C4×C13—21no—
212C2×C4×C13—21no—
213C2×C4×C13—42no—
214C2×C4×C13—42no—
215C2×C4×C13—41no—
216C2×C4×C13—81no—
217C2×C4×C13C2×C22⋊C411yescharacteristic
218C2×C4×C13C4×D411yescharacteristic
219C2×C4×C13#12011yescharacteristic
220C2×C4×C13#12111yescharacteristic
221C8×C13—42no—
222C8×C13—42no—
223C8×C13—41no—
224C8×C13—41no—
225C8×C13—81no—
226C2×H(5,𝔽2)C22×C1311yescharacteristic
227C2×AGL(1,ℤ/8)C4×C1311yescharacteristic, complemented
228C22×D8C4×C1311yescharacteristic, complemented
229#568—21no—
230#535C22×C1311yescharacteristic
231#449—21no—
232#449—21no—
233#447—21no—
234#447—21no—
235#421—21no—
236#418—21no—
237#418C4×C1311yescharacteristic, complemented
238#416C4×C1311yescharacteristic, complemented
239#413—22no—
240#413C22×C1311yescharacteristic
241#413C22×C1311yescharacteristic
242#413C22×C1311yescharacteristic
243C2×#100—21no—
244C2×#100—22no—
245#410C22×C1311yescharacteristic
246#408C22×C1311yescharacteristic
247#355—22no—
248AΣL(1,𝔽16)—22no—
249C22×C13—21no—
250C22×C13—21no—
251C22×C13—22no—
252C22×C13—21no—
253C22×C13—41no—
254C22×C13—41no—
255C22×C13—41no—
256C22×C13—41no—
257C22×C13—41no—
258C22×C13—81no—
259C22×C13—81no—
260C22×C13—81no—
261C22×C13—81no—
262C22×C13—81no—
263C22×C13—81no—
264C22×C13—162no—
265C22×C13—162no—
266C22×C13—162no—
267C22×C13—162no—
268C22×C13#38611yescharacteristic
269C4×C13—21no—
270C4×C13—21no—
271C4×C13—22no—
272C4×C13—21no—
273C4×C13—81no—
274C4×C13—161no—
275C4×C13C2×#9911yescharacteristic
276C4×C13C2×#9911yescharacteristic
277H(5,𝔽2)—42no—
278H(5,𝔽2)—42no—
279C2×#41—21no—
280C2×#41C2×C4×C1311yescharacteristic
281C2×#41D4×C1311yescharacteristic
282C2×#41D4×C1311yescharacteristic
283C2×#41C23×C1311yescharacteristic
284C22×D4—21no—
285C22×D4—21no—
286C22×D4—21no—
287C22×D4C2×C4×C1311yescharacteristic
288C22×D4C2×C4×C1311yescharacteristic
289C22×D4D4×C1311yescharacteristic
290C22×D4D4×C1311yescharacteristic
291AGL(1,ℤ/8)—42no—
292C2×SD16—21no—
293C2×D8—21no—
294C2×D8—21no—
295C2×D8—21no—
296C2×D8—42no—
297#131—42no—
298#131—42no—
299C2×M16—24no—
300C2×M16—21no—
301C2×M16—21no—
302C2×M16—21no—
303C2×M16C2×C4×C1311yescharacteristic
304C22×C8C2×C4×C1311yescharacteristic
305#127—21no—
306#124—21no—
307#121—21no—
308#121—21no—
309#120—21no—
310#120—21no—
311#117—21no—
312#117C2×C4×C1311yescharacteristic
313#104—42no—
314#103—21no—
315#102—21no—
316#102—21no—
317#102—21no—
318#102—42no—
319#101—21no—
320#101—21no—
321#101D4×C1312yes—
322#100—24no—
323#100—21no—
324#100—21no—
325#100D4×C1312yes—
326#99—21no—
327#99—21no—
328C22⋊C8—21no—
329C22⋊C8—21no—
330C2×C13—21no—
331C2×C13—41no—
332C2×C13—41no—
333C2×C13—41no—
334C2×C13—42no—
335C2×C13—81no—
336C2×C13—81no—
337C2×C13—161no—
338C2×C13#189811yescharacteristic
339C24—21no—
340C24—21no—
341C24—21no—
342C24—21no—
343#41—22no—
344#41—22no—
345#41—22no—
346#41—22no—
347#41—41no—
348#41—41no—
349#41—41no—
350#41—41no—
351#41—44no—
352C2×Q8C13×C22⋊C411yescharacteristic
353C2×Q8C2×D4×C1311yescharacteristic
354C2×D4—21no—
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—21no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—44no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—44no—
372C2×D4—44no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4C13×C22⋊C411yescharacteristic
376C2×D4C13×C22⋊C411yescharacteristic
377C2×D4C13×C22⋊C411yescharacteristic
378C2×D4C2×D4×C1311yescharacteristic
379C2×D4C13×#4111yescharacteristic
380C2×D4C13×#4111yescharacteristic
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4C22×C4×C1311yescharacteristic
385C22×C4C2×D4×C1311yescharacteristic
386C22×C4C2×D4×C1311yescharacteristic
387SD16—42no—
388D8—42no—
389D8—42no—
390D8—42no—
391M16—22no—
392M16—22no—
393M16—44no—
394M16—41no—
395M16—41no—
396M16—41no—
397M16—41no—
398M16—41no—
399C2×C8—21no—
400C2×C8—21no—
401C2×C8—44no—
402C2×C8—41no—
403C2×C8—41no—
404C2×C8—41no—
405C2×C8—41no—
406C4⋊C4—21no—
407C4⋊C4—41no—
408C22⋊C4—21no—
409C22⋊C4—41no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C42—21no—
413C42—41no—
414C13#1309911yescharacteristic, direct product factor, Sylow
415C23—21no—
416C23—21no—
417C23—21no—
418C23—42no—
419C23—42no—
420C23—42no—
421C23—41no—
422C23—81no—
423C23—161no—
424C23—161no—
425C23—161no—
426C23—161no—
427C23C4×D4×C1311yescharacteristic
428C23C13×#12111yescharacteristic
429C23C13×#12311yescharacteristic
430Q8—21no—
431Q8—41no—
432Q8C13×#9912yes—
433D4—24no—
434D4—21no—
435D4—21no—
436D4—21no—
437D4—21no—
438D4—21no—
439D4—41no—
440D4—41no—
441D4—41no—
442D4—42no—
443D4—42no—
444D4—42no—
445D4—42no—
446D4—42no—
447D4—41no—
448D4—41no—
449D4—81no—
450D4—161no—
451D4—161no—
452D4C13×#9912yes—
453C2×C4—24no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—41no—
464C2×C4—81no—
465C2×C4C2×C13×C22⋊C411yescharacteristic
466C2×C4C4×D4×C1311yescharacteristic
467C2×C4C13×#12011yescharacteristic
468C2×C4C13×#12111yescharacteristic
469C8—42no—
470C8—42no—
471C8—41no—
472C8—41no—
473C8—81no—
474C22—21no—
475C22—21no—
476C22—22no—
477C22—21no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22—41no—
482C22—41no—
483C22—81no—
484C22—81no—
485C22—81no—
486C22—81no—
487C22—81no—
488C22—81no—
489C22—162no—
490C22—162no—
491C22—162no—
492C22—162no—
493C22C13×#38611yescharacteristic
494C4—21no—
495C4—21no—
496C4—22no—
497C4—21no—
498C4—81no—
499C4—161no—
500C4C2×C13×#9911yescharacteristic
501C4C2×C13×#9911yescharacteristic
502C2—21no—
503C2—41no—
504C2—41no—
505C2—41no—
506C2—42no—
507C2—81no—
508C2—81no—
509C2—161no—
510C2C13×#189811yescharacteristic
subgroupG/H
center, socleC2×C13#1898
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×#41C23×C13
prime radicalC13×#3008C2
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
2. C13×#2888C2semidirect
3. C13×#2134C2semidirect
4. C13×#2122C2semidirect
5. C13×#1795C2semidirect
6. C13×#1395C2semidirect
7. C13×#1392C2semidirect
9. C2×C13×AGL(1,ℤ/8)C4semidirect
10. C22×C13×D8C4semidirect
19. C13×#418C4semidirect
20. C13×#416C4semidirect
84. #13099C13direct (N × H)
161. #2888C2×C13semidirect
162. #2134C2×C13semidirect
163. #2122C2×C13semidirect
164. #1795C2×C13semidirect
165. #1395C2×C13semidirect
166. #1392C2×C13semidirect
227. C2×AGL(1,ℤ/8)C4×C13semidirect
228. C22×D8C4×C13semidirect
237. #418C4×C13semidirect
238. #416C4×C13semidirect
414. C13#13099direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#30082
C13×#28882
C13×#21342
C13×#21222
C13×#17952
C13×#13952
C13×#13922
#1309913