Finite Group Databasebeta

← C13×#13098 #15699437

Subgroups — C13×#13098 #15699437

Order 3328.

640 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3010C211yesmaximal, characteristic
2C13×#2889C211yesmaximal, characteristic, complemented
3C13×#2134C211yesmaximal, characteristic, complemented
4C13×#2122C211yesmaximal, characteristic, complemented
5C13×#1796C211yesmaximal, characteristic, complemented
6C13×#1395C211yesmaximal, characteristic, complemented
7C13×#1392C211yesmaximal, characteristic, complemented
8C2×C13×2−1+4C2211yescharacteristic
9C2×C13×AGL(1,ℤ/8)C411yescharacteristic, complemented
10C22×C13×SD16C411yescharacteristic, complemented
11C13×#568—21no—
12C13×#535C2211yescharacteristic
13C13×#449—21no—
14C13×#449—21no—
15C13×#448—21no—
16C13×#448—21no—
17C13×#421—21no—
18C13×#419—21no—
19C13×#419C411yescharacteristic, complemented
20C13×#416C411yescharacteristic, complemented
21C13×#413—22no—
22C13×#413C2211yescharacteristic
23C13×#413C2211yescharacteristic
24C13×#413C2211yescharacteristic
25C2×C13×#101—21no—
26C2×C13×#101—22no—
27C13×#410C2211yescharacteristic
28C13×#408C2211yescharacteristic
29C13×#355—22no—
30C13×AΣL(1,𝔽16)—22no—
31C13×2−1+4—42no—
32C13×2−1+4—42no—
33C2×C13×#41—21no—
34C2×C13×#41—21no—
35C2×C13×#41—21no—
36C2×C13×#41C2×C411yescharacteristic
37C2×C13×#41D411yescharacteristic
38C2×C13×#41D411yescharacteristic
39C2×C13×#41C2311yescharacteristic
40C22×Q8×C13—21no—
41C22×Q8×C13C2×C411yescharacteristic
42C22×Q8×C13D411yescharacteristic
43C22×Q8×C13D411yescharacteristic
44C22×D4×C13C2×C411yescharacteristic
45C13×AGL(1,ℤ/8)—42no—
46C2×C13×SD16—21no—
47C2×C13×SD16—21no—
48C2×C13×SD16—21no—
49C2×C13×SD16—42no—
50C2×C13×D8—21no—
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×#103—21no—
70C13×#103—21no—
71C13×#103—42no—
72C13×#102—21no—
73C13×#101—24no—
74C13×#101—21no—
75C13×#101—21no—
76C13×#101D412yes—
77C13×#100—21no—
78C13×#100—21no—
79C13×#100D412yes—
80C13×#99—21no—
81C13×#99—21no—
82C13×C22⋊C8—21no—
83C13×C22⋊C8—21no—
84#13098C1311yesmaximal, characteristic, direct product factor, Sylow
85C24×C13—21no—
86C13×#41—22no—
87C13×#41—22no—
88C13×#41—22no—
89C13×#41—22no—
90C13×#41—41no—
91C13×#41—41no—
92C13×#41—41no—
93C13×#41—41no—
94C13×#41—44no—
95C13×#41—44no—
96C13×#41—44no—
97C2×Q8×C13—21no—
98C2×Q8×C13—21no—
99C2×Q8×C13—21no—
100C2×Q8×C13—22no—
101C2×Q8×C13—22no—
102C2×Q8×C13—41no—
103C2×Q8×C13—41no—
104C2×Q8×C13—41no—
105C2×Q8×C13—41no—
106C2×Q8×C13—44no—
107C2×Q8×C13C22⋊C411yescharacteristic
108C2×Q8×C13C22⋊C411yescharacteristic
109C2×Q8×C13C22⋊C411yescharacteristic
110C2×Q8×C13C2×D411yescharacteristic
111C2×D4×C13—21no—
112C2×D4×C13—21no—
113C2×D4×C13—21no—
114C2×D4×C13—21no—
115C2×D4×C13—21no—
116C2×D4×C13—41no—
117C2×D4×C13—41no—
118C2×D4×C13—41no—
119C2×D4×C13—41no—
120C2×D4×C13C22⋊C411yescharacteristic
121C2×D4×C13C2×D411yescharacteristic
122C2×D4×C13#4111yescharacteristic
123C2×D4×C13#4111yescharacteristic
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
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×SD16—42no—
135C13×SD16—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#3010C2×C1311yescharacteristic
161#2889C2×C1311yescharacteristic, complemented
162#2134C2×C1311yescharacteristic, complemented
163#2122C2×C1311yescharacteristic, complemented
164#1796C2×C1311yescharacteristic, complemented
165#1395C2×C1311yescharacteristic, complemented
166#1392C2×C1311yescharacteristic, complemented
167C23×C13—21no—
168C23×C13—41no—
169C23×C13—81no—
170C23×C13—161no—
171C23×C13C4×D411yescharacteristic
172C23×C13#12111yescharacteristic
173C23×C13#12311yescharacteristic
174Q8×C13—21no—
175Q8×C13—21no—
176Q8×C13—21no—
177Q8×C13—21no—
178Q8×C13—21no—
179Q8×C13—41no—
180Q8×C13—42no—
181Q8×C13—42no—
182Q8×C13—42no—
183Q8×C13#9912yes—
184D4×C13—24no—
185D4×C13—21no—
186D4×C13—41no—
187D4×C13—41no—
188D4×C13—41no—
189D4×C13—42no—
190D4×C13—42no—
191D4×C13—41no—
192D4×C13—41no—
193D4×C13—81no—
194D4×C13—161no—
195D4×C13—161no—
196D4×C13#9912yes—
197C2×C4×C13—24no—
198C2×C4×C13—21no—
199C2×C4×C13—21no—
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—81no—
214C2×C4×C13C2×C22⋊C411yescharacteristic
215C2×C4×C13C4×D411yescharacteristic
216C2×C4×C13#12011yescharacteristic
217C2×C4×C13#12111yescharacteristic
218C8×C13—42no—
219C8×C13—42no—
220C8×C13—41no—
221C8×C13—41no—
222C8×C13—81no—
223C2×2−1+4C22×C1311yescharacteristic
224C2×AGL(1,ℤ/8)C4×C1311yescharacteristic, complemented
225C22×SD16C4×C1311yescharacteristic, complemented
226#568—21no—
227#535C22×C1311yescharacteristic
228#449—21no—
229#449—21no—
230#448—21no—
231#448—21no—
232#421—21no—
233#419—21no—
234#419C4×C1311yescharacteristic, complemented
235#416C4×C1311yescharacteristic, complemented
236#413—22no—
237#413C22×C1311yescharacteristic
238#413C22×C1311yescharacteristic
239#413C22×C1311yescharacteristic
240C2×#101—21no—
241C2×#101—22no—
242#410C22×C1311yescharacteristic
243#408C22×C1311yescharacteristic
244#355—22no—
245AΣL(1,𝔽16)—22no—
246C22×C13—21no—
247C22×C13—21no—
248C22×C13—22no—
249C22×C13—21no—
250C22×C13—41no—
251C22×C13—41no—
252C22×C13—41no—
253C22×C13—81no—
254C22×C13—81no—
255C22×C13—81no—
256C22×C13—81no—
257C22×C13—162no—
258C22×C13#38611yescharacteristic
259C4×C13—21no—
260C4×C13—21no—
261C4×C13—22no—
262C4×C13—21no—
263C4×C13—41no—
264C4×C13—41no—
265C4×C13—81no—
266C4×C13—161no—
267C4×C13C2×#9911yescharacteristic
268C4×C13C2×#9911yescharacteristic
2692−1+4—42no—
2702−1+4—42no—
271C2×#41—21no—
272C2×#41—21no—
273C2×#41—21no—
274C2×#41C2×C4×C1311yescharacteristic
275C2×#41D4×C1311yescharacteristic
276C2×#41D4×C1311yescharacteristic
277C2×#41C23×C1311yescharacteristic
278C22×Q8—21no—
279C22×Q8C2×C4×C1311yescharacteristic
280C22×Q8D4×C1311yescharacteristic
281C22×Q8D4×C1311yescharacteristic
282C22×D4C2×C4×C1311yescharacteristic
283AGL(1,ℤ/8)—42no—
284C2×SD16—21no—
285C2×SD16—21no—
286C2×SD16—21no—
287C2×SD16—42no—
288C2×D8—21no—
289#131—42no—
290#131—42no—
291C2×M16—24no—
292C2×M16—21no—
293C2×M16—21no—
294C2×M16—21no—
295C2×M16C2×C4×C1311yescharacteristic
296C22×C8C2×C4×C1311yescharacteristic
297#127—21no—
298#124—21no—
299#121—21no—
300#121—21no—
301#120—21no—
302#120—21no—
303#117—21no—
304#117C2×C4×C1311yescharacteristic
305#104—42no—
306#103—21no—
307#103—21no—
308#103—21no—
309#103—42no—
310#102—21no—
311#101—24no—
312#101—21no—
313#101—21no—
314#101D4×C1312yes—
315#100—21no—
316#100—21no—
317#100D4×C1312yes—
318#99—21no—
319#99—21no—
320C22⋊C8—21no—
321C22⋊C8—21no—
322C2×C13—21no—
323C2×C13—41no—
324C2×C13—41no—
325C2×C13—41no—
326C2×C13—42no—
327C2×C13—161no—
328C2×C13#189811yescharacteristic
329C24—21no—
330#41—22no—
331#41—22no—
332#41—22no—
333#41—22no—
334#41—41no—
335#41—41no—
336#41—41no—
337#41—41no—
338#41—44no—
339#41—44no—
340#41—44no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8—21no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8—41no—
347C2×Q8—41no—
348C2×Q8—41no—
349C2×Q8—41no—
350C2×Q8—44no—
351C2×Q8C13×C22⋊C411yescharacteristic
352C2×Q8C13×C22⋊C411yescharacteristic
353C2×Q8C13×C22⋊C411yescharacteristic
354C2×Q8C2×D4×C1311yescharacteristic
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4C13×C22⋊C411yescharacteristic
365C2×D4C2×D4×C1311yescharacteristic
366C2×D4C13×#4111yescharacteristic
367C2×D4C13×#4111yescharacteristic
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4C22×C4×C1311yescharacteristic
375C22×C4C2×D4×C1311yescharacteristic
376C22×C4C2×D4×C1311yescharacteristic
377SD16—42no—
378SD16—42no—
379SD16—42no—
380D8—42no—
381M16—22no—
382M16—22no—
383M16—44no—
384M16—41no—
385M16—41no—
386M16—41no—
387M16—41no—
388M16—41no—
389C2×C8—21no—
390C2×C8—21no—
391C2×C8—44no—
392C2×C8—41no—
393C2×C8—41no—
394C2×C8—41no—
395C2×C8—41no—
396C4⋊C4—21no—
397C4⋊C4—41no—
398C22⋊C4—21no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—41no—
402C42—21no—
403C42—41no—
404C13#1309811yescharacteristic, direct product factor, Sylow
405C23—21no—
406C23—41no—
407C23—81no—
408C23—161no—
409C23C4×D4×C1311yescharacteristic
410C23C13×#12111yescharacteristic
411C23C13×#12311yescharacteristic
412Q8—21no—
413Q8—21no—
414Q8—21no—
415Q8—21no—
416Q8—21no—
417Q8—41no—
418Q8—42no—
419Q8—42no—
420Q8—42no—
421Q8C13×#9912yes—
422D4—24no—
423D4—21no—
424D4—41no—
425D4—41no—
426D4—41no—
427D4—42no—
428D4—42no—
429D4—41no—
430D4—41no—
431D4—81no—
432D4—161no—
433D4—161no—
434D4C13×#9912yes—
435C2×C4—24no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—81no—
452C2×C4C2×C13×C22⋊C411yescharacteristic
453C2×C4C4×D4×C1311yescharacteristic
454C2×C4C13×#12011yescharacteristic
455C2×C4C13×#12111yescharacteristic
456C8—42no—
457C8—42no—
458C8—41no—
459C8—41no—
460C8—81no—
461C22—21no—
462C22—21no—
463C22—22no—
464C22—21no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22—81no—
472C22—162no—
473C22C13×#38611yescharacteristic
474C4—21no—
475C4—21no—
476C4—22no—
477C4—21no—
478C4—41no—
479C4—41no—
480C4—81no—
481C4—161no—
482C4C2×C13×#9911yescharacteristic
483C4C2×C13×#9911yescharacteristic
484C2—21no—
485C2—41no—
486C2—41no—
487C2—41no—
488C2—42no—
489C2—161no—
490C2C13×#189811yescharacteristic
subgroupG/H
center, socleC2×C13#1898
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×#41C23×C13
prime radicalC13×#3010C2
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C13×2−1+4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2889C2semidirect
3. C13×#2134C2semidirect
4. C13×#2122C2semidirect
5. C13×#1796C2semidirect
6. C13×#1395C2semidirect
7. C13×#1392C2semidirect
9. C2×C13×AGL(1,ℤ/8)C4semidirect
10. C22×C13×SD16C4semidirect
19. C13×#419C4semidirect
20. C13×#416C4semidirect
84. #13098C13direct (N × H)
161. #2889C2×C13semidirect
162. #2134C2×C13semidirect
163. #2122C2×C13semidirect
164. #1796C2×C13semidirect
165. #1395C2×C13semidirect
166. #1392C2×C13semidirect
224. C2×AGL(1,ℤ/8)C4×C13semidirect
225. C22×SD16C4×C13semidirect
234. #419C4×C13semidirect
235. #416C4×C13semidirect
404. C13#13098direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#30102
C13×#28892
C13×#21342
C13×#21222
C13×#17962
C13×#13952
C13×#13922
#1309813