Finite Group Databasebeta

← C13×#13097 #15699436

Subgroups — C13×#13097 #15699436

Order 3328.

650 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3009C211yesmaximal, characteristic
2C13×#2888C211yesmaximal, characteristic
3C13×#2135C211yesmaximal, characteristic, complemented
4C13×#2123C211yesmaximal, characteristic, complemented
5C13×#1795C211yesmaximal, characteristic
6C13×#1395C211yesmaximal, characteristic, complemented
7C13×#1392C211yesmaximal, characteristic, complemented
8C2×C13×H(5,𝔽2)C2211yescharacteristic
9C2×C13×#137C411yescharacteristic, complemented
10C22×C13×SD16C411yescharacteristic, complemented
11C13×#568—21no—
12C13×#536C2211yescharacteristic
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×#413—22no—
22C13×#413C2211yescharacteristic
23C13×#413C2211yescharacteristic
24C13×#413C2211yescharacteristic
25C2×C13×#100—21no—
26C2×C13×#100—22no—
27C13×#410C2211yescharacteristic
28C13×#408C2211yescharacteristic
29C13×#356—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
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—
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×C4⋊Q8—21no—
60C13×#124—21no—
61C13×#123—21no—
62C13×#123—21no—
63C13×C22⋊Q8—21no—
64C13×C22⋊Q8—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#13097C1311yesmaximal, characteristic, direct product factor, Sylow
85C24×C13—21no—
86C24×C13—21no—
87C24×C13—21no—
88C13×#41—22no—
89C13×#41—22no—
90C13×#41—22no—
91C13×#41—22no—
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×C13C2×D411yescharacteristic
103C2×D4×C13—21no—
104C2×D4×C13—22no—
105C2×D4×C13—22no—
106C2×D4×C13—21no—
107C2×D4×C13—21no—
108C2×D4×C13—21no—
109C2×D4×C13—21no—
110C2×D4×C13—21no—
111C2×D4×C13—41no—
112C2×D4×C13—41no—
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×C13#4111yescharacteristic
123C2×D4×C13#4111yescharacteristic
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13C22×C411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C13×Q16—42no—
132C13×SD16—42no—
133C13×SD16—42no—
134C13×SD16—42no—
135C13×M16—22no—
136C13×M16—22no—
137C13×M16—44no—
138C13×M16—41no—
139C13×M16—41no—
140C13×M16—41no—
141C13×M16—41no—
142C13×M16—41no—
143C2×C8×C13—21no—
144C2×C8×C13—21no—
145C2×C8×C13—44no—
146C2×C8×C13—41no—
147C2×C8×C13—41no—
148C2×C8×C13—41no—
149C2×C8×C13—41no—
150C13×C4⋊C4—21no—
151C13×C4⋊C4—41no—
152C13×C4⋊C4—41no—
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#3009C2×C1311yescharacteristic
161#2888C2×C1311yescharacteristic
162#2135C2×C1311yescharacteristic, complemented
163#2123C2×C1311yescharacteristic, complemented
164#1795C2×C1311yescharacteristic
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—161no—
174C23×C13—161no—
175C23×C13—161no—
176C23×C13C4×D411yescharacteristic
177C23×C13#12111yescharacteristic
178C23×C13#12311yescharacteristic
179Q8×C13—21no—
180Q8×C13—41no—
181Q8×C13—41no—
182Q8×C13—41no—
183Q8×C13—81no—
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#9912yes—
200C2×C4×C13—24no—
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—21no—
208C2×C4×C13—42no—
209C2×C4×C13—42no—
210C2×C4×C13—41no—
211C2×C4×C13—41no—
212C2×C4×C13—81no—
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×H(5,𝔽2)C22×C1311yescharacteristic
224C2×#137C4×C1311yescharacteristic, complemented
225C22×SD16C4×C1311yescharacteristic, complemented
226#568—21no—
227#536C22×C1311yescharacteristic
228#452—21no—
229#452—21no—
230#450—21no—
231#450—21no—
232#421—21no—
233#418—21no—
234#418C4×C1311yescharacteristic, complemented
235#416C4×C1311yescharacteristic, complemented
236#413—22no—
237#413C22×C1311yescharacteristic
238#413C22×C1311yescharacteristic
239#413C22×C1311yescharacteristic
240C2×#100—21no—
241C2×#100—22no—
242#410C22×C1311yescharacteristic
243#408C22×C1311yescharacteristic
244#356—22no—
245#352—22no—
246C22×C13—21no—
247C22×C13—21no—
248C22×C13—21no—
249C22×C13—22no—
250C22×C13—41no—
251C22×C13—41no—
252C22×C13—41no—
253C22×C13—41no—
254C22×C13—41no—
255C22×C13—81no—
256C22×C13—81no—
257C22×C13—81no—
258C22×C13—162no—
259C22×C13—162no—
260C22×C13—162no—
261C22×C13#38611yescharacteristic
262C4×C13—21no—
263C4×C13—21no—
264C4×C13—22no—
265C4×C13—21no—
266C4×C13—81no—
267C4×C13—81no—
268C4×C13—161no—
269C4×C13C2×#9911yescharacteristic
270C4×C13C2×#9911yescharacteristic
271H(5,𝔽2)—42no—
272H(5,𝔽2)—42no—
273C2×#41—21no—
274C2×#41C2×C4×C1311yescharacteristic
275C2×#41D4×C1311yescharacteristic
276C2×#41D4×C1311yescharacteristic
277C2×#41C23×C1311yescharacteristic
278C22×Q8C2×C4×C1311yescharacteristic
279C22×D4—21no—
280C22×D4—21no—
281C22×D4—21no—
282C22×D4C2×C4×C1311yescharacteristic
283C22×D4D4×C1311yescharacteristic
284C22×D4D4×C1311yescharacteristic
285#137—42no—
286C2×Q16—21no—
287C2×SD16—21no—
288C2×SD16—21no—
289C2×SD16—21no—
290C2×SD16—42no—
291#131—42no—
292#131—42no—
293C2×M16—24no—
294C2×M16—21no—
295C2×M16—21no—
296C2×M16—21no—
297C2×M16C2×C4×C1311yescharacteristic
298C22×C8C2×C4×C1311yescharacteristic
299C4⋊Q8—21no—
300#124—21no—
301#123—21no—
302#123—21no—
303C22⋊Q8—21no—
304C22⋊Q8—21no—
305#117—21no—
306#117C2×C4×C1311yescharacteristic
307#104—42no—
308#103—21no—
309#102—21no—
310#102—21no—
311#102—21no—
312#102—42no—
313#101—21no—
314#101—21no—
315#101D4×C1312yes—
316#100—24no—
317#100—21no—
318#100—21no—
319#100D4×C1312yes—
320#99—21no—
321#99—21no—
322C22⋊C8—21no—
323C22⋊C8—21no—
324C2×C13—21no—
325C2×C13—41no—
326C2×C13—41no—
327C2×C13—41no—
328C2×C13—42no—
329C2×C13—81no—
330C2×C13—81no—
331C2×C13#189811yescharacteristic
332C24—21no—
333C24—21no—
334C24—21no—
335#41—22no—
336#41—22no—
337#41—22no—
338#41—22no—
339#41—41no—
340#41—41no—
341#41—41no—
342#41—41no—
343#41—44no—
344C2×Q8—21no—
345C2×Q8—21no—
346C2×Q8—41no—
347C2×Q8—41no—
348C2×Q8C13×C22⋊C411yescharacteristic
349C2×Q8C2×D4×C1311yescharacteristic
350C2×D4—21no—
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—41no—
359C2×D4—41no—
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—44no—
363C2×D4—44no—
364C2×D4—44no—
365C2×D4C13×C22⋊C411yescharacteristic
366C2×D4C13×C22⋊C411yescharacteristic
367C2×D4C13×C22⋊C411yescharacteristic
368C2×D4C2×D4×C1311yescharacteristic
369C2×D4C13×#4111yescharacteristic
370C2×D4C13×#4111yescharacteristic
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4C22×C4×C1311yescharacteristic
376C22×C4C2×D4×C1311yescharacteristic
377C22×C4C2×D4×C1311yescharacteristic
378Q16—42no—
379SD16—42no—
380SD16—42no—
381SD16—42no—
382M16—22no—
383M16—22no—
384M16—44no—
385M16—41no—
386M16—41no—
387M16—41no—
388M16—41no—
389M16—41no—
390C2×C8—21no—
391C2×C8—21no—
392C2×C8—44no—
393C2×C8—41no—
394C2×C8—41no—
395C2×C8—41no—
396C2×C8—41no—
397C4⋊C4—21no—
398C4⋊C4—41no—
399C4⋊C4—41no—
400C4⋊C4—41no—
401C22⋊C4—21no—
402C22⋊C4—41no—
403C22⋊C4—41no—
404C22⋊C4—41no—
405C42—21no—
406C42—41no—
407C13#1309711yescharacteristic, direct product factor, Sylow
408C23—21no—
409C23—21no—
410C23—21no—
411C23—42no—
412C23—42no—
413C23—42no—
414C23—161no—
415C23—161no—
416C23—161no—
417C23C4×D4×C1311yescharacteristic
418C23C13×#12111yescharacteristic
419C23C13×#12311yescharacteristic
420Q8—21no—
421Q8—41no—
422Q8—41no—
423Q8—41no—
424Q8—81no—
425Q8C13×#9912yes—
426D4—24no—
427D4—21no—
428D4—21no—
429D4—21no—
430D4—21no—
431D4—21no—
432D4—41no—
433D4—41no—
434D4—41no—
435D4—42no—
436D4—42no—
437D4—42no—
438D4—42no—
439D4—42no—
440D4C13×#9912yes—
441C2×C4—24no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—81no—
454C2×C4—81no—
455C2×C4C2×C13×C22⋊C411yescharacteristic
456C2×C4C4×D4×C1311yescharacteristic
457C2×C4C13×#12011yescharacteristic
458C2×C4C13×#12111yescharacteristic
459C8—42no—
460C8—42no—
461C8—41no—
462C8—41no—
463C8—81no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—22no—
468C22—41no—
469C22—41no—
470C22—41no—
471C22—41no—
472C22—41no—
473C22—81no—
474C22—81no—
475C22—81no—
476C22—162no—
477C22—162no—
478C22—162no—
479C22C13×#38611yescharacteristic
480C4—21no—
481C4—21no—
482C4—22no—
483C4—21no—
484C4—81no—
485C4—81no—
486C4—161no—
487C4C2×C13×#9911yescharacteristic
488C4C2×C13×#9911yescharacteristic
489C2—21no—
490C2—41no—
491C2—41no—
492C2—41no—
493C2—42no—
494C2—81no—
495C2—81no—
496C2C13×#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×#2135C2semidirect
4. C13×#2123C2semidirect
6. C13×#1395C2semidirect
7. C13×#1392C2semidirect
9. C2×C13×#137C4semidirect
10. C22×C13×SD16C4semidirect
19. C13×#418C4semidirect
20. C13×#416C4semidirect
84. #13097C13direct (N × H)
162. #2135C2×C13semidirect
163. #2123C2×C13semidirect
165. #1395C2×C13semidirect
166. #1392C2×C13semidirect
224. C2×#137C4×C13semidirect
225. C22×SD16C4×C13semidirect
234. #418C4×C13semidirect
235. #416C4×C13semidirect
407. C13#13097direct (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×#28882
C13×#21352
C13×#21232
C13×#17952
C13×#13952
C13×#13922
#1309713