Finite Group Databasebeta

← C13×#9265 #15695604

Subgroups — C13×#9265 #15695604

Order 3328.

438 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3211C211yesmaximal, characteristic
2C13×#2968C211yesmaximal, characteristic, complemented
3C13×#1532C211yesmaximal, characteristic, complemented
4C2×C13×#329C211yesmaximal, characteristic, complemented
5C13×#1469C211yesmaximal, characteristic, complemented
6C13×#1302C211yesmaximal, characteristic, complemented
7C13×#1281C211yesmaximal, characteristic, complemented
8C13×#529C2211yescharacteristic
9C2×C13×#124C2211yescharacteristic
10C13×#495—21no—
11C13×#488—21no—
12C13×#464—21no—
13C13×#463—21no—
14C13×#451C411yescharacteristic
15C13×#450C411yescharacteristic
16C13×#448C411yescharacteristic
17C13×#447C411yescharacteristic
18C13×#446—21no—
19C13×#435—21no—
20C13×#435—21no—
21C8×D4×C13—21no—
22C13×#433—21no—
23C13×#432C2211yescharacteristic
24C13×#431C2211yescharacteristic
25C13×#431C2211yescharacteristic
26C13×#405—21no—
27C2×C13×#97C2211yescharacteristic
28C2×C13×#97C2211yescharacteristic
29C13×#330—21no—
30C13×#329—21no—
31C13×#329—21no—
32C13×#329—21no—
33C13×#323—21no—
34C13×#323—21no—
35C22×Q8×C13C2×C411yescharacteristic
36C22×D4×C13C2×C411yescharacteristic
37C2×C13×Q16—21no—
38C2×C13×SD16—21no—
39C2×C13×SD16—21no—
40C2×C13×D8—21no—
41C2×C13×M16—21no—
42C22×C8×C13—21no—
43C22×C8×C13—21no—
44C22×C8×C13—21no—
45C13×#126—21no—
46C13×#125D411yescharacteristic
47C13×#124—21no—
48C13×#124—21no—
49C13×#124—21no—
50C13×#124—21no—
51C13×#124D411yescharacteristic
52C13×#123—21no—
53C13×C22⋊Q8C2×C411yescharacteristic
54C13×#121C2×C411yescharacteristic
55C4×Q8×C13D411yescharacteristic
56C4×D4×C13—21no—
57C4×D4×C13D411yescharacteristic
58C13×#117—21no—
59C2×C13×C22⋊C4—21no—
60C2×C13×C22⋊C4—21no—
61C2×C42×C13C2311yescharacteristic
62C13×C4⋊C8—21no—
63C13×C4⋊C8—21no—
64C13×C4⋊C8—21no—
65C13×C4⋊C8—21no—
66C13×C4⋊C8—21no—
67C13×#103—21no—
68C13×#103—21no—
69C13×#102—21no—
70C13×#102—21no—
71C13×C22⋊C8—21no—
72C13×C22⋊C8—21no—
73C13×C22⋊C8—21no—
74C13×C22⋊C8C2×C411yescharacteristic
75C13×C22⋊C8C2×C411yescharacteristic
76C13×C22⋊C8D411yescharacteristic
77C13×C22⋊C8D411yescharacteristic
78C13×#97—21no—
79C13×#97—21no—
80C13×#97—21no—
81C13×#97—21no—
82C13×#97—21no—
83C13×#97D411yescharacteristic
84C13×#97D411yescharacteristic
85C4×C8×C13—21no—
86C4×C8×C13—21no—
87C4×C8×C13—21no—
88#9265C1311yesmaximal, characteristic, direct product factor, Sylow
89C24×C13—21no—
90C2×Q8×C13—21no—
91C2×Q8×C13—21no—
92C2×Q8×C13—81no—
93C2×Q8×C13C22⋊C411yescharacteristic
94C2×D4×C13—21no—
95C2×D4×C13—21no—
96C2×D4×C13—21no—
97C2×D4×C13—81no—
98C2×D4×C13C22⋊C411yescharacteristic
99C22×C4×C13—21no—
100C22×C4×C13—21no—
101C22×C4×C13C22×C411yescharacteristic
102C22×C4×C13C2×D411yescharacteristic
103C22×C4×C13#4111yescharacteristic
104C13×Q16—81no—
105C13×SD16—81no—
106C13×SD16—81no—
107C13×D8—81no—
108C13×M16—42no—
109C2×C8×C13—21no—
110C2×C8×C13—22no—
111C2×C8×C13—21no—
112C2×C8×C13—21no—
113C2×C8×C13—21no—
114C2×C8×C13—21no—
115C2×C8×C13—21no—
116C2×C8×C13—42no—
117C2×C8×C13—42no—
118C2×C8×C13—41no—
119C2×C8×C13—41no—
120C2×C8×C13—41no—
121C13×C4⋊C4—21no—
122C13×C4⋊C4—21no—
123C13×C4⋊C4—21no—
124C13×C4⋊C4—21no—
125C13×C4⋊C4C22⋊C411yescharacteristic
126C13×C4⋊C4C22⋊C411yescharacteristic
127C13×C22⋊C4—21no—
128C13×C22⋊C4—21no—
129C13×C22⋊C4—21no—
130C13×C22⋊C4—21no—
131C13×C22⋊C4—21no—
132C13×C22⋊C4—41no—
133C13×C22⋊C4—41no—
134C13×C22⋊C4—41no—
135C13×C22⋊C4—41no—
136C42×C13—21no—
137C42×C13C2×D411yescharacteristic
138C42×C13C2×D411yescharacteristic
139C42×C13C2×D411yescharacteristic
140C42×C13#4111yescharacteristic
141#3211C2×C1311yescharacteristic
142#2968C2×C1311yescharacteristic, complemented
143#1532C2×C1311yescharacteristic, complemented
144C2×#329C2×C1311yescharacteristic, complemented
145#1469C2×C1311yescharacteristic, complemented
146#1302C2×C1311yescharacteristic, complemented
147#1281C2×C1311yescharacteristic, complemented
148C23×C13—21no—
149C23×C13—41no—
150C23×C13—41no—
151C23×C13—41no—
152C23×C13—81no—
153C23×C13—81no—
154C23×C13C4×D411yescharacteristic
155Q8×C13—41no—
156Q8×C13—41no—
157Q8×C13—41no—
158Q8×C13—81no—
159D4×C13—41no—
160D4×C13—41no—
161D4×C13—41no—
162D4×C13—41no—
163D4×C13—41no—
164D4×C13—81no—
165C2×C4×C13—21no—
166C2×C4×C13—21no—
167C2×C4×C13—21no—
168C2×C4×C13—21no—
169C2×C4×C13—21no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13—81no—
176C2×C4×C13C2×C22⋊C411yescharacteristic
177C2×C4×C13C4×D411yescharacteristic
178C2×C4×C13#12011yescharacteristic
179C2×C4×C13#12111yescharacteristic
180C2×C4×C13#12111yescharacteristic
181C2×C4×C13#12311yescharacteristic
182C8×C13—22no—
183C8×C13—42no—
184C8×C13—41no—
185C8×C13—41no—
186C8×C13—41no—
187C8×C13—41no—
188C8×C13—41no—
189C8×C13—81no—
190#529C22×C1311yescharacteristic
191C2×#124C22×C1311yescharacteristic
192#495—21no—
193#488—21no—
194#464—21no—
195#463—21no—
196#451C4×C1311yescharacteristic
197#450C4×C1311yescharacteristic
198#448C4×C1311yescharacteristic
199#447C4×C1311yescharacteristic
200#446—21no—
201#435—21no—
202#435—21no—
203C8×D4—21no—
204#433—21no—
205#432C22×C1311yescharacteristic
206#431C22×C1311yescharacteristic
207#431C22×C1311yescharacteristic
208#405—21no—
209C2×#97C22×C1311yescharacteristic
210C2×#97C22×C1311yescharacteristic
211#330—21no—
212#329—21no—
213#329—21no—
214#329—21no—
215#323—21no—
216#323—21no—
217C22×C13—21no—
218C22×C13—21no—
219C22×C13—41no—
220C22×C13—41no—
221C22×C13—41no—
222C22×C13—81no—
223C22×C13—81no—
224C22×C13—81no—
225C22×C13—161no—
226C22×C13—161no—
227C22×C13#38611yescharacteristic
228C22×C13#44311yescharacteristic
229C22×C13#44411yescharacteristic
230C4×C13—21no—
231C4×C13—21no—
232C4×C13—21no—
233C4×C13—21no—
234C4×C13—21no—
235C4×C13—21no—
236C4×C13—41no—
237C4×C13—41no—
238C4×C13—41no—
239C4×C13—81no—
240C22×Q8C2×C4×C1311yescharacteristic
241C22×D4C2×C4×C1311yescharacteristic
242C2×Q16—21no—
243C2×SD16—21no—
244C2×SD16—21no—
245C2×D8—21no—
246C2×M16—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250#126—21no—
251#125D4×C1311yescharacteristic
252#124—21no—
253#124—21no—
254#124—21no—
255#124—21no—
256#124D4×C1311yescharacteristic
257#123—21no—
258C22⋊Q8C2×C4×C1311yescharacteristic
259#121C2×C4×C1311yescharacteristic
260C4×Q8D4×C1311yescharacteristic
261C4×D4—21no—
262C4×D4D4×C1311yescharacteristic
263#117—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C42C23×C1311yescharacteristic
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272#103—21no—
273#103—21no—
274#102—21no—
275#102—21no—
276C22⋊C8—21no—
277C22⋊C8—21no—
278C22⋊C8—21no—
279C22⋊C8C2×C4×C1311yescharacteristic
280C22⋊C8C2×C4×C1311yescharacteristic
281C22⋊C8D4×C1311yescharacteristic
282C22⋊C8D4×C1311yescharacteristic
283#97—21no—
284#97—21no—
285#97—21no—
286#97—21no—
287#97—21no—
288#97D4×C1311yescharacteristic
289#97D4×C1311yescharacteristic
290C4×C8—21no—
291C4×C8—21no—
292C4×C8—21no—
293C2×C13—21no—
294C2×C13—21no—
295C2×C13—81no—
296C2×C13—161no—
297C2×C13#187611yescharacteristic
298C2×C13#190611yescharacteristic
299C2×C13#191411yescharacteristic
300C24—21no—
301C2×Q8—21no—
302C2×Q8—21no—
303C2×Q8—81no—
304C2×Q8C13×C22⋊C411yescharacteristic
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—81no—
309C2×D4C13×C22⋊C411yescharacteristic
310C22×C4—21no—
311C22×C4—21no—
312C22×C4C22×C4×C1311yescharacteristic
313C22×C4C2×D4×C1311yescharacteristic
314C22×C4C13×#4111yescharacteristic
315Q16—81no—
316SD16—81no—
317SD16—81no—
318D8—81no—
319M16—42no—
320C2×C8—21no—
321C2×C8—22no—
322C2×C8—21no—
323C2×C8—21no—
324C2×C8—21no—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—42no—
328C2×C8—42no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—41no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4C13×C22⋊C411yescharacteristic
337C4⋊C4C13×C22⋊C411yescharacteristic
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—21no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C42—21no—
348C42C2×D4×C1311yescharacteristic
349C42C2×D4×C1311yescharacteristic
350C42C2×D4×C1311yescharacteristic
351C42C13×#4111yescharacteristic
352C13#926511yescharacteristic, direct product factor, Sylow
353C23—21no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—81no—
358C23—81no—
359C23C4×D4×C1311yescharacteristic
360Q8—41no—
361Q8—41no—
362Q8—41no—
363Q8—81no—
364D4—41no—
365D4—41no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—81no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—81no—
381C2×C4C2×C13×C22⋊C411yescharacteristic
382C2×C4C4×D4×C1311yescharacteristic
383C2×C4C13×#12011yescharacteristic
384C2×C4C13×#12111yescharacteristic
385C2×C4C13×#12111yescharacteristic
386C2×C4C13×#12311yescharacteristic
387C8—22no—
388C8—42no—
389C8—41no—
390C8—41no—
391C8—41no—
392C8—41no—
393C8—41no—
394C8—81no—
395C22—21no—
396C22—21no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—81no—
401C22—81no—
402C22—81no—
403C22—161no—
404C22—161no—
405C22C13×#38611yescharacteristic
406C22C13×#44311yescharacteristic
407C22C13×#44411yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—41no—
415C4—41no—
416C4—41no—
417C4—81no—
418C2—21no—
419C2—21no—
420C2—81no—
421C2—161no—
422C2C13×#187611yescharacteristic
423C2C13×#190611yescharacteristic
424C2C13×#191411yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC13×#447C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2968C2semidirect
3. C13×#1532C2semidirect
4. C2×C13×#329C2semidirect
5. C13×#1469C2semidirect
6. C13×#1302C2semidirect
7. C13×#1281C2semidirect
88. #9265C13direct (N × H)
142. #2968C2×C13semidirect
143. #1532C2×C13semidirect
144. C2×#329C2×C13semidirect
145. #1469C2×C13semidirect
146. #1302C2×C13semidirect
147. #1281C2×C13semidirect
352. C13#9265direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#32112
C13×#29682
C13×#15322
C2×C13×#3292
C13×#14692
C13×#13022
C13×#12812
#926513