Finite Group Databasebeta

← C13×#9431 #15695770

Subgroups — C13×#9431 #15695770

Order 3328.

414 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3181C211yesmaximal, characteristic
2C13×#2968C211yesmaximal, characteristic
3C13×#1531C211yesmaximal, characteristic, complemented
4C13×#1518C211yesmaximal, characteristic, complemented
5C13×#1512C211yesmaximal, characteristic
6C13×#1302C211yesmaximal, characteristic, complemented
7C13×#1295C211yesmaximal, characteristic, complemented
8C13×#533C2211yescharacteristic
9C13×#529C2211yescharacteristic
10C13×#501C411yescharacteristic, complemented
11C13×#497C411yescharacteristic, complemented
12C13×#491C411yescharacteristic, complemented
13C13×#489C411yescharacteristic, complemented
14C13×#467—21no—
15C13×#465—21no—
16C13×#446—21no—
17C13×#441—21no—
18C13×#440—21no—
19C13×#435—21no—
20C13×#435—21no—
21C8×D4×C13—21no—
22C13×#433—21no—
23C13×#432C2211yescharacteristic
24C13×#431C2211yescharacteristic
25C13×#405—21no—
26C2×C13×#97C2211yescharacteristic
27C2×C13×#97C2211yescharacteristic
28C13×#382C2211yescharacteristic
29C13×#330—21no—
30C13×#330—21no—
31C13×#328—21no—
32C13×#328—21no—
33C13×#328—21no—
34C13×#327—21no—
35C2×C13×Q16—21no—
36C2×C13×SD16—21no—
37C2×C13×M16—21no—
38C22×C8×C13—21no—
39C22×C8×C13—21no—
40C22×C8×C13—21no—
41C13×C4⋊Q8C2×C411yescharacteristic
42C13×C4⋊Q8C2×C411yescharacteristic
43C13×#126—21no—
44C13×#125—21no—
45C13×#125C2×C411yescharacteristic
46C13×#124C2×C411yescharacteristic
47C13×#123—21no—
48C13×C22⋊Q8—21no—
49C13×C22⋊Q8—21no—
50C13×C22⋊Q8D411yescharacteristic
51C13×#121D411yescharacteristic
52C4×Q8×C13—21no—
53C4×Q8×C13—21no—
54C4×Q8×C13D411yescharacteristic
55C4×D4×C13—21no—
56C4×D4×C13D411yescharacteristic
57C13×#117—21no—
58C13×#117—21no—
59C2×C13×C4⋊C4—21no—
60C2×C42×C13C2311yescharacteristic
61C13×#107—21no—
62C13×#106—21no—
63C13×C4⋊C8—21no—
64C13×C4⋊C8—21no—
65C13×C4⋊C8—21no—
66C13×C4⋊C8—21no—
67C13×#103—21no—
68C13×#103—21no—
69C13×#103—21no—
70C13×#102—21no—
71C13×C22⋊C8—21no—
72C13×C22⋊C8—21no—
73C13×C22⋊C8—21no—
74C13×C22⋊C8D411yescharacteristic
75C13×C22⋊C8D411yescharacteristic
76C13×#97—21no—
77C13×#97—21no—
78C13×#97—21no—
79C13×#97—21no—
80C13×#97C2×C411yescharacteristic
81C13×#97C2×C411yescharacteristic
82C13×#97D411yescharacteristic
83C13×#97D411yescharacteristic
84C4×C8×C13—21no—
85C4×C8×C13—21no—
86C13×#95—21no—
87C13×#95—21no—
88#9431C1311yesmaximal, characteristic, direct product factor, Sylow
89C2×Q8×C13—21no—
90C2×Q8×C13—21no—
91C2×Q8×C13C22⋊C411yescharacteristic
92C2×D4×C13—21no—
93C2×D4×C13C22⋊C411yescharacteristic
94C22×C4×C13—21no—
95C22×C4×C13—41no—
96C22×C4×C13C2×D411yescharacteristic
97C22×C4×C13C2×D411yescharacteristic
98C22×C4×C13#4111yescharacteristic
99C13×Q16—42no—
100C13×SD16—42no—
101C13×M16—42no—
102C2×C8×C13—21no—
103C2×C8×C13—21no—
104C2×C8×C13—21no—
105C2×C8×C13—21no—
106C2×C8×C13—21no—
107C2×C8×C13—21no—
108C2×C8×C13—42no—
109C2×C8×C13—42no—
110C2×C8×C13—42no—
111C2×C8×C13—41no—
112C13×C4⋊C4—21no—
113C13×C4⋊C4—21no—
114C13×C4⋊C4—21no—
115C13×C4⋊C4—21no—
116C13×C4⋊C4—21no—
117C13×C4⋊C4—21no—
118C13×C4⋊C4—21no—
119C13×C4⋊C4—21no—
120C13×C4⋊C4—41no—
121C13×C4⋊C4—41no—
122C13×C4⋊C4—81no—
123C13×C4⋊C4C22⋊C411yescharacteristic
124C13×C4⋊C4C22⋊C411yescharacteristic
125C13×C22⋊C4—21no—
126C13×C22⋊C4—21no—
127C13×C22⋊C4—21no—
128C13×C22⋊C4—21no—
129C13×C22⋊C4—21no—
130C13×C22⋊C4—41no—
131C42×C13—21no—
132C42×C13—41no—
133C42×C13C22×C411yescharacteristic
134C42×C13C2×D411yescharacteristic
135C42×C13C2×D411yescharacteristic
136C42×C13#4111yescharacteristic
137#3181C2×C1311yescharacteristic
138#2968C2×C1311yescharacteristic
139#1531C2×C1311yescharacteristic, complemented
140#1518C2×C1311yescharacteristic, complemented
141#1512C2×C1311yescharacteristic
142#1302C2×C1311yescharacteristic, complemented
143#1295C2×C1311yescharacteristic, complemented
144C23×C13—21no—
145C23×C13#12111yescharacteristic
146Q8×C13—41no—
147Q8×C13—41no—
148Q8×C13—41no—
149Q8×C13—81no—
150D4×C13—41no—
151D4×C13—41no—
152D4×C13—41no—
153C2×C4×C13—21no—
154C2×C4×C13—21no—
155C2×C4×C13—21no—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—81no—
165C2×C4×C13—81no—
166C2×C4×C13—81no—
167C2×C4×C13C2×C22⋊C411yescharacteristic
168C2×C4×C13C4×D411yescharacteristic
169C2×C4×C13C4×D411yescharacteristic
170C2×C4×C13#12011yescharacteristic
171C2×C4×C13#12111yescharacteristic
172C2×C4×C13#12311yescharacteristic
173C8×C13—22no—
174C8×C13—22no—
175C8×C13—41no—
176C8×C13—41no—
177C8×C13—41no—
178C8×C13—41no—
179C8×C13—81no—
180#533C22×C1311yescharacteristic
181#529C22×C1311yescharacteristic
182#501C4×C1311yescharacteristic, complemented
183#497C4×C1311yescharacteristic, complemented
184#491C4×C1311yescharacteristic, complemented
185#489C4×C1311yescharacteristic, complemented
186#467—21no—
187#465—21no—
188#446—21no—
189#441—21no—
190#440—21no—
191#435—21no—
192#435—21no—
193C8×D4—21no—
194#433—21no—
195#432C22×C1311yescharacteristic
196#431C22×C1311yescharacteristic
197#405—21no—
198C2×#97C22×C1311yescharacteristic
199C2×#97C22×C1311yescharacteristic
200#382C22×C1311yescharacteristic
201#330—21no—
202#330—21no—
203#328—21no—
204#328—21no—
205#328—21no—
206#327—21no—
207C22×C13—21no—
208C22×C13—21no—
209C22×C13—41no—
210C22×C13—41no—
211C22×C13—41no—
212C22×C13#38611yescharacteristic
213C22×C13#47111yescharacteristic
214C22×C13#47311yescharacteristic
215C4×C13—21no—
216C4×C13—21no—
217C4×C13—21no—
218C4×C13—21no—
219C4×C13—21no—
220C4×C13—21no—
221C4×C13—41no—
222C4×C13—41no—
223C4×C13—41no—
224C4×C13—81no—
225C4×C13—81no—
226C4×C13—161no—
227C2×Q16—21no—
228C2×SD16—21no—
229C2×M16—21no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—21no—
233C4⋊Q8C2×C4×C1311yescharacteristic
234C4⋊Q8C2×C4×C1311yescharacteristic
235#126—21no—
236#125—21no—
237#125C2×C4×C1311yescharacteristic
238#124C2×C4×C1311yescharacteristic
239#123—21no—
240C22⋊Q8—21no—
241C22⋊Q8—21no—
242C22⋊Q8D4×C1311yescharacteristic
243#121D4×C1311yescharacteristic
244C4×Q8—21no—
245C4×Q8—21no—
246C4×Q8D4×C1311yescharacteristic
247C4×D4—21no—
248C4×D4D4×C1311yescharacteristic
249#117—21no—
250#117—21no—
251C2×C4⋊C4—21no—
252C2×C42C23×C1311yescharacteristic
253#107—21no—
254#106—21no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259#103—21no—
260#103—21no—
261#103—21no—
262#102—21no—
263C22⋊C8—21no—
264C22⋊C8—21no—
265C22⋊C8—21no—
266C22⋊C8D4×C1311yescharacteristic
267C22⋊C8D4×C1311yescharacteristic
268#97—21no—
269#97—21no—
270#97—21no—
271#97—21no—
272#97C2×C4×C1311yescharacteristic
273#97C2×C4×C1311yescharacteristic
274#97D4×C1311yescharacteristic
275#97D4×C1311yescharacteristic
276C4×C8—21no—
277C4×C8—21no—
278#95—21no—
279#95—21no—
280C2×C13—21no—
281C2×C13—21no—
282C2×C13—81no—
283C2×C13#188411yescharacteristic
284C2×C13#190611yescharacteristic
285C2×C13#190811yescharacteristic
286C2×Q8—21no—
287C2×Q8—21no—
288C2×Q8C13×C22⋊C411yescharacteristic
289C2×D4—21no—
290C2×D4C13×C22⋊C411yescharacteristic
291C22×C4—21no—
292C22×C4—41no—
293C22×C4C2×D4×C1311yescharacteristic
294C22×C4C2×D4×C1311yescharacteristic
295C22×C4C13×#4111yescharacteristic
296Q16—42no—
297SD16—42no—
298M16—42no—
299C2×C8—21no—
300C2×C8—21no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—42no—
306C2×C8—42no—
307C2×C8—42no—
308C2×C8—41no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—81no—
320C4⋊C4C13×C22⋊C411yescharacteristic
321C4⋊C4C13×C22⋊C411yescharacteristic
322C22⋊C4—21no—
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—41no—
328C42—21no—
329C42—41no—
330C42C22×C4×C1311yescharacteristic
331C42C2×D4×C1311yescharacteristic
332C42C2×D4×C1311yescharacteristic
333C42C13×#4111yescharacteristic
334C13#943111yescharacteristic, direct product factor, Sylow
335C23—21no—
336C23C13×#12111yescharacteristic
337Q8—41no—
338Q8—41no—
339Q8—41no—
340Q8—81no—
341D4—41no—
342D4—41no—
343D4—41no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4C2×C13×C22⋊C411yescharacteristic
359C2×C4C4×D4×C1311yescharacteristic
360C2×C4C4×D4×C1311yescharacteristic
361C2×C4C13×#12011yescharacteristic
362C2×C4C13×#12111yescharacteristic
363C2×C4C13×#12311yescharacteristic
364C8—22no—
365C8—22no—
366C8—41no—
367C8—41no—
368C8—41no—
369C8—41no—
370C8—81no—
371C22—21no—
372C22—21no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22C13×#38611yescharacteristic
377C22C13×#47111yescharacteristic
378C22C13×#47311yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—41no—
386C4—41no—
387C4—41no—
388C4—81no—
389C4—81no—
390C4—161no—
391C2—21no—
392C2—21no—
393C2—81no—
394C2C13×#188411yescharacteristic
395C2C13×#190611yescharacteristic
396C2C13×#190811yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC42C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC13×#121D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#1531C2semidirect
4. C13×#1518C2semidirect
6. C13×#1302C2semidirect
7. C13×#1295C2semidirect
10. C13×#501C4semidirect
11. C13×#497C4semidirect
12. C13×#491C4semidirect
13. C13×#489C4semidirect
88. #9431C13direct (N × H)
139. #1531C2×C13semidirect
140. #1518C2×C13semidirect
142. #1302C2×C13semidirect
143. #1295C2×C13semidirect
182. #501C4×C13semidirect
183. #497C4×C13semidirect
184. #491C4×C13semidirect
185. #489C4×C13semidirect
334. C13#9431direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31812
C13×#29682
C13×#15312
C13×#15182
C13×#15122
C13×#13022
C13×#12952
#943113