Finite Group Databasebeta

← C13×#9432 #15695771

Subgroups — C13×#9432 #15695771

Order 3328.

436 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3180C211yesmaximal, characteristic
2C13×#2968C211yesmaximal, characteristic, complemented
3C13×#1530C211yesmaximal, characteristic, complemented
4C13×#1517C211yesmaximal, characteristic, complemented
5C13×#1512C211yesmaximal, characteristic, complemented
6C13×#1302C211yesmaximal, characteristic, complemented
7C13×#1295C211yesmaximal, characteristic, complemented
8C13×#532C2211yescharacteristic
9C13×#529C2211yescharacteristic
10C13×#501C411yescharacteristic, complemented
11C13×#496C411yescharacteristic, complemented
12C13×#490C411yescharacteristic, complemented
13C13×#489C411yescharacteristic, complemented
14C13×#466—21no—
15C13×#465—21no—
16C13×#446—21no—
17C13×#442—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×#329—21no—
30C13×#329—21no—
31C13×#328—21no—
32C13×#327—21no—
33C13×#327—21no—
34C13×#327—21no—
35C2×C13×#41—21no—
36C2×C13×SD16—21no—
37C2×C13×D8—21no—
38C2×C13×M16—21no—
39C22×C8×C13—21no—
40C22×C8×C13—21no—
41C22×C8×C13—21no—
42C13×C4⋊Q8C2×C411yescharacteristic
43C13×#127C2×C411yescharacteristic
44C13×#126—21no—
45C13×#125C2×C411yescharacteristic
46C13×#124—21no—
47C13×#124C2×C411yescharacteristic
48C13×#123—21no—
49C13×C22⋊Q8D411yescharacteristic
50C13×#121—21no—
51C13×#121—21no—
52C13×#121D411yescharacteristic
53C4×Q8×C13D411yescharacteristic
54C4×D4×C13—21no—
55C4×D4×C13—21no—
56C4×D4×C13—21no—
57C4×D4×C13D411yescharacteristic
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×#102—21no—
69C13×#102—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#9432C1311yesmaximal, characteristic, direct product factor, Sylow
89C13×#41—81no—
90C13×#41—81no—
91C2×Q8×C13—21no—
92C2×Q8×C13C22⋊C411yescharacteristic
93C2×D4×C13—21no—
94C2×D4×C13—21no—
95C2×D4×C13—21no—
96C2×D4×C13—21no—
97C2×D4×C13—41no—
98C2×D4×C13C22⋊C411yescharacteristic
99C22×C4×C13—21no—
100C22×C4×C13—41no—
101C22×C4×C13—41no—
102C22×C4×C13C2×D411yescharacteristic
103C22×C4×C13C2×D411yescharacteristic
104C22×C4×C13#4111yescharacteristic
105C13×SD16—42no—
106C13×D8—42no—
107C13×M16—42no—
108C2×C8×C13—21no—
109C2×C8×C13—21no—
110C2×C8×C13—21no—
111C2×C8×C13—21no—
112C2×C8×C13—21no—
113C2×C8×C13—21no—
114C2×C8×C13—42no—
115C2×C8×C13—42no—
116C2×C8×C13—42no—
117C2×C8×C13—41no—
118C13×C4⋊C4—21no—
119C13×C4⋊C4—21no—
120C13×C4⋊C4—21no—
121C13×C4⋊C4—21no—
122C13×C4⋊C4—21no—
123C13×C4⋊C4—21no—
124C13×C4⋊C4—81no—
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—
134C42×C13—21no—
135C42×C13C22×C411yescharacteristic
136C42×C13C2×D411yescharacteristic
137C42×C13C2×D411yescharacteristic
138C42×C13#4111yescharacteristic
139#3180C2×C1311yescharacteristic
140#2968C2×C1311yescharacteristic, complemented
141#1530C2×C1311yescharacteristic, complemented
142#1517C2×C1311yescharacteristic, complemented
143#1512C2×C1311yescharacteristic, complemented
144#1302C2×C1311yescharacteristic, complemented
145#1295C2×C1311yescharacteristic, complemented
146C23×C13—21no—
147C23×C13—41no—
148C23×C13#12111yescharacteristic
149Q8×C13—41no—
150Q8×C13—81no—
151D4×C13—41no—
152D4×C13—41no—
153D4×C13—41no—
154D4×C13—41no—
155D4×C13—41no—
156D4×C13—81no—
157D4×C13—81no—
158D4×C13—81no—
159D4×C13—81no—
160C2×C4×C13—21no—
161C2×C4×C13—21no—
162C2×C4×C13—21no—
163C2×C4×C13—21no—
164C2×C4×C13—21no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—82no—
171C2×C4×C13—81no—
172C2×C4×C13—81no—
173C2×C4×C13—81no—
174C2×C4×C13C2×C22⋊C411yescharacteristic
175C2×C4×C13C4×D411yescharacteristic
176C2×C4×C13C4×D411yescharacteristic
177C2×C4×C13#12011yescharacteristic
178C2×C4×C13#12111yescharacteristic
179C2×C4×C13#12311yescharacteristic
180C8×C13—22no—
181C8×C13—22no—
182C8×C13—41no—
183C8×C13—41no—
184C8×C13—41no—
185C8×C13—41no—
186C8×C13—81no—
187#532C22×C1311yescharacteristic
188#529C22×C1311yescharacteristic
189#501C4×C1311yescharacteristic, complemented
190#496C4×C1311yescharacteristic, complemented
191#490C4×C1311yescharacteristic, complemented
192#489C4×C1311yescharacteristic, complemented
193#466—21no—
194#465—21no—
195#446—21no—
196#442—21no—
197#440—21no—
198#435—21no—
199#435—21no—
200C8×D4—21no—
201#433—21no—
202#432C22×C1311yescharacteristic
203#431C22×C1311yescharacteristic
204#405—21no—
205C2×#97C22×C1311yescharacteristic
206C2×#97C22×C1311yescharacteristic
207#382C22×C1311yescharacteristic
208#329—21no—
209#329—21no—
210#328—21no—
211#327—21no—
212#327—21no—
213#327—21no—
214C22×C13—21no—
215C22×C13—21no—
216C22×C13—41no—
217C22×C13—41no—
218C22×C13—41no—
219C22×C13—81no—
220C22×C13—81no—
221C22×C13—81no—
222C22×C13#38611yescharacteristic
223C22×C13#47111yescharacteristic
224C22×C13#47211yescharacteristic
225C4×C13—21no—
226C4×C13—21no—
227C4×C13—21no—
228C4×C13—21no—
229C4×C13—21no—
230C4×C13—21no—
231C4×C13—41no—
232C4×C13—41no—
233C4×C13—41no—
234C4×C13—81no—
235C4×C13—161no—
236C2×#41—21no—
237C2×SD16—21no—
238C2×D8—21no—
239C2×M16—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C4⋊Q8C2×C4×C1311yescharacteristic
244#127C2×C4×C1311yescharacteristic
245#126—21no—
246#125C2×C4×C1311yescharacteristic
247#124—21no—
248#124C2×C4×C1311yescharacteristic
249#123—21no—
250C22⋊Q8D4×C1311yescharacteristic
251#121—21no—
252#121—21no—
253#121D4×C1311yescharacteristic
254C4×Q8D4×C1311yescharacteristic
255C4×D4—21no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4D4×C1311yescharacteristic
259#117—21no—
260C2×C4⋊C4—21no—
261C2×C42C23×C1311yescharacteristic
262#107—21no—
263#106—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268#103—21no—
269#102—21no—
270#102—21no—
271#102—21no—
272C22⋊C8—21no—
273C22⋊C8—21no—
274C22⋊C8—21no—
275C22⋊C8D4×C1311yescharacteristic
276C22⋊C8D4×C1311yescharacteristic
277#97—21no—
278#97—21no—
279#97—21no—
280#97—21no—
281#97C2×C4×C1311yescharacteristic
282#97C2×C4×C1311yescharacteristic
283#97D4×C1311yescharacteristic
284#97D4×C1311yescharacteristic
285C4×C8—21no—
286C4×C8—21no—
287#95—21no—
288#95—21no—
289C2×C13—21no—
290C2×C13—21no—
291C2×C13—81no—
292C2×C13—161no—
293C2×C13#188411yescharacteristic
294C2×C13#190611yescharacteristic
295C2×C13#190711yescharacteristic
296#41—81no—
297#41—81no—
298C2×Q8—21no—
299C2×Q8C13×C22⋊C411yescharacteristic
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—41no—
305C2×D4C13×C22⋊C411yescharacteristic
306C22×C4—21no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4C2×D4×C1311yescharacteristic
310C22×C4C2×D4×C1311yescharacteristic
311C22×C4C13×#4111yescharacteristic
312SD16—42no—
313D8—42no—
314M16—42no—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—21no—
320C2×C8—21no—
321C2×C8—42no—
322C2×C8—42no—
323C2×C8—42no—
324C2×C8—41no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—81no—
332C4⋊C4C13×C22⋊C411yescharacteristic
333C4⋊C4C13×C22⋊C411yescharacteristic
334C22⋊C4—21no—
335C22⋊C4—21no—
336C22⋊C4—21no—
337C22⋊C4—21no—
338C22⋊C4—21no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C42—21no—
342C42C22×C4×C1311yescharacteristic
343C42C2×D4×C1311yescharacteristic
344C42C2×D4×C1311yescharacteristic
345C42C13×#4111yescharacteristic
346C13#943211yescharacteristic, direct product factor, Sylow
347C23—21no—
348C23—41no—
349C23C13×#12111yescharacteristic
350Q8—41no—
351Q8—81no—
352D4—41no—
353D4—41no—
354D4—41no—
355D4—41no—
356D4—41no—
357D4—81no—
358D4—81no—
359D4—81no—
360D4—81no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—82no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4C2×C13×C22⋊C411yescharacteristic
376C2×C4C4×D4×C1311yescharacteristic
377C2×C4C4×D4×C1311yescharacteristic
378C2×C4C13×#12011yescharacteristic
379C2×C4C13×#12111yescharacteristic
380C2×C4C13×#12311yescharacteristic
381C8—22no—
382C8—22no—
383C8—41no—
384C8—41no—
385C8—41no—
386C8—41no—
387C8—81no—
388C22—21no—
389C22—21no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22C13×#38611yescharacteristic
397C22C13×#47111yescharacteristic
398C22C13×#47211yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—41no—
406C4—41no—
407C4—41no—
408C4—81no—
409C4—161no—
410C2—21no—
411C2—21no—
412C2—81no—
413C2—161no—
414C2C13×#188411yescharacteristic
415C2C13×#190611yescharacteristic
416C2C13×#190711yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC42C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC13×#3180C2
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
2. C13×#2968C2semidirect
3. C13×#1530C2semidirect
4. C13×#1517C2semidirect
5. C13×#1512C2semidirect
6. C13×#1302C2semidirect
7. C13×#1295C2semidirect
10. C13×#501C4semidirect
11. C13×#496C4semidirect
12. C13×#490C4semidirect
13. C13×#489C4semidirect
88. #9432C13direct (N × H)
140. #2968C2×C13semidirect
141. #1530C2×C13semidirect
142. #1517C2×C13semidirect
143. #1512C2×C13semidirect
144. #1302C2×C13semidirect
145. #1295C2×C13semidirect
189. #501C4×C13semidirect
190. #496C4×C13semidirect
191. #490C4×C13semidirect
192. #489C4×C13semidirect
346. C13#9432direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31802
C13×#29682
C13×#15302
C13×#15172
C13×#15122
C13×#13022
C13×#12952
#943213