Finite Group Databasebeta

← C13×#8997 #15695336

Subgroups — C13×#8997 #15695336

Order 3328.

452 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3171C211yesmaximal, characteristic
2C13×#2995C211yesmaximal, characteristic, complemented
3C13×#1963C211yesmaximal, characteristic, complemented
4C13×#1500C211yesmaximal, characteristic, complemented
5C13×#1496C211yesmaximal, characteristic, complemented
6C13×#1300C211yesmaximal, characteristic, complemented
7C13×#1299C211yesmaximal, characteristic, complemented
8C13×#532C2211yescharacteristic
9C13×#529C2211yescharacteristic
10C13×#501C411yescharacteristic, complemented
11C13×#496C411yescharacteristic, complemented
12C13×#490C411yescharacteristic, complemented
13C13×#489C411yescharacteristic, complemented
14C13×#469—21no—
15C13×#468—21no—
16C13×#446—21no—
17C4×C13×SD16—21no—
18C4×C13×D8—21no—
19C13×#436—21no—
20C13×#435—21no—
21C13×#435—21no—
22C13×#433—21no—
23C13×#432C2211yescharacteristic
24C13×#431C2211yescharacteristic
25C13×#424—21no—
26C13×#423C2211yescharacteristic
27C2×C13×#104—21no—
28C2×C13×#104—21no—
29C4×C13×M16C2211yescharacteristic
30C13×#376C2211yescharacteristic
31C13×#328—21no—
32C13×#327—21no—
33C13×D4⋊C8—21no—
34C13×D4⋊C8—21no—
35C2×C13×#41—21no—
36C2×C13×SD16—21no—
37C2×C13×D8—21no—
38C2×C13×M16—21no—
39C2×C13×M16—21no—
40C2×C13×M16D411yescharacteristic
41C2×C13×M16D411yescharacteristic
42C22×C8×C13—21no—
43C13×C4⋊Q8C2×C411yescharacteristic
44C13×#127C2×C411yescharacteristic
45C13×#126—21no—
46C13×#125C2×C411yescharacteristic
47C13×#124—21no—
48C13×#124C2×C411yescharacteristic
49C13×#123—21no—
50C13×C22⋊Q8D411yescharacteristic
51C13×#121—21no—
52C13×#121—21no—
53C13×#121D411yescharacteristic
54C4×Q8×C13D411yescharacteristic
55C4×D4×C13—21no—
56C4×D4×C13—21no—
57C4×D4×C13—21no—
58C4×D4×C13D411yescharacteristic
59C13×#117—21no—
60C2×C42×C13—21no—
61C2×C42×C13C2311yescharacteristic
62C13×#107—21no—
63C13×#106—21no—
64C13×C4⋊C8—21no—
65C13×C4⋊C8—21no—
66C13×C4⋊C8—21no—
67C13×C4⋊C8—21no—
68C13×C4⋊C8—21no—
69C13×C4⋊C8D411yescharacteristic
70C13×C4⋊C8D411yescharacteristic
71C13×#104—42no—
72C13×#104—42no—
73C13×#103—21no—
74C13×#102—21no—
75C13×#102—21no—
76C13×#102—21no—
77C13×C22⋊C8—21no—
78C13×C22⋊C8—21no—
79C13×C22⋊C8—21no—
80C13×C22⋊C8—21no—
81C13×#97—21no—
82C13×#97—21no—
83C13×#97C2×C411yescharacteristic
84C13×#97C2×C411yescharacteristic
85C4×C8×C13—21no—
86C4×C8×C13—21no—
87C4×C8×C13—21no—
88C13×#95—21no—
89C13×#95—21no—
90#8997C1311yesmaximal, characteristic, direct product factor, Sylow
91C13×#41—41no—
92C13×#41—41no—
93C13×#41—41no—
94C13×#41—41no—
95C2×Q8×C13—21no—
96C2×Q8×C13C22⋊C411yescharacteristic
97C2×D4×C13—21no—
98C2×D4×C13—21no—
99C2×D4×C13—21no—
100C2×D4×C13—21no—
101C2×D4×C13—41no—
102C2×D4×C13C22⋊C411yescharacteristic
103C22×C4×C13—21no—
104C22×C4×C13—41no—
105C22×C4×C13—41no—
106C22×C4×C13C2×D411yescharacteristic
107C22×C4×C13C2×D411yescharacteristic
108C22×C4×C13#4111yescharacteristic
109C13×SD16—42no—
110C13×D8—42no—
111C13×M16—42no—
112C13×M16—41no—
113C13×M16—41no—
114C13×M16—81no—
115C2×C8×C13—21no—
116C2×C8×C13—21no—
117C2×C8×C13—21no—
118C2×C8×C13—21no—
119C2×C8×C13—21no—
120C2×C8×C13—21no—
121C2×C8×C13—41no—
122C2×C8×C13—81no—
123C13×C4⋊C4—21no—
124C13×C4⋊C4—21no—
125C13×C4⋊C4—21no—
126C13×C4⋊C4—21no—
127C13×C4⋊C4—21no—
128C13×C4⋊C4—21no—
129C13×C4⋊C4C22⋊C411yescharacteristic
130C13×C4⋊C4C22⋊C411yescharacteristic
131C13×C22⋊C4—21no—
132C13×C22⋊C4—21no—
133C13×C22⋊C4—21no—
134C13×C22⋊C4—21no—
135C13×C22⋊C4—21no—
136C13×C22⋊C4—41no—
137C13×C22⋊C4—41no—
138C42×C13—21no—
139C42×C13—22no—
140C42×C13—41no—
141C42×C13C22×C411yescharacteristic
142C42×C13C2×D411yescharacteristic
143C42×C13C2×D411yescharacteristic
144C42×C13#4111yescharacteristic
145#3171C2×C1311yescharacteristic
146#2995C2×C1311yescharacteristic, complemented
147#1963C2×C1311yescharacteristic, complemented
148#1500C2×C1311yescharacteristic, complemented
149#1496C2×C1311yescharacteristic, complemented
150#1300C2×C1311yescharacteristic, complemented
151#1299C2×C1311yescharacteristic, complemented
152C23×C13—21no—
153C23×C13—41no—
154C23×C13#12111yescharacteristic
155Q8×C13—41no—
156Q8×C13—41no—
157Q8×C13—41no—
158D4×C13—41no—
159D4×C13—41no—
160D4×C13—41no—
161D4×C13—42no—
162D4×C13—41no—
163D4×C13—41no—
164D4×C13—81no—
165D4×C13—81no—
166D4×C13—81no—
167C2×C4×C13—21no—
168C2×C4×C13—21no—
169C2×C4×C13—21no—
170C2×C4×C13—21no—
171C2×C4×C13—21no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13—41no—
176C2×C4×C13—42no—
177C2×C4×C13—41no—
178C2×C4×C13—81no—
179C2×C4×C13—81no—
180C2×C4×C13—81no—
181C2×C4×C13—81no—
182C2×C4×C13C2×C22⋊C411yescharacteristic
183C2×C4×C13C4×D411yescharacteristic
184C2×C4×C13C4×D411yescharacteristic
185C2×C4×C13#12011yescharacteristic
186C2×C4×C13#12111yescharacteristic
187C2×C4×C13#12311yescharacteristic
188C8×C13—22no—
189C8×C13—41no—
190C8×C13—41no—
191C8×C13—41no—
192C8×C13—41no—
193C8×C13—41no—
194C8×C13—81no—
195#532C22×C1311yescharacteristic
196#529C22×C1311yescharacteristic
197#501C4×C1311yescharacteristic, complemented
198#496C4×C1311yescharacteristic, complemented
199#490C4×C1311yescharacteristic, complemented
200#489C4×C1311yescharacteristic, complemented
201#469—21no—
202#468—21no—
203#446—21no—
204C4×SD16—21no—
205C4×D8—21no—
206#436—21no—
207#435—21no—
208#435—21no—
209#433—21no—
210#432C22×C1311yescharacteristic
211#431C22×C1311yescharacteristic
212#424—21no—
213#423C22×C1311yescharacteristic
214C2×#104—21no—
215C2×#104—21no—
216C4×M16C22×C1311yescharacteristic
217#376C22×C1311yescharacteristic
218#328—21no—
219#327—21no—
220D4⋊C8—21no—
221D4⋊C8—21no—
222C22×C13—21no—
223C22×C13—21no—
224C22×C13—21no—
225C22×C13—41no—
226C22×C13—41no—
227C22×C13—41no—
228C22×C13—81no—
229C22×C13—81no—
230C22×C13—81no—
231C22×C13#38611yescharacteristic
232C4×C13—21no—
233C4×C13—21no—
234C4×C13—21no—
235C4×C13—21no—
236C4×C13—21no—
237C4×C13—41no—
238C4×C13—41no—
239C4×C13—41no—
240C4×C13—82no—
241C4×C13—81no—
242C4×C13#45311yescharacteristic
243C4×C13#45411yescharacteristic
244C2×#41—21no—
245C2×SD16—21no—
246C2×D8—21no—
247C2×M16—21no—
248C2×M16—21no—
249C2×M16D4×C1311yescharacteristic
250C2×M16D4×C1311yescharacteristic
251C22×C8—21no—
252C4⋊Q8C2×C4×C1311yescharacteristic
253#127C2×C4×C1311yescharacteristic
254#126—21no—
255#125C2×C4×C1311yescharacteristic
256#124—21no—
257#124C2×C4×C1311yescharacteristic
258#123—21no—
259C22⋊Q8D4×C1311yescharacteristic
260#121—21no—
261#121—21no—
262#121D4×C1311yescharacteristic
263C4×Q8D4×C1311yescharacteristic
264C4×D4—21no—
265C4×D4—21no—
266C4×D4—21no—
267C4×D4D4×C1311yescharacteristic
268#117—21no—
269C2×C42—21no—
270C2×C42C23×C1311yescharacteristic
271#107—21no—
272#106—21no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8—21no—
276C4⋊C8—21no—
277C4⋊C8—21no—
278C4⋊C8D4×C1311yescharacteristic
279C4⋊C8D4×C1311yescharacteristic
280#104—42no—
281#104—42no—
282#103—21no—
283#102—21no—
284#102—21no—
285#102—21no—
286C22⋊C8—21no—
287C22⋊C8—21no—
288C22⋊C8—21no—
289C22⋊C8—21no—
290#97—21no—
291#97—21no—
292#97C2×C4×C1311yescharacteristic
293#97C2×C4×C1311yescharacteristic
294C4×C8—21no—
295C4×C8—21no—
296C4×C8—21no—
297#95—21no—
298#95—21no—
299C2×C13—41no—
300C2×C13—81no—
301C2×C13—161no—
302C2×C13#188111yescharacteristic
303C2×C13#188311yescharacteristic
304C2×C13#188411yescharacteristic
305#41—41no—
306#41—41no—
307#41—41no—
308#41—41no—
309C2×Q8—21no—
310C2×Q8C13×C22⋊C411yescharacteristic
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—41no—
316C2×D4C13×C22⋊C411yescharacteristic
317C22×C4—21no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4C2×D4×C1311yescharacteristic
321C22×C4C2×D4×C1311yescharacteristic
322C22×C4C13×#4111yescharacteristic
323SD16—42no—
324D8—42no—
325M16—42no—
326M16—41no—
327M16—41no—
328M16—81no—
329C2×C8—21no—
330C2×C8—21no—
331C2×C8—21no—
332C2×C8—21no—
333C2×C8—21no—
334C2×C8—21no—
335C2×C8—41no—
336C2×C8—81no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4C13×C22⋊C411yescharacteristic
344C4⋊C4C13×C22⋊C411yescharacteristic
345C22⋊C4—21no—
346C22⋊C4—21no—
347C22⋊C4—21no—
348C22⋊C4—21no—
349C22⋊C4—21no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C42—21no—
353C42—22no—
354C42—41no—
355C42C22×C4×C1311yescharacteristic
356C42C2×D4×C1311yescharacteristic
357C42C2×D4×C1311yescharacteristic
358C42C13×#4111yescharacteristic
359C13#899711yescharacteristic, direct product factor, Sylow
360C23—21no—
361C23—41no—
362C23C13×#12111yescharacteristic
363Q8—41no—
364Q8—41no—
365Q8—41no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—42no—
370D4—41no—
371D4—41no—
372D4—81no—
373D4—81no—
374D4—81no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4C2×C13×C22⋊C411yescharacteristic
391C2×C4C4×D4×C1311yescharacteristic
392C2×C4C4×D4×C1311yescharacteristic
393C2×C4C13×#12011yescharacteristic
394C2×C4C13×#12111yescharacteristic
395C2×C4C13×#12311yescharacteristic
396C8—22no—
397C8—41no—
398C8—41no—
399C8—41no—
400C8—41no—
401C8—41no—
402C8—81no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22C13×#38611yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—82no—
422C4—81no—
423C4C13×#45311yescharacteristic
424C4C13×#45411yescharacteristic
425C2—41no—
426C2—81no—
427C2—161no—
428C2C13×#188111yescharacteristic
429C2C13×#188311yescharacteristic
430C2C13×#188411yescharacteristic
subgroupG/H
centerC2×C4×C13#120
commutatorC42C22×C4×C13
Frattini, cosocleC2×C42C23×C13
socleC22×C13#386
prime radicalC13×#3171C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2995C2semidirect
3. C13×#1963C2semidirect
4. C13×#1500C2semidirect
5. C13×#1496C2semidirect
6. C13×#1300C2semidirect
7. C13×#1299C2semidirect
10. C13×#501C4semidirect
11. C13×#496C4semidirect
12. C13×#490C4semidirect
13. C13×#489C4semidirect
90. #8997C13direct (N × H)
146. #2995C2×C13semidirect
147. #1963C2×C13semidirect
148. #1500C2×C13semidirect
149. #1496C2×C13semidirect
150. #1300C2×C13semidirect
151. #1299C2×C13semidirect
197. #501C4×C13semidirect
198. #496C4×C13semidirect
199. #490C4×C13semidirect
200. #489C4×C13semidirect
359. C13#8997direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31712
C13×#29952
C13×#19632
C13×#15002
C13×#14962
C13×#13002
C13×#12992
#899713