Finite Group Databasebeta

← C13×#8992 #15695331

Subgroups — C13×#8992 #15695331

Order 3328.

500 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3103C211yesmaximal, characteristic
2Q8×C13×M16C211yesmaximal, characteristic, complemented
3C13×#1980C211yesmaximal, characteristic
4C4×C13×#103C211yesmaximal, characteristic, complemented
5C13×#1492C211yesmaximal, characteristic
6C13×#1303C211yesmaximal, characteristic, complemented
7C13×#1278C211yesmaximal, characteristic, complemented
8C13×#532C2211yescharacteristic
9C2×C4×Q8×C13C2211yescharacteristic
10C13×#481—21no—
11C13×#475C411yescharacteristic, complemented
12C13×#475C411yescharacteristic, complemented
13C13×#460C411yescharacteristic, complemented
14C13×#460C411yescharacteristic, complemented
15C13×#448—21no—
16C13×#446—21no—
17C13×#446—22no—
18C8×Q8×C13—21no—
19C4×C13×SD16—21no—
20C4×C13×SD16—21no—
21C13×#431C2211yescharacteristic
22C13×#423—21no—
23C13×#423C2211yescharacteristic
24C2×C13×#104—21no—
25C2×C13×#104—21no—
26C2×C13×#103—21no—
27C4×C13×M16—21no—
28C4×C13×M16C2211yescharacteristic
29C2×C4×C8×C13C2211yescharacteristic
30C4×C13×C4⋊C4C2211yescharacteristic
31C13×#340—21no—
32C13×D4⋊C8—22no—
33C2×C13×#41—21no—
34C22×Q8×C13D411yescharacteristic
35C2×C13×SD16—21no—
36C2×C13×SD16—21no—
37C2×C13×M16—21no—
38C2×C13×M16D411yescharacteristic
39C2×C13×M16D411yescharacteristic
40C22×C8×C13—21no—
41C13×C4⋊Q8C2×C411yescharacteristic
42C13×#127C2×C411yescharacteristic
43C13×#124—21no—
44C13×#121—21no—
45C13×#121—21no—
46C4×Q8×C13—21no—
47C4×Q8×C13—21no—
48C4×Q8×C13C2×C411yescharacteristic
49C4×Q8×C13C2×C411yescharacteristic
50C4×Q8×C13D411yescharacteristic
51C4×Q8×C13D411yescharacteristic
52C4×D4×C13—21no—
53C4×D4×C13—21no—
54C2×C13×C4⋊C4—21no—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4D411yescharacteristic
57C2×C42×C13—21no—
58C2×C42×C13—21no—
59C2×C42×C13C2311yescharacteristic
60C13×#106—21no—
61C13×#106—21no—
62C13×C4⋊C8—22no—
63C13×C4⋊C8—22no—
64C13×C4⋊C8—21no—
65C13×C4⋊C8C2×C411yescharacteristic
66C13×C4⋊C8C2×C411yescharacteristic
67C13×C4⋊C8D412yes—
68C13×#104—42no—
69C13×#104—42no—
70C13×#103—24no—
71C13×#103—21no—
72C13×#103—21no—
73C13×#102—21no—
74C13×#102—21no—
75C13×C22⋊C8—21no—
76C13×#97—22no—
77C13×#97—21no—
78C4×C8×C13—22no—
79C4×C8×C13—21no—
80C4×C8×C13—21no—
81C4×C8×C13—21no—
82C4×C8×C13—21no—
83C13×#95—21no—
84#8992C1311yesmaximal, characteristic, direct product factor, Sylow
85C13×#41—41no—
86C13×#41—41no—
87C13×#41—41no—
88C13×#41—41no—
89C2×Q8×C13—21no—
90C2×Q8×C13—22no—
91C2×Q8×C13—21no—
92C2×Q8×C13—41no—
93C2×Q8×C13C22⋊C411yescharacteristic
94C2×Q8×C13C22⋊C411yescharacteristic
95C2×D4×C13—21no—
96C2×D4×C13—21no—
97C2×D4×C13—21no—
98C2×D4×C13—41no—
99C22×C4×C13—21no—
100C22×C4×C13—21no—
101C22×C4×C13—41no—
102C22×C4×C13—41no—
103C22×C4×C13C2×D411yescharacteristic
104C22×C4×C13C2×D411yescharacteristic
105C22×C4×C13#4111yescharacteristic
106C13×SD16—42no—
107C13×SD16—42no—
108C13×M16—21no—
109C13×M16—21no—
110C13×M16—21no—
111C13×M16—41no—
112C13×M16—41no—
113C13×M16SD1612yescomplemented
114C2×C8×C13—21no—
115C2×C8×C13—22no—
116C2×C8×C13—21no—
117C2×C8×C13—21no—
118C2×C8×C13—21no—
119C2×C8×C13—22no—
120C2×C8×C13—41no—
121C2×C8×C13—41no—
122C13×C4⋊C4—21no—
123C13×C4⋊C4—21no—
124C13×C4⋊C4—21no—
125C13×C4⋊C4—21no—
126C13×C4⋊C4—21no—
127C13×C4⋊C4—22no—
128C13×C4⋊C4—21no—
129C13×C4⋊C4—21no—
130C13×C4⋊C4—41no—
131C13×C4⋊C4C22⋊C411yescharacteristic
132C13×C4⋊C4C22⋊C411yescharacteristic
133C13×C22⋊C4—41no—
134C13×C22⋊C4—41no—
135C42×C13—21no—
136C42×C13—21no—
137C42×C13—21no—
138C42×C13—21no—
139C42×C13—41no—
140C42×C13—41no—
141C42×C13C22×C411yescharacteristic
142C42×C13C2×D411yescharacteristic
143C42×C13C2×D411yescharacteristic
144C42×C13#4111yescharacteristic
145#3103C2×C1311yescharacteristic
146Q8×M16C2×C1311yescharacteristic, complemented
147#1980C2×C1311yescharacteristic
148C4×#103C2×C1311yescharacteristic, complemented
149#1492C2×C1311yescharacteristic
150#1303C2×C1311yescharacteristic, complemented
151#1278C2×C1311yescharacteristic, complemented
152C23×C13—41no—
153C23×C13#12111yescharacteristic
154Q8×C13—21no—
155Q8×C13—21no—
156Q8×C13—21no—
157Q8×C13—42no—
158Q8×C13—41no—
159Q8×C13—41no—
160Q8×C13#10412yescomplemented
161D4×C13—42no—
162D4×C13—41no—
163D4×C13—41no—
164D4×C13—41no—
165D4×C13—41no—
166D4×C13—81no—
167D4×C13—81no—
168C2×C4×C13—21no—
169C2×C4×C13—21no—
170C2×C4×C13—21no—
171C2×C4×C13—21no—
172C2×C4×C13—21no—
173C2×C4×C13—21no—
174C2×C4×C13—41no—
175C2×C4×C13—42no—
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×C13—81no—
183C2×C4×C13C2×C22⋊C411yescharacteristic
184C2×C4×C13C4×D411yescharacteristic
185C2×C4×C13C4×D411yescharacteristic
186C2×C4×C13#12011yescharacteristic
187C2×C4×C13#12111yescharacteristic
188C2×C4×C13#12311yescharacteristic
189C2×C4×C13C2×SD1611yescharacteristic
190C2×C4×C13#13511yescharacteristic
191C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C13#13711yescharacteristic
193C8×C13—22no—
194C8×C13—42no—
195C8×C13—41no—
196C8×C13—41no—
197C8×C13—41no—
198C8×C13—42no—
199#532C22×C1311yescharacteristic
200C2×C4×Q8C22×C1311yescharacteristic
201#481—21no—
202#475C4×C1311yescharacteristic, complemented
203#475C4×C1311yescharacteristic, complemented
204#460C4×C1311yescharacteristic, complemented
205#460C4×C1311yescharacteristic, complemented
206#448—21no—
207#446—21no—
208#446—22no—
209C8×Q8—21no—
210C4×SD16—21no—
211C4×SD16—21no—
212#431C22×C1311yescharacteristic
213#423—21no—
214#423C22×C1311yescharacteristic
215C2×#104—21no—
216C2×#104—21no—
217C2×#103—21no—
218C4×M16—21no—
219C4×M16C22×C1311yescharacteristic
220C2×C4×C8C22×C1311yescharacteristic
221C4×C4⋊C4C22×C1311yescharacteristic
222#340—21no—
223D4⋊C8—22no—
224C22×C13—21no—
225C22×C13—21no—
226C22×C13—81no—
227C22×C13—81no—
228C22×C13—81no—
229C22×C13#38611yescharacteristic
230C22×C13#46011yescharacteristic
231C22×C13#46411yescharacteristic
232C4×C13—21no—
233C4×C13—22no—
234C4×C13—21no—
235C4×C13—21no—
236C4×C13—41no—
237C4×C13—41no—
238C4×C13—41no—
239C4×C13—82no—
240C4×C13—81no—
241C4×C13C2×#10411yescharacteristic
242C4×C13#42111yescharacteristic
243C4×C13C4×SD1611yescharacteristic
244C4×C13#44011yescharacteristic
245C4×C13#44811yescharacteristic
246C4×C13#44911yescharacteristic
247C2×#41—21no—
248C22×Q8D4×C1311yescharacteristic
249C2×SD16—21no—
250C2×SD16—21no—
251C2×M16—21no—
252C2×M16D4×C1311yescharacteristic
253C2×M16D4×C1311yescharacteristic
254C22×C8—21no—
255C4⋊Q8C2×C4×C1311yescharacteristic
256#127C2×C4×C1311yescharacteristic
257#124—21no—
258#121—21no—
259#121—21no—
260C4×Q8—21no—
261C4×Q8—21no—
262C4×Q8C2×C4×C1311yescharacteristic
263C4×Q8C2×C4×C1311yescharacteristic
264C4×Q8D4×C1311yescharacteristic
265C4×Q8D4×C1311yescharacteristic
266C4×D4—21no—
267C4×D4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4D4×C1311yescharacteristic
271C2×C42—21no—
272C2×C42—21no—
273C2×C42C23×C1311yescharacteristic
274#106—21no—
275#106—21no—
276C4⋊C8—22no—
277C4⋊C8—22no—
278C4⋊C8—21no—
279C4⋊C8C2×C4×C1311yescharacteristic
280C4⋊C8C2×C4×C1311yescharacteristic
281C4⋊C8D4×C1312yes—
282#104—42no—
283#104—42no—
284#103—24no—
285#103—21no—
286#103—21no—
287#102—21no—
288#102—21no—
289C22⋊C8—21no—
290#97—22no—
291#97—21no—
292C4×C8—22no—
293C4×C8—21no—
294C4×C8—21no—
295C4×C8—21no—
296C4×C8—21no—
297#95—21no—
298C2×C13—21no—
299C2×C13—21no—
300C2×C13—161no—
301C2×C13#187111yescharacteristic
302C2×C13#188011yescharacteristic
303C2×C13#188111yescharacteristic
304#41—41no—
305#41—41no—
306#41—41no—
307#41—41no—
308C2×Q8—21no—
309C2×Q8—22no—
310C2×Q8—21no—
311C2×Q8—41no—
312C2×Q8C13×C22⋊C411yescharacteristic
313C2×Q8C13×C22⋊C411yescharacteristic
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—41no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4C2×D4×C1311yescharacteristic
323C22×C4C2×D4×C1311yescharacteristic
324C22×C4C13×#4111yescharacteristic
325SD16—42no—
326SD16—42no—
327M16—21no—
328M16—21no—
329M16—21no—
330M16—41no—
331M16—41no—
332M16C13×SD1612yescomplemented
333C2×C8—21no—
334C2×C8—22no—
335C2×C8—21no—
336C2×C8—21no—
337C2×C8—21no—
338C2×C8—22no—
339C2×C8—41no—
340C2×C8—41no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—22no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—41no—
350C4⋊C4C13×C22⋊C411yescharacteristic
351C4⋊C4C13×C22⋊C411yescharacteristic
352C22⋊C4—41no—
353C22⋊C4—41no—
354C42—21no—
355C42—21no—
356C42—21no—
357C42—21no—
358C42—41no—
359C42—41no—
360C42C22×C4×C1311yescharacteristic
361C42C2×D4×C1311yescharacteristic
362C42C2×D4×C1311yescharacteristic
363C42C13×#4111yescharacteristic
364C13#899211yescharacteristic, direct product factor, Sylow
365C23—41no—
366C23C13×#12111yescharacteristic
367Q8—21no—
368Q8—21no—
369Q8—21no—
370Q8—42no—
371Q8—41no—
372Q8—41no—
373Q8C13×#10412yescomplemented
374D4—42no—
375D4—41no—
376D4—41no—
377D4—41no—
378D4—41no—
379D4—81no—
380D4—81no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—41no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4C2×C13×C22⋊C411yescharacteristic
397C2×C4C4×D4×C1311yescharacteristic
398C2×C4C4×D4×C1311yescharacteristic
399C2×C4C13×#12011yescharacteristic
400C2×C4C13×#12111yescharacteristic
401C2×C4C13×#12311yescharacteristic
402C2×C4C2×C13×SD1611yescharacteristic
403C2×C4C13×#13511yescharacteristic
404C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
405C2×C4C13×#13711yescharacteristic
406C8—22no—
407C8—42no—
408C8—41no—
409C8—41no—
410C8—41no—
411C8—42no—
412C22—21no—
413C22—21no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22C13×#38611yescharacteristic
418C22C13×#46011yescharacteristic
419C22C13×#46411yescharacteristic
420C4—21no—
421C4—22no—
422C4—21no—
423C4—21no—
424C4—41no—
425C4—41no—
426C4—41no—
427C4—82no—
428C4—81no—
429C4C2×C13×#10411yescharacteristic
430C4C13×#42111yescharacteristic
431C4C4×C13×SD1611yescharacteristic
432C4C13×#44011yescharacteristic
433C4C13×#44811yescharacteristic
434C4C13×#44911yescharacteristic
435C2—21no—
436C2—21no—
437C2—161no—
438C2C13×#187111yescharacteristic
439C2C13×#188011yescharacteristic
440C2C13×#188111yescharacteristic
subgroupG/H
centerC2×C4×C13#120
commutatorC42C22×C4×C13
Frattini, cosocleC2×C42C23×C13
socleC22×C13#386
prime radicalC13×#532C22
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. Q8×C13×M16C2semidirect
4. C4×C13×#103C2semidirect
6. C13×#1303C2semidirect
7. C13×#1278C2semidirect
11. C13×#475C4semidirect
12. C13×#475C4semidirect
13. C13×#460C4semidirect
14. C13×#460C4semidirect
84. #8992C13direct (N × H)
113. C13×M16SD16semidirect
146. Q8×M16C2×C13semidirect
148. C4×#103C2×C13semidirect
150. #1303C2×C13semidirect
151. #1278C2×C13semidirect
160. Q8×C13#104semidirect
202. #475C4×C13semidirect
203. #475C4×C13semidirect
204. #460C4×C13semidirect
205. #460C4×C13semidirect
332. M16C13×SD16semidirect
364. C13#8992direct (N × H)
373. Q8C13×#104semidirect

Maximal subgroups

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

subgroupindex
C13×#31032
Q8×C13×M162
C13×#19802
C4×C13×#1032
C13×#14922
C13×#13032
C13×#12782
#899213