Finite Group Databasebeta

← C13×#9381 #15695720

Subgroups — C13×#9381 #15695720

Order 3328.

530 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3213C211yesmaximal, characteristic
2C13×#2337C211yesmaximal, characteristic, complemented
3C13×#1980C211yesmaximal, characteristic, complemented
4C13×#1527C211yesmaximal, characteristic, complemented
5C13×#1514C211yesmaximal, characteristic, complemented
6C13×#1288C211yesmaximal, characteristic, complemented
7C13×#1285C211yesmaximal, characteristic, complemented
8C13×#532C2211yescharacteristic
9C2×C13×#124C2211yescharacteristic
10C13×#496C412yescomplemented
11C13×#489C412yescomplemented
12C13×#463—22no—
13C13×#448—21no—
14C13×#447—21no—
15C13×#432C2211yescharacteristic
16C13×#432C2211yescharacteristic
17C2×C13×#104—21no—
18C2×C13×#104—21no—
19C4×C13×M16C2211yescharacteristic
20C13×#391—21no—
21C13×#388—21no—
22C13×#388—21no—
23C13×#386—21no—
24C13×#385—21no—
25C13×#383C2211yescharacteristic
26C4×C13×C4⋊C4C2211yescharacteristic
27C4×C13×C22⋊C4—21no—
28C13×#329—22no—
29C13×#327—21no—
30C13×#327—21no—
31C2×C13×#41—21no—
32C22×Q8×C13D411yescharacteristic
33C22×D4×C13D411yescharacteristic
34C23×C4×C13—21no—
35C2×C13×SD16—22no—
36C2×C13×D8—22no—
37C2×C13×M16—21no—
38C13×C4⋊Q8C2×C411yescharacteristic, complemented
39C13×#127C2×C411yescharacteristic, complemented
40C13×#124—21no—
41C13×#124—21no—
42C13×#124—21no—
43C13×#124C2×C412yes—
44C13×#124D412yes—
45C13×#121—21no—
46C13×#121—21no—
47C4×D4×C13—21no—
48C4×D4×C13—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C22⋊C4—21no—
52C2×C13×C22⋊C4—21no—
53C2×C13×C22⋊C4—21no—
54C2×C13×C22⋊C4—21no—
55C2×C13×C22⋊C4—21no—
56C2×C42×C13—21no—
57C2×C42×C13D411yescharacteristic
58C2×C42×C13D411yescharacteristic
59C2×C42×C13C2311yescharacteristic
60C13×C4⋊C8—21no—
61C13×C4⋊C8—21no—
62C13×#104—42no—
63C13×#104—42no—
64C13×#103—22no—
65C13×#102—22no—
66C13×C22⋊C8—21no—
67C13×C22⋊C8—21no—
68C13×#97—21no—
69C13×#97—21no—
70C13×#97C2×C412yescomplemented
71C4×C8×C13—21no—
72C13×#95—21no—
73C13×#95—21no—
74C13×#95—21no—
75C13×#95—21no—
76C13×#95—21no—
77C13×#95D411yescharacteristic
78C13×#95D411yescharacteristic
79#9381C1311yesmaximal, characteristic, direct product factor, Sylow
80C24×C13—21no—
81C13×#41—41no—
82C13×#41—41no—
83C13×#41—41no—
84C13×#41—41no—
85C2×Q8×C13—21no—
86C2×Q8×C13—21no—
87C2×Q8×C13—81no—
88C2×Q8×C13C22⋊C412yes—
89C2×D4×C13—21no—
90C2×D4×C13—21no—
91C2×D4×C13—21no—
92C2×D4×C13—21no—
93C2×D4×C13—41no—
94C2×D4×C13—81no—
95C2×D4×C13C22⋊C412yes—
96C22×C4×C13—21no—
97C22×C4×C13—21no—
98C22×C4×C13—21no—
99C22×C4×C13—21no—
100C22×C4×C13—21no—
101C22×C4×C13—42no—
102C22×C4×C13—41no—
103C22×C4×C13—81no—
104C22×C4×C13—81no—
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13C2×D411yescharacteristic
107C22×C4×C13C2×D411yescharacteristic
108C13×SD16—82no—
109C13×D8—82no—
110C13×M16—22no—
111C13×M16—41no—
112C2×C8×C13—22no—
113C2×C8×C13—41no—
114C2×C8×C13—41no—
115C13×C4⋊C4—21no—
116C13×C4⋊C4—21no—
117C13×C4⋊C4—42no—
118C13×C4⋊C4—81no—
119C13×C22⋊C4—22no—
120C13×C22⋊C4—22no—
121C13×C22⋊C4—22no—
122C13×C22⋊C4—22no—
123C13×C22⋊C4—42no—
124C13×C22⋊C4—41no—
125C13×C22⋊C4—41no—
126C13×C22⋊C4—81no—
127C13×C22⋊C4—81no—
128C42×C13—41no—
129C42×C13—41no—
130C42×C13—81no—
131C42×C13C22×C411yescharacteristic
132C42×C13C2×D411yescharacteristic
133C42×C13#4111yescharacteristic
134C42×C13#4111yescharacteristic
135#3213C2×C1311yescharacteristic
136#2337C2×C1311yescharacteristic, complemented
137#1980C2×C1311yescharacteristic, complemented
138#1527C2×C1311yescharacteristic, complemented
139#1514C2×C1311yescharacteristic, complemented
140#1288C2×C1311yescharacteristic, complemented
141#1285C2×C1311yescharacteristic, complemented
142C23×C13—22no—
143C23×C13—41no—
144C23×C13—41no—
145C23×C13—41no—
146C23×C13—41no—
147C23×C13—41no—
148C23×C13—41no—
149C23×C13—41no—
150C23×C13#12011yescharacteristic
151Q8×C13—42no—
152Q8×C13—41no—
153Q8×C13—41no—
154Q8×C13—81no—
155D4×C13—42no—
156D4×C13—42no—
157D4×C13—41no—
158D4×C13—41no—
159D4×C13—81no—
160D4×C13—81no—
161D4×C13—81no—
162D4×C13—81no—
163C2×C4×C13—21no—
164C2×C4×C13—21no—
165C2×C4×C13—22no—
166C2×C4×C13—22no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13—41no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13—41no—
179C2×C4×C13—41no—
180C2×C4×C13—41no—
181C2×C4×C13—41no—
182C2×C4×C13—41no—
183C2×C4×C13—81no—
184C2×C4×C13—81no—
185C2×C4×C13—84no—
186C2×C4×C13C2×C22⋊C411yescharacteristic
187C2×C4×C13C4×D411yescharacteristic
188C2×C4×C13C4×D411yescharacteristic
189C2×C4×C13#12111yescharacteristic
190C2×C4×C13#12111yescharacteristic
191C2×C4×C13#12311yescharacteristic
192C8×C13—42no—
193C8×C13—42no—
194C8×C13—81no—
195#532C22×C1311yescharacteristic
196C2×#124C22×C1311yescharacteristic
197#496C4×C1312yescomplemented
198#489C4×C1312yescomplemented
199#463—22no—
200#448—21no—
201#447—21no—
202#432C22×C1311yescharacteristic
203#432C22×C1311yescharacteristic
204C2×#104—21no—
205C2×#104—21no—
206C4×M16C22×C1311yescharacteristic
207#391—21no—
208#388—21no—
209#388—21no—
210#386—21no—
211#385—21no—
212#383C22×C1311yescharacteristic
213C4×C4⋊C4C22×C1311yescharacteristic
214C4×C22⋊C4—21no—
215#329—22no—
216#327—21no—
217#327—21no—
218C22×C13—21no—
219C22×C13—21no—
220C22×C13—42no—
221C22×C13—42no—
222C22×C13—42no—
223C22×C13—81no—
224C22×C13—81no—
225C22×C13—81no—
226C22×C13—81no—
227C22×C13—81no—
228C22×C13—81no—
229C22×C13—81no—
230C22×C13#38611yescharacteristic
231C22×C13#45311yescharacteristic
232C22×C13#45411yescharacteristic
233C4×C13—21no—
234C4×C13—21no—
235C4×C13—21no—
236C4×C13—21no—
237C4×C13—21no—
238C4×C13—21no—
239C4×C13—42no—
240C4×C13—42no—
241C4×C13—81no—
242C4×C13—81no—
243C4×C13—81no—
244C4×C13—81no—
245C2×#41—21no—
246C22×Q8D4×C1311yescharacteristic
247C22×D4D4×C1311yescharacteristic
248C23×C4—21no—
249C2×SD16—22no—
250C2×D8—22no—
251C2×M16—21no—
252C4⋊Q8C2×C4×C1311yescharacteristic, complemented
253#127C2×C4×C1311yescharacteristic, complemented
254#124—21no—
255#124—21no—
256#124—21no—
257#124C2×C4×C1312yes—
258#124D4×C1312yes—
259#121—21no—
260#121—21no—
261C4×D4—21no—
262C4×D4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C42—21no—
271C2×C42D4×C1311yescharacteristic
272C2×C42D4×C1311yescharacteristic
273C2×C42C23×C1311yescharacteristic
274C4⋊C8—21no—
275C4⋊C8—21no—
276#104—42no—
277#104—42no—
278#103—22no—
279#102—22no—
280C22⋊C8—21no—
281C22⋊C8—21no—
282#97—21no—
283#97—21no—
284#97C2×C4×C1312yescomplemented
285C4×C8—21no—
286#95—21no—
287#95—21no—
288#95—21no—
289#95—21no—
290#95—21no—
291#95D4×C1311yescharacteristic
292#95D4×C1311yescharacteristic
293C2×C13—21no—
294C2×C13—21no—
295C2×C13—82no—
296C2×C13—161no—
297C2×C13#188311yescharacteristic
298C2×C13#190611yescharacteristic
299C2×C13#191111yescharacteristic
300C24—21no—
301#41—41no—
302#41—41no—
303#41—41no—
304#41—41no—
305C2×Q8—21no—
306C2×Q8—21no—
307C2×Q8—81no—
308C2×Q8C13×C22⋊C412yes—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—41no—
314C2×D4—81no—
315C2×D4C13×C22⋊C412yes—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—42no—
322C22×C4—41no—
323C22×C4—81no—
324C22×C4—81no—
325C22×C4C2×D4×C1311yescharacteristic
326C22×C4C2×D4×C1311yescharacteristic
327C22×C4C2×D4×C1311yescharacteristic
328SD16—82no—
329D8—82no—
330M16—22no—
331M16—41no—
332C2×C8—22no—
333C2×C8—41no—
334C2×C8—41no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—42no—
338C4⋊C4—81no—
339C22⋊C4—22no—
340C22⋊C4—22no—
341C22⋊C4—22no—
342C22⋊C4—22no—
343C22⋊C4—42no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—81no—
347C22⋊C4—81no—
348C42—41no—
349C42—41no—
350C42—81no—
351C42C22×C4×C1311yescharacteristic
352C42C2×D4×C1311yescharacteristic
353C42C13×#4111yescharacteristic
354C42C13×#4111yescharacteristic
355C13#938111yescharacteristic, direct product factor, Sylow
356C23—22no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23C13×#12011yescharacteristic
365Q8—42no—
366Q8—41no—
367Q8—41no—
368Q8—81no—
369D4—42no—
370D4—42no—
371D4—41no—
372D4—41no—
373D4—81no—
374D4—81no—
375D4—81no—
376D4—81no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—84no—
400C2×C4C2×C13×C22⋊C411yescharacteristic
401C2×C4C4×D4×C1311yescharacteristic
402C2×C4C4×D4×C1311yescharacteristic
403C2×C4C13×#12111yescharacteristic
404C2×C4C13×#12111yescharacteristic
405C2×C4C13×#12311yescharacteristic
406C8—42no—
407C8—42no—
408C8—81no—
409C22—21no—
410C22—21no—
411C22—42no—
412C22—42no—
413C22—42no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22C13×#38611yescharacteristic
422C22C13×#45311yescharacteristic
423C22C13×#45411yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—21no—
428C4—21no—
429C4—21no—
430C4—42no—
431C4—42no—
432C4—81no—
433C4—81no—
434C4—81no—
435C4—81no—
436C2—21no—
437C2—21no—
438C2—82no—
439C2—161no—
440C2C13×#188311yescharacteristic
441C2C13×#190611yescharacteristic
442C2C13×#191111yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC42C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC13×#3213C2
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×#2337C2semidirect
3. C13×#1980C2semidirect
4. C13×#1527C2semidirect
5. C13×#1514C2semidirect
6. C13×#1288C2semidirect
7. C13×#1285C2semidirect
10. C13×#496C4semidirect
11. C13×#489C4semidirect
38. C13×C4⋊Q8C2×C4semidirect
39. C13×#127C2×C4semidirect
70. C13×#97C2×C4semidirect
79. #9381C13direct (N × H)
136. #2337C2×C13semidirect
137. #1980C2×C13semidirect
138. #1527C2×C13semidirect
139. #1514C2×C13semidirect
140. #1288C2×C13semidirect
141. #1285C2×C13semidirect
197. #496C4×C13semidirect
198. #489C4×C13semidirect
252. C4⋊Q8C2×C4×C13semidirect
253. #127C2×C4×C13semidirect
284. #97C2×C4×C13semidirect
355. C13#9381direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#32132
C13×#23372
C13×#19802
C13×#15272
C13×#15142
C13×#12882
C13×#12852
#938113