Finite Group Databasebeta

← C13×#9386 #15695725

Subgroups — C13×#9386 #15695725

Order 3328.

618 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×#2973C211yesmaximal, characteristic, complemented
2C13×#2543C211yesmaximal, characteristic
3C13×#1799C211yesmaximal, characteristic, complemented
4C13×#1519C212yesmaximal, complemented
5C13×#1294C212yesmaximal, complemented
6C2×C13×#121—21no—
7C2×C13×#121C2211yescharacteristic
8C2×C4×D4×C13C2211yescharacteristic
9C13×#435—24no—
10C13×#432—21no—
11C2×C13×#99—21no—
12C13×#407—21no—
13C2×C13×C22⋊C8C2212yes—
14C13×#398C411yescharacteristic, complemented
15C13×#397C411yescharacteristic, complemented
16C13×#394C411yescharacteristic, complemented
17C13×#392C411yescharacteristic, complemented
18C13×#388—21no—
19C13×#386—21no—
20C13×#386—21no—
21C13×#380C2212yes—
22C2×C13×#95C2211yescharacteristic
23C13×#342—21no—
24C13×#327—24no—
25C22×D4×C13—21no—
26C22×D4×C13—21no—
27C22×D4×C13C2×C411yescharacteristic
28C22×D4×C13D411yescharacteristic
29C23×C4×C13—21no—
30C23×C4×C13D411yescharacteristic
31C23×C4×C13C2311yescharacteristic
32C2×C13×M16—22no—
33C22×C8×C13—22no—
34C13×#121—22no—
35C13×#121—22no—
36C13×#121—44no—
37C4×D4×C13—22no—
38C4×D4×C13—22no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4—22no—
41C2×C13×C4⋊C4C2×C411yescharacteristic
42C2×C13×C4⋊C4C2×C411yescharacteristic
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—21no—
47C2×C13×C22⋊C4—22no—
48C2×C13×C22⋊C4—21no—
49C2×C13×C22⋊C4C2×C411yescharacteristic
50C2×C13×C22⋊C4D411yescharacteristic
51C2×C42×C13D411yescharacteristic
52C13×C4⋊C8—22no—
53C13×#99—42no—
54C13×C22⋊C8—22no—
55C13×C22⋊C8—22no—
56C13×C22⋊C8D414yescomplemented
57C13×#97—22no—
58C13×#95—21no—
59C13×#95—21no—
60C13×#95—21no—
61C13×#95—22no—
62C13×#95C2×C411yescharacteristic
63C13×#95C2×C411yescharacteristic
64#9386C1311yesmaximal, characteristic, direct product factor, Sylow
65C24×C13—21no—
66C24×C13C22⋊C411yescharacteristic
67C24×C13C2×D411yescharacteristic
68C2×D4×C13—22no—
69C2×D4×C13—21no—
70C2×D4×C13—22no—
71C2×D4×C13—21no—
72C2×D4×C13—22no—
73C2×D4×C13—42no—
74C2×D4×C13—42no—
75C2×D4×C13—42no—
76C2×D4×C13—42no—
77C2×D4×C13—41no—
78C2×D4×C13—41no—
79C2×D4×C13—81no—
80C2×D4×C13—81no—
81C22×C4×C13—21no—
82C22×C4×C13—21no—
83C22×C4×C13—21no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—42no—
87C22×C4×C13—42no—
88C22×C4×C13—42no—
89C22×C4×C13—81no—
90C22×C4×C13—81no—
91C22×C4×C13—81no—
92C22×C4×C13C22⋊C411yescharacteristic
93C22×C4×C13C22⋊C411yescharacteristic
94C22×C4×C13C22⋊C411yescharacteristic
95C22×C4×C13C22×C411yescharacteristic
96C22×C4×C13C2×D412yes—
97C22×C4×C13C2×D411yescharacteristic
98C22×C4×C13#4112yes—
99C13×M16—82no—
100C2×C8×C13—24no—
101C2×C8×C13—82no—
102C13×C4⋊C4—22no—
103C13×C4⋊C4—22no—
104C13×C4⋊C4—42no—
105C13×C4⋊C4—82no—
106C13×C22⋊C4—22no—
107C13×C22⋊C4—22no—
108C13×C22⋊C4—42no—
109C13×C22⋊C4—42no—
110C13×C22⋊C4—42no—
111C13×C22⋊C4—41no—
112C13×C22⋊C4—41no—
113C13×C22⋊C4—42no—
114C13×C22⋊C4—42no—
115C13×C22⋊C4—81no—
116C42×C13—21no—
117C42×C13—21no—
118#2973C2×C1311yescharacteristic, complemented
119#2543C2×C1311yescharacteristic
120#1799C2×C1311yescharacteristic, complemented
121#1519C2×C1312yescomplemented
122#1294C2×C1312yescomplemented
123C23×C13—21no—
124C23×C13—21no—
125C23×C13—21no—
126C23×C13—41no—
127C23×C13—41no—
128C23×C13—41no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13—41no—
132C23×C13—41no—
133C23×C13—41no—
134C23×C13—41no—
135C23×C13—41no—
136C23×C13—41no—
137C23×C13C2×C22⋊C411yescharacteristic
138C23×C13#12112yes—
139C23×C13AGL(1,ℤ/8)11yescharacteristic
140C23×C13AGL(1,ℤ/8)12yes—
141C23×C13#13711yescharacteristic
142D4×C13—42no—
143D4×C13—42no—
144D4×C13—82no—
145D4×C13—84no—
146D4×C13—82no—
147D4×C13—82no—
148C2×C4×C13—22no—
149C2×C4×C13—21no—
150C2×C4×C13—21no—
151C2×C4×C13—21no—
152C2×C4×C13—21no—
153C2×C4×C13—21no—
154C2×C4×C13—42no—
155C2×C4×C13—42no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—42no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—81no—
170C2×C4×C13—84no—
171C2×C4×C13—82no—
172C2×C4×C13—82no—
173C2×C4×C13—82no—
174C2×C4×C13C4×D412yes—
175C2×C4×C13#12011yescharacteristic
176C2×C4×C13#12311yescharacteristic
177C8×C13—44no—
178C2×#121—21no—
179C2×#121C22×C1311yescharacteristic
180C2×C4×D4C22×C1311yescharacteristic
181#435—24no—
182#432—21no—
183C2×#99—21no—
184#407—21no—
185C2×C22⋊C8C22×C1312yes—
186#398C4×C1311yescharacteristic, complemented
187#397C4×C1311yescharacteristic, complemented
188#394C4×C1311yescharacteristic, complemented
189#392C4×C1311yescharacteristic, complemented
190#388—21no—
191#386—21no—
192#386—21no—
193#380C22×C1312yes—
194C2×#95C22×C1311yescharacteristic
195#342—21no—
196#327—24no—
197C22×C13—21no—
198C22×C13—22no—
199C22×C13—21no—
200C22×C13—22no—
201C22×C13—42no—
202C22×C13—41no—
203C22×C13—41no—
204C22×C13—42no—
205C22×C13—41no—
206C22×C13—41no—
207C22×C13—41no—
208C22×C13—81no—
209C22×C13—81no—
210C22×C13—81no—
211C22×C13—81no—
212C22×C13—81no—
213C22×C13—81no—
214C22×C13—81no—
215C22×C13—81no—
216C22×C13#38611yescharacteristic
217C22×C13#41711yescharacteristic
218C22×C13#41811yescharacteristic
219C22×C13#46812yes—
220C22×C13#46912yes—
221C4×C13—21no—
222C4×C13—21no—
223C4×C13—22no—
224C4×C13—42no—
225C4×C13—41no—
226C4×C13—41no—
227C4×C13—41no—
228C4×C13—81no—
229C4×C13—81no—
230C4×C13—162no—
231C22×D4—21no—
232C22×D4—21no—
233C22×D4C2×C4×C1311yescharacteristic
234C22×D4D4×C1311yescharacteristic
235C23×C4—21no—
236C23×C4D4×C1311yescharacteristic
237C23×C4C23×C1311yescharacteristic
238C2×M16—22no—
239C22×C8—22no—
240#121—22no—
241#121—22no—
242#121—44no—
243C4×D4—22no—
244C4×D4—22no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4C2×C4×C1311yescharacteristic
248C2×C4⋊C4C2×C4×C1311yescharacteristic
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—22no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4C2×C4×C1311yescharacteristic
256C2×C22⋊C4D4×C1311yescharacteristic
257C2×C42D4×C1311yescharacteristic
258C4⋊C8—22no—
259#99—42no—
260C22⋊C8—22no—
261C22⋊C8—22no—
262C22⋊C8D4×C1314yescomplemented
263#97—22no—
264#95—21no—
265#95—21no—
266#95—21no—
267#95—22no—
268#95C2×C4×C1311yescharacteristic
269#95C2×C4×C1311yescharacteristic
270C2×C13—21no—
271C2×C13—22no—
272C2×C13—21no—
273C2×C13—22no—
274C2×C13—81no—
275C2×C13—161no—
276C2×C13#188411yescharacteristic
277C2×C13#189511yescharacteristic
278C2×C13#191311yescharacteristic
279C24—21no—
280C24C13×C22⋊C411yescharacteristic
281C24C2×D4×C1311yescharacteristic
282C2×D4—22no—
283C2×D4—21no—
284C2×D4—22no—
285C2×D4—21no—
286C2×D4—22no—
287C2×D4—42no—
288C2×D4—42no—
289C2×D4—42no—
290C2×D4—42no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—81no—
294C2×D4—81no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—81no—
304C22×C4—81no—
305C22×C4—81no—
306C22×C4C13×C22⋊C411yescharacteristic
307C22×C4C13×C22⋊C411yescharacteristic
308C22×C4C13×C22⋊C411yescharacteristic
309C22×C4C22×C4×C1311yescharacteristic
310C22×C4C2×D4×C1312yes—
311C22×C4C2×D4×C1311yescharacteristic
312C22×C4C13×#4112yes—
313M16—82no—
314C2×C8—24no—
315C2×C8—82no—
316C4⋊C4—22no—
317C4⋊C4—22no—
318C4⋊C4—42no—
319C4⋊C4—82no—
320C22⋊C4—22no—
321C22⋊C4—22no—
322C22⋊C4—42no—
323C22⋊C4—42no—
324C22⋊C4—42no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—42no—
328C22⋊C4—42no—
329C22⋊C4—81no—
330C42—21no—
331C42—21no—
332C13#938611yescharacteristic, direct product factor, Sylow
333C23—21no—
334C23—21no—
335C23—21no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23C2×C13×C22⋊C411yescharacteristic
348C23C13×#12112yes—
349C23C13×AGL(1,ℤ/8)11yescharacteristic
350C23C13×AGL(1,ℤ/8)12yes—
351C23C13×#13711yescharacteristic
352D4—42no—
353D4—42no—
354D4—82no—
355D4—84no—
356D4—82no—
357D4—82no—
358C2×C4—22no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—81no—
380C2×C4—84no—
381C2×C4—82no—
382C2×C4—82no—
383C2×C4—82no—
384C2×C4C4×D4×C1312yes—
385C2×C4C13×#12011yescharacteristic
386C2×C4C13×#12311yescharacteristic
387C8—44no—
388C22—21no—
389C22—22no—
390C22—21no—
391C22—22no—
392C22—42no—
393C22—41no—
394C22—41no—
395C22—42no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—81no—
400C22—81no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—81no—
407C22C13×#38611yescharacteristic
408C22C13×#41711yescharacteristic
409C22C13×#41811yescharacteristic
410C22C13×#46812yes—
411C22C13×#46912yes—
412C4—21no—
413C4—21no—
414C4—22no—
415C4—42no—
416C4—41no—
417C4—41no—
418C4—41no—
419C4—81no—
420C4—81no—
421C4—162no—
422C2—21no—
423C2—22no—
424C2—21no—
425C2—22no—
426C2—81no—
427C2—161no—
428C2C13×#188411yescharacteristic
429C2C13×#189511yescharacteristic
430C2C13×#191311yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC22×C4C22×C4×C13
Frattini, cosocleC23×C4C23×C13
prime radicalC13×#2543C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2973C2semidirect
3. C13×#1799C2semidirect
4. C13×#1519C2semidirect
5. C13×#1294C2semidirect
14. C13×#398C4semidirect
15. C13×#397C4semidirect
16. C13×#394C4semidirect
17. C13×#392C4semidirect
56. C13×C22⋊C8D4semidirect
64. #9386C13direct (N × H)
118. #2973C2×C13semidirect
120. #1799C2×C13semidirect
121. #1519C2×C13semidirect
122. #1294C2×C13semidirect
186. #398C4×C13semidirect
187. #397C4×C13semidirect
188. #394C4×C13semidirect
189. #392C4×C13semidirect
262. C22⋊C8D4×C13semidirect
332. C13#9386direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#29732
C13×#25432
C13×#17992
C13×#15192
C13×#12942
#938613