Finite Group Databasebeta

← C13×#9107 #15695446

Subgroups — C13×#9107 #15695446

Order 3328.

674 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2972C211yesmaximal, characteristic, complemented
2C13×#2321C211yesmaximal, characteristic
3C13×#1459C211yesmaximal, characteristic, complemented
4C2×C13×#323C212yesmaximal, complemented
5C13×#1282C212yesmaximal, complemented
6C2×C13×#120C411yescharacteristic
7C2×C4×D4×C13C2211yescharacteristic
8C22×C13×C22⋊C4C2211yescharacteristic
9C8×D4×C13—24no—
10C13×#431—21no—
11C2×C13×C22⋊C8—21no—
12C2×C13×C22⋊C8C2212yes—
13C2×C13×C22⋊C8C2212yes—
14C13×#390—21no—
15C13×#388—21no—
16C13×#388—21no—
17C13×#386—21no—
18C13×#386C411yescharacteristic
19C13×#385C411yescharacteristic
20C13×#379C411yescharacteristic
21C4×C13×C22⋊C4C2211yescharacteristic
22C13×#324—21no—
23C13×#323—21no—
24C13×#323—24no—
25C25×C13C2×C411yescharacteristic
26C22×D4×C13—21no—
27C22×D4×C13C2×C411yescharacteristic
28C23×C4×C13C2×C411yescharacteristic
29C23×C4×C13D411yescharacteristic
30C23×C4×C13C2311yescharacteristic
31C22×C8×C13—22no—
32C22×C8×C13—22no—
33C22×C8×C13—22no—
34C13×#120—22no—
35C13×#120C814yescomplemented
36C4×D4×C13—22no—
37C4×D4×C13—22no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4D411yescharacteristic
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—22no—
44C2×C13×C22⋊C4—22no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—21no—
47C2×C13×C22⋊C4—21no—
48C2×C13×C22⋊C4C2×C411yescharacteristic
49C2×C13×C22⋊C4C2×C411yescharacteristic
50C2×C13×C22⋊C4C2×C411yescharacteristic
51C2×C13×C22⋊C4D411yescharacteristic
52C2×C42×C13—21no—
53C2×C42×C13D411yescharacteristic
54C13×C4⋊C8—22no—
55C13×C22⋊C8—22no—
56C13×C22⋊C8—22no—
57C13×C22⋊C8—22no—
58C13×C22⋊C8—22no—
59C13×C22⋊C8D414yescomplemented
60C4×C8×C13—22no—
61C13×#95—21no—
62C13×#95—21no—
63C13×#95—21no—
64#9107C1311yesmaximal, characteristic, direct product factor, Sylow
65C24×C13—21no—
66C24×C13—22no—
67C24×C13—21no—
68C24×C13—22no—
69C24×C13—81no—
70C24×C13—81no—
71C24×C13C22⋊C411yescharacteristic
72C24×C13C2×C812yescomplemented
73C24×C13C22×C411yescharacteristic
74C2×D4×C13—22no—
75C2×D4×C13—22no—
76C2×D4×C13—24no—
77C2×D4×C13—81no—
78C2×D4×C13—81no—
79C2×D4×C13C2×C812yes—
80C2×D4×C13M1612yes—
81C22×C4×C13—21no—
82C22×C4×C13—21no—
83C22×C4×C13—21no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—22no—
87C22×C4×C13—81no—
88C22×C4×C13—81no—
89C22×C4×C13—81no—
90C22×C4×C13C22⋊C411yescharacteristic
91C22×C4×C13C22⋊C411yescharacteristic
92C22×C4×C13C22⋊C411yescharacteristic
93C22×C4×C13C2×D412yes—
94C22×C4×C13C2×D411yescharacteristic
95C22×C4×C13C2×D411yescharacteristic
96C22×C4×C13#4112yes—
97C2×C8×C13—24no—
98C2×C8×C13—42no—
99C2×C8×C13—82no—
100C2×C8×C13—82no—
101C2×C8×C13—82no—
102C13×C4⋊C4—22no—
103C13×C4⋊C4—81no—
104C13×C22⋊C4—22no—
105C13×C22⋊C4—21no—
106C13×C22⋊C4—24no—
107C13×C22⋊C4—22no—
108C13×C22⋊C4—22no—
109C13×C22⋊C4—41no—
110C13×C22⋊C4—42no—
111C13×C22⋊C4—41no—
112C13×C22⋊C4—81no—
113C13×C22⋊C4—81no—
114C13×C22⋊C4—81no—
115C13×C22⋊C4C2×C812yescomplemented
116C42×C13—21no—
117C42×C13—21no—
118C42×C13—81no—
119#2972C2×C1311yescharacteristic, complemented
120#2321C2×C1311yescharacteristic
121#1459C2×C1311yescharacteristic, complemented
122C2×#323C2×C1312yescomplemented
123#1282C2×C1312yescomplemented
124C23×C13—21no—
125C23×C13—21no—
126C23×C13—22no—
127C23×C13—24no—
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×C13—41no—
138C23×C13—42no—
139C23×C13—82no—
140C23×C13—82no—
141C23×C13—82no—
142C23×C13—82no—
143C23×C13—84no—
144C23×C13C22⋊C812yes—
145C23×C13C2×C22⋊C411yescharacteristic
146C23×C13C4×D412yes—
147C23×C13C22×C811yescharacteristic
148C23×C13C2×M1611yescharacteristic
149C23×C13#13112yes—
150D4×C13—24no—
151D4×C13—24no—
152D4×C13—84no—
153C2×C4×C13—21no—
154C2×C4×C13—21no—
155C2×C4×C13—21no—
156C2×C4×C13—21no—
157C2×C4×C13—22no—
158C2×C4×C13—41no—
159C2×C4×C13—42no—
160C2×C4×C13—42no—
161C2×C4×C13—41no—
162C2×C4×C13—42no—
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—41no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—41no—
173C2×C4×C13—81no—
174C2×C4×C13—82no—
175C2×C4×C13C22⋊C812yes—
176C2×C4×C13#12011yescharacteristic
177C2×C4×C13#12112yes—
178C2×C4×C13#12311yescharacteristic
179C8×C13—44no—
180C8×C13—82no—
181C2×#120C4×C1311yescharacteristic
182C2×C4×D4C22×C1311yescharacteristic
183C22×C22⋊C4C22×C1311yescharacteristic
184C8×D4—24no—
185#431—21no—
186C2×C22⋊C8—21no—
187C2×C22⋊C8C22×C1312yes—
188C2×C22⋊C8C22×C1312yes—
189#390—21no—
190#388—21no—
191#388—21no—
192#386—21no—
193#386C4×C1311yescharacteristic
194#385C4×C1311yescharacteristic
195#379C4×C1311yescharacteristic
196C4×C22⋊C4C22×C1311yescharacteristic
197#324—21no—
198#323—21no—
199#323—24no—
200C22×C13—21no—
201C22×C13—22no—
202C22×C13—21no—
203C22×C13—22no—
204C22×C13—22no—
205C22×C13—41no—
206C22×C13—41no—
207C22×C13—42no—
208C22×C13—42no—
209C22×C13—42no—
210C22×C13—42no—
211C22×C13—41no—
212C22×C13—41no—
213C22×C13—42no—
214C22×C13—81no—
215C22×C13—84no—
216C22×C13—81no—
217C22×C13—81no—
218C22×C13—84no—
219C22×C13—81no—
220C22×C13—81no—
221C22×C13#38611yescharacteristic
222C22×C13C2×C22⋊C811yescharacteristic
223C22×C13#40811yescharacteristic
224C22×C13C8×D412yes—
225C22×C13#43512yes—
226C4×C13—22no—
227C4×C13—21no—
228C4×C13—22no—
229C4×C13—21no—
230C4×C13—42no—
231C4×C13—41no—
232C4×C13—41no—
233C4×C13—81no—
234C4×C13—81no—
235C25C2×C4×C1311yescharacteristic
236C22×D4—21no—
237C22×D4C2×C4×C1311yescharacteristic
238C23×C4C2×C4×C1311yescharacteristic
239C23×C4D4×C1311yescharacteristic
240C23×C4C23×C1311yescharacteristic
241C22×C8—22no—
242C22×C8—22no—
243C22×C8—22no—
244#120—22no—
245#120C8×C1314yescomplemented
246C4×D4—22no—
247C4×D4—22no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4D4×C1311yescharacteristic
250C2×C22⋊C4—21no—
251C2×C22⋊C4—22no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—22no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4C2×C4×C1311yescharacteristic
259C2×C22⋊C4C2×C4×C1311yescharacteristic
260C2×C22⋊C4C2×C4×C1311yescharacteristic
261C2×C22⋊C4D4×C1311yescharacteristic
262C2×C42—21no—
263C2×C42D4×C1311yescharacteristic
264C4⋊C8—22no—
265C22⋊C8—22no—
266C22⋊C8—22no—
267C22⋊C8—22no—
268C22⋊C8—22no—
269C22⋊C8D4×C1314yescomplemented
270C4×C8—22no—
271#95—21no—
272#95—21no—
273#95—21no—
274C2×C13—21no—
275C2×C13—21no—
276C2×C13—22no—
277C2×C13—22no—
278C2×C13—42no—
279C2×C13—82no—
280C2×C13#186911yescharacteristic
281C2×C13#191311yescharacteristic
282C2×C13#191411yescharacteristic
283C24—21no—
284C24—22no—
285C24—21no—
286C24—22no—
287C24—81no—
288C24—81no—
289C24C13×C22⋊C411yescharacteristic
290C24C2×C8×C1312yescomplemented
291C24C22×C4×C1311yescharacteristic
292C2×D4—22no—
293C2×D4—22no—
294C2×D4—24no—
295C2×D4—81no—
296C2×D4—81no—
297C2×D4C2×C8×C1312yes—
298C2×D4C13×M1612yes—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—22no—
305C22×C4—81no—
306C22×C4—81no—
307C22×C4—81no—
308C22×C4C13×C22⋊C411yescharacteristic
309C22×C4C13×C22⋊C411yescharacteristic
310C22×C4C13×C22⋊C411yescharacteristic
311C22×C4C2×D4×C1312yes—
312C22×C4C2×D4×C1311yescharacteristic
313C22×C4C2×D4×C1311yescharacteristic
314C22×C4C13×#4112yes—
315C2×C8—24no—
316C2×C8—42no—
317C2×C8—82no—
318C2×C8—82no—
319C2×C8—82no—
320C4⋊C4—22no—
321C4⋊C4—81no—
322C22⋊C4—22no—
323C22⋊C4—21no—
324C22⋊C4—24no—
325C22⋊C4—22no—
326C22⋊C4—22no—
327C22⋊C4—41no—
328C22⋊C4—42no—
329C22⋊C4—41no—
330C22⋊C4—81no—
331C22⋊C4—81no—
332C22⋊C4—81no—
333C22⋊C4C2×C8×C1312yescomplemented
334C42—21no—
335C42—21no—
336C42—81no—
337C13#910711yescharacteristic, direct product factor, Sylow
338C23—21no—
339C23—21no—
340C23—22no—
341C23—24no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—42no—
353C23—82no—
354C23—82no—
355C23—82no—
356C23—82no—
357C23—84no—
358C23C13×C22⋊C812yes—
359C23C2×C13×C22⋊C411yescharacteristic
360C23C4×D4×C1312yes—
361C23C22×C8×C1311yescharacteristic
362C23C2×C13×M1611yescharacteristic
363C23C13×#13112yes—
364D4—24no—
365D4—24no—
366D4—84no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—22no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—81no—
388C2×C4—82no—
389C2×C4C13×C22⋊C812yes—
390C2×C4C13×#12011yescharacteristic
391C2×C4C13×#12112yes—
392C2×C4C13×#12311yescharacteristic
393C8—44no—
394C8—82no—
395C22—21no—
396C22—22no—
397C22—21no—
398C22—22no—
399C22—22no—
400C22—41no—
401C22—41no—
402C22—42no—
403C22—42no—
404C22—42no—
405C22—42no—
406C22—41no—
407C22—41no—
408C22—42no—
409C22—81no—
410C22—84no—
411C22—81no—
412C22—81no—
413C22—84no—
414C22—81no—
415C22—81no—
416C22C13×#38611yescharacteristic
417C22C2×C13×C22⋊C811yescharacteristic
418C22C13×#40811yescharacteristic
419C22C8×D4×C1312yes—
420C22C13×#43512yes—
421C4—22no—
422C4—21no—
423C4—22no—
424C4—21no—
425C4—42no—
426C4—41no—
427C4—41no—
428C4—81no—
429C4—81no—
430C2—21no—
431C2—21no—
432C2—22no—
433C2—22no—
434C2—42no—
435C2—82no—
436C2C13×#186911yescharacteristic
437C2C13×#191311yescharacteristic
438C2C13×#191411yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC23C22×C8×C13
Frattini, cosocleC23×C4C23×C13
prime radicalC2×C13×#120C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2972C2semidirect
3. C13×#1459C2semidirect
4. C2×C13×#323C2semidirect
5. C13×#1282C2semidirect
35. C13×#120C8semidirect
59. C13×C22⋊C8D4semidirect
64. #9107C13direct (N × H)
72. C24×C13C2×C8semidirect
115. C13×C22⋊C4C2×C8semidirect
119. #2972C2×C13semidirect
121. #1459C2×C13semidirect
122. C2×#323C2×C13semidirect
123. #1282C2×C13semidirect
245. #120C8×C13semidirect
269. C22⋊C8D4×C13semidirect
290. C24C2×C8×C13semidirect
333. C22⋊C4C2×C8×C13semidirect
337. C13#9107direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#29722
C13×#23212
C13×#14592
C2×C13×#3232
C13×#12822
#910713