Finite Group Databasebeta

← C13×#11796 #15698135

Subgroups — C13×#11796 #15698135

Order 3328.

1068 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#392C211yesmaximal, characteristic
2C13×#1819C211yesmaximal, characteristic, complemented
3C13×#1462C211yesmaximal, characteristic, complemented
4C13×#1343C214yesmaximal, complemented
5C23×D4×C13—21no—
6C23×D4×C13C411yescharacteristic, complemented
7C22×C13×C22⋊C4—21no—
8C22×C13×C22⋊C4C2211yescharacteristic
9C13×#407—21no—
10C13×#392—21no—
11C13×#392—21no—
12C13×#392C412yescomplemented
13C13×#392C2212yes—
14C13×#379—21no—
15C2×C13×#95C411yescharacteristic, complemented
16C13×#342—21no—
17C13×#342C2212yescomplemented
18C13×#323—21no—
19C13×#323C2212yescomplemented
20C25×C13—21no—
21C25×C13D411yescharacteristic
22C22×D4×C13—22no—
23C22×D4×C13—22no—
24C22×D4×C13—21no—
25C22×D4×C13—41no—
26C22×D4×C13—41no—
27C22×D4×C13—44no—
28C22×D4×C13—44no—
29C22×D4×C13—44no—
30C22×D4×C13—44no—
31C22×D4×C13C2×C412yes—
32C23×C4×C13—21no—
33C23×C4×C13C2×C411yescharacteristic
34C23×C4×C13D411yescharacteristic
35C2×C13×M16—41no—
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4—41no—
40C2×C13×C22⋊C4—41no—
41C2×C13×C22⋊C4—44no—
42C2×C13×C22⋊C4—41no—
43C2×C13×C22⋊C4—41no—
44C2×C13×C22⋊C4C2×C411yescharacteristic
45C2×C13×C22⋊C4D411yescharacteristic
46C2×C13×C22⋊C4D411yescharacteristic
47C2×C13×C22⋊C4C2311yescharacteristic
48C13×C22⋊C8—22no—
49C13×C22⋊C8—41no—
50C13×#95—21no—
51C13×#95C2×C412yes—
52#11796C1311yesmaximal, characteristic, direct product factor, Sylow
53C24×C13—24no—
54C24×C13—22no—
55C24×C13—22no—
56C24×C13—21no—
57C24×C13—21no—
58C24×C13—41no—
59C24×C13—42no—
60C24×C13—42no—
61C24×C13—42no—
62C24×C13—42no—
63C24×C13—42no—
64C24×C13—42no—
65C24×C13—42no—
66C24×C13—41no—
67C24×C13—41no—
68C24×C13C22⋊C411yescharacteristic
69C24×C13C22⋊C411yescharacteristic
70C24×C13C2×D411yescharacteristic
71C2×D4×C13—42no—
72C2×D4×C13—44no—
73C2×D4×C13—44no—
74C2×D4×C13—42no—
75C2×D4×C13—44no—
76C2×D4×C13—44no—
77C2×D4×C13—44no—
78C2×D4×C13—44no—
79C2×D4×C13—44no—
80C2×D4×C13—432no—
81C2×D4×C13—48no—
82C2×D4×C13—44no—
83C2×D4×C13—44no—
84C2×D4×C13—44no—
85C22×C4×C13—24no—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13—22no—
90C22×C4×C13—21no—
91C22×C4×C13—42no—
92C22×C4×C13—42no—
93C22×C4×C13—42no—
94C22×C4×C13—42no—
95C22×C4×C13—42no—
96C22×C4×C13C22⋊C411yescharacteristic
97C22×C4×C13C22⋊C411yescharacteristic
98C22×C4×C13C22×C411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C13×M16—82no—
101C2×C8×C13—42no—
102C13×C22⋊C4—41no—
103C13×C22⋊C4—41no—
104C13×C22⋊C4—41no—
105C13×C22⋊C4—41no—
106C13×C22⋊C4—44no—
107C13×C22⋊C4—44no—
108C13×C22⋊C4—42no—
109C13×C22⋊C4—42no—
110C13×C22⋊C4—82no—
111C13×C22⋊C4—82no—
112C2×#392C2×C1311yescharacteristic
113#1819C2×C1311yescharacteristic, complemented
114#1462C2×C1311yescharacteristic, complemented
115#1343C2×C1314yescomplemented
116C23×C13—22no—
117C23×C13—22no—
118C23×C13—21no—
119C23×C13—21no—
120C23×C13—21no—
121C23×C13—21no—
122C23×C13—24no—
123C23×C13—21no—
124C23×C13—21no—
125C23×C13—21no—
126C23×C13—42no—
127C23×C13—42no—
128C23×C13—41no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13—41no—
132C23×C13—42no—
133C23×C13—48no—
134C23×C13—48no—
135C23×C13—42no—
136C23×C13—44no—
137C23×C13—42no—
138C23×C13—48no—
139C23×C13—42no—
140C23×C13—44no—
141C23×C13—42no—
142C23×C13—42no—
143C23×C13—42no—
144C23×C13—42no—
145C23×C13—81no—
146C23×C13—81no—
147C23×C13—84no—
148C23×C13—84no—
149C23×C13—84no—
150C23×C13—82no—
151C23×C13—82no—
152C23×C13—82no—
153C23×C13—82no—
154C23×C13#9911yescharacteristic
155C23×C13#9911yescharacteristic
156C23×C13C2×C22⋊C411yescharacteristic
157C23×C13AGL(1,ℤ/8)12yes—
158D4×C13—416no—
159D4×C13—416no—
160D4×C13—44no—
161D4×C13—48no—
162D4×C13—44no—
163C2×C4×C13—24no—
164C2×C4×C13—21no—
165C2×C4×C13—21no—
166C2×C4×C13—21no—
167C2×C4×C13—21no—
168C2×C4×C13—48no—
169C2×C4×C13—42no—
170C2×C4×C13—42no—
171C2×C4×C13—42no—
172C2×C4×C13—42no—
173C2×C4×C13—42no—
174C2×C4×C13—41no—
175C2×C4×C13—41no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13—81no—
179C2×C4×C13—82no—
180C2×C4×C13—82no—
181C2×C4×C13—82no—
182C8×C13—82no—
183C23×D4—21no—
184C23×D4C4×C1311yescharacteristic, complemented
185C22×C22⋊C4—21no—
186C22×C22⋊C4C22×C1311yescharacteristic
187#407—21no—
188#392—21no—
189#392—21no—
190#392C4×C1312yescomplemented
191#392C22×C1312yes—
192#379—21no—
193C2×#95C4×C1311yescharacteristic, complemented
194#342—21no—
195#342C22×C1312yescomplemented
196#323—21no—
197#323C22×C1312yescomplemented
198C22×C13—24no—
199C22×C13—24no—
200C22×C13—21no—
201C22×C13—21no—
202C22×C13—21no—
203C22×C13—21no—
204C22×C13—21no—
205C22×C13—21no—
206C22×C13—22no—
207C22×C13—42no—
208C22×C13—42no—
209C22×C13—44no—
210C22×C13—44no—
211C22×C13—41no—
212C22×C13—41no—
213C22×C13—44no—
214C22×C13—41no—
215C22×C13—41no—
216C22×C13—41no—
217C22×C13—81no—
218C22×C13—84no—
219C22×C13—84no—
220C22×C13—81no—
221C22×C13—82no—
222C22×C13—82no—
223C22×C13—88no—
224C22×C13—88no—
225C22×C13—82no—
226C22×C13—82no—
227C22×C13AΣL(1,𝔽16)12yes—
228C22×C13#35312yes—
229C22×C13C2×#9911yescharacteristic
230C22×C13#41811yescharacteristic
231C22×C13#42111yescharacteristic
232C4×C13—44no—
233C4×C13—41no—
234C4×C13—41no—
235C4×C13—41no—
236C4×C13—41no—
237C4×C13—162no—
238C25—21no—
239C25D4×C1311yescharacteristic
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—21no—
243C22×D4—41no—
244C22×D4—41no—
245C22×D4—44no—
246C22×D4—44no—
247C22×D4—44no—
248C22×D4—44no—
249C22×D4C2×C4×C1312yes—
250C23×C4—21no—
251C23×C4C2×C4×C1311yescharacteristic
252C23×C4D4×C1311yescharacteristic
253C2×M16—41no—
254C2×C22⋊C4—22no—
255C2×C22⋊C4—22no—
256C2×C22⋊C4—22no—
257C2×C22⋊C4—41no—
258C2×C22⋊C4—41no—
259C2×C22⋊C4—44no—
260C2×C22⋊C4—41no—
261C2×C22⋊C4—41no—
262C2×C22⋊C4C2×C4×C1311yescharacteristic
263C2×C22⋊C4D4×C1311yescharacteristic
264C2×C22⋊C4D4×C1311yescharacteristic
265C2×C22⋊C4C23×C1311yescharacteristic
266C22⋊C8—22no—
267C22⋊C8—41no—
268#95—21no—
269#95C2×C4×C1312yes—
270C2×C13—21no—
271C2×C13—21no—
272C2×C13—22no—
273C2×C13—22no—
274C2×C13—42no—
275C2×C13—81no—
276C2×C13—84no—
277C2×C13#151011yescharacteristic
278C2×C13C2×AΣL(1,𝔽16)11yescharacteristic
279C2×C13C2×#35311yescharacteristic
280C24—24no—
281C24—22no—
282C24—22no—
283C24—21no—
284C24—21no—
285C24—41no—
286C24—42no—
287C24—42no—
288C24—42no—
289C24—42no—
290C24—42no—
291C24—42no—
292C24—42no—
293C24—41no—
294C24—41no—
295C24C13×C22⋊C411yescharacteristic
296C24C13×C22⋊C411yescharacteristic
297C24C2×D4×C1311yescharacteristic
298C2×D4—42no—
299C2×D4—44no—
300C2×D4—44no—
301C2×D4—42no—
302C2×D4—44no—
303C2×D4—44no—
304C2×D4—44no—
305C2×D4—44no—
306C2×D4—44no—
307C2×D4—48no—
308C2×D4—432no—
309C2×D4—44no—
310C2×D4—44no—
311C2×D4—44no—
312C22×C4—24no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—22no—
317C22×C4—21no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4C13×C22⋊C411yescharacteristic
324C22×C4C13×C22⋊C411yescharacteristic
325C22×C4C22×C4×C1311yescharacteristic
326C22×C4C2×D4×C1311yescharacteristic
327M16—82no—
328C2×C8—42no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—44no—
334C22⋊C4—44no—
335C22⋊C4—42no—
336C22⋊C4—42no—
337C22⋊C4—82no—
338C22⋊C4—82no—
339C13#1179611yescharacteristic, direct product factor, Sylow
340C23—21no—
341C23—21no—
342C23—22no—
343C23—22no—
344C23—21no—
345C23—21no—
346C23—24no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—42no—
351C23—42no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—42no—
357C23—48no—
358C23—48no—
359C23—42no—
360C23—44no—
361C23—42no—
362C23—48no—
363C23—42no—
364C23—42no—
365C23—42no—
366C23—42no—
367C23—44no—
368C23—42no—
369C23—81no—
370C23—81no—
371C23—84no—
372C23—84no—
373C23—84no—
374C23—82no—
375C23—82no—
376C23—82no—
377C23—82no—
378C23C13×#9911yescharacteristic
379C23C13×#9911yescharacteristic
380C23C2×C13×C22⋊C411yescharacteristic
381C23C13×AGL(1,ℤ/8)12yes—
382D4—44no—
383D4—416no—
384D4—416no—
385D4—44no—
386D4—48no—
387C2×C4—24no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—48no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—81no—
403C2×C4—82no—
404C2×C4—82no—
405C2×C4—82no—
406C8—82no—
407C22—24no—
408C22—24no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—22no—
416C22—42no—
417C22—42no—
418C22—44no—
419C22—44no—
420C22—41no—
421C22—41no—
422C22—41no—
423C22—44no—
424C22—41no—
425C22—41no—
426C22—81no—
427C22—84no—
428C22—84no—
429C22—81no—
430C22—82no—
431C22—82no—
432C22—88no—
433C22—88no—
434C22—82no—
435C22—82no—
436C22C13×AΣL(1,𝔽16)12yes—
437C22C13×#35312yes—
438C22C2×C13×#9911yescharacteristic
439C22C13×#41811yescharacteristic
440C22C13×#42111yescharacteristic
441C4—44no—
442C4—41no—
443C4—41no—
444C4—41no—
445C4—41no—
446C4—162no—
447C2—21no—
448C2—21no—
449C2—22no—
450C2—22no—
451C2—42no—
452C2—81no—
453C2—84no—
454C2C13×#151011yescharacteristic
455C2C2×C13×AΣL(1,𝔽16)11yescharacteristic
456C2C2×C13×#35311yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC2×C13×#392C2
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C24×C13 ◁ C22×C13×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#1819C2semidirect
3. C13×#1462C2semidirect
4. C13×#1343C2semidirect
6. C23×D4×C13C4semidirect
12. C13×#392C4semidirect
15. C2×C13×#95C4semidirect
17. C13×#342C22semidirect
19. C13×#323C22semidirect
52. #11796C13direct (N × H)
113. #1819C2×C13semidirect
114. #1462C2×C13semidirect
115. #1343C2×C13semidirect
184. C23×D4C4×C13semidirect
190. #392C4×C13semidirect
193. C2×#95C4×C13semidirect
195. #342C22×C13semidirect
197. #323C22×C13semidirect
339. C13#11796direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3922
C13×#18192
C13×#14622
C13×#13432
#1179613