Finite Group Databasebeta

← C13×#10331 #15696670

Subgroups — C13×#10331 #15696670

Order 3328.

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

normal subgroups only

This group has 672 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
1C13×#3193C211yesmaximal, characteristic
2C13×#2502C211yesmaximal, characteristic, complemented
3C13×#2501C211yesmaximal, characteristic
4C13×#1821C211yesmaximal, characteristic, complemented
5C13×#1508C211yesmaximal, characteristic, complemented
6C13×#1507C211yesmaximal, characteristic
7C13×#1297C211yesmaximal, characteristic, complemented
8C2×C13×#123—22no—
9C2×C13×C22⋊Q8C2211yescharacteristic
10C2×C13×#121C2211yescharacteristic
11C22×C13×C4⋊C4C2211yescharacteristic
12C13×#484—21no—
13C13×#480—21no—
14C13×#468—22no—
15C13×#450—21no—
16C13×#448—21no—
17C13×#407C2211yescharacteristic
18C13×#407C2211yescharacteristic
19C13×#399—22no—
20C13×#398—22no—
21C13×#391—21no—
22C13×#390—21no—
23C13×#385—22no—
24C13×#384—21no—
25C13×#384—21no—
26C4×C13×C22⋊C4C2211yescharacteristic
27C4×C13×C22⋊C4C2211yescharacteristic
28C13×#343—22no—
29C13×#328—22no—
30C13×#327—22no—
31C22×Q8×C13D411yescharacteristic
32C22×D4×C13—21no—
33C22×D4×C13D411yescharacteristic
34C23×C4×C13D412yes—
35C23×C4×C13C2311yescharacteristic
36C2×C13×SD16—22no—
37C2×C13×M16—21no—
38C2×C13×M16D412yes—
39C13×#123—48no—
40C13×C22⋊Q8—21no—
41C13×C22⋊Q8—21no—
42C13×C22⋊Q8—21no—
43C13×C22⋊Q8—21no—
44C13×#121—21no—
45C13×#121—21no—
46C13×#121—21no—
47C13×#121—21no—
48C2×C13×C4⋊C4—24no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4—21no—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4—24no—
57C2×C13×C4⋊C4D411yescharacteristic
58C2×C13×C4⋊C4D411yescharacteristic
59C2×C13×C22⋊C4—21no—
60C2×C13×C22⋊C4—21no—
61C2×C13×C22⋊C4—24no—
62C2×C13×C22⋊C4—21no—
63C2×C13×C22⋊C4—21no—
64C2×C42×C13—21no—
65C2×C42×C13—21no—
66C13×#107—22no—
67C13×#103—22no—
68C13×#102—22no—
69C13×C22⋊C8—21no—
70C13×C22⋊C8—21no—
71C13×C22⋊C8—21no—
72C13×C22⋊C8—21no—
73C13×#95—24no—
74C13×#95D412yes—
75C13×#95D412yes—
76#10331C1311yesmaximal, characteristic, direct product factor, Sylow
77C24×C13—21no—
78C24×C13C2×D411yescharacteristic
79C2×Q8×C13—21no—
80C2×Q8×C13—21no—
81C2×Q8×C13—42no—
82C2×D4×C13—21no—
83C2×D4×C13—21no—
84C2×D4×C13—42no—
85C2×D4×C13—44no—
86C2×D4×C13—41no—
87C2×D4×C13—41no—
88C22×C4×C13—22no—
89C22×C4×C13—22no—
90C22×C4×C13—21no—
91C22×C4×C13—22no—
92C22×C4×C13—22no—
93C22×C4×C13—21no—
94C22×C4×C13—21no—
95C22×C4×C13—22no—
96C22×C4×C13—42no—
97C22×C4×C13—44no—
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13C2×D411yescharacteristic
103C22×C4×C13#4111yescharacteristic
104C13×SD16—82no—
105C13×M16—42no—
106C13×M16—42no—
107C2×C8×C13—22no—
108C2×C8×C13—41no—
109C13×C4⋊C4—21no—
110C13×C4⋊C4—21no—
111C13×C4⋊C4—21no—
112C13×C4⋊C4—21no—
113C13×C4⋊C4—48no—
114C13×C4⋊C4—41no—
115C13×C4⋊C4—41no—
116C13×C4⋊C4—41no—
117C13×C4⋊C4—41no—
118C13×C4⋊C4—41no—
119C13×C4⋊C4—41no—
120C13×C4⋊C4—84no—
121C13×C22⋊C4—24no—
122C13×C22⋊C4—24no—
123C13×C22⋊C4—48no—
124C13×C22⋊C4—41no—
125C13×C22⋊C4—41no—
126C13×C22⋊C4—41no—
127C13×C22⋊C4—41no—
128C42×C13—42no—
129C42×C13—42no—
130#3193C2×C1311yescharacteristic
131#2502C2×C1311yescharacteristic, complemented
132#2501C2×C1311yescharacteristic
133#1821C2×C1311yescharacteristic, complemented
134#1508C2×C1311yescharacteristic, complemented
135#1507C2×C1311yescharacteristic
136#1297C2×C1311yescharacteristic, complemented
137C23×C13—22no—
138C23×C13—22no—
139C23×C13—41no—
140C23×C13—42no—
141C23×C13—42no—
142C23×C13—41no—
143C23×C13—42no—
144C23×C13#12011yescharacteristic
145C23×C13#12011yescharacteristic
146C23×C13#12111yescharacteristic
147Q8×C13—42no—
148Q8×C13—81no—
149D4×C13—42no—
150D4×C13—81no—
151D4×C13—82no—
152D4×C13—82no—
153C2×C4×C13—22no—
154C2×C4×C13—22no—
155C2×C4×C13—22no—
156C2×C4×C13—24no—
157C2×C4×C13—24no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—42no—
162C2×C4×C13—42no—
163C2×C4×C13—42no—
164C2×C4×C13—42no—
165C2×C4×C13—44no—
166C2×C4×C13—42no—
167C2×C4×C13—42no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13—42no—
172C2×C4×C13—42no—
173C2×C4×C13—44no—
174C2×C4×C13—82no—
175C2×C4×C13#12011yescharacteristic
176C2×C4×C13#12111yescharacteristic
177C2×C4×C13#12111yescharacteristic
178C2×C4×C13#12711yescharacteristic
179C8×C13—42no—
180C8×C13—81no—
181C2×#123—22no—
182C2×C22⋊Q8C22×C1311yescharacteristic
183C2×#121C22×C1311yescharacteristic
184C22×C4⋊C4C22×C1311yescharacteristic
185#484—21no—
186#480—21no—
187#468—22no—
188#450—21no—
189#448—21no—
190#407C22×C1311yescharacteristic
191#407C22×C1311yescharacteristic
192#399—22no—
193#398—22no—
194#391—21no—
195#390—21no—
196#385—22no—
197#384—21no—
198#384—21no—
199C4×C22⋊C4C22×C1311yescharacteristic
200C4×C22⋊C4C22×C1311yescharacteristic
201#343—22no—
202#328—22no—
203#327—22no—
204C22×C13—21no—
205C22×C13—21no—
206C22×C13—21no—
207C22×C13—21no—
208C22×C13—21no—
209C22×C13—21no—
210C22×C13—21no—
211C22×C13—44no—
212C22×C13—84no—
213C22×C13—81no—
214C22×C13—81no—
215C22×C13—81no—
216C22×C13#39211yescharacteristic
217C22×C13#45312yes—
218C22×C13#45612yes—
219C4×C13—21no—
220C4×C13—21no—
221C4×C13—21no—
222C4×C13—44no—
223C4×C13—44no—
224C4×C13—81no—
225C4×C13—82no—
226C4×C13—81no—
227C4×C13—81no—
228C4×C13#45812yes—
229C22×Q8D4×C1311yescharacteristic
230C22×D4—21no—
231C22×D4D4×C1311yescharacteristic
232C23×C4D4×C1312yes—
233C23×C4C23×C1311yescharacteristic
234C2×SD16—22no—
235C2×M16—21no—
236C2×M16D4×C1312yes—
237#123—48no—
238C22⋊Q8—21no—
239C22⋊Q8—21no—
240C22⋊Q8—21no—
241C22⋊Q8—21no—
242#121—21no—
243#121—21no—
244#121—21no—
245#121—21no—
246C2×C4⋊C4—24no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—24no—
255C2×C4⋊C4D4×C1311yescharacteristic
256C2×C4⋊C4D4×C1311yescharacteristic
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—24no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C42—21no—
263C2×C42—21no—
264#107—22no—
265#103—22no—
266#102—22no—
267C22⋊C8—21no—
268C22⋊C8—21no—
269C22⋊C8—21no—
270C22⋊C8—21no—
271#95—24no—
272#95D4×C1312yes—
273#95D4×C1312yes—
274C2×C13—22no—
275C2×C13—22no—
276C2×C13—41no—
277C2×C13—161no—
278C2×C13#200211yescharacteristic
279C2×C13#200511yescharacteristic
280C2×C13#202211yescharacteristic
281C24—21no—
282C24C2×D4×C1311yescharacteristic
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—42no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—42no—
289C2×D4—44no—
290C2×D4—41no—
291C2×D4—41no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—21no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—22no—
300C22×C4—42no—
301C22×C4—44no—
302C22×C4C2×D4×C1311yescharacteristic
303C22×C4C2×D4×C1311yescharacteristic
304C22×C4C2×D4×C1311yescharacteristic
305C22×C4C2×D4×C1311yescharacteristic
306C22×C4C2×D4×C1311yescharacteristic
307C22×C4C13×#4111yescharacteristic
308SD16—82no—
309M16—42no—
310M16—42no—
311C2×C8—22no—
312C2×C8—41no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—48no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—84no—
325C22⋊C4—24no—
326C22⋊C4—24no—
327C22⋊C4—48no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C42—42no—
333C42—42no—
334C13#1033111yescharacteristic, direct product factor, Sylow
335C23—22no—
336C23—22no—
337C23—41no—
338C23—42no—
339C23—42no—
340C23—41no—
341C23—42no—
342C23C13×#12011yescharacteristic
343C23C13×#12011yescharacteristic
344C23C13×#12111yescharacteristic
345Q8—42no—
346Q8—81no—
347D4—42no—
348D4—81no—
349D4—82no—
350D4—82no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—24no—
355C2×C4—24no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—44no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—44no—
372C2×C4—82no—
373C2×C4C13×#12011yescharacteristic
374C2×C4C13×#12111yescharacteristic
375C2×C4C13×#12111yescharacteristic
376C2×C4C13×#12711yescharacteristic
377C8—42no—
378C8—81no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—44no—
387C22—84no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22C13×#39211yescharacteristic
392C22C13×#45312yes—
393C22C13×#45612yes—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—44no—
398C4—44no—
399C4—81no—
400C4—82no—
401C4—81no—
402C4—81no—
403C4C13×#45812yes—
404C2—22no—
405C2—22no—
406C2—41no—
407C2—161no—
408C2C13×#200211yescharacteristic
409C2C13×#200511yescharacteristic
410C2C13×#202211yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC2×C13×#121C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2502C2semidirect
4. C13×#1821C2semidirect
5. C13×#1508C2semidirect
7. C13×#1297C2semidirect
76. #10331C13direct (N × H)
131. #2502C2×C13semidirect
133. #1821C2×C13semidirect
134. #1508C2×C13semidirect
136. #1297C2×C13semidirect
334. C13#10331direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31932
C13×#25022
C13×#25012
C13×#18212
C13×#15082
C13×#15072
C13×#12972
#1033113