Finite Group Databasebeta

← C13×#9185 #15695524

Subgroups — C13×#9185 #15695524

Order 3328.

582 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 122 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×#2973C211yesmaximal, characteristic, complemented
2C13×#2635C211yesmaximal, characteristic
3C4×C13×#99C211yesmaximal, characteristic, complemented
4C13×#1507C212yesmaximal, complemented
5C13×#1284C212yesmaximal, complemented
6C2×C13×#121C2211yescharacteristic
7C2×C4×D4×C13C2211yescharacteristic
8C13×#435—24no—
9C13×#432—21no—
10C2×C13×#99—21no—
11C13×#407C2212yes—
12C2×C13×C22⋊C8—21no—
13C13×#400C411yescharacteristic, complemented
14C13×#399C411yescharacteristic, complemented
15C13×#394—21no—
16C13×#394C411yescharacteristic, complemented
17C13×#392—21no—
18C13×#392C411yescharacteristic, complemented
19C13×#388—21no—
20C13×#386—21no—
21C13×#381C2211yescharacteristic
22C4×C13×C22⋊C4C2212yes—
23C13×#342—21no—
24C13×#327—24no—
25C22×D4×C13—21no—
26C22×D4×C13—21no—
27C22×D4×C13C2×C411yescharacteristic
28C22×D4×C13D411yescharacteristic
29C23×C4×C13D411yescharacteristic
30C23×C4×C13C2311yescharacteristic
31C2×C13×M16—22no—
32C22×C8×C13—22no—
33C13×#121—22no—
34C13×#121—22no—
35C4×D4×C13—22no—
36C4×D4×C13—22no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4C2×C411yescharacteristic
39C2×C13×C4⋊C4C2×C411yescharacteristic
40C2×C13×C22⋊C4—22no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—21no—
47C2×C13×C22⋊C4C2×C411yescharacteristic
48C2×C13×C22⋊C4D411yescharacteristic
49C2×C42×C13—22no—
50C2×C42×C13D411yescharacteristic
51C13×C4⋊C8—22no—
52C13×#99—24no—
53C13×C22⋊C8—22no—
54C13×C22⋊C8—22no—
55C13×C22⋊C8D414yescomplemented
56C13×#97—22no—
57C13×#95—21no—
58C13×#95—21no—
59C13×#95—21no—
60C13×#95—22no—
61C13×#95C2×C411yescharacteristic
62C13×#95C2×C411yescharacteristic
63#9185C1311yesmaximal, characteristic, direct product factor, Sylow
64C24×C13—21no—
65C24×C13C22⋊C411yescharacteristic
66C24×C13C2×D411yescharacteristic
67C2×D4×C13—22no—
68C2×D4×C13—22no—
69C2×D4×C13—22no—
70C2×D4×C13—41no—
71C2×D4×C13—42no—
72C2×D4×C13—42no—
73C2×D4×C13—81no—
74C2×D4×C13—81no—
75C2×D4×C13—81no—
76C2×D4×C13—81no—
77C2×D4×C13—81no—
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—21no—
81C22×C4×C13—21no—
82C22×C4×C13—21no—
83C22×C4×C13—42no—
84C22×C4×C13—81no—
85C22×C4×C13—81no—
86C22×C4×C13C22⋊C411yescharacteristic
87C22×C4×C13C22⋊C411yescharacteristic
88C22×C4×C13C22⋊C411yescharacteristic
89C22×C4×C13C22×C411yescharacteristic
90C22×C4×C13C2×D412yes—
91C22×C4×C13C2×D411yescharacteristic
92C22×C4×C13#4112yes—
93C13×M16—82no—
94C2×C8×C13—24no—
95C2×C8×C13—82no—
96C13×C4⋊C4—22no—
97C13×C4⋊C4—22no—
98C13×C4⋊C4—81no—
99C13×C22⋊C4—22no—
100C13×C22⋊C4—22no—
101C13×C22⋊C4—24no—
102C13×C22⋊C4—42no—
103C13×C22⋊C4—42no—
104C13×C22⋊C4—41no—
105C13×C22⋊C4—41no—
106C13×C22⋊C4—81no—
107C13×C22⋊C4—81no—
108C13×C22⋊C4—81no—
109C13×C22⋊C4—81no—
110C42×C13—21no—
111C42×C13—21no—
112C42×C13—82no—
113#2973C2×C1311yescharacteristic, complemented
114#2635C2×C1311yescharacteristic
115C4×#99C2×C1311yescharacteristic, complemented
116#1507C2×C1312yescomplemented
117#1284C2×C1312yescomplemented
118C23×C13—21no—
119C23×C13—21no—
120C23×C13—21no—
121C23×C13—21no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13—41no—
126C23×C13—41no—
127C23×C13—41no—
128C23×C13—41no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13—41no—
132C23×C13—41no—
133C23×C13#10412yes—
134C23×C13C2×C22⋊C411yescharacteristic
135C23×C13#12112yes—
136D4×C13—44no—
137D4×C13—82no—
138D4×C13—84no—
139D4×C13—84no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—42no—
146C2×C4×C13—42no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—42no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—44no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—81no—
163C2×C4×C13—82no—
164C2×C4×C13—82no—
165C2×C4×C13C4×D412yes—
166C2×C4×C13#12011yescharacteristic
167C2×C4×C13#12311yescharacteristic
168C8×C13—44no—
169C2×#121C22×C1311yescharacteristic
170C2×C4×D4C22×C1311yescharacteristic
171#435—24no—
172#432—21no—
173C2×#99—21no—
174#407C22×C1312yes—
175C2×C22⋊C8—21no—
176#400C4×C1311yescharacteristic, complemented
177#399C4×C1311yescharacteristic, complemented
178#394—21no—
179#394C4×C1311yescharacteristic, complemented
180#392—21no—
181#392C4×C1311yescharacteristic, complemented
182#388—21no—
183#386—21no—
184#381C22×C1311yescharacteristic
185C4×C22⋊C4C22×C1312yes—
186#342—21no—
187#327—24no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13—22no—
191C22×C13—22no—
192C22×C13—22no—
193C22×C13—22no—
194C22×C13—42no—
195C22×C13—41no—
196C22×C13—41no—
197C22×C13—81no—
198C22×C13—81no—
199C22×C13—81no—
200C22×C13—81no—
201C22×C13—81no—
202C22×C13—81no—
203C22×C13—81no—
204C22×C13—81no—
205C22×C13—81no—
206C22×C13—81no—
207C22×C13#38611yescharacteristic
208C22×C13C2×#10411yescharacteristic
209C22×C13#42111yescharacteristic
210C4×C13—21no—
211C4×C13—21no—
212C4×C13—22no—
213C4×C13—41no—
214C4×C13—41no—
215C4×C13—41no—
216C4×C13—81no—
217C4×C13—81no—
218C4×C13—84no—
219C4×C13—81no—
220C22×D4—21no—
221C22×D4—21no—
222C22×D4C2×C4×C1311yescharacteristic
223C22×D4D4×C1311yescharacteristic
224C23×C4D4×C1311yescharacteristic
225C23×C4C23×C1311yescharacteristic
226C2×M16—22no—
227C22×C8—22no—
228#121—22no—
229#121—22no—
230C4×D4—22no—
231C4×D4—22no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4C2×C4×C1311yescharacteristic
234C2×C4⋊C4C2×C4×C1311yescharacteristic
235C2×C22⋊C4—22no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4C2×C4×C1311yescharacteristic
243C2×C22⋊C4D4×C1311yescharacteristic
244C2×C42—22no—
245C2×C42D4×C1311yescharacteristic
246C4⋊C8—22no—
247#99—24no—
248C22⋊C8—22no—
249C22⋊C8—22no—
250C22⋊C8D4×C1314yescomplemented
251#97—22no—
252#95—21no—
253#95—21no—
254#95—21no—
255#95—22no—
256#95C2×C4×C1311yescharacteristic
257#95C2×C4×C1311yescharacteristic
258C2×C13—21no—
259C2×C13—21no—
260C2×C13—42no—
261C2×C13—42no—
262C2×C13—161no—
263C2×C13#187111yescharacteristic
264C2×C13#191011yescharacteristic
265C2×C13#191311yescharacteristic
266C24—21no—
267C24C13×C22⋊C411yescharacteristic
268C24C2×D4×C1311yescharacteristic
269C2×D4—22no—
270C2×D4—22no—
271C2×D4—22no—
272C2×D4—41no—
273C2×D4—42no—
274C2×D4—42no—
275C2×D4—81no—
276C2×D4—81no—
277C2×D4—81no—
278C2×D4—81no—
279C2×D4—81no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—42no—
286C22×C4—81no—
287C22×C4—81no—
288C22×C4C13×C22⋊C411yescharacteristic
289C22×C4C13×C22⋊C411yescharacteristic
290C22×C4C13×C22⋊C411yescharacteristic
291C22×C4C22×C4×C1311yescharacteristic
292C22×C4C2×D4×C1312yes—
293C22×C4C2×D4×C1311yescharacteristic
294C22×C4C13×#4112yes—
295M16—82no—
296C2×C8—24no—
297C2×C8—82no—
298C4⋊C4—22no—
299C4⋊C4—22no—
300C4⋊C4—81no—
301C22⋊C4—22no—
302C22⋊C4—22no—
303C22⋊C4—24no—
304C22⋊C4—42no—
305C22⋊C4—42no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—81no—
309C22⋊C4—81no—
310C22⋊C4—81no—
311C22⋊C4—81no—
312C42—21no—
313C42—21no—
314C42—82no—
315C13#918511yescharacteristic, direct product factor, Sylow
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23C13×#10412yes—
332C23C2×C13×C22⋊C411yescharacteristic
333C23C13×#12112yes—
334D4—44no—
335D4—82no—
336D4—84no—
337D4—84no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—44no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—81no—
361C2×C4—82no—
362C2×C4—82no—
363C2×C4C4×D4×C1312yes—
364C2×C4C13×#12011yescharacteristic
365C2×C4C13×#12311yescharacteristic
366C8—44no—
367C22—21no—
368C22—21no—
369C22—22no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—42no—
374C22—41no—
375C22—41no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22C13×#38611yescharacteristic
387C22C2×C13×#10411yescharacteristic
388C22C13×#42111yescharacteristic
389C4—21no—
390C4—21no—
391C4—22no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—81no—
396C4—81no—
397C4—84no—
398C4—81no—
399C2—21no—
400C2—21no—
401C2—42no—
402C2—42no—
403C2—161no—
404C2C13×#187111yescharacteristic
405C2C13×#191011yescharacteristic
406C2C13×#191311yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC22×C4C22×C4×C13
Frattini, cosocleC23×C4C23×C13
prime radicalC13×#2635C2
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. C4×C13×#99C2semidirect
4. C13×#1507C2semidirect
5. C13×#1284C2semidirect
13. C13×#400C4semidirect
14. C13×#399C4semidirect
16. C13×#394C4semidirect
18. C13×#392C4semidirect
55. C13×C22⋊C8D4semidirect
63. #9185C13direct (N × H)
113. #2973C2×C13semidirect
115. C4×#99C2×C13semidirect
116. #1507C2×C13semidirect
117. #1284C2×C13semidirect
176. #400C4×C13semidirect
177. #399C4×C13semidirect
179. #394C4×C13semidirect
181. #392C4×C13semidirect
250. C22⋊C8D4×C13semidirect
315. C13#9185direct (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×#26352
C4×C13×#992
C13×#15072
C13×#12842
#918513