Finite Group Databasebeta

← C13×#11566 #15697905

Subgroups — C13×#11566 #15697905

Order 3328.

494 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2544C211yesmaximal, characteristic
2C13×#1465C211yesmaximal, characteristic, complemented
3C13×#1459C211yesmaximal, characteristic, complemented
4C13×#1319C212yesmaximal, complemented
5C13×#1318C212yesmaximal, complemented
6C2×C13×#127C411yescharacteristic
7C2×C13×#124C411yescharacteristic
8C2×C13×#124C411yescharacteristic
9C2×C4×D4×C13C2211yescharacteristic
10C13×#407—21no—
11C2×C13×C22⋊C8—21no—
12C13×#394—21no—
13C13×#394—21no—
14C13×#391C2211yescharacteristic
15C13×#390C2211yescharacteristic
16C13×#386—21no—
17C13×#386—21no—
18C4×C13×C4⋊C4C411yescharacteristic
19C13×#324C2212yes—
20C13×#324C2212yes—
21C13×#323—21no—
22C13×#323—21no—
23C22×Q8×C13C2×C411yescharacteristic
24C22×D4×C13—21no—
25C22×D4×C13—21no—
26C22×D4×C13C2×C411yescharacteristic
27C22×D4×C13C2×C411yescharacteristic
28C23×C4×C13D411yescharacteristic
29C23×C4×C13D411yescharacteristic
30C2×C13×M16—41no—
31C22×C8×C13—41no—
32C13×#127—42no—
33C13×#124—41no—
34C13×#124—41no—
35C13×#124—42no—
36C4×D4×C13—41no—
37C4×D4×C13—41no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4C2311yescharacteristic
40C2×C13×C22⋊C4—21no—
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⋊C4D411yescharacteristic
47C2×C13×C22⋊C4D411yescharacteristic
48C2×C42×C13C2×C411yescharacteristic
49C2×C42×C13C2×C411yescharacteristic
50C2×C42×C13C2×C411yescharacteristic
51C13×C22⋊C8—22no—
52C13×C22⋊C8—22no—
53C13×C22⋊C8—41no—
54C13×C22⋊C8—41no—
55C13×#95—21no—
56C13×#95—21no—
57C13×#95—21no—
58#11566C1311yesmaximal, characteristic, direct product factor, Sylow
59C24×C13—21no—
60C24×C13C22⋊C411yescharacteristic
61C24×C13C22⋊C411yescharacteristic
62C2×Q8×C13—22no—
63C2×Q8×C13—41no—
64C2×Q8×C13—41no—
65C2×D4×C13—22no—
66C2×D4×C13—22no—
67C2×D4×C13—22no—
68C2×D4×C13—41no—
69C2×D4×C13—41no—
70C2×D4×C13—41no—
71C2×D4×C13—42no—
72C2×D4×C13—42no—
73C2×D4×C13—42no—
74C2×D4×C13—42no—
75C2×D4×C13—81no—
76C2×D4×C13—81no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—21no—
81C22×C4×C13—21no—
82C22×C4×C13—21no—
83C22×C4×C13—21no—
84C22×C4×C13—81no—
85C22×C4×C13—81no—
86C22×C4×C13C22⋊C411yescharacteristic
87C22×C4×C13C22⋊C411yescharacteristic
88C22×C4×C13C22×C411yescharacteristic
89C22×C4×C13C2×D411yescharacteristic
90C22×C4×C13C2×D411yescharacteristic
91C13×M16—82no—
92C2×C8×C13—42no—
93C2×C8×C13—42no—
94C2×C8×C13—82no—
95C13×C4⋊C4—41no—
96C13×C4⋊C4—42no—
97C13×C22⋊C4—41no—
98C13×C22⋊C4—41no—
99C13×C22⋊C4—42no—
100C13×C22⋊C4—42no—
101C13×C22⋊C4—42no—
102C13×C22⋊C4—41no—
103C13×C22⋊C4—41no—
104C13×C22⋊C4—81no—
105C13×C22⋊C4—81no—
106C42×C13—21no—
107C42×C13—21no—
108C42×C13—41no—
109C42×C13—41no—
110#2544C2×C1311yescharacteristic
111#1465C2×C1311yescharacteristic, complemented
112#1459C2×C1311yescharacteristic, complemented
113#1319C2×C1312yescomplemented
114#1318C2×C1312yescomplemented
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—21no—
118C23×C13—21no—
119C23×C13—21no—
120C23×C13—41no—
121C23×C13—41no—
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#10012yes—
132C23×C13C2×C22⋊C411yescharacteristic
133Q8×C13—82no—
134D4×C13—44no—
135D4×C13—82no—
136D4×C13—84no—
137D4×C13—84no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—22no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—41no—
145C2×C4×C13—42no—
146C2×C4×C13—42no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—81no—
159C2×C4×C13—81no—
160C2×C4×C13#9911yescharacteristic
161C2×C4×C13#9911yescharacteristic
162C2×C4×C13#13112yes—
163C8×C13—82no—
164C8×C13—82no—
165C2×#127C4×C1311yescharacteristic
166C2×#124C4×C1311yescharacteristic
167C2×#124C4×C1311yescharacteristic
168C2×C4×D4C22×C1311yescharacteristic
169#407—21no—
170C2×C22⋊C8—21no—
171#394—21no—
172#394—21no—
173#391C22×C1311yescharacteristic
174#390C22×C1311yescharacteristic
175#386—21no—
176#386—21no—
177C4×C4⋊C4C4×C1311yescharacteristic
178#324C22×C1312yes—
179#324C22×C1312yes—
180#323—21no—
181#323—21no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—22no—
185C22×C13—42no—
186C22×C13—42no—
187C22×C13—41no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13—41no—
191C22×C13—41no—
192C22×C13—81no—
193C22×C13—81no—
194C22×C13—81no—
195C22×C13—81no—
196C22×C13—81no—
197C22×C13—81no—
198C22×C13—81no—
199C22×C13—81no—
200C22×C13—81no—
201C22×C13#40811yescharacteristic
202C22×C13C2×#9911yescharacteristic
203C22×C13C2×#10011yescharacteristic
204C4×C13—21no—
205C4×C13—21no—
206C4×C13—22no—
207C4×C13—42no—
208C4×C13—41no—
209C4×C13—41no—
210C4×C13—41no—
211C4×C13—81no—
212C4×C13—81no—
213C22×Q8C2×C4×C1311yescharacteristic
214C22×D4—21no—
215C22×D4—21no—
216C22×D4C2×C4×C1311yescharacteristic
217C22×D4C2×C4×C1311yescharacteristic
218C23×C4D4×C1311yescharacteristic
219C23×C4D4×C1311yescharacteristic
220C2×M16—41no—
221C22×C8—41no—
222#127—42no—
223#124—41no—
224#124—41no—
225#124—42no—
226C4×D4—41no—
227C4×D4—41no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4C23×C1311yescharacteristic
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4D4×C1311yescharacteristic
237C2×C22⋊C4D4×C1311yescharacteristic
238C2×C42C2×C4×C1311yescharacteristic
239C2×C42C2×C4×C1311yescharacteristic
240C2×C42C2×C4×C1311yescharacteristic
241C22⋊C8—22no—
242C22⋊C8—22no—
243C22⋊C8—41no—
244C22⋊C8—41no—
245#95—21no—
246#95—21no—
247#95—21no—
248C2×C13—21no—
249C2×C13—21no—
250C2×C13—42no—
251C2×C13—81no—
252C2×C13—161no—
253C2×C13#147111yescharacteristic
254C2×C13#212711yescharacteristic
255C2×C13#213211yescharacteristic
256C24—21no—
257C24C13×C22⋊C411yescharacteristic
258C24C13×C22⋊C411yescharacteristic
259C2×Q8—22no—
260C2×Q8—41no—
261C2×Q8—41no—
262C2×D4—22no—
263C2×D4—22no—
264C2×D4—22no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—42no—
269C2×D4—42no—
270C2×D4—42no—
271C2×D4—42no—
272C2×D4—81no—
273C2×D4—81no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—81no—
282C22×C4—81no—
283C22×C4C13×C22⋊C411yescharacteristic
284C22×C4C13×C22⋊C411yescharacteristic
285C22×C4C22×C4×C1311yescharacteristic
286C22×C4C2×D4×C1311yescharacteristic
287C22×C4C2×D4×C1311yescharacteristic
288M16—82no—
289C2×C8—42no—
290C2×C8—42no—
291C2×C8—82no—
292C4⋊C4—41no—
293C4⋊C4—42no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—42no—
297C22⋊C4—42no—
298C22⋊C4—42no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—81no—
302C22⋊C4—81no—
303C42—21no—
304C42—21no—
305C42—41no—
306C42—41no—
307C13#1156611yescharacteristic, direct product factor, Sylow
308C23—21no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23C13×#10012yes—
325C23C2×C13×C22⋊C411yescharacteristic
326Q8—82no—
327D4—44no—
328D4—82no—
329D4—84no—
330D4—84no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—22no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4C13×#9911yescharacteristic
354C2×C4C13×#9911yescharacteristic
355C2×C4C13×#13112yes—
356C8—82no—
357C8—82no—
358C22—21no—
359C22—21no—
360C22—22no—
361C22—42no—
362C22—42no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22C13×#40811yescharacteristic
378C22C2×C13×#9911yescharacteristic
379C22C2×C13×#10011yescharacteristic
380C4—22no—
381C4—21no—
382C4—21no—
383C4—42no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—81no—
388C4—81no—
389C2—21no—
390C2—21no—
391C2—42no—
392C2—81no—
393C2—161no—
394C2C13×#147111yescharacteristic
395C2C13×#212711yescharacteristic
396C2C13×#213211yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C4⋊C4C23×C13
prime radicalC2×C13×#127C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C4×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#1465C2semidirect
3. C13×#1459C2semidirect
4. C13×#1319C2semidirect
5. C13×#1318C2semidirect
58. #11566C13direct (N × H)
111. #1465C2×C13semidirect
112. #1459C2×C13semidirect
113. #1319C2×C13semidirect
114. #1318C2×C13semidirect
307. C13#11566direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25442
C13×#14652
C13×#14592
C13×#13192
C13×#13182
#1156613