Finite Group Databasebeta

← C13×#34973 #15721312

Subgroups — C13×#34973 #15721312

Order 3328.

1716 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2524C214yesmaximal, complemented
2C13×#2519C214yesmaximal
3C13×#2469C214yesmaximal
4C13×#2462C214yesmaximal, complemented
5C13×#2402C211yesmaximal, characteristic, complemented
6C13×#2399C211yesmaximal, characteristic, complemented
7C13×#2396C212yesmaximal
8C4×C13×#125C214yesmaximal, complemented
9C4×C13×#126C214yesmaximal
10C13×#2298C211yesmaximal, characteristic
11C42×Q8×C13C212yesmaximal, complemented
12C2×C13×#126C2214yes—
13C2×C13×#125C2214yes—
14C2×C4×Q8×C13C2212yes—
15C2×C4×Q8×C13C2214yes—
16C2×C13×#117C2211yescharacteristic
17C13×#400C2212yes—
18C13×#400C2214yes—
19C13×#399C2212yes—
20C13×#398C2214yes—
21C13×#398C2214yes—
22C13×#398C2214yes—
23C13×#396C2214yes—
24C13×#395C2212yes—
25C13×#395C2214yes—
26C13×#393C2212yes—
27C13×#389C2214yes—
28C13×#389C2214yes—
29C13×#388C2214yes—
30C13×#388C2214yes—
31C13×#388C2214yes—
32C13×#388C2214yes—
33C13×#387C2214yes—
34C13×#387C2214yes—
35C13×#387C2214yes—
36C13×#387C2214yes—
37C13×#387C2214yes—
38C13×#387C2214yes—
39C13×#387C2214yes—
40C13×#387C2214yes—
41C13×#383C2214yes—
42C13×#382C2214yes—
43C4×C13×C4⋊C4C2214yes—
44C4×C13×C4⋊C4C2214yes—
45C4×C13×C4⋊C4C2214yes—
46C4×C13×C4⋊C4C2214yes—
47C4×C13×C4⋊C4C2212yes—
48C4×C13×C4⋊C4C2212yes—
49C4×C13×C4⋊C4C2214yes—
50C4×C13×C4⋊C4C2214yes—
51C4×C13×C4⋊C4C2214yes—
52C4×C13×C22⋊C4C2212yes—
53C4×C13×C22⋊C4C2214yes—
54C13×#376C2211yescharacteristic
55C43×C13C2211yescharacteristic
56C43×C13C2214yes—
57C22×Q8×C13C2312yes—
58C23×C4×C13C2311yescharacteristic
59C13×#126—216no—
60C13×#125—216no—
61C4×Q8×C13—216no—
62C4×Q8×C13—28no—
63C13×#117—24no—
64C2×C13×C4⋊C4C2314yes—
65C2×C13×C4⋊C4C2314yes—
66C2×C13×C4⋊C4C2314yes—
67C2×C13×C4⋊C4C2312yes—
68C2×C13×C4⋊C4C2314yes—
69C2×C13×C4⋊C4C2314yes—
70C2×C13×C4⋊C4C2314yes—
71C2×C13×C4⋊C4C2314yes—
72C2×C13×C4⋊C4C2314yes—
73C2×C13×C4⋊C4C2314yes—
74C2×C13×C4⋊C4C2314yes—
75C2×C13×C4⋊C4C2312yes—
76C2×C13×C4⋊C4C2314yes—
77C2×C13×C22⋊C4C2314yes—
78C2×C13×C22⋊C4C2314yes—
79C2×C13×C22⋊C4C2314yes—
80C2×C13×C22⋊C4C2312yes—
81C2×C42×C13C2314yes—
82C2×C42×C13C2314yes—
83C2×C42×C13C2314yes—
84C2×C42×C13C2314yes—
85C2×C42×C13C2314yes—
86C2×C42×C13C2314yes—
87C2×C42×C13C2312yes—
88C2×C42×C13C2314yes—
89C2×C42×C13C2312yes—
90C2×C42×C13C2311yescharacteristic
91C2×C42×C13C2311yescharacteristic
92C13×#95C2314yes—
93C13×#95C2314yes—
94C13×#95C2314yes—
95C13×#95C2314yes—
96C13×#95C2314yes—
97C13×#95C2312yes—
98C13×#95C2312yes—
99C13×#95C2314yes—
100C13×#95C2314yes—
101C13×#95C2314yes—
102C13×#95C2314yes—
103C13×#95C2314yes—
104C13×#95C2314yes—
105C13×#95C2314yes—
106C13×#95C2314yes—
107#34973C1311yesmaximal, characteristic, direct product factor, Sylow
108C24×C13C2411yescharacteristic
109C2×Q8×C13—28no—
110C2×Q8×C13—24no—
111C22×C4×C13—22no—
112C22×C4×C13—24no—
113C22×C4×C13C2411yescharacteristic
114C22×C4×C13C2414yes—
115C22×C4×C13C2414yes—
116C22×C4×C13C2414yes—
117C22×C4×C13C2412yes—
118C22×C4×C13C2414yes—
119C22×C4×C13C2414yes—
120C22×C4×C13C2414yes—
121C22×C4×C13C2412yes—
122C22×C4×C13C2411yescharacteristic
123C13×C4⋊C4—24no—
124C13×C4⋊C4—28no—
125C13×C4⋊C4—28no—
126C13×C4⋊C4—28no—
127C13×C4⋊C4—24no—
128C13×C4⋊C4—28no—
129C13×C4⋊C4—28no—
130C13×C4⋊C4—28no—
131C13×C4⋊C4—28no—
132C13×C4⋊C4—28no—
133C13×C4⋊C4—28no—
134C13×C4⋊C4—28no—
135C13×C4⋊C4#41116yes—
136C13×C22⋊C4—24no—
137C13×C22⋊C4—28no—
138C13×C22⋊C4—28no—
139C13×C22⋊C4—28no—
140C42×C13—22no—
141C42×C13—28no—
142C42×C13—28no—
143C42×C13—28no—
144C42×C13—28no—
145C42×C13—28no—
146C42×C13—28no—
147C42×C13—24no—
148C42×C13—28no—
149C42×C13—24no—
150C42×C13#4114yes—
151#2524C2×C1314yescomplemented
152#2519C2×C1314yes—
153#2469C2×C1314yes—
154#2462C2×C1314yescomplemented
155#2402C2×C1311yescharacteristic, complemented
156#2399C2×C1311yescharacteristic, complemented
157#2396C2×C1312yes—
158C4×#125C2×C1314yescomplemented
159C4×#126C2×C1314yes—
160#2298C2×C1311yescharacteristic
161C42×Q8C2×C1312yescomplemented
162C23×C13—24no—
163C23×C13—21no—
164C23×C13—22no—
165C23×C13C2511yescharacteristic
166Q8×C13—216no—
167C2×C4×C13—24no—
168C2×C4×C13—24no—
169C2×C4×C13—24no—
170C2×C4×C13—24no—
171C2×C4×C13—24no—
172C2×C4×C13—24no—
173C2×C4×C13—24no—
174C2×C4×C13—22no—
175C2×C4×C13—24no—
176C2×C4×C13—24no—
177C2×C4×C13—24no—
178C2×C4×C13—24no—
179C2×C4×C13—24no—
180C2×C4×C13—24no—
181C2×C4×C13—24no—
182C2×C4×C13—24no—
183C2×C4×C13—21no—
184C2×C4×C13—24no—
185C2×C4×C13—24no—
186C2×C4×C13—22no—
187C2×C4×C13—44no—
188C2×C4×C13C2×#4118yes—
189C2×C4×C13C2×#4118yes—
190C2×C4×C13C2×#4118yes—
191C2×C4×C13C2×#4114yes—
192C2×C4×C13C2×#4112yes—
193C2×C4×C132−1+414yes—
194C2×#126C22×C1314yes—
195C2×#125C22×C1314yes—
196C2×C4×Q8C22×C1312yes—
197C2×C4×Q8C22×C1314yes—
198C2×#117C22×C1311yescharacteristic
199#400C22×C1312yes—
200#400C22×C1314yes—
201#399C22×C1312yes—
202#398C22×C1314yes—
203#398C22×C1314yes—
204#398C22×C1314yes—
205#396C22×C1314yes—
206#395C22×C1312yes—
207#395C22×C1314yes—
208#393C22×C1312yes—
209#389C22×C1314yes—
210#389C22×C1314yes—
211#388C22×C1314yes—
212#388C22×C1314yes—
213#388C22×C1314yes—
214#388C22×C1314yes—
215#387C22×C1314yes—
216#387C22×C1314yes—
217#387C22×C1314yes—
218#387C22×C1314yes—
219#387C22×C1314yes—
220#387C22×C1314yes—
221#387C22×C1314yes—
222#387C22×C1314yes—
223#383C22×C1314yes—
224#382C22×C1314yes—
225C4×C4⋊C4C22×C1314yes—
226C4×C4⋊C4C22×C1314yes—
227C4×C4⋊C4C22×C1314yes—
228C4×C4⋊C4C22×C1314yes—
229C4×C4⋊C4C22×C1312yes—
230C4×C4⋊C4C22×C1312yes—
231C4×C4⋊C4C22×C1314yes—
232C4×C4⋊C4C22×C1314yes—
233C4×C4⋊C4C22×C1314yes—
234C4×C22⋊C4C22×C1314yes—
235C4×C22⋊C4C22×C1312yes—
236#376C22×C1311yescharacteristic
237C43C22×C1314yes—
238C43C22×C1311yescharacteristic
239C22×C13—42no—
240C22×C13—41no—
241C22×C13—44no—
242C22×C13C22×#4111yescharacteristic
243C22×C13C22×#4114yes—
244C22×C13C2×2−1+412yes—
245C4×C13—28no—
246C4×C13—24no—
247C4×C13—28no—
248C4×C13—28no—
249C4×C13—44no—
250C4×C13—42no—
251C4×C13—41no—
252C4×C13—44no—
253C4×C13—44no—
254C4×C13#54114yes—
255C22×Q8C23×C1312yes—
256C23×C4C23×C1311yescharacteristic
257#126—216no—
258#125—216no—
259C4×Q8—216no—
260C4×Q8—28no—
261#117—24no—
262C2×C4⋊C4C23×C1312yes—
263C2×C4⋊C4C23×C1314yes—
264C2×C4⋊C4C23×C1314yes—
265C2×C4⋊C4C23×C1314yes—
266C2×C4⋊C4C23×C1312yes—
267C2×C4⋊C4C23×C1314yes—
268C2×C4⋊C4C23×C1314yes—
269C2×C4⋊C4C23×C1314yes—
270C2×C4⋊C4C23×C1314yes—
271C2×C4⋊C4C23×C1314yes—
272C2×C4⋊C4C23×C1314yes—
273C2×C4⋊C4C23×C1314yes—
274C2×C4⋊C4C23×C1314yes—
275C2×C22⋊C4C23×C1312yes—
276C2×C22⋊C4C23×C1314yes—
277C2×C22⋊C4C23×C1314yes—
278C2×C22⋊C4C23×C1314yes—
279C2×C42C23×C1311yescharacteristic
280C2×C42C23×C1314yes—
281C2×C42C23×C1314yes—
282C2×C42C23×C1314yes—
283C2×C42C23×C1314yes—
284C2×C42C23×C1314yes—
285C2×C42C23×C1314yes—
286C2×C42C23×C1312yes—
287C2×C42C23×C1314yes—
288C2×C42C23×C1312yes—
289C2×C42C23×C1311yescharacteristic
290#95C23×C1314yes—
291#95C23×C1314yes—
292#95C23×C1314yes—
293#95C23×C1314yes—
294#95C23×C1314yes—
295#95C23×C1314yes—
296#95C23×C1312yes—
297#95C23×C1312yes—
298#95C23×C1314yes—
299#95C23×C1314yes—
300#95C23×C1314yes—
301#95C23×C1314yes—
302#95C23×C1314yes—
303#95C23×C1314yes—
304#95C23×C1314yes—
305C2×C13—81no—
306C2×C13#344412yes—
307C2×C13C2×#54111yescharacteristic
308C2×C13#348214yes—
309C24C24×C1311yescharacteristic
310C2×Q8—28no—
311C2×Q8—24no—
312C22×C4—22no—
313C22×C4—24no—
314C22×C4C24×C1311yescharacteristic
315C22×C4C24×C1314yes—
316C22×C4C24×C1314yes—
317C22×C4C24×C1314yes—
318C22×C4C24×C1312yes—
319C22×C4C24×C1314yes—
320C22×C4C24×C1314yes—
321C22×C4C24×C1314yes—
322C22×C4C24×C1312yes—
323C22×C4C24×C1311yescharacteristic
324C4⋊C4—24no—
325C4⋊C4—28no—
326C4⋊C4—28no—
327C4⋊C4—28no—
328C4⋊C4—24no—
329C4⋊C4—28no—
330C4⋊C4—28no—
331C4⋊C4—28no—
332C4⋊C4—28no—
333C4⋊C4—28no—
334C4⋊C4—28no—
335C4⋊C4—28no—
336C4⋊C4C13×#41116yes—
337C22⋊C4—24no—
338C22⋊C4—28no—
339C22⋊C4—28no—
340C22⋊C4—28no—
341C42—22no—
342C42—28no—
343C42—28no—
344C42—28no—
345C42—28no—
346C42—28no—
347C42—28no—
348C42—24no—
349C42—28no—
350C42—24no—
351C42C13×#4114yes—
352C13#3497311yescharacteristic, direct product factor, Sylow
353C23—24no—
354C23—21no—
355C23—22no—
356C23C25×C1311yescharacteristic
357Q8—216no—
358C2×C4—24no—
359C2×C4—24no—
360C2×C4—24no—
361C2×C4—24no—
362C2×C4—24no—
363C2×C4—24no—
364C2×C4—24no—
365C2×C4—22no—
366C2×C4—24no—
367C2×C4—24no—
368C2×C4—24no—
369C2×C4—24no—
370C2×C4—24no—
371C2×C4—24no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—21no—
375C2×C4—24no—
376C2×C4—24no—
377C2×C4—22no—
378C2×C4—44no—
379C2×C4C2×C13×#4118yes—
380C2×C4C2×C13×#4118yes—
381C2×C4C2×C13×#4118yes—
382C2×C4C2×C13×#4114yes—
383C2×C4C2×C13×#4112yes—
384C2×C4C13×2−1+414yes—
385C22—42no—
386C22—41no—
387C22—44no—
388C22C22×C13×#4111yescharacteristic
389C22C22×C13×#4114yes—
390C22C2×C13×2−1+412yes—
391C4—28no—
392C4—24no—
393C4—28no—
394C4—28no—
395C4—44no—
396C4—42no—
397C4—41no—
398C4—44no—
399C4—44no—
400C4C13×#54114yes—
401C2—81no—
402C2C13×#344412yes—
403C2C2×C13×#54111yescharacteristic
404C2C13×#348214yes—
subgroupG/H
centerC22×C4×C13C24
commutator, Frattini, cosocleC23C25×C13
socleC23×C13C25
prime radicalC24×C13C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2524C2semidirect
4. C13×#2462C2semidirect
5. C13×#2402C2semidirect
6. C13×#2399C2semidirect
8. C4×C13×#125C2semidirect
11. C42×Q8×C13C2semidirect
107. #34973C13direct (N × H)
151. #2524C2×C13semidirect
154. #2462C2×C13semidirect
155. #2402C2×C13semidirect
156. #2399C2×C13semidirect
158. C4×#125C2×C13semidirect
161. C42×Q8C2×C13semidirect
352. C13#34973direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25242
C13×#25192
C13×#24692
C13×#24622
C13×#24022
C13×#23992
C13×#23962
C4×C13×#1252
C4×C13×#1262
C13×#22982
C42×Q8×C132
#3497313