Finite Group Databasebeta

← C13×#34551 #15720890

Subgroups — C13×#34551 #15720890

Order 3328.

2082 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2402C213yesmaximal, complemented
2C13×#2401C216yesmaximal, complemented
3C13×#2398C213yesmaximal, complemented
4C13×#2396C213yesmaximal, complemented
5C13×#2395C216yesmaximal, complemented
6C13×#2392C213yesmaximal
7C42×Q8×C13C211yesmaximal, characteristic, complemented
8C42×D4×C13C213yesmaximal, complemented
9C4×C13×#117C213yesmaximal, complemented
10C2×C4×Q8×C13C2213yes—
11C2×C4×D4×C13C2216yes—
12C2×C4×D4×C13C2213yes—
13C2×C13×#117C2213yes—
14C2×C13×#117C2213yes—
15C22×C42×C13C2213yes—
16C13×#401C2212yes—
17C13×#400C2216yes—
18C13×#400C2213yes—
19C13×#400C2216yes—
20C13×#399C2213yes—
21C13×#398C2213yes—
22C13×#398C2216yes—
23C13×#397C2213yes—
24C13×#397C2216yes—
25C13×#397C2216yes—
26C13×#396C2216yes—
27C13×#395C2211yescharacteristic
28C13×#394C2213yes—
29C13×#394C2216yes—
30C13×#393C2213yes—
31C13×#392C2211yescharacteristic
32C4×C13×C4⋊C4C2216yes—
33C4×C13×C4⋊C4C2216yes—
34C4×C13×C4⋊C4C2213yes—
35C4×C13×C4⋊C4C2216yes—
36C4×C13×C4⋊C4C2213yes—
37C4×C13×C4⋊C4C2216yes—
38C4×C13×C22⋊C4C2216yes—
39C4×C13×C22⋊C4C2216yes—
40C4×C13×C22⋊C4C2216yes—
41C4×C13×C22⋊C4C2216yes—
42C4×C13×C22⋊C4C2216yes—
43C13×#376C2213yes—
44C13×#376C2213yes—
45C43×C13C2211yescharacteristic
46C43×C13C2213yes—
47C22×Q8×C13C2311yescharacteristic
48C22×D4×C13C2313yes—
49C23×C4×C13C2316yes—
50C23×C4×C13C2313yes—
51C4×Q8×C13—212no—
52C4×D4×C13—224no—
53C4×D4×C13—212no—
54C13×#117—212no—
55C13×#117—212no—
56C2×C13×C4⋊C4C2316yes—
57C2×C13×C4⋊C4C2313yes—
58C2×C13×C4⋊C4C2313yes—
59C2×C13×C4⋊C4C2316yes—
60C2×C13×C4⋊C4C2313yes—
61C2×C13×C4⋊C4C2316yes—
62C2×C13×C4⋊C4C2313yes—
63C2×C13×C22⋊C4C2313yes—
64C2×C13×C22⋊C4C2313yes—
65C2×C13×C22⋊C4C2316yes—
66C2×C13×C22⋊C4C2316yes—
67C2×C13×C22⋊C4C2316yes—
68C2×C13×C22⋊C4C2316yes—
69C2×C42×C13—212no—
70C2×C42×C13C2316yes—
71C2×C42×C13C2316yes—
72C2×C42×C13C2313yes—
73C2×C42×C13C2313yes—
74C2×C42×C13C2313yes—
75C2×C42×C13C2313yes—
76C2×C42×C13C2316yes—
77C2×C42×C13C2313yes—
78C2×C42×C13C2311yescharacteristic
79C13×#95C2313yes—
80C13×#95C2313yes—
81C13×#95C2316yes—
82C13×#95C2316yes—
83C13×#95C2316yes—
84C13×#95C2316yes—
85C13×#95C2316yes—
86C13×#95C2316yes—
87C13×#95C2311yescharacteristic
88C13×#95C2313yes—
89C13×#95C2312yes—
90#34551C1311yesmaximal, characteristic, direct product factor, Sylow
91C24×C13C2413yes—
92C2×Q8×C13—26no—
93C2×D4×C13—212no—
94C2×D4×C13—26no—
95C22×C4×C13—26no—
96C22×C4×C13—26no—
97C22×C4×C13—212no—
98C22×C4×C13—212no—
99C22×C4×C13—212no—
100C22×C4×C13#41112yes—
101C22×C4×C13C2416yes—
102C22×C4×C13C2416yes—
103C22×C4×C13C2413yes—
104C22×C4×C13C2411yescharacteristic
105C22×C4×C13C2413yes—
106C22×C4×C13C2413yes—
107C22×C4×C13C2413yes—
108C22×C4×C13C2413yes—
109C13×C4⋊C4—26no—
110C13×C4⋊C4—26no—
111C13×C4⋊C4—212no—
112C13×C4⋊C4—212no—
113C13×C4⋊C4—26no—
114C13×C4⋊C4—212no—
115C13×C4⋊C4—26no—
116C13×C22⋊C4—212no—
117C13×C22⋊C4—212no—
118C13×C22⋊C4—26no—
119C13×C22⋊C4—26no—
120C13×C22⋊C4—212no—
121C13×C22⋊C4—212no—
122C42×C13—212no—
123C42×C13—26no—
124C42×C13—26no—
125C42×C13—26no—
126C42×C13—26no—
127C42×C13—212no—
128C42×C13—212no—
129C42×C13#4114yes—
130C42×C13#41112yes—
131#2402C2×C1313yescomplemented
132#2401C2×C1316yescomplemented
133#2398C2×C1313yescomplemented
134#2396C2×C1313yescomplemented
135#2395C2×C1316yescomplemented
136#2392C2×C1313yes—
137C42×Q8C2×C1311yescharacteristic, complemented
138C42×D4C2×C1313yescomplemented
139C4×#117C2×C1313yescomplemented
140C23×C13—23no—
141C23×C13—26no—
142C23×C13—26no—
143C23×C13—23no—
144C23×C13C2×#4116yes—
145C23×C13C2511yescharacteristic
146Q8×C13—28no—
147D4×C13—224no—
148C2×C4×C13—23no—
149C2×C4×C13—26no—
150C2×C4×C13—26no—
151C2×C4×C13—23no—
152C2×C4×C13—224no—
153C2×C4×C13—26no—
154C2×C4×C13—26no—
155C2×C4×C13—26no—
156C2×C4×C13—26no—
157C2×C4×C13—23no—
158C2×C4×C13—23no—
159C2×C4×C13—26no—
160C2×C4×C13—26no—
161C2×C4×C13—26no—
162C2×C4×C13—424no—
163C2×C4×C13C2×#4116yes—
164C2×C4×C13C2×#4116yes—
165C2×C4×C13C2×#4116yes—
166C2×C4×C13C2×#4116yes—
167C2×C4×C13C2×#4116yes—
168C2×C4×C13C2×#4116yes—
169C2×C4×Q8C22×C1313yes—
170C2×C4×D4C22×C1316yes—
171C2×C4×D4C22×C1313yes—
172C2×#117C22×C1313yes—
173C2×#117C22×C1313yes—
174C22×C42C22×C1313yes—
175#401C22×C1312yes—
176#400C22×C1316yes—
177#400C22×C1313yes—
178#400C22×C1316yes—
179#399C22×C1313yes—
180#398C22×C1313yes—
181#398C22×C1316yes—
182#397C22×C1313yes—
183#397C22×C1316yes—
184#397C22×C1316yes—
185#396C22×C1316yes—
186#395C22×C1311yescharacteristic
187#394C22×C1313yes—
188#394C22×C1316yes—
189#393C22×C1313yes—
190#392C22×C1311yescharacteristic
191C4×C4⋊C4C22×C1313yes—
192C4×C4⋊C4C22×C1316yes—
193C4×C4⋊C4C22×C1316yes—
194C4×C4⋊C4C22×C1316yes—
195C4×C4⋊C4C22×C1313yes—
196C4×C4⋊C4C22×C1316yes—
197C4×C22⋊C4C22×C1316yes—
198C4×C22⋊C4C22×C1316yes—
199C4×C22⋊C4C22×C1316yes—
200C4×C22⋊C4C22×C1316yes—
201C4×C22⋊C4C22×C1316yes—
202#376C22×C1313yes—
203#376C22×C1313yes—
204C43C22×C1311yescharacteristic
205C43C22×C1313yes—
206C22×C13—26no—
207C22×C13—212no—
208C22×C13—46no—
209C22×C13—43no—
210C22×C13—43no—
211C22×C13C22×#4111yescharacteristic
212C22×C13C22×#4113yes—
213C22×C13C22×#4113yes—
214C4×C13—26no—
215C4×C13—26no—
216C4×C13—26no—
217C4×C13—46no—
218C4×C13—41no—
219C4×C13—46no—
220C4×C13—43no—
221C4×C13#529112yes—
222C22×Q8C23×C1311yescharacteristic
223C22×D4C23×C1313yes—
224C23×C4C23×C1316yes—
225C23×C4C23×C1313yes—
226C4×Q8—212no—
227C4×D4—224no—
228C4×D4—212no—
229#117—212no—
230#117—212no—
231C2×C4⋊C4C23×C1313yes—
232C2×C4⋊C4C23×C1313yes—
233C2×C4⋊C4C23×C1316yes—
234C2×C4⋊C4C23×C1316yes—
235C2×C4⋊C4C23×C1313yes—
236C2×C4⋊C4C23×C1316yes—
237C2×C4⋊C4C23×C1313yes—
238C2×C22⋊C4C23×C1313yes—
239C2×C22⋊C4C23×C1313yes—
240C2×C22⋊C4C23×C1316yes—
241C2×C22⋊C4C23×C1316yes—
242C2×C22⋊C4C23×C1316yes—
243C2×C22⋊C4C23×C1316yes—
244C2×C42—212no—
245C2×C42C23×C1313yes—
246C2×C42C23×C1313yes—
247C2×C42C23×C1313yes—
248C2×C42C23×C1316yes—
249C2×C42C23×C1316yes—
250C2×C42C23×C1313yes—
251C2×C42C23×C1316yes—
252C2×C42C23×C1313yes—
253C2×C42C23×C1311yescharacteristic
254#95C23×C1316yes—
255#95C23×C1316yes—
256#95C23×C1316yes—
257#95C23×C1316yes—
258#95C23×C1313yes—
259#95C23×C1313yes—
260#95C23×C1316yes—
261#95C23×C1316yes—
262#95C23×C1311yescharacteristic
263#95C23×C1313yes—
264#95C23×C1312yes—
265C2×C13—46no—
266C2×C13C2×#52913yes—
267C2×C13#344411yescharacteristic
268C2×C13#344413yes—
269C24C24×C1313yes—
270C2×Q8—26no—
271C2×D4—212no—
272C2×D4—26no—
273C22×C4—26no—
274C22×C4—26no—
275C22×C4—212no—
276C22×C4—212no—
277C22×C4—212no—
278C22×C4C13×#41112yes—
279C22×C4C24×C1316yes—
280C22×C4C24×C1316yes—
281C22×C4C24×C1313yes—
282C22×C4C24×C1311yescharacteristic
283C22×C4C24×C1313yes—
284C22×C4C24×C1313yes—
285C22×C4C24×C1313yes—
286C22×C4C24×C1313yes—
287C4⋊C4—26no—
288C4⋊C4—26no—
289C4⋊C4—212no—
290C4⋊C4—212no—
291C4⋊C4—26no—
292C4⋊C4—212no—
293C4⋊C4—26no—
294C22⋊C4—212no—
295C22⋊C4—212no—
296C22⋊C4—26no—
297C22⋊C4—26no—
298C22⋊C4—212no—
299C22⋊C4—212no—
300C42—212no—
301C42—26no—
302C42—26no—
303C42—26no—
304C42—26no—
305C42—212no—
306C42—212no—
307C42C13×#4114yes—
308C42C13×#41112yes—
309C13#3455111yescharacteristic, direct product factor, Sylow
310C23—23no—
311C23—26no—
312C23—26no—
313C23—23no—
314C23C2×C13×#4116yes—
315C23C25×C1311yescharacteristic
316Q8—28no—
317D4—224no—
318C2×C4—23no—
319C2×C4—26no—
320C2×C4—26no—
321C2×C4—23no—
322C2×C4—224no—
323C2×C4—26no—
324C2×C4—26no—
325C2×C4—26no—
326C2×C4—26no—
327C2×C4—23no—
328C2×C4—23no—
329C2×C4—26no—
330C2×C4—26no—
331C2×C4—26no—
332C2×C4—424no—
333C2×C4C2×C13×#4116yes—
334C2×C4C2×C13×#4116yes—
335C2×C4C2×C13×#4116yes—
336C2×C4C2×C13×#4116yes—
337C2×C4C2×C13×#4116yes—
338C2×C4C2×C13×#4116yes—
339C22—26no—
340C22—212no—
341C22—46no—
342C22—43no—
343C22—43no—
344C22C22×C13×#4111yescharacteristic
345C22C22×C13×#4113yes—
346C22C22×C13×#4113yes—
347C4—26no—
348C4—26no—
349C4—26no—
350C4—46no—
351C4—41no—
352C4—46no—
353C4—43no—
354C4C13×#529112yes—
355C2—46no—
356C2C2×C13×#52913yes—
357C2C13×#344411yescharacteristic
358C2C13×#344413yes—
subgroupG/H
centerC2×C42×C13C23
commutator, Frattini, cosocleC23C25×C13
socleC23×C13C25
prime radicalC13×#392C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2402C2semidirect
2. C13×#2401C2semidirect
3. C13×#2398C2semidirect
4. C13×#2396C2semidirect
5. C13×#2395C2semidirect
7. C42×Q8×C13C2semidirect
8. C42×D4×C13C2semidirect
9. C4×C13×#117C2semidirect
90. #34551C13direct (N × H)
131. #2402C2×C13semidirect
132. #2401C2×C13semidirect
133. #2398C2×C13semidirect
134. #2396C2×C13semidirect
135. #2395C2×C13semidirect
137. C42×Q8C2×C13semidirect
138. C42×D4C2×C13semidirect
139. C4×#117C2×C13semidirect
309. C13#34551direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#24022
C13×#24012
C13×#23982
C13×#23962
C13×#23952
C13×#23922
C42×Q8×C132
C42×D4×C132
C4×C13×#1172
#3455113