Finite Group Databasebeta

← C13×#29110 #15715449

Subgroups — C13×#29110 #15715449

Order 3328.

1078 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2851C211yesmaximal, characteristic, complemented
2C2×C13×#390C211yesmaximal, characteristic
3C13×#2073C212yesmaximal, complemented
4C13×#2025C212yesmaximal, complemented
5C13×#1936C214yesmaximal, complemented
6C13×#1823C212yesmaximal, complemented
7C13×#1786C212yesmaximal
8C13×#1749C211yesmaximal, characteristic, complemented
9C23×D4×C13C2211yescharacteristic
10C2×C13×#125C2211yescharacteristic, complemented
11C22×C13×C4⋊C4C2211yescharacteristic
12C22×C13×C22⋊C4—22no—
13C22×C42×C13C2211yescharacteristic
14C2×C13×#102C2214yes—
15C2×C13×#102C2214yes—
16C2×C13×C22⋊C8C2212yes—
17C2×C13×#97C2212yescomplemented
18C13×#390—22no—
19C13×#390C2212yes—
20C13×#390C2212yes—
21C13×#389C2212yescomplemented
22C13×#387—22no—
23C13×#385—22no—
24C13×#382C2211yescharacteristic, complemented
25C13×#380C2212yes—
26C13×#340C2214yescomplemented
27C13×#340C2214yescomplemented
28C13×#336C2212yescomplemented
29C25×C13—21no—
30C22×D4×C13—24no—
31C22×D4×C13—21no—
32C22×D4×C13—24no—
33C22×D4×C13—42no—
34C22×D4×C13C2312yes—
35C23×C4×C13—21no—
36C23×C4×C13D412yes—
37C23×C4×C13C2311yescharacteristic
38C22×C8×C13C2314yes—
39C13×#125—42no—
40C2×C13×C4⋊C4—24no—
41C2×C13×C4⋊C4—22no—
42C2×C13×C4⋊C4—22no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4C2312yes—
45C2×C13×C4⋊C4C2312yes—
46C2×C13×C4⋊C4C2312yes—
47C2×C13×C22⋊C4—22no—
48C2×C13×C22⋊C4—24no—
49C2×C13×C22⋊C4—24no—
50C2×C13×C22⋊C4—48no—
51C2×C42×C13—42no—
52C2×C42×C13D412yes—
53C2×C42×C13C2311yescharacteristic
54C2×C42×C13C2311yescharacteristic
55C13×#102—28no—
56C13×#102—44no—
57C13×C22⋊C8—24no—
58C13×#97—42no—
59C13×#95—22no—
60C13×#95—22no—
61C13×#95—22no—
62#29110C1311yesmaximal, characteristic, direct product factor, Sylow
63C24×C13—24no—
64C24×C13—22no—
65C24×C13—42no—
66C24×C13—44no—
67C24×C13—42no—
68C24×C13—44no—
69C24×C13C2×D411yescharacteristic
70C2×D4×C13—24no—
71C2×D4×C13—24no—
72C2×D4×C13—22no—
73C2×D4×C13—24no—
74C2×D4×C13—416no—
75C2×D4×C13—42no—
76C2×D4×C13—42no—
77C2×D4×C13#4114yes—
78C22×C4×C13—22no—
79C22×C4×C13—22no—
80C22×C4×C13—24no—
81C22×C4×C13—22no—
82C22×C4×C13—22no—
83C22×C4×C13—22no—
84C22×C4×C13—42no—
85C22×C4×C13—42no—
86C22×C4×C13—42no—
87C22×C4×C13—44no—
88C22×C4×C13C2×D412yes—
89C22×C4×C13C2×D412yes—
90C22×C4×C13C2×D411yescharacteristic
91C22×C4×C13#4114yes—
92C22×C4×C13C2411yescharacteristic
93C2×C8×C13—24no—
94C2×C8×C13—24no—
95C2×C8×C13—24no—
96C13×C4⋊C4—24no—
97C13×C4⋊C4—24no—
98C13×C4⋊C4—24no—
99C13×C4⋊C4—44no—
100C13×C4⋊C4—44no—
101C13×C4⋊C4—42no—
102C13×C22⋊C4—48no—
103C13×C22⋊C4—48no—
104C13×C22⋊C4—44no—
105C42×C13—22no—
106C42×C13—22no—
107C42×C13—42no—
108#2851C2×C1311yescharacteristic, complemented
109C2×#390C2×C1311yescharacteristic
110#2073C2×C1312yescomplemented
111#2025C2×C1312yescomplemented
112#1936C2×C1314yescomplemented
113#1823C2×C1312yescomplemented
114#1786C2×C1312yes—
115#1749C2×C1311yescharacteristic, complemented
116C23×C13—21no—
117C23×C13—21no—
118C23×C13—22no—
119C23×C13—24no—
120C23×C13—48no—
121C23×C13—416no—
122C23×C13—42no—
123C23×C13—42no—
124C23×C13—44no—
125C23×C13—44no—
126C23×C13—84no—
127C23×C13—88no—
128C23×C13—84no—
129C23×C13#12412yes—
130C23×C13AGL(1,ℤ/8)14yes—
131C23×C13C22×D411yescharacteristic
132D4×C13—28no—
133D4×C13—48no—
134D4×C13—44no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—28no—
138C2×C4×C13—22no—
139C2×C4×C13—22no—
140C2×C4×C13—22no—
141C2×C4×C13—22no—
142C2×C4×C13—22no—
143C2×C4×C13—22no—
144C2×C4×C13—48no—
145C2×C4×C13—42no—
146C2×C4×C13—42no—
147C2×C4×C13—42no—
148C2×C4×C13—44no—
149C2×C4×C13—42no—
150C2×C4×C13—42no—
151C2×C4×C13—42no—
152C2×C4×C13—42no—
153C2×C4×C13—84no—
154C2×C4×C13#12412yes—
155C2×C4×C13C2×#4112yes—
156C2×C4×C13C2×#4112yes—
157C2×C4×C13H(5,𝔽2)12yes—
158C8×C13—44no—
159C23×D4C22×C1311yescharacteristic
160C2×#125C22×C1311yescharacteristic, complemented
161C22×C4⋊C4C22×C1311yescharacteristic
162C22×C22⋊C4—22no—
163C22×C42C22×C1311yescharacteristic
164C2×#102C22×C1314yes—
165C2×#102C22×C1314yes—
166C2×C22⋊C8C22×C1312yes—
167C2×#97C22×C1312yescomplemented
168#390—22no—
169#390C22×C1312yes—
170#390C22×C1312yes—
171#389C22×C1312yescomplemented
172#387—22no—
173#385—22no—
174#382C22×C1311yescharacteristic, complemented
175#380C22×C1312yes—
176#340C22×C1314yescomplemented
177#340C22×C1314yescomplemented
178#336C22×C1312yescomplemented
179C22×C13—22no—
180C22×C13—24no—
181C22×C13—22no—
182C22×C13—24no—
183C22×C13—44no—
184C22×C13—48no—
185C22×C13—816no—
186C22×C13—82no—
187C22×C13—82no—
188C22×C13—84no—
189C22×C13#49014yes—
190C22×C13#52511yescharacteristic
191C22×C13C2×#12411yescharacteristic
192C22×C13#53411yescharacteristic
193C22×C13C2×AGL(1,ℤ/8)12yes—
194C22×C13#57512yes—
195C4×C13—22no—
196C4×C13—42no—
197C4×C13—42no—
198C4×C13—82no—
199C4×C13—82no—
200C4×C13—82no—
201C4×C13#55114yes—
202C25—21no—
203C22×D4—24no—
204C22×D4—21no—
205C22×D4—24no—
206C22×D4—42no—
207C22×D4C23×C1312yes—
208C23×C4—21no—
209C23×C4D4×C1312yes—
210C23×C4C23×C1311yescharacteristic
211C22×C8C23×C1314yes—
212#125—42no—
213C2×C4⋊C4—24no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4C23×C1312yes—
218C2×C4⋊C4C23×C1312yes—
219C2×C4⋊C4C23×C1312yes—
220C2×C22⋊C4—22no—
221C2×C22⋊C4—24no—
222C2×C22⋊C4—24no—
223C2×C22⋊C4—48no—
224C2×C42—42no—
225C2×C42D4×C1312yes—
226C2×C42C23×C1311yescharacteristic
227C2×C42C23×C1311yescharacteristic
228#102—28no—
229#102—44no—
230C22⋊C8—24no—
231#97—42no—
232#95—22no—
233#95—22no—
234#95—22no—
235C2×C13—24no—
236C2×C13—84no—
237C2×C13#256111yescharacteristic
238C2×C13#311412yes—
239C2×C13C2×#49011yescharacteristic
240C2×C13#314011yescharacteristic
241C2×C13#319412yes—
242C24—24no—
243C24—22no—
244C24—42no—
245C24—44no—
246C24—42no—
247C24—44no—
248C24C2×D4×C1311yescharacteristic
249C2×D4—24no—
250C2×D4—24no—
251C2×D4—22no—
252C2×D4—24no—
253C2×D4—416no—
254C2×D4—42no—
255C2×D4—42no—
256C2×D4C13×#4114yes—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—24no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—42no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4—44no—
267C22×C4C2×D4×C1312yes—
268C22×C4C2×D4×C1312yes—
269C22×C4C2×D4×C1311yescharacteristic
270C22×C4C13×#4114yes—
271C22×C4C24×C1311yescharacteristic
272C2×C8—24no—
273C2×C8—24no—
274C2×C8—24no—
275C4⋊C4—24no—
276C4⋊C4—24no—
277C4⋊C4—24no—
278C4⋊C4—44no—
279C4⋊C4—44no—
280C4⋊C4—42no—
281C22⋊C4—48no—
282C22⋊C4—48no—
283C22⋊C4—44no—
284C42—22no—
285C42—22no—
286C42—42no—
287C13#2911011yescharacteristic, direct product factor, Sylow
288C23—21no—
289C23—21no—
290C23—22no—
291C23—24no—
292C23—48no—
293C23—416no—
294C23—42no—
295C23—42no—
296C23—44no—
297C23—44no—
298C23—84no—
299C23—88no—
300C23—84no—
301C23C13×#12412yes—
302C23C13×AGL(1,ℤ/8)14yes—
303C23C22×D4×C1311yescharacteristic
304D4—28no—
305D4—48no—
306D4—44no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—28no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—48no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—44no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—84no—
326C2×C4C13×#12412yes—
327C2×C4C2×C13×#4112yes—
328C2×C4C2×C13×#4112yes—
329C2×C4C13×H(5,𝔽2)12yes—
330C8—44no—
331C22—22no—
332C22—24no—
333C22—22no—
334C22—24no—
335C22—44no—
336C22—48no—
337C22—816no—
338C22—82no—
339C22—82no—
340C22—84no—
341C22C13×#49014yes—
342C22C13×#52511yescharacteristic
343C22C2×C13×#12411yescharacteristic
344C22C13×#53411yescharacteristic
345C22C2×C13×AGL(1,ℤ/8)12yes—
346C22C13×#57512yes—
347C4—22no—
348C4—42no—
349C4—42no—
350C4—82no—
351C4—82no—
352C4—82no—
353C4C13×#55114yes—
354C2—24no—
355C2—84no—
356C2C13×#256111yescharacteristic
357C2C13×#311412yes—
358C2C2×C13×#49011yescharacteristic
359C2C13×#314011yescharacteristic
360C2C13×#319412yes—
subgroupG/H
center, socleC23×C13C22×D4
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC23×D4×C13C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C13 ◁ C22×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2851C2semidirect
3. C13×#2073C2semidirect
4. C13×#2025C2semidirect
5. C13×#1936C2semidirect
6. C13×#1823C2semidirect
8. C13×#1749C2semidirect
10. C2×C13×#125C22semidirect
17. C2×C13×#97C22semidirect
21. C13×#389C22semidirect
24. C13×#382C22semidirect
26. C13×#340C22semidirect
27. C13×#340C22semidirect
28. C13×#336C22semidirect
62. #29110C13direct (N × H)
108. #2851C2×C13semidirect
110. #2073C2×C13semidirect
111. #2025C2×C13semidirect
112. #1936C2×C13semidirect
113. #1823C2×C13semidirect
115. #1749C2×C13semidirect
160. C2×#125C22×C13semidirect
167. C2×#97C22×C13semidirect
171. #389C22×C13semidirect
174. #382C22×C13semidirect
176. #340C22×C13semidirect
177. #340C22×C13semidirect
178. #336C22×C13semidirect
287. C13#29110direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28512
C2×C13×#3902
C13×#20732
C13×#20252
C13×#19362
C13×#18232
C13×#17862
C13×#17492
#2911013