Finite Group Databasebeta

← C13×#19056 #15705395

Subgroups — C13×#19056 #15705395

Order 3328.

992 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 992 conjugacy classes of subgroups — too many to draw. Only its 222 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×#3549C211yesmaximal, characteristic
2C13×#3216C212yesmaximal, complemented
3C13×#3135C211yesmaximal, characteristic, complemented
4C13×#1659C218yesmaximal, complemented
5C13×#1536C211yesmaximal, characteristic, complemented
6C13×#1530C212yesmaximal, complemented
7C13×H(3,𝔽4)C2214yes—
8C13×#555—22no—
9C13×#555—21no—
10D42×C13—22no—
11D42×C13—21no—
12C13×#535—22no—
13C13×#535—24no—
14C13×#533C2211yescharacteristic, complemented
15C13×#532C2212yes—
16C13×#532C2211yescharacteristic
17C13×#497C2214yescomplemented
18C13×#491—21no—
19C13×#490—21no—
20C13×#489C2214yescomplemented
21C13×#489C2214yescomplemented
22C13×#462—22no—
23C13×#460—22no—
24C13×#452—24no—
25C13×#432C2212yescomplemented
26C13×#416—22no—
27C2×C13×#97C2211yescharacteristic, complemented
28C13×#329C2218yescomplemented
29C13×#329C2214yescomplemented
30C2×C13×#41D412yes—
31C2×C13×#41D414yes—
32C22×D4×C13—24no—
33C22×D4×C13—22no—
34C2×C13×Q16—24no—
35C2×C13×SD16—24no—
36C22×C8×C13—21no—
37C13×C4⋊Q8D412yes—
38C13×C4⋊Q8D411yescharacteristic
39C13×C4⋊Q8C2312yes—
40C13×#127—24no—
41C13×#127D412yes—
42C13×#127D411yescharacteristic
43C13×#125—21no—
44C13×#124—24no—
45C13×#124—28no—
46C13×#124C2312yes—
47C13×#124C2314yes—
48C13×C22⋊Q8—22no—
49C13×#121—24no—
50C13×#121—24no—
51C13×#121—24no—
52C13×#121—22no—
53C13×#121—22no—
54C13×#121—22no—
55C13×#120—24no—
56C13×#120—24no—
57C13×#120—28no—
58C4×Q8×C13—22no—
59C4×D4×C13—22no—
60C4×D4×C13—22no—
61C4×D4×C13—22no—
62C13×#117—24no—
63C13×#117—22no—
64C13×#117—21no—
65C2×C42×C13C2311yescharacteristic
66C13×C4⋊C8—22no—
67C13×#103—24no—
68C13×#103—24no—
69C13×#102—24no—
70C13×#102—24no—
71C13×C22⋊C8—22no—
72C13×#97—21no—
73C13×#97C2312yes—
74C13×#97C2314yes—
75#19056C1311yesmaximal, characteristic, direct product factor, Sylow
76C24×C13—24no—
77C13×#41—44no—
78C13×#41—84no—
79C2×Q8×C13—22no—
80C2×Q8×C13C2×D412yes—
81C2×Q8×C13C2×D414yes—
82C2×D4×C13—24no—
83C2×D4×C13—28no—
84C2×D4×C13—22no—
85C2×D4×C13—24no—
86C2×D4×C13—22no—
87C2×D4×C13—22no—
88C2×D4×C13—22no—
89C2×D4×C13—88no—
90C2×D4×C13—84no—
91C2×D4×C13C2×D412yes—
92C2×D4×C13C2×D414yes—
93C22×C4×C13—24no—
94C22×C4×C13—22no—
95C22×C4×C13C2×D411yescharacteristic
96C22×C4×C13C2×D412yes—
97C13×Q16—84no—
98C13×SD16—84no—
99C2×C8×C13—22no—
100C2×C8×C13—24no—
101C2×C8×C13—42no—
102C13×C4⋊C4—22no—
103C13×C4⋊C4—22no—
104C13×C4⋊C4—22no—
105C13×C4⋊C4—22no—
106C13×C4⋊C4—22no—
107C13×C4⋊C4—42no—
108C13×C22⋊C4—28no—
109C13×C22⋊C4—24no—
110C13×C22⋊C4—24no—
111C13×C22⋊C4—24no—
112C13×C22⋊C4—24no—
113C13×C22⋊C4—41no—
114C42×C13—24no—
115C42×C13—41no—
116C42×C13C2×D411yescharacteristic
117C42×C13C2×D412yes—
118C42×C13C2411yescharacteristic
119#3549C2×C1311yescharacteristic
120#3216C2×C1312yescomplemented
121#3135C2×C1311yescharacteristic, complemented
122#1659C2×C1318yescomplemented
123#1536C2×C1311yescharacteristic, complemented
124#1530C2×C1312yescomplemented
125C23×C13—22no—
126C23×C13—24no—
127C23×C13—84no—
128C23×C13—88no—
129C23×C13#12011yescharacteristic
130Q8×C13—44no—
131Q8×C13—42no—
132Q8×C13—42no—
133Q8×C13—42no—
134D4×C13—44no—
135D4×C13—44no—
136D4×C13—44no—
137D4×C13—42no—
138D4×C13—44no—
139D4×C13—82no—
140D4×C13—84no—
141D4×C13—84no—
142D4×C13—88no—
143C2×C4×C13—22no—
144C2×C4×C13—22no—
145C2×C4×C13—24no—
146C2×C4×C13—42no—
147C2×C4×C13—48no—
148C2×C4×C13—44no—
149C2×C4×C13—42no—
150C2×C4×C13#12012yes—
151C2×C4×C13#12011yescharacteristic
152C2×C4×C13C22×D411yescharacteristic
153C2×C4×C13C22×D412yes—
154C8×C13—42no—
155C8×C13—44no—
156H(3,𝔽4)C22×C1314yes—
157#555—22no—
158#555—21no—
159D42—22no—
160D42—21no—
161#535—22no—
162#535—24no—
163#533C22×C1311yescharacteristic, complemented
164#532C22×C1311yescharacteristic
165#532C22×C1312yes—
166#497C22×C1314yescomplemented
167#491—21no—
168#490—21no—
169#489C22×C1314yescomplemented
170#489C22×C1314yescomplemented
171#462—22no—
172#460—22no—
173#452—24no—
174#432C22×C1312yescomplemented
175#416—22no—
176C2×#97C22×C1311yescharacteristic, complemented
177#329C22×C1314yescomplemented
178#329C22×C1318yescomplemented
179C22×C13—21no—
180C22×C13—22no—
181C22×C13—42no—
182C22×C13—44no—
183C22×C13—44no—
184C22×C13—44no—
185C22×C13—44no—
186C22×C13—168no—
187C22×C13C2×#12011yescharacteristic
188C4×C13—21no—
189C4×C13—22no—
190C4×C13—22no—
191C4×C13—42no—
192C4×C13—44no—
193C4×C13—82no—
194C4×C13#45512yes—
195C2×#41D4×C1312yes—
196C2×#41D4×C1314yes—
197C22×D4—24no—
198C22×D4—22no—
199C2×Q16—24no—
200C2×SD16—24no—
201C22×C8—21no—
202C4⋊Q8D4×C1312yes—
203C4⋊Q8D4×C1311yescharacteristic
204C4⋊Q8C23×C1312yes—
205#127—24no—
206#127D4×C1312yes—
207#127D4×C1311yescharacteristic
208#125—21no—
209#124—24no—
210#124—28no—
211#124C23×C1312yes—
212#124C23×C1314yes—
213C22⋊Q8—22no—
214#121—24no—
215#121—24no—
216#121—24no—
217#121—22no—
218#121—22no—
219#121—22no—
220#120—24no—
221#120—24no—
222#120—28no—
223C4×Q8—22no—
224C4×D4—22no—
225C4×D4—22no—
226C4×D4—22no—
227#117—24no—
228#117—22no—
229#117—21no—
230C2×C42C23×C1311yescharacteristic
231C4⋊C8—22no—
232#103—24no—
233#103—24no—
234#102—24no—
235#102—24no—
236C22⋊C8—22no—
237#97—21no—
238#97C23×C1312yes—
239#97C23×C1314yes—
240C2×C13—41no—
241C2×C13—82no—
242C2×C13—84no—
243C2×C13C2×#45511yescharacteristic
244C2×C13#301912yes—
245C24—24no—
246#41—44no—
247#41—84no—
248C2×Q8—22no—
249C2×Q8C2×D4×C1312yes—
250C2×Q8C2×D4×C1314yes—
251C2×D4—24no—
252C2×D4—28no—
253C2×D4—22no—
254C2×D4—24no—
255C2×D4—22no—
256C2×D4—22no—
257C2×D4—22no—
258C2×D4—88no—
259C2×D4—84no—
260C2×D4C2×D4×C1312yes—
261C2×D4C2×D4×C1314yes—
262C22×C4—24no—
263C22×C4—22no—
264C22×C4C2×D4×C1311yescharacteristic
265C22×C4C2×D4×C1312yes—
266Q16—84no—
267SD16—84no—
268C2×C8—22no—
269C2×C8—24no—
270C2×C8—42no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—42no—
277C22⋊C4—28no—
278C22⋊C4—24no—
279C22⋊C4—24no—
280C22⋊C4—24no—
281C22⋊C4—24no—
282C22⋊C4—41no—
283C42—24no—
284C42—41no—
285C42C2×D4×C1311yescharacteristic
286C42C2×D4×C1312yes—
287C42C24×C1311yescharacteristic
288C13#1905611yescharacteristic, direct product factor, Sylow
289C23—22no—
290C23—24no—
291C23—84no—
292C23—88no—
293C23C13×#12011yescharacteristic
294Q8—44no—
295Q8—42no—
296Q8—42no—
297Q8—42no—
298D4—44no—
299D4—42no—
300D4—44no—
301D4—44no—
302D4—44no—
303D4—82no—
304D4—84no—
305D4—84no—
306D4—88no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—24no—
310C2×C4—42no—
311C2×C4—48no—
312C2×C4—44no—
313C2×C4—42no—
314C2×C4C13×#12012yes—
315C2×C4C13×#12011yescharacteristic
316C2×C4C22×D4×C1311yescharacteristic
317C2×C4C22×D4×C1312yes—
318C8—42no—
319C8—44no—
320C22—21no—
321C22—22no—
322C22—42no—
323C22—44no—
324C22—44no—
325C22—44no—
326C22—44no—
327C22—168no—
328C22C2×C13×#12011yescharacteristic
329C4—21no—
330C4—22no—
331C4—22no—
332C4—42no—
333C4—44no—
334C4—82no—
335C4C13×#45512yes—
336C2—41no—
337C2—82no—
338C2—84no—
339C2C2×C13×#45511yescharacteristic
340C2C13×#301912yes—
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC42C24×C13
prime radicalC13×#3549C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#3216C2semidirect
3. C13×#3135C2semidirect
4. C13×#1659C2semidirect
5. C13×#1536C2semidirect
6. C13×#1530C2semidirect
14. C13×#533C22semidirect
17. C13×#497C22semidirect
20. C13×#489C22semidirect
21. C13×#489C22semidirect
25. C13×#432C22semidirect
27. C2×C13×#97C22semidirect
28. C13×#329C22semidirect
29. C13×#329C22semidirect
75. #19056C13direct (N × H)
120. #3216C2×C13semidirect
121. #3135C2×C13semidirect
122. #1659C2×C13semidirect
123. #1536C2×C13semidirect
124. #1530C2×C13semidirect
163. #533C22×C13semidirect
166. #497C22×C13semidirect
169. #489C22×C13semidirect
170. #489C22×C13semidirect
174. #432C22×C13semidirect
176. C2×#97C22×C13semidirect
177. #329C22×C13semidirect
178. #329C22×C13semidirect
288. C13#19056direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35492
C13×#32162
C13×#31352
C13×#16592
C13×#15362
C13×#15302
#1905613