Finite Group Databasebeta

← C13×#18997 #15705336

Subgroups — C13×#18997 #15705336

Order 3328.

1066 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 1066 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
1C2×C13×H(3,𝔽4)C211yesmaximal, characteristic
2C13×#3215C212yesmaximal, complemented
3C13×#3140C211yesmaximal, characteristic, complemented
4C13×#1659C218yesmaximal, complemented
5C13×#1533C211yesmaximal, characteristic, complemented
6C13×#1527C212yesmaximal, complemented
7C13×H(3,𝔽4)—24no—
8C13×H(3,𝔽4)—22no—
9C13×H(3,𝔽4)C2214yes—
10C13×#533C2211yescharacteristic, complemented
11C2×C13×#124—21no—
12C2×C13×#124—22no—
13C2×C13×#124C2212yes—
14C2×C13×#124C2211yescharacteristic
15C2×C13×#120—21no—
16C2×C13×#120—22no—
17C13×#497C2214yescomplemented
18C13×#489C2214yescomplemented
19C13×#489C2214yescomplemented
20C13×#488—22no—
21C13×#464—24no—
22C13×#451—22no—
23C13×#450—22no—
24C13×#432C2212yescomplemented
25C13×#419—21no—
26C13×#418—21no—
27C4×C13×M16C2211yescharacteristic, complemented
28C13×#329C2218yescomplemented
29C13×#329C2214yescomplemented
30C25×C13—21no—
31C22×Q8×C13D411yescharacteristic
32C22×Q8×C13D412yes—
33C22×D4×C13—22no—
34C22×D4×C13—21no—
35C22×D4×C13D411yescharacteristic
36C22×D4×C13D412yes—
37C2×C13×Q16—24no—
38C2×C13×SD16—24no—
39C2×C13×M16—21no—
40C13×C4⋊Q8C2312yescomplemented
41C13×#125—21no—
42C13×#124—24no—
43C13×#124—28no—
44C13×#124—24no—
45C13×#124—28no—
46C13×#124—22no—
47C13×#124—22no—
48C13×#124—22no—
49C13×#124D414yes—
50C13×#124D412yes—
51C13×#124C2312yes—
52C13×#124C2314yes—
53C13×C22⋊Q8—22no—
54C13×#120—24no—
55C13×#120—28no—
56C13×#120—24no—
57C13×#120—28no—
58C4×Q8×C13—22no—
59C13×#117—21no—
60C2×C13×C22⋊C4—21no—
61C2×C13×C22⋊C4—22no—
62C2×C13×C22⋊C4—22no—
63C2×C13×C22⋊C4—22no—
64C2×C13×C22⋊C4—22no—
65C2×C42×C13—21no—
66C2×C42×C13C2311yescharacteristic
67C13×C4⋊C8—22no—
68C13×#103—24no—
69C13×#103—24no—
70C13×#102—24no—
71C13×#102—24no—
72C13×C22⋊C8—22no—
73C13×#97C2312yescomplemented
74C13×#97C2314yescomplemented
75C4×C8×C13—21no—
76#18997C1311yesmaximal, characteristic, direct product factor, Sylow
77C24×C13—24no—
78C24×C13—21no—
79C24×C13—22no—
80C24×C13—84no—
81C24×C13—82no—
82C2×Q8×C13—21no—
83C2×Q8×C13—22no—
84C2×Q8×C13—22no—
85C2×Q8×C13—42no—
86C2×Q8×C13—82no—
87C2×Q8×C13C2×D412yes—
88C2×Q8×C13C2×D414yes—
89C2×D4×C13—24no—
90C2×D4×C13—28no—
91C2×D4×C13—21no—
92C2×D4×C13—22no—
93C2×D4×C13—42no—
94C2×D4×C13—82no—
95C2×D4×C13—84no—
96C2×D4×C13—82no—
97C2×D4×C13C2×D412yes—
98C2×D4×C13C2×D414yes—
99C22×C4×C13—22no—
100C22×C4×C13—21no—
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13C2×D412yes—
103C13×Q16—84no—
104C13×SD16—84no—
105C13×M16—42no—
106C2×C8×C13—22no—
107C2×C8×C13—24no—
108C13×C4⋊C4—22no—
109C13×C4⋊C4—22no—
110C13×C4⋊C4—42no—
111C13×C22⋊C4—28no—
112C13×C22⋊C4—24no—
113C13×C22⋊C4—24no—
114C13×C22⋊C4—24no—
115C13×C22⋊C4—24no—
116C13×C22⋊C4—24no—
117C13×C22⋊C4—24no—
118C13×C22⋊C4—24no—
119C13×C22⋊C4—41no—
120C42×C13—24no—
121C42×C13—41no—
122C42×C13C2×D411yescharacteristic
123C42×C13C2×D412yes—
124C42×C13C2411yescharacteristic
125C2×H(3,𝔽4)C2×C1311yescharacteristic
126#3215C2×C1312yescomplemented
127#3140C2×C1311yescharacteristic, complemented
128#1659C2×C1318yescomplemented
129#1533C2×C1311yescharacteristic, complemented
130#1527C2×C1312yescomplemented
131C23×C13—22no—
132C23×C13—24no—
133C23×C13—44no—
134C23×C13—44no—
135C23×C13—44no—
136C23×C13—42no—
137C23×C13—44no—
138C23×C13—84no—
139C23×C13—88no—
140C23×C13—816no—
141C23×C13#12011yescharacteristic
142Q8×C13—44no—
143Q8×C13—42no—
144Q8×C13—44no—
145Q8×C13—81no—
146Q8×C13—82no—
147D4×C13—44no—
148D4×C13—42no—
149D4×C13—81no—
150D4×C13—82no—
151D4×C13—84no—
152D4×C13—88no—
153C2×C4×C13—22no—
154C2×C4×C13—22no—
155C2×C4×C13—24no—
156C2×C4×C13—42no—
157C2×C4×C13—44no—
158C2×C4×C13—42no—
159C2×C4×C13—42no—
160C2×C4×C13#12011yescharacteristic
161C2×C4×C13#12012yes—
162C2×C4×C13C22×D411yescharacteristic
163C2×C4×C13C22×D412yes—
164C8×C13—42no—
165C8×C13—44no—
166H(3,𝔽4)—24no—
167H(3,𝔽4)—22no—
168H(3,𝔽4)C22×C1314yes—
169#533C22×C1311yescharacteristic, complemented
170C2×#124—21no—
171C2×#124—22no—
172C2×#124C22×C1311yescharacteristic
173C2×#124C22×C1312yes—
174C2×#120—21no—
175C2×#120—22no—
176#497C22×C1314yescomplemented
177#489C22×C1314yescomplemented
178#489C22×C1314yescomplemented
179#488—22no—
180#464—24no—
181#451—22no—
182#450—22no—
183#432C22×C1312yescomplemented
184#419—21no—
185#418—21no—
186C4×M16C22×C1311yescharacteristic, complemented
187#329C22×C1318yescomplemented
188#329C22×C1314yescomplemented
189C22×C13—22no—
190C22×C13—42no—
191C22×C13—44no—
192C22×C13—44no—
193C22×C13—44no—
194C22×C13—44no—
195C22×C13—84no—
196C22×C13—88no—
197C22×C13—816no—
198C22×C13#45512yes—
199C22×C13C2×#12011yescharacteristic
200C4×C13—21no—
201C4×C13—21no—
202C4×C13—22no—
203C4×C13—22no—
204C4×C13—42no—
205C4×C13—44no—
206C4×C13—82no—
207C25—21no—
208C22×Q8D4×C1311yescharacteristic
209C22×Q8D4×C1312yes—
210C22×D4—22no—
211C22×D4—21no—
212C22×D4D4×C1311yescharacteristic
213C22×D4D4×C1312yes—
214C2×Q16—24no—
215C2×SD16—24no—
216C2×M16—21no—
217C4⋊Q8C23×C1312yescomplemented
218#125—21no—
219#124—24no—
220#124—28no—
221#124—24no—
222#124—28no—
223#124—22no—
224#124—22no—
225#124—22no—
226#124D4×C1314yes—
227#124D4×C1312yes—
228#124C23×C1312yes—
229#124C23×C1314yes—
230C22⋊Q8—22no—
231#120—24no—
232#120—28no—
233#120—24no—
234#120—28no—
235C4×Q8—22no—
236#117—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—22no—
239C2×C22⋊C4—22no—
240C2×C22⋊C4—22no—
241C2×C22⋊C4—22no—
242C2×C42—21no—
243C2×C42C23×C1311yescharacteristic
244C4⋊C8—22no—
245#103—24no—
246#103—24no—
247#102—24no—
248#102—24no—
249C22⋊C8—22no—
250#97C23×C1312yescomplemented
251#97C23×C1314yescomplemented
252C4×C8—21no—
253C2×C13—22no—
254C2×C13—82no—
255C2×C13—84no—
256C2×C13C2×#45511yescharacteristic
257C2×C13#301912yes—
258C24—24no—
259C24—21no—
260C24—22no—
261C24—84no—
262C24—82no—
263C2×Q8—21no—
264C2×Q8—22no—
265C2×Q8—22no—
266C2×Q8—42no—
267C2×Q8—82no—
268C2×Q8C2×D4×C1312yes—
269C2×Q8C2×D4×C1314yes—
270C2×D4—24no—
271C2×D4—28no—
272C2×D4—21no—
273C2×D4—22no—
274C2×D4—42no—
275C2×D4—82no—
276C2×D4—84no—
277C2×D4—82no—
278C2×D4C2×D4×C1312yes—
279C2×D4C2×D4×C1314yes—
280C22×C4—22no—
281C22×C4—21no—
282C22×C4C2×D4×C1311yescharacteristic
283C22×C4C2×D4×C1312yes—
284Q16—84no—
285SD16—84no—
286M16—42no—
287C2×C8—22no—
288C2×C8—24no—
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—42no—
292C22⋊C4—28no—
293C22⋊C4—24no—
294C22⋊C4—24no—
295C22⋊C4—24no—
296C22⋊C4—24no—
297C22⋊C4—24no—
298C22⋊C4—24no—
299C22⋊C4—24no—
300C22⋊C4—41no—
301C42—24no—
302C42—41no—
303C42C2×D4×C1311yescharacteristic
304C42C2×D4×C1312yes—
305C42C24×C1311yescharacteristic
306C13#1899711yescharacteristic, direct product factor, Sylow
307C23—22no—
308C23—24no—
309C23—44no—
310C23—44no—
311C23—44no—
312C23—42no—
313C23—44no—
314C23—84no—
315C23—88no—
316C23—816no—
317C23C13×#12011yescharacteristic
318Q8—44no—
319Q8—42no—
320Q8—44no—
321Q8—81no—
322Q8—82no—
323D4—44no—
324D4—42no—
325D4—81no—
326D4—82no—
327D4—84no—
328D4—88no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—24no—
332C2×C4—42no—
333C2×C4—44no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4C13×#12011yescharacteristic
337C2×C4C13×#12012yes—
338C2×C4C22×D4×C1311yescharacteristic
339C2×C4C22×D4×C1312yes—
340C8—42no—
341C8—44no—
342C22—22no—
343C22—42no—
344C22—44no—
345C22—44no—
346C22—44no—
347C22—44no—
348C22—84no—
349C22—88no—
350C22—816no—
351C22C13×#45512yes—
352C22C2×C13×#12011yescharacteristic
353C4—21no—
354C4—21no—
355C4—22no—
356C4—22no—
357C4—42no—
358C4—44no—
359C4—82no—
360C2—22no—
361C2—82no—
362C2—84no—
363C2C2×C13×#45511yescharacteristic
364C2C13×#301912yes—
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC42C24×C13
prime radicalC2×C13×H(3,𝔽4)C2
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×#3215C2semidirect
3. C13×#3140C2semidirect
4. C13×#1659C2semidirect
5. C13×#1533C2semidirect
6. C13×#1527C2semidirect
10. C13×#533C22semidirect
17. C13×#497C22semidirect
18. C13×#489C22semidirect
19. C13×#489C22semidirect
24. C13×#432C22semidirect
27. C4×C13×M16C22semidirect
28. C13×#329C22semidirect
29. C13×#329C22semidirect
40. C13×C4⋊Q8C23semidirect
73. C13×#97C23semidirect
74. C13×#97C23semidirect
76. #18997C13direct (N × H)
126. #3215C2×C13semidirect
127. #3140C2×C13semidirect
128. #1659C2×C13semidirect
129. #1533C2×C13semidirect
130. #1527C2×C13semidirect
169. #533C22×C13semidirect
176. #497C22×C13semidirect
177. #489C22×C13semidirect
178. #489C22×C13semidirect
183. #432C22×C13semidirect
186. C4×M16C22×C13semidirect
187. #329C22×C13semidirect
188. #329C22×C13semidirect
217. C4⋊Q8C23×C13semidirect
250. #97C23×C13semidirect
251. #97C23×C13semidirect
306. C13#18997direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×H(3,𝔽4)2
C13×#32152
C13×#31402
C13×#16592
C13×#15332
C13×#15272
#1899713