Finite Group Databasebeta

← C13×#13360 #15699699

Subgroups — C13×#13360 #15699699

Order 3328.

702 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 702 conjugacy classes of subgroups — too many to draw. Only its 94 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×#3199C211yesmaximal, characteristic, complemented
2C13×#3021C212yesmaximal, complemented
3C13×#2122C212yesmaximal, complemented
4C13×#1794C211yesmaximal, characteristic, complemented
5C13×#1392C211yesmaximal, characteristic, complemented
6C13×#585C2211yescharacteristic
7C2×C13×AGL(1,ℤ/8)—22no—
8C13×#535C2212yes—
9C13×#482—22no—
10C13×#469—21no—
11C13×#466—21no—
12C13×#454—24no—
13C13×#453—24no—
14C13×#447—22no—
15C13×#421—22no—
16C13×#421—21no—
17C13×#416—21no—
18C13×#413C2212yes—
19C13×#410C2211yescharacteristic
20C13×#408C2211yescharacteristic
21C13×AΣL(1,𝔽16)—24no—
22C13×2−1+4—41no—
23C13×2−1+4D412yes—
24C13×H(5,𝔽2)—22no—
25C13×H(5,𝔽2)—21no—
26C13×H(5,𝔽2)—41no—
27C2×C13×#41—21no—
28C2×C13×#41—22no—
29C2×C13×#41—42no—
30C2×C13×#41C2311yescharacteristic
31C22×D4×C13D412yes—
32C13×AGL(1,ℤ/8)—28no—
33C13×AGL(1,ℤ/8)—44no—
34C2×C13×SD16—42no—
35C2×C13×D8—21no—
36C2×C13×D8—21no—
37C2×C13×D8—42no—
38C2×C13×M16—22no—
39C2×C13×M16D411yescharacteristic
40C22×C8×C13D411yescharacteristic
41C13×#127—22no—
42C13×#124—22no—
43C13×#121—22no—
44C13×#121—22no—
45C13×#120—22no—
46C13×#120—22no—
47C13×#117—21no—
48C13×#117D412yes—
49C13×#107—21no—
50C13×#106—21no—
51C13×#104—28no—
52C13×#104—42no—
53C13×#103—41no—
54C13×#102—22no—
55C13×#102—22no—
56C13×#102—41no—
57C13×#101—22no—
58C13×#100D414yes—
59C13×#99—22no—
60C13×C22⋊C8—22no—
61#13360C1311yesmaximal, characteristic, direct product factor, Sylow
62C24×C13—22no—
63C13×#41—22no—
64C13×#41—24no—
65C13×#41—24no—
66C13×#41—22no—
67C13×#41—41no—
68C13×#41—41no—
69C13×#41—41no—
70C13×#41—42no—
71C13×#41—42no—
72C13×#41—44no—
73C13×#41—42no—
74C13×#41—41no—
75C2×Q8×C13—21no—
76C2×Q8×C13—22no—
77C2×Q8×C13—42no—
78C2×Q8×C13C2×D411yescharacteristic
79C2×D4×C13—21no—
80C2×D4×C13—22no—
81C2×D4×C13—22no—
82C2×D4×C13—22no—
83C2×D4×C13—42no—
84C2×D4×C13—42no—
85C2×D4×C13—44no—
86C2×D4×C13—42no—
87C2×D4×C13—42no—
88C2×D4×C13—41no—
89C2×D4×C13—42no—
90C2×D4×C13—42no—
91C2×D4×C13C2×D412yes—
92C2×D4×C13#4111yescharacteristic
93C22×C4×C13—41no—
94C22×C4×C13—42no—
95C22×C4×C13C2×D412yes—
96C22×C4×C13C2×D411yescharacteristic
97C13×SD16—48no—
98C13×D8—48no—
99C13×D8—81no—
100C13×D8—81no—
101C13×M16—24no—
102C13×M16—42no—
103C13×M16—41no—
104C2×C8×C13—21no—
105C2×C8×C13—21no—
106C2×C8×C13—42no—
107C2×C8×C13—41no—
108C13×C4⋊C4—22no—
109C13×C4⋊C4—41no—
110C13×C22⋊C4—22no—
111C13×C22⋊C4—42no—
112C13×C22⋊C4—42no—
113C13×C22⋊C4—41no—
114C42×C13—22no—
115C42×C13—41no—
116#3199C2×C1311yescharacteristic, complemented
117#3021C2×C1312yescomplemented
118#2122C2×C1312yescomplemented
119#1794C2×C1311yescharacteristic, complemented
120#1392C2×C1311yescharacteristic, complemented
121C23×C13—41no—
122C23×C13—42no—
123C23×C13—42no—
124C23×C13—82no—
125C23×C13—162no—
126C23×C13#12112yes—
127C23×C13#12711yescharacteristic
128Q8×C13—24no—
129Q8×C13—22no—
130Q8×C13—41no—
131Q8×C13—41no—
132D4×C13—24no—
133D4×C13—22no—
134D4×C13—42no—
135D4×C13—41no—
136D4×C13—44no—
137D4×C13—42no—
138D4×C13—44no—
139D4×C13—42no—
140D4×C13—41no—
141D4×C13—42no—
142D4×C13—42no—
143D4×C13—162no—
144D4×C13—162no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—22no—
148C2×C4×C13—22no—
149C2×C4×C13—44no—
150C2×C4×C13—42no—
151C2×C4×C13—41no—
152C2×C4×C13—42no—
153C2×C4×C13—42no—
154C2×C4×C13—42no—
155C2×C4×C13—81no—
156C2×C4×C13#12012yes—
157C2×C4×C13#12011yescharacteristic
158C2×C4×C13#12111yescharacteristic
159C8×C13—44no—
160C8×C13—41no—
161C8×C13—41no—
162#585C22×C1311yescharacteristic
163C2×AGL(1,ℤ/8)—22no—
164#535C22×C1312yes—
165#482—22no—
166#469—21no—
167#466—21no—
168#454—24no—
169#453—24no—
170#447—22no—
171#421—22no—
172#421—21no—
173#416—21no—
174#413C22×C1312yes—
175#410C22×C1311yescharacteristic
176#408C22×C1311yescharacteristic
177AΣL(1,𝔽16)—24no—
178C22×C13—21no—
179C22×C13—22no—
180C22×C13—41no—
181C22×C13—42no—
182C22×C13—42no—
183C22×C13—82no—
184C22×C13—82no—
185C22×C13—82no—
186C22×C13—161no—
187C22×C13—162no—
188C22×C13—164no—
189C22×C13#39211yescharacteristic
190C4×C13—22no—
191C4×C13—21no—
192C4×C13—42no—
193C4×C13—82no—
194C4×C13—161no—
195C4×C13B(4,𝔽2)11yescharacteristic
196C4×C13B(4,𝔽2)11yescharacteristic
1972−1+4—41no—
1982−1+4D4×C1312yes—
199H(5,𝔽2)—22no—
200H(5,𝔽2)—21no—
201H(5,𝔽2)—41no—
202C2×#41—22no—
203C2×#41—21no—
204C2×#41—42no—
205C2×#41C23×C1311yescharacteristic
206C22×D4D4×C1312yes—
207AGL(1,ℤ/8)—28no—
208AGL(1,ℤ/8)—44no—
209C2×SD16—42no—
210C2×D8—21no—
211C2×D8—21no—
212C2×D8—42no—
213C2×M16—22no—
214C2×M16D4×C1311yescharacteristic
215C22×C8D4×C1311yescharacteristic
216#127—22no—
217#124—22no—
218#121—22no—
219#121—22no—
220#120—22no—
221#120—22no—
222#117—21no—
223#117D4×C1312yes—
224#107—21no—
225#106—21no—
226#104—28no—
227#104—42no—
228#103—41no—
229#102—22no—
230#102—22no—
231#102—41no—
232#101—22no—
233#100D4×C1314yes—
234#99—22no—
235C22⋊C8—22no—
236C2×C13—21no—
237C2×C13—41no—
238C2×C13—42no—
239C2×C13—82no—
240C2×C13—162no—
241C2×C13#202111yescharacteristic
242C24—22no—
243#41—22no—
244#41—24no—
245#41—24no—
246#41—22no—
247#41—41no—
248#41—41no—
249#41—41no—
250#41—42no—
251#41—42no—
252#41—44no—
253#41—42no—
254#41—41no—
255C2×Q8—21no—
256C2×Q8—22no—
257C2×Q8—42no—
258C2×Q8C2×D4×C1311yescharacteristic
259C2×D4—21no—
260C2×D4—22no—
261C2×D4—22no—
262C2×D4—22no—
263C2×D4—42no—
264C2×D4—42no—
265C2×D4—44no—
266C2×D4—42no—
267C2×D4—42no—
268C2×D4—41no—
269C2×D4—42no—
270C2×D4—42no—
271C2×D4C2×D4×C1312yes—
272C2×D4C13×#4111yescharacteristic
273C22×C4—41no—
274C22×C4—42no—
275C22×C4C2×D4×C1312yes—
276C22×C4C2×D4×C1311yescharacteristic
277SD16—48no—
278D8—48no—
279D8—81no—
280D8—81no—
281M16—24no—
282M16—42no—
283M16—41no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—42no—
287C2×C8—41no—
288C4⋊C4—22no—
289C4⋊C4—41no—
290C22⋊C4—22no—
291C22⋊C4—42no—
292C22⋊C4—42no—
293C22⋊C4—41no—
294C42—22no—
295C42—41no—
296C13#1336011yescharacteristic, direct product factor, Sylow
297C23—41no—
298C23—42no—
299C23—42no—
300C23—82no—
301C23—162no—
302C23C13×#12112yes—
303C23C13×#12711yescharacteristic
304Q8—24no—
305Q8—22no—
306Q8—41no—
307Q8—41no—
308D4—24no—
309D4—22no—
310D4—42no—
311D4—41no—
312D4—44no—
313D4—42no—
314D4—44no—
315D4—42no—
316D4—41no—
317D4—42no—
318D4—42no—
319D4—162no—
320D4—162no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—44no—
326C2×C4—42no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—81no—
332C2×C4C13×#12012yes—
333C2×C4C13×#12011yescharacteristic
334C2×C4C13×#12111yescharacteristic
335C8—44no—
336C8—41no—
337C8—41no—
338C22—21no—
339C22—22no—
340C22—41no—
341C22—42no—
342C22—42no—
343C22—82no—
344C22—82no—
345C22—82no—
346C22—161no—
347C22—162no—
348C22—164no—
349C22C13×#39211yescharacteristic
350C4—22no—
351C4—21no—
352C4—42no—
353C4—82no—
354C4—161no—
355C4C13×B(4,𝔽2)11yescharacteristic
356C4C13×B(4,𝔽2)11yescharacteristic
357C2—21no—
358C2—41no—
359C2—42no—
360C2—82no—
361C2—162no—
362C2C13×#202111yescharacteristic
subgroupG/H
center, socleC2×C13#2021
commutator, Frattini, cosocleC2×#41C23×C13
LCSG ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C13×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3199C2semidirect
2. C13×#3021C2semidirect
3. C13×#2122C2semidirect
4. C13×#1794C2semidirect
5. C13×#1392C2semidirect
61. #13360C13direct (N × H)
116. #3199C2×C13semidirect
117. #3021C2×C13semidirect
118. #2122C2×C13semidirect
119. #1794C2×C13semidirect
120. #1392C2×C13semidirect
296. C13#13360direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31992
C13×#30212
C13×#21222
C13×#17942
C13×#13922
#1336013