Finite Group Databasebeta

← C13×#13359 #15699698

Subgroups — C13×#13359 #15699698

Order 3328.

704 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 98 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×#456C212yesmaximal
2C13×#2734C211yesmaximal, characteristic, complemented
3C2×C13×#356C212yesmaximal, complemented
4C13×#1793C211yesmaximal, characteristic
5C13×#1394C211yesmaximal, characteristic, complemented
6C2×C13×2−1+4C2211yescharacteristic
7C2×C13×#137—22no—
8C2×C13×C4⋊Q8C2212yes—
9C13×#456—24no—
10C13×#456—24no—
11C2×C13×#104—22no—
12C2×C13×#104—21no—
13C13×#417—21no—
14C2×C13×#101C2211yescharacteristic
15C2×C13×#101C2212yes—
16C13×#398—21no—
17C13×#395—22no—
18C13×#391C2211yescharacteristic
19C13×#389—21no—
20C13×#387—22no—
21C13×#356—24no—
22C13×2−1+4—22no—
23C13×2−1+4—21no—
24C13×2−1+4—42no—
25C13×2−1+4D412yes—
26C2×C13×#41—21no—
27C2×C13×#41—22no—
28C2×C13×#41—41no—
29C22×Q8×C13—41no—
30C22×Q8×C13D412yes—
31C22×Q8×C13C2311yescharacteristic
32C13×#137—28no—
33C13×#137—44no—
34C2×C13×Q16—42no—
35C2×C13×SD16—42no—
36C2×C13×M16—22no—
37C2×C13×M16—21no—
38C13×C4⋊Q8—22no—
39C13×C4⋊Q8—22no—
40C13×C4⋊Q8—22no—
41C13×C4⋊Q8—22no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—22no—
44C2×C13×C4⋊C4—22no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4D411yescharacteristic
48C2×C42×C13D412yes—
49C2×C42×C13D411yescharacteristic
50C13×#104—28no—
51C13×#104—42no—
52C13×#103—41no—
53C13×#102—41no—
54C13×#101—22no—
55C13×#101—22no—
56C13×#101D414yes—
57C13×#95—21no—
58C13×#95—22no—
59C13×#95—22no—
60C13×#95—22no—
61#13359C1311yesmaximal, characteristic, direct product factor, Sylow
62C13×#41—22no—
63C13×#41—24no—
64C13×#41—24no—
65C13×#41—22no—
66C13×#41—41no—
67C13×#41—42no—
68C13×#41—42no—
69C13×#41—44no—
70C13×#41—42no—
71C13×#41—42no—
72C13×#41—41no—
73C2×Q8×C13—21no—
74C2×Q8×C13—22no—
75C2×Q8×C13—22no—
76C2×Q8×C13—22no—
77C2×Q8×C13—41no—
78C2×Q8×C13—41no—
79C2×Q8×C13—42no—
80C2×Q8×C13—42no—
81C2×Q8×C13—42no—
82C2×Q8×C13—44no—
83C2×Q8×C13—42no—
84C2×Q8×C13C2×D411yescharacteristic
85C2×Q8×C13C2×D412yes—
86C2×Q8×C13#4111yescharacteristic
87C2×D4×C13—21no—
88C2×D4×C13—22no—
89C2×D4×C13—41no—
90C22×C4×C13—21no—
91C22×C4×C13—22no—
92C22×C4×C13—21no—
93C22×C4×C13—22no—
94C22×C4×C13—41no—
95C22×C4×C13—42no—
96C22×C4×C13C2×D412yes—
97C22×C4×C13C2×D411yescharacteristic
98C13×Q16—48no—
99C13×SD16—48no—
100C13×M16—24no—
101C13×M16—42no—
102C13×M16—41no—
103C13×M16—41no—
104C2×C8×C13—42no—
105C2×C8×C13—41no—
106C13×C4⋊C4—24no—
107C13×C4⋊C4—41no—
108C13×C4⋊C4—42no—
109C13×C4⋊C4—42no—
110C13×C4⋊C4—42no—
111C13×C4⋊C4—42no—
112C13×C4⋊C4—81no—
113C13×C4⋊C4—81no—
114C42×C13—22no—
115C42×C13—22no—
116C42×C13—41no—
117C2×#456C2×C1312yes—
118#2734C2×C1311yescharacteristic, complemented
119C2×#356C2×C1312yescomplemented
120#1793C2×C1311yescharacteristic
121#1394C2×C1311yescharacteristic, complemented
122C23×C13—41no—
123C23×C13#12011yescharacteristic
124Q8×C13—24no—
125Q8×C13—22no—
126Q8×C13—41no—
127Q8×C13—42no—
128Q8×C13—41no—
129Q8×C13—41no—
130Q8×C13—42no—
131Q8×C13—44no—
132Q8×C13—82no—
133D4×C13—24no—
134D4×C13—22no—
135D4×C13—41no—
136D4×C13—42no—
137D4×C13—42no—
138D4×C13—42no—
139C2×C4×C13—21no—
140C2×C4×C13—22no—
141C2×C4×C13—21no—
142C2×C4×C13—22no—
143C2×C4×C13—22no—
144C2×C4×C13—24no—
145C2×C4×C13—44no—
146C2×C4×C13—42no—
147C2×C4×C13—42no—
148C2×C4×C13—44no—
149C2×C4×C13—41no—
150C2×C4×C13—42no—
151C2×C4×C13—42no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—42no—
155C2×C4×C13—42no—
156C2×C4×C13—42no—
157C2×C4×C13—41no—
158C2×C4×C13—42no—
159C2×C4×C13#12012yes—
160C2×C4×C13#12112yes—
161C2×C4×C13#12111yescharacteristic
162C2×C4×C13#12711yescharacteristic
163C8×C13—44no—
164C8×C13—81no—
165C2×2−1+4C22×C1311yescharacteristic
166C2×#137—22no—
167C2×C4⋊Q8C22×C1312yes—
168#456—24no—
169#456—24no—
170C2×#104—22no—
171C2×#104—21no—
172#417—21no—
173C2×#101C22×C1311yescharacteristic
174C2×#101C22×C1312yes—
175#398—21no—
176#395—22no—
177#391C22×C1311yescharacteristic
178#389—21no—
179#387—22no—
180#356—24no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—42no—
184C22×C13—81no—
185C22×C13—81no—
186C22×C13#39211yescharacteristic
187C22×C13B(4,𝔽2)11yescharacteristic
188C22×C13B(4,𝔽2)11yescharacteristic
189C4×C13—22no—
190C4×C13—21no—
191C4×C13—21no—
192C4×C13—22no—
193C4×C13—44no—
194C4×C13—42no—
195C4×C13—42no—
196C4×C13—81no—
197C4×C13—82no—
1982−1+4—22no—
1992−1+4—21no—
2002−1+4—42no—
2012−1+4D4×C1312yes—
202C2×#41—22no—
203C2×#41—21no—
204C2×#41—41no—
205C22×Q8—41no—
206C22×Q8D4×C1312yes—
207C22×Q8C23×C1311yescharacteristic
208#137—28no—
209#137—44no—
210C2×Q16—42no—
211C2×SD16—42no—
212C2×M16—22no—
213C2×M16—21no—
214C4⋊Q8—22no—
215C4⋊Q8—22no—
216C4⋊Q8—22no—
217C4⋊Q8—22no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4D4×C1311yescharacteristic
224C2×C42D4×C1312yes—
225C2×C42D4×C1311yescharacteristic
226#104—28no—
227#104—42no—
228#103—41no—
229#102—41no—
230#101—22no—
231#101—22no—
232#101D4×C1314yes—
233#95—21no—
234#95—22no—
235#95—22no—
236#95—22no—
237C2×C13—21no—
238C2×C13—21no—
239C2×C13—82no—
240C2×C13#202111yescharacteristic
241C2×C13#220311yescharacteristic
242C2×C13#220511yescharacteristic
243#41—22no—
244#41—24no—
245#41—24no—
246#41—22no—
247#41—41no—
248#41—42no—
249#41—42no—
250#41—44no—
251#41—42no—
252#41—42no—
253#41—41no—
254C2×Q8—21no—
255C2×Q8—22no—
256C2×Q8—22no—
257C2×Q8—22no—
258C2×Q8—41no—
259C2×Q8—41no—
260C2×Q8—42no—
261C2×Q8—42no—
262C2×Q8—42no—
263C2×Q8—44no—
264C2×Q8—42no—
265C2×Q8C2×D4×C1311yescharacteristic
266C2×Q8C2×D4×C1312yes—
267C2×Q8C13×#4111yescharacteristic
268C2×D4—21no—
269C2×D4—22no—
270C2×D4—41no—
271C22×C4—21no—
272C22×C4—22no—
273C22×C4—21no—
274C22×C4—22no—
275C22×C4—41no—
276C22×C4—42no—
277C22×C4C2×D4×C1312yes—
278C22×C4C2×D4×C1311yescharacteristic
279Q16—48no—
280SD16—48no—
281M16—24no—
282M16—42no—
283M16—41no—
284M16—41no—
285C2×C8—42no—
286C2×C8—41no—
287C4⋊C4—24no—
288C4⋊C4—41no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C4⋊C4—42no—
292C4⋊C4—42no—
293C4⋊C4—81no—
294C4⋊C4—81no—
295C42—22no—
296C42—22no—
297C42—41no—
298C13#1335911yescharacteristic, direct product factor, Sylow
299C23—41no—
300C23C13×#12011yescharacteristic
301Q8—24no—
302Q8—22no—
303Q8—41no—
304Q8—42no—
305Q8—41no—
306Q8—41no—
307Q8—42no—
308Q8—44no—
309Q8—82no—
310D4—24no—
311D4—22no—
312D4—41no—
313D4—42no—
314D4—42no—
315D4—42no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—24no—
322C2×C4—44no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—44no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4C13×#12012yes—
337C2×C4C13×#12112yes—
338C2×C4C13×#12111yescharacteristic
339C2×C4C13×#12711yescharacteristic
340C8—44no—
341C8—81no—
342C22—21no—
343C22—21no—
344C22—42no—
345C22—81no—
346C22—81no—
347C22C13×#39211yescharacteristic
348C22C13×B(4,𝔽2)11yescharacteristic
349C22C13×B(4,𝔽2)11yescharacteristic
350C4—22no—
351C4—21no—
352C4—21no—
353C4—22no—
354C4—44no—
355C4—42no—
356C4—42no—
357C4—82no—
358C4—81no—
359C2—21no—
360C2—21no—
361C2—82no—
362C2C13×#202111yescharacteristic
363C2C13×#220311yescharacteristic
364C2C13×#220511yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC22×Q8C23×C13
prime radicalC2×C13×2−1+4C22
LCSG ▷ C22×Q8 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C13 ◁ C22×Q8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2734C2semidirect
3. C2×C13×#356C2semidirect
5. C13×#1394C2semidirect
61. #13359C13direct (N × H)
118. #2734C2×C13semidirect
119. C2×#356C2×C13semidirect
121. #1394C2×C13semidirect
298. C13#13359direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#4562
C13×#27342
C2×C13×#3562
C13×#17932
C13×#13942
#1335913