Finite Group Databasebeta

← C13×#10338 #15696677

Subgroups — C13×#10338 #15696677

Order 3328.

998 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 998 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2483C211yesmaximal, characteristic, complemented
2C13×#2405C212yesmaximal
3C13×#1819C212yesmaximal, complemented
4C13×#1781C211yesmaximal, characteristic
5C13×#1304C211yesmaximal, characteristic, complemented
6C23×D4×C13C2211yescharacteristic
7C2×C13×#123—22no—
8C22×C13×C22⋊C4C2212yes—
9C2×C13×#99—22no—
10C13×#397—22no—
11C13×#394—24no—
12C13×#386—22no—
13C13×#385—22no—
14C13×#385—22no—
15C13×#381—22no—
16C13×#379—22no—
17C13×#379C2211yescharacteristic
18C13×#379C2211yescharacteristic
19C13×#379C2212yes—
20C13×#342—24no—
21C25×C13D411yescharacteristic
22C25×C13C2311yescharacteristic
23C22×D4×C13—22no—
24C22×D4×C13—21no—
25C22×D4×C13—22no—
26C22×D4×C13—21no—
27C22×D4×C13—44no—
28C23×C4×C13D412yes—
29C23×C4×C13D411yescharacteristic
30C23×C4×C13D412yes—
31C13×#123—48no—
32C2×C13×C4⋊C4—24no—
33C2×C13×C4⋊C4—22no—
34C2×C13×C22⋊C4—24no—
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4—22no—
40C2×C13×C22⋊C4—22no—
41C2×C13×C22⋊C4—22no—
42C2×C13×C22⋊C4—22no—
43C2×C13×C22⋊C4—22no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—22no—
46C2×C13×C22⋊C4—24no—
47C2×C13×C22⋊C4D414yes—
48C2×C13×C22⋊C4D412yes—
49C13×#99—44no—
50C13×#95—22no—
51C13×#95—24no—
52C13×#95—24no—
53#10338C1311yesmaximal, characteristic, direct product factor, Sylow
54C24×C13—22no—
55C24×C13—21no—
56C24×C13—42no—
57C24×C13—42no—
58C24×C13—44no—
59C24×C13—44no—
60C24×C13C2×D411yescharacteristic
61C24×C13C2×D412yes—
62C24×C13C2×D411yescharacteristic
63C24×C13C2×D412yes—
64C24×C13#4111yescharacteristic
65C2×D4×C13—24no—
66C2×D4×C13—28no—
67C2×D4×C13—44no—
68C2×D4×C13—42no—
69C2×D4×C13—44no—
70C2×D4×C13—42no—
71C2×D4×C13—44no—
72C2×D4×C13—42no—
73C2×D4×C13—41no—
74C2×D4×C13—42no—
75C2×D4×C13—41no—
76C22×C4×C13—22no—
77C22×C4×C13—21no—
78C22×C4×C13—22no—
79C22×C4×C13—22no—
80C22×C4×C13—22no—
81C22×C4×C13—22no—
82C22×C4×C13—24no—
83C22×C4×C13—22no—
84C22×C4×C13—22no—
85C22×C4×C13—22no—
86C22×C4×C13—42no—
87C22×C4×C13—44no—
88C22×C4×C13—44no—
89C22×C4×C13—41no—
90C13×C4⋊C4—48no—
91C13×C4⋊C4—82no—
92C13×C22⋊C4—44no—
93C13×C22⋊C4—44no—
94C13×C22⋊C4—44no—
95C13×C22⋊C4—48no—
96C13×C22⋊C4—42no—
97C13×C22⋊C4—42no—
98C13×C22⋊C4—42no—
99C13×C22⋊C4—42no—
100C13×C22⋊C4—42no—
101C13×C22⋊C4—44no—
102C13×C22⋊C4—42no—
103C13×C22⋊C4—44no—
104C13×C22⋊C4—84no—
105#2483C2×C1311yescharacteristic, complemented
106#2405C2×C1312yes—
107#1819C2×C1312yescomplemented
108#1781C2×C1311yescharacteristic
109#1304C2×C1311yescharacteristic, complemented
110C23×C13—24no—
111C23×C13—24no—
112C23×C13—24no—
113C23×C13—22no—
114C23×C13—24no—
115C23×C13—24no—
116C23×C13—22no—
117C23×C13—41no—
118C23×C13—42no—
119C23×C13—42no—
120C23×C13—41no—
121C23×C13—42no—
122C23×C13—42no—
123C23×C13—42no—
124C23×C13—42no—
125C23×C13—41no—
126C23×C13—44no—
127C23×C13—41no—
128C23×C13—44no—
129C23×C13—82no—
130C23×C13—88no—
131C23×C13—88no—
132C23×C13#12011yescharacteristic
133C23×C13#12012yes—
134C23×C13#12111yescharacteristic
135C23×C13#12112yes—
136C23×C13#12711yescharacteristic
137D4×C13—48no—
138D4×C13—44no—
139D4×C13—44no—
140C2×C4×C13—24no—
141C2×C4×C13—22no—
142C2×C4×C13—42no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—44no—
146C2×C4×C13—44no—
147C2×C4×C13—44no—
148C2×C4×C13—44no—
149C2×C4×C13—44no—
150C2×C4×C13—42no—
151C2×C4×C13—42no—
152C2×C4×C13—42no—
153C2×C4×C13—44no—
154C2×C4×C13—44no—
155C2×C4×C13—44no—
156C2×C4×C13—82no—
157C2×C4×C13—82no—
158C2×C4×C13—81no—
159C2×C4×C13—82no—
160C23×D4C22×C1311yescharacteristic
161C2×#123—22no—
162C22×C22⋊C4C22×C1312yes—
163C2×#99—22no—
164#397—22no—
165#394—24no—
166#386—22no—
167#385—22no—
168#385—22no—
169#381—22no—
170#379—22no—
171#379C22×C1311yescharacteristic
172#379C22×C1312yes—
173#379C22×C1311yescharacteristic
174#342—24no—
175C22×C13—22no—
176C22×C13—22no—
177C22×C13—22no—
178C22×C13—21no—
179C22×C13—22no—
180C22×C13—21no—
181C22×C13—22no—
182C22×C13—22no—
183C22×C13—22no—
184C22×C13—22no—
185C22×C13—48no—
186C22×C13—44no—
187C22×C13—48no—
188C22×C13—42no—
189C22×C13—84no—
190C22×C13—82no—
191C22×C13—84no—
192C22×C13—82no—
193C22×C13—82no—
194C22×C13—82no—
195C22×C13—82no—
196C22×C13#39211yescharacteristic
197C22×C13B(4,𝔽2)12yes—
198C22×C13#45814yes—
199C4×C13—42no—
200C4×C13—84no—
201C4×C13—82no—
202C4×C13—82no—
203C4×C13—82no—
204C4×C13—161no—
205C25D4×C1311yescharacteristic
206C25C23×C1311yescharacteristic
207C22×D4—22no—
208C22×D4—21no—
209C22×D4—22no—
210C22×D4—21no—
211C22×D4—44no—
212C23×C4D4×C1312yes—
213C23×C4D4×C1312yes—
214C23×C4D4×C1311yescharacteristic
215#123—48no—
216C2×C4⋊C4—24no—
217C2×C4⋊C4—22no—
218C2×C22⋊C4—24no—
219C2×C22⋊C4—22no—
220C2×C22⋊C4—22no—
221C2×C22⋊C4—22no—
222C2×C22⋊C4—22no—
223C2×C22⋊C4—22no—
224C2×C22⋊C4—22no—
225C2×C22⋊C4—22no—
226C2×C22⋊C4—22no—
227C2×C22⋊C4—22no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—24no—
231C2×C22⋊C4D4×C1314yes—
232C2×C22⋊C4D4×C1312yes—
233#99—44no—
234#95—22no—
235#95—24no—
236#95—24no—
237C2×C13—24no—
238C2×C13—22no—
239C2×C13—41no—
240C2×C13—42no—
241C2×C13—41no—
242C2×C13—82no—
243C2×C13#202111yescharacteristic
244C2×C13#202212yes—
245C24—22no—
246C24—21no—
247C24—42no—
248C24—42no—
249C24—44no—
250C24—44no—
251C24C2×D4×C1311yescharacteristic
252C24C2×D4×C1312yes—
253C24C2×D4×C1311yescharacteristic
254C24C2×D4×C1312yes—
255C24C13×#4111yescharacteristic
256C2×D4—24no—
257C2×D4—28no—
258C2×D4—44no—
259C2×D4—42no—
260C2×D4—44no—
261C2×D4—42no—
262C2×D4—44no—
263C2×D4—42no—
264C2×D4—41no—
265C2×D4—42no—
266C2×D4—41no—
267C22×C4—22no—
268C22×C4—21no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—24no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—42no—
278C22×C4—44no—
279C22×C4—44no—
280C22×C4—41no—
281C4⋊C4—48no—
282C4⋊C4—82no—
283C22⋊C4—44no—
284C22⋊C4—48no—
285C22⋊C4—44no—
286C22⋊C4—44no—
287C22⋊C4—42no—
288C22⋊C4—42no—
289C22⋊C4—42no—
290C22⋊C4—42no—
291C22⋊C4—42no—
292C22⋊C4—44no—
293C22⋊C4—42no—
294C22⋊C4—44no—
295C22⋊C4—84no—
296C13#1033811yescharacteristic, direct product factor, Sylow
297C23—24no—
298C23—24no—
299C23—24no—
300C23—22no—
301C23—24no—
302C23—24no—
303C23—22no—
304C23—41no—
305C23—42no—
306C23—42no—
307C23—41no—
308C23—42no—
309C23—42no—
310C23—42no—
311C23—42no—
312C23—41no—
313C23—44no—
314C23—41no—
315C23—44no—
316C23—82no—
317C23—88no—
318C23—88no—
319C23C13×#12011yescharacteristic
320C23C13×#12012yes—
321C23C13×#12111yescharacteristic
322C23C13×#12112yes—
323C23C13×#12711yescharacteristic
324D4—48no—
325D4—44no—
326D4—44no—
327C2×C4—24no—
328C2×C4—22no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—44no—
333C2×C4—44no—
334C2×C4—44no—
335C2×C4—44no—
336C2×C4—44no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—44no—
341C2×C4—44no—
342C2×C4—44no—
343C2×C4—82no—
344C2×C4—82no—
345C2×C4—81no—
346C2×C4—82no—
347C22—22no—
348C22—22no—
349C22—22no—
350C22—21no—
351C22—22no—
352C22—21no—
353C22—22no—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—48no—
358C22—44no—
359C22—48no—
360C22—42no—
361C22—84no—
362C22—82no—
363C22—84no—
364C22—82no—
365C22—82no—
366C22—82no—
367C22—82no—
368C22C13×#39211yescharacteristic
369C22C13×B(4,𝔽2)12yes—
370C22C13×#45814yes—
371C4—42no—
372C4—84no—
373C4—82no—
374C4—82no—
375C4—82no—
376C4—161no—
377C2—24no—
378C2—22no—
379C2—41no—
380C2—41no—
381C2—42no—
382C2—82no—
383C2C13×#202111yescharacteristic
384C2C13×#202212yes—
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC25C23×C13
prime radicalC23×D4×C13C22
LCSG ▷ C25 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C25×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2483C2semidirect
3. C13×#1819C2semidirect
5. C13×#1304C2semidirect
53. #10338C13direct (N × H)
105. #2483C2×C13semidirect
107. #1819C2×C13semidirect
109. #1304C2×C13semidirect
296. C13#10338direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#24832
C13×#24052
C13×#18192
C13×#17812
C13×#13042
#1033813