Finite Group Databasebeta

← C13×#10324 #15696663

Subgroups — C13×#10324 #15696663

Order 3328.

910 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 910 conjugacy classes of subgroups — too many to draw. Only its 122 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×#3189C211yesmaximal, characteristic, complemented
2C13×#2848C212yesmaximal
3C13×#1779C211yesmaximal, characteristic
4C13×#1520C212yesmaximal, complemented
5C13×#1289C211yesmaximal, characteristic, complemented
6C24×C4×C13C2211yescharacteristic
7C2×C13×C22⋊Q8—22no—
8C2×C13×C22⋊Q8C2212yes—
9C13×#484—22no—
10C13×#467—22no—
11C13×#451—22no—
12C2×C13×C22⋊C8—22no—
13C2×C13×C22⋊C8C2211yescharacteristic
14C2×C13×C22⋊C8C2211yescharacteristic
15C13×#385—22no—
16C13×#385—24no—
17C13×#380—22no—
18C13×#380C2212yes—
19C13×#379—22no—
20C13×#328—24no—
21C25×C13D411yescharacteristic
22C22×Q8×C13D412yes—
23C23×C4×C13—22no—
24C23×C4×C13—21no—
25C23×C4×C13—22no—
26C23×C4×C13—21no—
27C23×C4×C13—44no—
28C23×C4×C13D411yescharacteristic
29C23×C4×C13C2311yescharacteristic
30C2×C13×Q16—22no—
31C22×C8×C13—21no—
32C22×C8×C13D412yes—
33C13×C22⋊Q8—22no—
34C13×C22⋊Q8—22no—
35C13×C22⋊Q8—22no—
36C13×C22⋊Q8—22no—
37C13×C22⋊Q8—48no—
38C2×C13×C4⋊C4—24no—
39C2×C13×C4⋊C4—22no—
40C2×C13×C4⋊C4—22no—
41C2×C13×C4⋊C4D412yes—
42C2×C13×C22⋊C4—24no—
43C2×C13×C22⋊C4—24no—
44C2×C13×C22⋊C4—22no—
45C2×C13×C22⋊C4—22no—
46C13×#107—22no—
47C13×#103—24no—
48C13×C22⋊C8—22no—
49C13×C22⋊C8—22no—
50C13×C22⋊C8—44no—
51C13×#95—24no—
52C13×#95D414yes—
53#10324C1311yesmaximal, characteristic, direct product factor, Sylow
54C24×C13—22no—
55C24×C13—21no—
56C24×C13—21no—
57C24×C13—22no—
58C24×C13—42no—
59C24×C13—42no—
60C24×C13Q1612yescomplemented
61C24×C13C2×D411yescharacteristic
62C2×Q8×C13—22no—
63C2×Q8×C13—22no—
64C2×Q8×C13—44no—
65C22×C4×C13—24no—
66C22×C4×C13—28no—
67C22×C4×C13—22no—
68C22×C4×C13—21no—
69C22×C4×C13—22no—
70C22×C4×C13—24no—
71C22×C4×C13—22no—
72C22×C4×C13—42no—
73C22×C4×C13—42no—
74C22×C4×C13—44no—
75C22×C4×C13—42no—
76C22×C4×C13—44no—
77C22×C4×C13—42no—
78C22×C4×C13—44no—
79C22×C4×C13—42no—
80C22×C4×C13—41no—
81C22×C4×C13—42no—
82C22×C4×C13—41no—
83C22×C4×C13C2×D412yes—
84C22×C4×C13C2×D411yescharacteristic
85C22×C4×C13C2×D412yes—
86C22×C4×C13#4111yescharacteristic
87C13×Q16—82no—
88C2×C8×C13—22no—
89C2×C8×C13—42no—
90C2×C8×C13—42no—
91C2×C8×C13—41no—
92C13×C4⋊C4—22no—
93C13×C4⋊C4—22no—
94C13×C4⋊C4—44no—
95C13×C4⋊C4—48no—
96C13×C4⋊C4—42no—
97C13×C4⋊C4—42no—
98C13×C22⋊C4—48no—
99C13×C22⋊C4—48no—
100C13×C22⋊C4—42no—
101C13×C22⋊C4—42no—
102C13×C22⋊C4—42no—
103C13×C22⋊C4—42no—
104#3189C2×C1311yescharacteristic, complemented
105#2848C2×C1312yes—
106#1779C2×C1311yescharacteristic
107#1520C2×C1312yescomplemented
108#1289C2×C1311yescharacteristic, complemented
109C23×C13—24no—
110C23×C13—24no—
111C23×C13—22no—
112C23×C13—22no—
113C23×C13—24no—
114C23×C13—22no—
115C23×C13—41no—
116C23×C13—44no—
117C23×C13—41no—
118C23×C13—42no—
119C23×C13—41no—
120C23×C13—42no—
121C23×C13—41no—
122C23×C13—44no—
123C23×C13—48no—
124C23×C13—41no—
125C23×C13—42no—
126C23×C13—41no—
127C23×C13#12012yes—
128C23×C13#12111yescharacteristic
129C23×C13C2×Q1611yescharacteristic
130C23×C13#13511yescharacteristic
131C23×C13#13712yes—
132Q8×C13—44no—
133Q8×C13—82no—
134C2×C4×C13—24no—
135C2×C4×C13—22no—
136C2×C4×C13—24no—
137C2×C4×C13—22no—
138C2×C4×C13—42no—
139C2×C4×C13—41no—
140C2×C4×C13—44no—
141C2×C4×C13—48no—
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—44no—
153C2×C4×C13#12011yescharacteristic
154C2×C4×C13#12112yes—
155C2×C4×C13#12711yescharacteristic
156C8×C13—42no—
157C8×C13—81no—
158C24×C4C22×C1311yescharacteristic
159C2×C22⋊Q8—22no—
160C2×C22⋊Q8C22×C1312yes—
161#484—22no—
162#467—22no—
163#451—22no—
164C2×C22⋊C8—22no—
165C2×C22⋊C8C22×C1311yescharacteristic
166C2×C22⋊C8C22×C1311yescharacteristic
167#385—22no—
168#385—24no—
169#380—22no—
170#380C22×C1312yes—
171#379—22no—
172#328—24no—
173C22×C13—22no—
174C22×C13—21no—
175C22×C13—22no—
176C22×C13—21no—
177C22×C13—28no—
178C22×C13—24no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—42no—
182C22×C13—44no—
183C22×C13—44no—
184C22×C13—44no—
185C22×C13—42no—
186C22×C13—42no—
187C22×C13—42no—
188C22×C13—42no—
189C22×C13—42no—
190C22×C13—42no—
191C22×C13#39211yescharacteristic
192C22×C13#45112yes—
193C22×C13#45212yes—
194C22×C13#46711yescharacteristic
195C22×C13#47011yescharacteristic
196C4×C13—21no—
197C4×C13—22no—
198C4×C13—42no—
199C4×C13—84no—
200C4×C13—82no—
201C4×C13—82no—
202C4×C13B(4,𝔽2)12yes—
203C25D4×C1311yescharacteristic
204C22×Q8D4×C1312yes—
205C23×C4—22no—
206C23×C4—21no—
207C23×C4—22no—
208C23×C4—21no—
209C23×C4—44no—
210C23×C4D4×C1311yescharacteristic
211C23×C4C23×C1311yescharacteristic
212C2×Q16—22no—
213C22×C8—21no—
214C22×C8D4×C1312yes—
215C22⋊Q8—22no—
216C22⋊Q8—22no—
217C22⋊Q8—22no—
218C22⋊Q8—22no—
219C22⋊Q8—48no—
220C2×C4⋊C4—24no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4D4×C1312yes—
224C2×C22⋊C4—24no—
225C2×C22⋊C4—24no—
226C2×C22⋊C4—22no—
227C2×C22⋊C4—22no—
228#107—22no—
229#103—24no—
230C22⋊C8—22no—
231C22⋊C8—22no—
232C22⋊C8—44no—
233#95—24no—
234#95D4×C1314yes—
235C2×C13—22no—
236C2×C13—22no—
237C2×C13—21no—
238C2×C13—21no—
239C2×C13—44no—
240C2×C13#200111yescharacteristic
241C2×C13#201011yescharacteristic
242C2×C13#202111yescharacteristic
243C24—22no—
244C24—21no—
245C24—21no—
246C24—22no—
247C24—42no—
248C24—42no—
249C24C13×Q1612yescomplemented
250C24C2×D4×C1311yescharacteristic
251C2×Q8—22no—
252C2×Q8—22no—
253C2×Q8—44no—
254C22×C4—24no—
255C22×C4—28no—
256C22×C4—22no—
257C22×C4—21no—
258C22×C4—22no—
259C22×C4—24no—
260C22×C4—22no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—44no—
264C22×C4—42no—
265C22×C4—44no—
266C22×C4—42no—
267C22×C4—44no—
268C22×C4—42no—
269C22×C4—41no—
270C22×C4—42no—
271C22×C4—41no—
272C22×C4C2×D4×C1312yes—
273C22×C4C2×D4×C1311yescharacteristic
274C22×C4C2×D4×C1312yes—
275C22×C4C13×#4111yescharacteristic
276Q16—82no—
277C2×C8—22no—
278C2×C8—42no—
279C2×C8—42no—
280C2×C8—41no—
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—44no—
284C4⋊C4—48no—
285C4⋊C4—42no—
286C4⋊C4—42no—
287C22⋊C4—48no—
288C22⋊C4—48no—
289C22⋊C4—42no—
290C22⋊C4—42no—
291C22⋊C4—42no—
292C22⋊C4—42no—
293C13#1032411yescharacteristic, direct product factor, Sylow
294C23—24no—
295C23—24no—
296C23—22no—
297C23—22no—
298C23—24no—
299C23—22no—
300C23—41no—
301C23—44no—
302C23—41no—
303C23—42no—
304C23—41no—
305C23—42no—
306C23—41no—
307C23—44no—
308C23—48no—
309C23—41no—
310C23—42no—
311C23—41no—
312C23C13×#12012yes—
313C23C13×#12111yescharacteristic
314C23C2×C13×Q1611yescharacteristic
315C23C13×#13511yescharacteristic
316C23C13×#13712yes—
317Q8—44no—
318Q8—82no—
319C2×C4—24no—
320C2×C4—22no—
321C2×C4—24no—
322C2×C4—22no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—44no—
326C2×C4—48no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—44no—
331C2×C4—44no—
332C2×C4—44no—
333C2×C4—44no—
334C2×C4—44no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—44no—
338C2×C4C13×#12011yescharacteristic
339C2×C4C13×#12112yes—
340C2×C4C13×#12711yescharacteristic
341C8—42no—
342C8—81no—
343C22—22no—
344C22—21no—
345C22—22no—
346C22—21no—
347C22—28no—
348C22—24no—
349C22—41no—
350C22—41no—
351C22—42no—
352C22—44no—
353C22—44no—
354C22—44no—
355C22—42no—
356C22—42no—
357C22—42no—
358C22—42no—
359C22—42no—
360C22—42no—
361C22C13×#39211yescharacteristic
362C22C13×#45112yes—
363C22C13×#45212yes—
364C22C13×#46711yescharacteristic
365C22C13×#47011yescharacteristic
366C4—21no—
367C4—22no—
368C4—42no—
369C4—84no—
370C4—82no—
371C4—82no—
372C4C13×B(4,𝔽2)12yes—
373C2—22no—
374C2—22no—
375C2—21no—
376C2—21no—
377C2—44no—
378C2C13×#200111yescharacteristic
379C2C13×#201011yescharacteristic
380C2C13×#202111yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC25×C13D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3189C2semidirect
4. C13×#1520C2semidirect
5. C13×#1289C2semidirect
53. #10324C13direct (N × H)
60. C24×C13Q16semidirect
104. #3189C2×C13semidirect
107. #1520C2×C13semidirect
108. #1289C2×C13semidirect
249. C24C13×Q16semidirect
293. C13#10324direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31892
C13×#28482
C13×#17792
C13×#15202
C13×#12892
#1032413