Finite Group Databasebeta

← C13×#9966 #15696305

Subgroups — C13×#9966 #15696305

Order 3328.

1020 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 1020 conjugacy classes of subgroups — too many to draw. Only its 138 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×#450C212yesmaximal
2C13×#2659C211yesmaximal, characteristic, complemented
3C2×C13×#328C212yesmaximal, complemented
4C13×#1438C211yesmaximal, characteristic
5C13×#1280C211yesmaximal, characteristic, complemented
6C23×D4×C13C2211yescharacteristic
7C22×C13×SD16—22no—
8C2×C13×C22⋊Q8C2212yes—
9C22×C13×C22⋊C4—22no—
10C13×#450—24no—
11C13×#450—24no—
12C2×C13×#102—22no—
13C2×C13×C22⋊C8C2212yes—
14C13×#398—22no—
15C13×#395—22no—
16C13×#380—22no—
17C2×C13×#95C2211yescharacteristic
18C2×C13×#95C2211yescharacteristic
19C13×#328—24no—
20C25×C13—21no—
21C22×Q8×C13D412yes—
22C22×D4×C13—22no—
23C22×D4×C13—22no—
24C22×D4×C13—21no—
25C22×D4×C13—44no—
26C22×D4×C13D412yes—
27C23×C4×C13—21no—
28C23×C4×C13D412yes—
29C23×C4×C13C2311yescharacteristic
30C2×C13×SD16—28no—
31C2×C13×SD16—48no—
32C22×C8×C13—22no—
33C13×C22⋊Q8—22no—
34C13×C22⋊Q8—22no—
35C13×C22⋊Q8—22no—
36C13×C22⋊Q8—22no—
37C2×C13×C4⋊C4—22no—
38C2×C13×C4⋊C4—22no—
39C2×C13×C4⋊C4—22no—
40C2×C13×C4⋊C4D412yes—
41C2×C13×C22⋊C4—22no—
42C2×C13×C22⋊C4—44no—
43C2×C13×C22⋊C4—44no—
44C2×C13×C22⋊C4—44no—
45C13×#102—28no—
46C13×C22⋊C8—22no—
47C13×C22⋊C8D414yes—
48C13×#95—24no—
49C13×#95—22no—
50C13×#95—22no—
51#9966C1311yesmaximal, characteristic, direct product factor, Sylow
52C24×C13—24no—
53C24×C13—22no—
54C24×C13—42no—
55C24×C13—42no—
56C24×C13—42no—
57C24×C13—41no—
58C24×C13—41no—
59C24×C13—42no—
60C24×C13—42no—
61C24×C13C2×D411yescharacteristic
62C2×Q8×C13—22no—
63C2×Q8×C13—22no—
64C2×Q8×C13—44no—
65C2×D4×C13—28no—
66C2×D4×C13—24no—
67C2×D4×C13—44no—
68C2×D4×C13—44no—
69C2×D4×C13—48no—
70C2×D4×C13—44no—
71C2×D4×C13—42no—
72C22×C4×C13—22no—
73C22×C4×C13—22no—
74C22×C4×C13—22no—
75C22×C4×C13—22no—
76C22×C4×C13—22no—
77C22×C4×C13—42no—
78C22×C4×C13—42no—
79C22×C4×C13—42no—
80C22×C4×C13—42no—
81C22×C4×C13—41no—
82C22×C4×C13—41no—
83C22×C4×C13—42no—
84C22×C4×C13SD1614yescomplemented
85C22×C4×C13C2×D412yes—
86C22×C4×C13C2×D411yescharacteristic
87C22×C4×C13C2×D412yes—
88C22×C4×C13#4111yescharacteristic
89C13×SD16—416no—
90C2×C8×C13—24no—
91C2×C8×C13—44no—
92C13×C4⋊C4—22no—
93C13×C4⋊C4—22no—
94C13×C4⋊C4—42no—
95C13×C4⋊C4—42no—
96C13×C4⋊C4—82no—
97C13×C4⋊C4—82no—
98C13×C22⋊C4—416no—
99C13×C22⋊C4—42no—
100C13×C22⋊C4—42no—
101C2×#450C2×C1312yes—
102#2659C2×C1311yescharacteristic, complemented
103C2×#328C2×C1312yescomplemented
104#1438C2×C1311yescharacteristic
105#1280C2×C1311yescharacteristic, complemented
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—22no—
109C23×C13—24no—
110C23×C13—44no—
111C23×C13—44no—
112C23×C13—42no—
113C23×C13—44no—
114C23×C13—44no—
115C23×C13—44no—
116C23×C13—44no—
117C23×C13—42no—
118C23×C13—44no—
119C23×C13—44no—
120C23×C13—82no—
121C23×C13—82no—
122C23×C13—82no—
123C23×C13—82no—
124C23×C13—82no—
125C23×C13—82no—
126C23×C13—81no—
127C23×C13—81no—
128C23×C13—81no—
129C23×C13—81no—
130C23×C13#12011yescharacteristic
131C23×C13#12111yescharacteristic
132C23×C13#12711yescharacteristic
133C23×C13C2×SD1612yes—
134C23×C13#13712yes—
135Q8×C13—44no—
136Q8×C13—82no—
137D4×C13—28no—
138D4×C13—44no—
139D4×C13—48no—
140C2×C4×C13—24no—
141C2×C4×C13—24no—
142C2×C4×C13—41no—
143C2×C4×C13—42no—
144C2×C4×C13—41no—
145C2×C4×C13—42no—
146C2×C4×C13—42no—
147C2×C4×C13—44no—
148C2×C4×C13—44no—
149C2×C4×C13—42no—
150C2×C4×C13—42no—
151C2×C4×C13—42no—
152C2×C4×C13—42no—
153C2×C4×C13—42no—
154C2×C4×C13—44no—
155C2×C4×C13—82no—
156C2×C4×C13—82no—
157C2×C4×C13—81no—
158C2×C4×C13—81no—
159C2×C4×C13#12012yes—
160C2×C4×C13#12112yes—
161C8×C13—44no—
162C23×D4C22×C1311yescharacteristic
163C22×SD16—22no—
164C2×C22⋊Q8C22×C1312yes—
165C22×C22⋊C4—22no—
166#450—24no—
167#450—24no—
168C2×#102—22no—
169C2×C22⋊C8C22×C1312yes—
170#398—22no—
171#395—22no—
172#380—22no—
173C2×#95C22×C1311yescharacteristic
174C2×#95C22×C1311yescharacteristic
175#328—24no—
176C22×C13—22no—
177C22×C13—22no—
178C22×C13—22no—
179C22×C13—22no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—48no—
185C22×C13—44no—
186C22×C13—84no—
187C22×C13—84no—
188C22×C13—84no—
189C22×C13—84no—
190C22×C13—84no—
191C22×C13—82no—
192C22×C13—82no—
193C22×C13#39211yescharacteristic
194C22×C13#44812yes—
195C22×C13#45311yescharacteristic
196C22×C13#45411yescharacteristic
197C22×C13B(4,𝔽2)12yes—
198C22×C13#46112yes—
199C22×C13#49211yescharacteristic
200C22×C13#49711yescharacteristic
201C4×C13—22no—
202C4×C13—22no—
203C4×C13—44no—
204C4×C13—82no—
205C4×C13—82no—
206C4×C13—82no—
207C25—21no—
208C22×Q8D4×C1312yes—
209C22×D4—22no—
210C22×D4—22no—
211C22×D4—21no—
212C22×D4—44no—
213C22×D4D4×C1312yes—
214C23×C4—21no—
215C23×C4D4×C1312yes—
216C23×C4C23×C1311yescharacteristic
217C2×SD16—28no—
218C2×SD16—48no—
219C22×C8—22no—
220C22⋊Q8—22no—
221C22⋊Q8—22no—
222C22⋊Q8—22no—
223C22⋊Q8—22no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4D4×C1312yes—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—44no—
230C2×C22⋊C4—44no—
231C2×C22⋊C4—44no—
232#102—28no—
233C22⋊C8—22no—
234C22⋊C8D4×C1314yes—
235#95—24no—
236#95—22no—
237#95—22no—
238C2×C13—21no—
239C2×C13—22no—
240C2×C13—21no—
241C2×C13—84no—
242C2×C13#159612yes—
243C2×C13#159912yes—
244C2×C13#200611yescharacteristic
245C2×C13#201311yescharacteristic
246C2×C13#202111yescharacteristic
247C24—24no—
248C24—22no—
249C24—42no—
250C24—42no—
251C24—42no—
252C24—41no—
253C24—41no—
254C24—42no—
255C24—42no—
256C24C2×D4×C1311yescharacteristic
257C2×Q8—22no—
258C2×Q8—22no—
259C2×Q8—44no—
260C2×D4—28no—
261C2×D4—24no—
262C2×D4—44no—
263C2×D4—44no—
264C2×D4—48no—
265C2×D4—44no—
266C2×D4—42no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—42no—
279C22×C4C13×SD1614yescomplemented
280C22×C4C2×D4×C1312yes—
281C22×C4C2×D4×C1311yescharacteristic
282C22×C4C2×D4×C1312yes—
283C22×C4C13×#4111yescharacteristic
284SD16—416no—
285C2×C8—24no—
286C2×C8—44no—
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C4⋊C4—82no—
292C4⋊C4—82no—
293C22⋊C4—416no—
294C22⋊C4—42no—
295C22⋊C4—42no—
296C13#996611yescharacteristic, direct product factor, Sylow
297C23—21no—
298C23—21no—
299C23—22no—
300C23—24no—
301C23—44no—
302C23—44no—
303C23—42no—
304C23—44no—
305C23—44no—
306C23—44no—
307C23—44no—
308C23—42no—
309C23—44no—
310C23—44no—
311C23—82no—
312C23—82no—
313C23—82no—
314C23—82no—
315C23—82no—
316C23—82no—
317C23—81no—
318C23—81no—
319C23—81no—
320C23—81no—
321C23C13×#12011yescharacteristic
322C23C13×#12111yescharacteristic
323C23C13×#12711yescharacteristic
324C23C2×C13×SD1612yes—
325C23C13×#13712yes—
326Q8—44no—
327Q8—82no—
328D4—28no—
329D4—44no—
330D4—48no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—44no—
339C2×C4—44no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—44no—
346C2×C4—82no—
347C2×C4—81no—
348C2×C4—82no—
349C2×C4—81no—
350C2×C4C13×#12012yes—
351C2×C4C13×#12112yes—
352C8—44no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—22no—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—48no—
362C22—44no—
363C22—84no—
364C22—84no—
365C22—84no—
366C22—82no—
367C22—82no—
368C22—84no—
369C22—84no—
370C22C13×#39211yescharacteristic
371C22C13×#44812yes—
372C22C13×#45311yescharacteristic
373C22C13×#45411yescharacteristic
374C22C13×B(4,𝔽2)12yes—
375C22C13×#46112yes—
376C22C13×#49211yescharacteristic
377C22C13×#49711yescharacteristic
378C4—22no—
379C4—22no—
380C4—44no—
381C4—82no—
382C4—82no—
383C4—82no—
384C2—21no—
385C2—22no—
386C2—21no—
387C2—84no—
388C2C13×#159612yes—
389C2C13×#159912yes—
390C2C13×#200611yescharacteristic
391C2C13×#201311yescharacteristic
392C2C13×#202111yescharacteristic
subgroupG/H
center, socleC23×C13#120
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC23×D4×C13C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2659C2semidirect
3. C2×C13×#328C2semidirect
5. C13×#1280C2semidirect
51. #9966C13direct (N × H)
84. C22×C4×C13SD16semidirect
102. #2659C2×C13semidirect
103. C2×#328C2×C13semidirect
105. #1280C2×C13semidirect
279. C22×C4C13×SD16semidirect
296. C13#9966direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#4502
C13×#26592
C2×C13×#3282
C13×#14382
C13×#12802
#996613