Finite Group Databasebeta

← C13×#10337 #15696676

Subgroups — C13×#10337 #15696676

Order 3328.

1274 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 1274 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×#2405C212yesmaximal, complemented
2C13×#2403C211yesmaximal, characteristic
3C13×#1819C211yesmaximal, characteristic, complemented
4C13×#1781C212yesmaximal, complemented
5C13×#1304C211yesmaximal, characteristic, complemented
6C23×D4×C13C2212yes—
7C2×C13×#123—22no—
8C2×C13×#120—22no—
9C22×C13×C22⋊C4C2211yescharacteristic
10C2×C13×#99—24no—
11C13×#394—24no—
12C13×#392—22no—
13C13×#386—22no—
14C13×#386—22no—
15C13×#385—22no—
16C13×#379—22no—
17C13×#379C2211yescharacteristic
18C13×#379C2211yescharacteristic
19C13×#379C2212yes—
20C13×#342—22no—
21C25×C13D412yes—
22C25×C13C2311yescharacteristic
23C22×D4×C13—22no—
24C22×D4×C13—22no—
25C22×D4×C13—22no—
26C22×D4×C13—22no—
27C22×D4×C13—22no—
28C22×D4×C13—22no—
29C22×D4×C13—22no—
30C22×D4×C13—48no—
31C23×C4×C13D412yes—
32C23×C4×C13D412yescomplemented
33C13×#123—48no—
34C13×#120—48no—
35C2×C13×C4⋊C4—24no—
36C2×C13×C22⋊C4—24no—
37C2×C13×C22⋊C4—24no—
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—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—22no—
46C2×C13×C22⋊C4—21no—
47C2×C13×C22⋊C4—24no—
48C2×C13×C22⋊C4D412yes—
49C2×C13×C22⋊C4D414yescomplemented
50C13×#99—48no—
51C13×#95—24no—
52C13×#95—22no—
53#10337C1311yesmaximal, characteristic, direct product factor, Sylow
54C24×C13—22no—
55C24×C13—22no—
56C24×C13—22no—
57C24×C13—44no—
58C24×C13—44no—
59C24×C13—42no—
60C24×C13—44no—
61C24×C13—44no—
62C24×C13C2×D412yes—
63C24×C13C2×D411yescharacteristic
64C24×C13C2×D411yescharacteristic
65C24×C13C2×D412yes—
66C24×C13#4111yescharacteristic
67C2×D4×C13—28no—
68C2×D4×C13—28no—
69C2×D4×C13—28no—
70C2×D4×C13—44no—
71C2×D4×C13—44no—
72C2×D4×C13—44no—
73C2×D4×C13—44no—
74C2×D4×C13—44no—
75C2×D4×C13—44no—
76C2×D4×C13—44no—
77C2×D4×C13—44no—
78C2×D4×C13—44no—
79C2×D4×C13—42no—
80C2×D4×C13—42no—
81C2×D4×C13—42no—
82C2×D4×C13—42no—
83C2×D4×C13—48no—
84C2×D4×C13—82no—
85C22×C4×C13—22no—
86C22×C4×C13—22no—
87C22×C4×C13—22no—
88C22×C4×C13—22no—
89C22×C4×C13—22no—
90C22×C4×C13—24no—
91C22×C4×C13—22no—
92C22×C4×C13—22no—
93C22×C4×C13—44no—
94C22×C4×C13—44no—
95C22×C4×C13—41no—
96C13×C4⋊C4—48no—
97C13×C22⋊C4—48no—
98C13×C22⋊C4—44no—
99C13×C22⋊C4—44no—
100C13×C22⋊C4—44no—
101C13×C22⋊C4—48no—
102C13×C22⋊C4—41no—
103C13×C22⋊C4—42no—
104C13×C22⋊C4—41no—
105C13×C22⋊C4—44no—
106C13×C22⋊C4—42no—
107C13×C22⋊C4—44no—
108C13×C22⋊C4—42no—
109C13×C22⋊C4—84no—
110#2405C2×C1312yescomplemented
111#2403C2×C1311yescharacteristic
112#1819C2×C1311yescharacteristic, complemented
113#1781C2×C1312yescomplemented
114#1304C2×C1311yescharacteristic, complemented
115C23×C13—24no—
116C23×C13—24no—
117C23×C13—24no—
118C23×C13—24no—
119C23×C13—22no—
120C23×C13—24no—
121C23×C13—24no—
122C23×C13—24no—
123C23×C13—42no—
124C23×C13—41no—
125C23×C13—42no—
126C23×C13—42no—
127C23×C13—42no—
128C23×C13—42no—
129C23×C13—41no—
130C23×C13—44no—
131C23×C13—42no—
132C23×C13—42no—
133C23×C13—42no—
134C23×C13—44no—
135C23×C13—42no—
136C23×C13—44no—
137C23×C13—44no—
138C23×C13—82no—
139C23×C13—82no—
140C23×C13—88no—
141C23×C13—816no—
142C23×C13#12012yes—
143C23×C13#12011yescharacteristic
144C23×C13#12112yes—
145C23×C13#12111yescharacteristic
146C23×C13#12711yescharacteristic
147D4×C13—48no—
148D4×C13—48no—
149D4×C13—48no—
150D4×C13—48no—
151D4×C13—88no—
152C2×C4×C13—24no—
153C2×C4×C13—24no—
154C2×C4×C13—24no—
155C2×C4×C13—42no—
156C2×C4×C13—42no—
157C2×C4×C13—42no—
158C2×C4×C13—42no—
159C2×C4×C13—44no—
160C2×C4×C13—44no—
161C2×C4×C13—44no—
162C2×C4×C13—44no—
163C2×C4×C13—42no—
164C2×C4×C13—44no—
165C2×C4×C13—44no—
166C2×C4×C13—42no—
167C2×C4×C13—82no—
168C2×C4×C13—82no—
169C2×C4×C13—81no—
170C23×D4C22×C1312yes—
171C2×#123—22no—
172C2×#120—22no—
173C22×C22⋊C4C22×C1311yescharacteristic
174C2×#99—24no—
175#394—24no—
176#392—22no—
177#386—22no—
178#386—22no—
179#385—22no—
180#379—22no—
181#379C22×C1311yescharacteristic
182#379C22×C1311yescharacteristic
183#379C22×C1312yes—
184#342—22no—
185C22×C13—22no—
186C22×C13—22no—
187C22×C13—22no—
188C22×C13—22no—
189C22×C13—22no—
190C22×C13—22no—
191C22×C13—22no—
192C22×C13—21no—
193C22×C13—22no—
194C22×C13—21no—
195C22×C13—44no—
196C22×C13—48no—
197C22×C13—48no—
198C22×C13—48no—
199C22×C13—44no—
200C22×C13—82no—
201C22×C13—84no—
202C22×C13—84no—
203C22×C13—84no—
204C22×C13—82no—
205C22×C13—84no—
206C22×C13—84no—
207C22×C13—82no—
208C22×C13—82no—
209C22×C13#39211yescharacteristic
210C22×C13B(4,𝔽2)14yes—
211C22×C13#45812yes—
212C4×C13—44no—
213C4×C13—84no—
214C4×C13—82no—
215C4×C13—82no—
216C4×C13—161no—
217C25D4×C1312yes—
218C25C23×C1311yescharacteristic
219C22×D4—22no—
220C22×D4—22no—
221C22×D4—22no—
222C22×D4—22no—
223C22×D4—22no—
224C22×D4—22no—
225C22×D4—22no—
226C22×D4—48no—
227C23×C4D4×C1312yes—
228C23×C4D4×C1312yescomplemented
229#123—48no—
230#120—48no—
231C2×C4⋊C4—24no—
232C2×C22⋊C4—24no—
233C2×C22⋊C4—24no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—22no—
236C2×C22⋊C4—22no—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—22no—
239C2×C22⋊C4—22no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—22no—
243C2×C22⋊C4—24no—
244C2×C22⋊C4D4×C1312yes—
245C2×C22⋊C4D4×C1314yescomplemented
246#99—48no—
247#95—24no—
248#95—22no—
249C2×C13—22no—
250C2×C13—24no—
251C2×C13—41no—
252C2×C13—41no—
253C2×C13—42no—
254C2×C13—84no—
255C2×C13#202112yes—
256C2×C13#202211yescharacteristic
257C24—22no—
258C24—22no—
259C24—22no—
260C24—44no—
261C24—44no—
262C24—42no—
263C24—44no—
264C24—44no—
265C24C2×D4×C1312yes—
266C24C2×D4×C1311yescharacteristic
267C24C2×D4×C1311yescharacteristic
268C24C2×D4×C1312yes—
269C24C13×#4111yescharacteristic
270C2×D4—28no—
271C2×D4—28no—
272C2×D4—28no—
273C2×D4—44no—
274C2×D4—44no—
275C2×D4—44no—
276C2×D4—44no—
277C2×D4—44no—
278C2×D4—44no—
279C2×D4—44no—
280C2×D4—44no—
281C2×D4—44no—
282C2×D4—42no—
283C2×D4—42no—
284C2×D4—42no—
285C2×D4—42no—
286C2×D4—48no—
287C2×D4—82no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—24no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—44no—
297C22×C4—44no—
298C22×C4—41no—
299C4⋊C4—48no—
300C22⋊C4—48no—
301C22⋊C4—44no—
302C22⋊C4—44no—
303C22⋊C4—48no—
304C22⋊C4—44no—
305C22⋊C4—41no—
306C22⋊C4—42no—
307C22⋊C4—41no—
308C22⋊C4—44no—
309C22⋊C4—42no—
310C22⋊C4—44no—
311C22⋊C4—42no—
312C22⋊C4—84no—
313C13#1033711yescharacteristic, direct product factor, Sylow
314C23—24no—
315C23—24no—
316C23—24no—
317C23—24no—
318C23—22no—
319C23—24no—
320C23—24no—
321C23—24no—
322C23—42no—
323C23—41no—
324C23—42no—
325C23—42no—
326C23—42no—
327C23—42no—
328C23—41no—
329C23—44no—
330C23—42no—
331C23—42no—
332C23—42no—
333C23—44no—
334C23—42no—
335C23—44no—
336C23—44no—
337C23—82no—
338C23—82no—
339C23—88no—
340C23—816no—
341C23C13×#12012yes—
342C23C13×#12011yescharacteristic
343C23C13×#12112yes—
344C23C13×#12111yescharacteristic
345C23C13×#12711yescharacteristic
346D4—48no—
347D4—48no—
348D4—48no—
349D4—48no—
350D4—88no—
351C2×C4—24no—
352C2×C4—24no—
353C2×C4—24no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—44no—
359C2×C4—44no—
360C2×C4—44no—
361C2×C4—44no—
362C2×C4—42no—
363C2×C4—44no—
364C2×C4—44no—
365C2×C4—42no—
366C2×C4—82no—
367C2×C4—82no—
368C2×C4—81no—
369C22—22no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—21no—
377C22—22no—
378C22—21no—
379C22—44no—
380C22—48no—
381C22—48no—
382C22—48no—
383C22—44no—
384C22—82no—
385C22—84no—
386C22—84no—
387C22—84no—
388C22—82no—
389C22—84no—
390C22—84no—
391C22—82no—
392C22—82no—
393C22C13×#39211yescharacteristic
394C22C13×B(4,𝔽2)14yes—
395C22C13×#45812yes—
396C4—44no—
397C4—84no—
398C4—82no—
399C4—82no—
400C4—161no—
401C2—22no—
402C2—24no—
403C2—41no—
404C2—42no—
405C2—41no—
406C2—84no—
407C2C13×#202112yes—
408C2C13×#202211yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC25C23×C13
prime radicalC13×#2403C2
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×#2405C2semidirect
3. C13×#1819C2semidirect
4. C13×#1781C2semidirect
5. C13×#1304C2semidirect
32. C23×C4×C13D4semidirect
49. C2×C13×C22⋊C4D4semidirect
53. #10337C13direct (N × H)
110. #2405C2×C13semidirect
112. #1819C2×C13semidirect
113. #1781C2×C13semidirect
114. #1304C2×C13semidirect
228. C23×C4D4×C13semidirect
245. C2×C22⋊C4D4×C13semidirect
313. C13#10337direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#24052
C13×#24032
C13×#18192
C13×#17812
C13×#13042
#1033713