Finite Group Databasebeta

← C13×#9496 #15695835

Subgroups — C13×#9496 #15695835

Order 3328.

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

normal subgroups only

This group has 900 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×#2405C211yesmaximal, characteristic
2C13×#2312C211yesmaximal, characteristic, complemented
3C13×#1819C211yesmaximal, characteristic, complemented
4C13×#1781C212yesmaximal
5C13×#1304C212yesmaximal, complemented
6C23×D4×C13C2211yescharacteristic
7C2×C13×#123—21no—
8C22×C13×C22⋊C4C2211yescharacteristic
9C2×C13×#99—24no—
10C13×#394—22no—
11C13×#388—24no—
12C13×#386—21no—
13C13×#385C412yescomplemented
14C13×#380—21no—
15C13×#379C412yescomplemented
16C13×#379C2212yes—
17C13×#379C2211yescharacteristic
18C13×#379C2212yes—
19C4×C13×C22⋊C4—21no—
20C13×#342—22no—
21C25×C13C2×C411yescharacteristic
22C25×C13C2311yescharacteristic
23C22×D4×C13—21no—
24C22×D4×C13—22no—
25C22×D4×C13—21no—
26C22×D4×C13—22no—
27C22×D4×C13—44no—
28C23×C4×C13C2×C411yescharacteristic
29C23×C4×C13D411yescharacteristic
30C23×C4×C13D411yescharacteristic
31C13×#123—44no—
32C2×C13×C4⋊C4—22no—
33C2×C13×C4⋊C4—22no—
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4—22no—
40C2×C13×C22⋊C4—22no—
41C2×C13×C22⋊C4—22no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—22no—
44C2×C13×C22⋊C4—22no—
45C2×C13×C22⋊C4C2×C412yes—
46C2×C13×C22⋊C4C2×C412yes—
47C2×C13×C22⋊C4D412yes—
48C2×C13×C22⋊C4D414yes—
49C2×C42×C13—22no—
50C13×#99—48no—
51C13×#95—22no—
52C13×#95—22no—
53C13×#95—22no—
54#9496C1311yesmaximal, characteristic, direct product factor, Sylow
55C24×C13—21no—
56C24×C13—22no—
57C24×C13—42no—
58C24×C13—42no—
59C24×C13—42no—
60C24×C13—42no—
61C24×C13—81no—
62C24×C13—81no—
63C24×C13C22×C411yescharacteristic
64C24×C13C2×D411yescharacteristic
65C24×C13C2×D411yescharacteristic
66C24×C13C2×D412yes—
67C24×C13#4112yes—
68C2×D4×C13—28no—
69C2×D4×C13—24no—
70C2×D4×C13—42no—
71C2×D4×C13—44no—
72C2×D4×C13—42no—
73C2×D4×C13—44no—
74C2×D4×C13—42no—
75C2×D4×C13—44no—
76C2×D4×C13—41no—
77C2×D4×C13—42no—
78C2×D4×C13—41no—
79C22×C4×C13—21no—
80C22×C4×C13—22no—
81C22×C4×C13—21no—
82C22×C4×C13—21no—
83C22×C4×C13—21no—
84C22×C4×C13—21no—
85C22×C4×C13—22no—
86C22×C4×C13—24no—
87C22×C4×C13—42no—
88C22×C4×C13—42no—
89C22×C4×C13—42no—
90C22×C4×C13—81no—
91C22×C4×C13C22⋊C412yes—
92C22×C4×C13C22⋊C412yes—
93C13×C4⋊C4—44no—
94C13×C4⋊C4—82no—
95C13×C22⋊C4—24no—
96C13×C22⋊C4—24no—
97C13×C22⋊C4—44no—
98C13×C22⋊C4—44no—
99C13×C22⋊C4—42no—
100C13×C22⋊C4—44no—
101C13×C22⋊C4—42no—
102C13×C22⋊C4—44no—
103C13×C22⋊C4—44no—
104C13×C22⋊C4—82no—
105C13×C22⋊C4—81no—
106C13×C22⋊C4—82no—
107C13×C22⋊C4—82no—
108C42×C13—82no—
109#2405C2×C1311yescharacteristic
110#2312C2×C1311yescharacteristic, complemented
111#1819C2×C1311yescharacteristic, complemented
112#1781C2×C1312yes—
113#1304C2×C1312yescomplemented
114C23×C13—22no—
115C23×C13—22no—
116C23×C13—22no—
117C23×C13—22no—
118C23×C13—24no—
119C23×C13—22no—
120C23×C13—24no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13—42no—
125C23×C13—41no—
126C23×C13—42no—
127C23×C13—41no—
128C23×C13—42no—
129C23×C13—42no—
130C23×C13—42no—
131C23×C13—42no—
132C23×C13—41no—
133C23×C13—42no—
134C23×C13—41no—
135C23×C13—42no—
136C23×C13—82no—
137C23×C13—82no—
138C23×C13—88no—
139C23×C13—88no—
140C23×C13C2×C22⋊C411yescharacteristic
141C23×C13C4×D412yes—
142C23×C13#12011yescharacteristic
143C23×C13#12112yes—
144C23×C13#12311yescharacteristic
145D4×C13—48no—
146D4×C13—44no—
147D4×C13—44no—
148C2×C4×C13—22no—
149C2×C4×C13—24no—
150C2×C4×C13—22no—
151C2×C4×C13—22no—
152C2×C4×C13—42no—
153C2×C4×C13—41no—
154C2×C4×C13—42no—
155C2×C4×C13—41no—
156C2×C4×C13—42no—
157C2×C4×C13—42no—
158C2×C4×C13—42no—
159C2×C4×C13—42no—
160C2×C4×C13—44no—
161C2×C4×C13—42no—
162C2×C4×C13—44no—
163C2×C4×C13—42no—
164C2×C4×C13—44no—
165C2×C4×C13—81no—
166C2×C4×C13—81no—
167C2×C4×C13—82no—
168C2×C4×C13—82no—
169C2×C4×C13—82no—
170C23×D4C22×C1311yescharacteristic
171C2×#123—21no—
172C22×C22⋊C4C22×C1311yescharacteristic
173C2×#99—24no—
174#394—22no—
175#388—24no—
176#386—21no—
177#385C4×C1312yescomplemented
178#380—21no—
179#379C4×C1312yescomplemented
180#379C22×C1312yes—
181#379C22×C1311yescharacteristic
182#379C22×C1312yes—
183C4×C22⋊C4—21no—
184#342—22no—
185C22×C13—21no—
186C22×C13—21no—
187C22×C13—21no—
188C22×C13—21no—
189C22×C13—22no—
190C22×C13—22no—
191C22×C13—21no—
192C22×C13—22no—
193C22×C13—22no—
194C22×C13—21no—
195C22×C13—22no—
196C22×C13—21no—
197C22×C13—22no—
198C22×C13—44no—
199C22×C13—44no—
200C22×C13—44no—
201C22×C13—42no—
202C22×C13—84no—
203C22×C13—82no—
204C22×C13—82no—
205C22×C13—84no—
206C22×C13—84no—
207C22×C13—84no—
208C22×C13—81no—
209C22×C13—81no—
210C22×C13#38611yescharacteristic
211C22×C13#41012yes—
212C22×C13B(4,𝔽2)12yes—
213C4×C13—42no—
214C4×C13—42no—
215C4×C13—42no—
216C4×C13—84no—
217C4×C13—82no—
218C4×C13—162no—
219C25C2×C4×C1311yescharacteristic
220C25C23×C1311yescharacteristic
221C22×D4—21no—
222C22×D4—22no—
223C22×D4—21no—
224C22×D4—22no—
225C22×D4—44no—
226C23×C4C2×C4×C1311yescharacteristic
227C23×C4D4×C1311yescharacteristic
228C23×C4D4×C1311yescharacteristic
229#123—44no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—22no—
232C2×C22⋊C4—22no—
233C2×C22⋊C4—22no—
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—22no—
242C2×C22⋊C4—22no—
243C2×C22⋊C4C2×C4×C1312yes—
244C2×C22⋊C4C2×C4×C1312yes—
245C2×C22⋊C4D4×C1312yes—
246C2×C22⋊C4D4×C1314yes—
247C2×C42—22no—
248#99—48no—
249#95—22no—
250#95—22no—
251#95—22no—
252C2×C13—22no—
253C2×C13—22no—
254C2×C13—42no—
255C2×C13—41no—
256C2×C13—42no—
257C2×C13—82no—
258C2×C13#188911yescharacteristic
259C2×C13#189911yescharacteristic
260C2×C13#191311yescharacteristic
261C24—21no—
262C24—22no—
263C24—42no—
264C24—42no—
265C24—42no—
266C24—42no—
267C24—81no—
268C24—81no—
269C24C22×C4×C1311yescharacteristic
270C24C2×D4×C1311yescharacteristic
271C24C2×D4×C1311yescharacteristic
272C24C2×D4×C1312yes—
273C24C13×#4112yes—
274C2×D4—28no—
275C2×D4—24no—
276C2×D4—42no—
277C2×D4—44no—
278C2×D4—42no—
279C2×D4—44no—
280C2×D4—42no—
281C2×D4—44no—
282C2×D4—41no—
283C2×D4—42no—
284C2×D4—41no—
285C22×C4—21no—
286C22×C4—22no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—22no—
292C22×C4—24no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—81no—
297C22×C4C13×C22⋊C412yes—
298C22×C4C13×C22⋊C412yes—
299C4⋊C4—44no—
300C4⋊C4—82no—
301C22⋊C4—24no—
302C22⋊C4—24no—
303C22⋊C4—44no—
304C22⋊C4—42no—
305C22⋊C4—44no—
306C22⋊C4—44no—
307C22⋊C4—42no—
308C22⋊C4—44no—
309C22⋊C4—44no—
310C22⋊C4—82no—
311C22⋊C4—81no—
312C22⋊C4—82no—
313C22⋊C4—82no—
314C42—82no—
315C13#949611yescharacteristic, direct product factor, Sylow
316C23—22no—
317C23—22no—
318C23—22no—
319C23—22no—
320C23—24no—
321C23—22no—
322C23—24no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—42no—
327C23—41no—
328C23—42no—
329C23—41no—
330C23—42no—
331C23—42no—
332C23—42no—
333C23—42no—
334C23—41no—
335C23—42no—
336C23—41no—
337C23—42no—
338C23—82no—
339C23—82no—
340C23—88no—
341C23—88no—
342C23C2×C13×C22⋊C411yescharacteristic
343C23C4×D4×C1312yes—
344C23C13×#12011yescharacteristic
345C23C13×#12112yes—
346C23C13×#12311yescharacteristic
347D4—48no—
348D4—44no—
349D4—44no—
350C2×C4—22no—
351C2×C4—24no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—44no—
363C2×C4—42no—
364C2×C4—44no—
365C2×C4—42no—
366C2×C4—44no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—82no—
370C2×C4—82no—
371C2×C4—82no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—22no—
377C22—22no—
378C22—21no—
379C22—22no—
380C22—22no—
381C22—21no—
382C22—22no—
383C22—21no—
384C22—22no—
385C22—44no—
386C22—44no—
387C22—44no—
388C22—42no—
389C22—84no—
390C22—82no—
391C22—82no—
392C22—84no—
393C22—84no—
394C22—84no—
395C22—81no—
396C22—81no—
397C22C13×#38611yescharacteristic
398C22C13×#41012yes—
399C22C13×B(4,𝔽2)12yes—
400C4—42no—
401C4—42no—
402C4—42no—
403C4—84no—
404C4—82no—
405C4—162no—
406C2—22no—
407C2—22no—
408C2—42no—
409C2—42no—
410C2—41no—
411C2—82no—
412C2C13×#188911yescharacteristic
413C2C13×#189911yescharacteristic
414C2C13×#191311yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC24C22×C4×C13
Frattini, cosocleC25C23×C13
prime radicalC23×D4×C13C22
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C25×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2312C2semidirect
3. C13×#1819C2semidirect
5. C13×#1304C2semidirect
13. C13×#385C4semidirect
15. C13×#379C4semidirect
54. #9496C13direct (N × H)
110. #2312C2×C13semidirect
111. #1819C2×C13semidirect
113. #1304C2×C13semidirect
177. #385C4×C13semidirect
179. #379C4×C13semidirect
315. C13#9496direct (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×#23122
C13×#18192
C13×#17812
C13×#13042
#949613