Finite Group Databasebeta

← C13×#9501 #15695840

Subgroups — C13×#9501 #15695840

Order 3328.

928 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 928 conjugacy classes of subgroups — too many to draw. Only its 130 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×#2309C211yesmaximal, characteristic
3C13×#1819C212yesmaximal, complemented
4C13×#1781C211yesmaximal, characteristic
5C13×#1304C212yesmaximal, complemented
6C23×D4×C13C2211yescharacteristic
7C2×C13×#123C412yescomplemented
8C2×C13×#117—21no—
9C22×C13×C22⋊C4C2211yescharacteristic
10C2×C13×#99—22no—
11C13×#394—22no—
12C13×#390—24no—
13C13×#386C412yescomplemented
14C13×#385—21no—
15C13×#379—21no—
16C13×#379—21no—
17C13×#379C2212yes—
18C13×#379C2211yescharacteristic
19C13×#379C2212yes—
20C13×#342—24no—
21C25×C13D411yescharacteristic
22C25×C13C2311yescharacteristic
23C22×D4×C13—22no—
24C22×D4×C13—22no—
25C22×D4×C13—44no—
26C22×D4×C13C2×C412yes—
27C22×D4×C13D412yes—
28C23×C4×C13C2×C411yescharacteristic
29C23×C4×C13C2×C411yescharacteristic
30C23×C4×C13D411yescharacteristic
31C13×#123—44no—
32C13×#117—44no—
33C2×C13×C4⋊C4—22no—
34C2×C13×C4⋊C4—22no—
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—22no—
41C2×C13×C22⋊C4—22no—
42C2×C13×C22⋊C4—22no—
43C2×C13×C22⋊C4—22no—
44C2×C13×C22⋊C4—22no—
45C2×C13×C22⋊C4—22no—
46C2×C13×C22⋊C4—22no—
47C2×C13×C22⋊C4—22no—
48C2×C13×C22⋊C4—21no—
49C2×C13×C22⋊C4—22no—
50C2×C13×C22⋊C4C2×C412yes—
51C2×C13×C22⋊C4D414yes—
52C2×C42×C13—22no—
53C13×#99—44no—
54C13×#95—22no—
55#9501C1311yesmaximal, characteristic, direct product factor, Sylow
56C24×C13—21no—
57C24×C13—21no—
58C24×C13—42no—
59C24×C13—42no—
60C24×C13—42no—
61C24×C13—42no—
62C24×C13—81no—
63C24×C13—81no—
64C24×C13C22⋊C412yes—
65C24×C13C22×C411yescharacteristic
66C24×C13C2×D411yescharacteristic
67C24×C13C2×D411yescharacteristic
68C24×C13C2×D412yes—
69C24×C13#4112yes—
70C2×D4×C13—24no—
71C2×D4×C13—24no—
72C2×D4×C13—24no—
73C2×D4×C13—24no—
74C2×D4×C13—42no—
75C2×D4×C13—42no—
76C2×D4×C13—44no—
77C2×D4×C13—44no—
78C2×D4×C13—48no—
79C22×C4×C13—21no—
80C22×C4×C13—21no—
81C22×C4×C13—24no—
82C22×C4×C13—21no—
83C22×C4×C13—22no—
84C22×C4×C13—21no—
85C22×C4×C13—24no—
86C22×C4×C13—22no—
87C22×C4×C13—22no—
88C22×C4×C13—42no—
89C22×C4×C13—42no—
90C22×C4×C13—81no—
91C22×C4×C13C22⋊C412yes—
92C13×C4⋊C4—44no—
93C13×C4⋊C4—44no—
94C13×C22⋊C4—42no—
95C13×C22⋊C4—44no—
96C13×C22⋊C4—44no—
97C13×C22⋊C4—41no—
98C13×C22⋊C4—42no—
99C13×C22⋊C4—41no—
100C13×C22⋊C4—42no—
101C13×C22⋊C4—44no—
102C13×C22⋊C4—44no—
103C13×C22⋊C4—44no—
104C13×C22⋊C4—82no—
105C13×C22⋊C4—81no—
106C13×C22⋊C4—82no—
107C13×C22⋊C4—82no—
108C13×C22⋊C4—82no—
109C13×C22⋊C4—82no—
110C42×C13—44no—
111#2405C2×C1311yescharacteristic
112#2309C2×C1311yescharacteristic
113#1819C2×C1312yescomplemented
114#1781C2×C1311yescharacteristic
115#1304C2×C1312yescomplemented
116C23×C13—22no—
117C23×C13—22no—
118C23×C13—22no—
119C23×C13—22no—
120C23×C13—24no—
121C23×C13—22no—
122C23×C13—22no—
123C23×C13—22no—
124C23×C13—41no—
125C23×C13—41no—
126C23×C13—41no—
127C23×C13—41no—
128C23×C13—42no—
129C23×C13—42no—
130C23×C13—42no—
131C23×C13—42no—
132C23×C13—41no—
133C23×C13—42no—
134C23×C13—42no—
135C23×C13—42no—
136C23×C13—42no—
137C23×C13—42no—
138C23×C13—42no—
139C23×C13—42no—
140C23×C13—81no—
141C23×C13—81no—
142C23×C13—88no—
143C23×C13—88no—
144C23×C13C2×C22⋊C411yescharacteristic
145C23×C13C4×D412yes—
146C23×C13#12011yescharacteristic
147C23×C13#12112yes—
148C23×C13#12311yescharacteristic
149D4×C13—48no—
150D4×C13—48no—
151C2×C4×C13—22no—
152C2×C4×C13—22no—
153C2×C4×C13—24no—
154C2×C4×C13—22no—
155C2×C4×C13—22no—
156C2×C4×C13—44no—
157C2×C4×C13—42no—
158C2×C4×C13—42no—
159C2×C4×C13—44no—
160C2×C4×C13—42no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—42no—
164C2×C4×C13—42no—
165C2×C4×C13—44no—
166C2×C4×C13—82no—
167C2×C4×C13—82no—
168C2×C4×C13—82no—
169C2×C4×C13—82no—
170C2×C4×C13—82no—
171C2×C4×C13#9914yes—
172C23×D4C22×C1311yescharacteristic
173C2×#123C4×C1312yescomplemented
174C2×#117—21no—
175C22×C22⋊C4C22×C1311yescharacteristic
176C2×#99—22no—
177#394—22no—
178#390—24no—
179#386C4×C1312yescomplemented
180#385—21no—
181#379—21no—
182#379—21no—
183#379C22×C1312yes—
184#379C22×C1311yescharacteristic
185#379C22×C1312yes—
186#342—24no—
187C22×C13—21no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13—22no—
192C22×C13—21no—
193C22×C13—22no—
194C22×C13—21no—
195C22×C13—22no—
196C22×C13—22no—
197C22×C13—22no—
198C22×C13—22no—
199C22×C13—21no—
200C22×C13—44no—
201C22×C13—44no—
202C22×C13—44no—
203C22×C13—42no—
204C22×C13—42no—
205C22×C13—42no—
206C22×C13—84no—
207C22×C13—82no—
208C22×C13—82no—
209C22×C13—84no—
210C22×C13—84no—
211C22×C13—84no—
212C22×C13#38611yescharacteristic
213C22×C13C2×#9912yes—
214C22×C13#45812yes—
215C4×C13—24no—
216C4×C13—84no—
217C4×C13—82no—
218C4×C13—81no—
219C4×C13—81no—
220C4×C13—162no—
221C25D4×C1311yescharacteristic
222C25C23×C1311yescharacteristic
223C22×D4—22no—
224C22×D4—22no—
225C22×D4—44no—
226C22×D4C2×C4×C1312yes—
227C22×D4D4×C1312yes—
228C23×C4C2×C4×C1311yescharacteristic
229C23×C4C2×C4×C1311yescharacteristic
230C23×C4D4×C1311yescharacteristic
231#123—44no—
232#117—44no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—22no—
235C2×C22⋊C4—22no—
236C2×C22⋊C4—22no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—22no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—22no—
242C2×C22⋊C4—22no—
243C2×C22⋊C4—22no—
244C2×C22⋊C4—22no—
245C2×C22⋊C4—22no—
246C2×C22⋊C4—22no—
247C2×C22⋊C4—22no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—22no—
250C2×C22⋊C4C2×C4×C1312yes—
251C2×C22⋊C4D4×C1314yes—
252C2×C42—22no—
253#99—44no—
254#95—22no—
255C2×C13—22no—
256C2×C13—22no—
257C2×C13—42no—
258C2×C13—42no—
259C2×C13—41no—
260C2×C13—82no—
261C2×C13#189011yescharacteristic
262C2×C13#189811yescharacteristic
263C2×C13#191311yescharacteristic
264C24—21no—
265C24—21no—
266C24—42no—
267C24—42no—
268C24—42no—
269C24—42no—
270C24—81no—
271C24—81no—
272C24C13×C22⋊C412yes—
273C24C22×C4×C1311yescharacteristic
274C24C2×D4×C1311yescharacteristic
275C24C2×D4×C1311yescharacteristic
276C24C2×D4×C1312yes—
277C24C13×#4112yes—
278C2×D4—24no—
279C2×D4—24no—
280C2×D4—24no—
281C2×D4—24no—
282C2×D4—42no—
283C2×D4—42no—
284C2×D4—44no—
285C2×D4—44no—
286C2×D4—48no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—24no—
290C22×C4—21no—
291C22×C4—22no—
292C22×C4—21no—
293C22×C4—24no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—81no—
299C22×C4C13×C22⋊C412yes—
300C4⋊C4—44no—
301C4⋊C4—44no—
302C22⋊C4—44no—
303C22⋊C4—44no—
304C22⋊C4—42no—
305C22⋊C4—41no—
306C22⋊C4—42no—
307C22⋊C4—41no—
308C22⋊C4—42no—
309C22⋊C4—44no—
310C22⋊C4—44no—
311C22⋊C4—44no—
312C22⋊C4—82no—
313C22⋊C4—81no—
314C22⋊C4—82no—
315C22⋊C4—82no—
316C22⋊C4—82no—
317C22⋊C4—82no—
318C42—44no—
319C13#950111yescharacteristic, direct product factor, Sylow
320C23—22no—
321C23—22no—
322C23—22no—
323C23—22no—
324C23—24no—
325C23—22no—
326C23—22no—
327C23—22no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—42no—
333C23—42no—
334C23—42no—
335C23—42no—
336C23—41no—
337C23—42no—
338C23—42no—
339C23—42no—
340C23—42no—
341C23—42no—
342C23—42no—
343C23—42no—
344C23—81no—
345C23—81no—
346C23—88no—
347C23—88no—
348C23C2×C13×C22⋊C411yescharacteristic
349C23C4×D4×C1312yes—
350C23C13×#12011yescharacteristic
351C23C13×#12112yes—
352C23C13×#12311yescharacteristic
353D4—48no—
354D4—48no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—24no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—44no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—44no—
364C2×C4—42no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—44no—
370C2×C4—82no—
371C2×C4—82no—
372C2×C4—82no—
373C2×C4—82no—
374C2×C4—82no—
375C2×C4C13×#9914yes—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—22no—
381C22—21no—
382C22—22no—
383C22—21no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22—22no—
388C22—21no—
389C22—44no—
390C22—44no—
391C22—44no—
392C22—42no—
393C22—42no—
394C22—42no—
395C22—84no—
396C22—82no—
397C22—82no—
398C22—84no—
399C22—84no—
400C22—84no—
401C22C13×#38611yescharacteristic
402C22C2×C13×#9912yes—
403C22C13×#45812yes—
404C4—24no—
405C4—84no—
406C4—82no—
407C4—81no—
408C4—81no—
409C4—162no—
410C2—22no—
411C2—22no—
412C2—42no—
413C2—41no—
414C2—42no—
415C2—82no—
416C2C13×#189011yescharacteristic
417C2C13×#189811yescharacteristic
418C2C13×#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
3. C13×#1819C2semidirect
5. C13×#1304C2semidirect
7. C2×C13×#123C4semidirect
13. C13×#386C4semidirect
55. #9501C13direct (N × H)
113. #1819C2×C13semidirect
115. #1304C2×C13semidirect
173. C2×#123C4×C13semidirect
179. #386C4×C13semidirect
319. C13#9501direct (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×#23092
C13×#18192
C13×#17812
C13×#13042
#950113