Finite Group Databasebeta

← C13×#11845 #15698184

Subgroups — C13×#11845 #15698184

Order 3328.

506 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2561C211yesmaximal, characteristic
2C13×#1819C211yesmaximal, characteristic
3C2×C13×#323C211yesmaximal, characteristic
4C13×#1351C212yesmaximal, complemented
5C13×#1344C212yesmaximal, complemented
6C2×C13×C22⋊Q8C411yescharacteristic, complemented
7C22×C13×C22⋊C4C2211yescharacteristic
8C2×C13×C22⋊C8—21no—
9C13×#397C411yescharacteristic, complemented
10C13×#397C2211yescharacteristic
11C13×#393C411yescharacteristic, complemented
12C13×#393C2211yescharacteristic
13C13×#388—21no—
14C13×#388—21no—
15C13×#381—21no—
16C13×#379—21no—
17C13×#379—21no—
18C4×C13×C22⋊C4C411yescharacteristic, complemented
19C13×#342—21no—
20C13×#342C2212yes—
21C13×#323—21no—
22C13×#323C2212yes—
23C25×C13D411yescharacteristic
24C22×Q8×C13C2×C411yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C22×C8×C13—41no—
28C13×C22⋊Q8—41no—
29C13×C22⋊Q8—41no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C22⋊C4—21no—
33C2×C13×C22⋊C4—21no—
34C2×C13×C22⋊C4—21no—
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—41no—
40C2×C13×C22⋊C4—41no—
41C2×C13×C22⋊C4—41no—
42C2×C13×C22⋊C4—41no—
43C2×C13×C22⋊C4C2×C411yescharacteristic
44C2×C13×C22⋊C4D411yescharacteristic
45C2×C13×C22⋊C4D411yescharacteristic
46C2×C13×C22⋊C4C2311yescharacteristic
47C2×C42×C13—21no—
48C13×C22⋊C8—22no—
49C13×C22⋊C8—41no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95C2×C411yescharacteristic
55C13×#95C2×C411yescharacteristic
56#11845C1311yesmaximal, characteristic, direct product factor, Sylow
57C24×C13—21no—
58C24×C13—21no—
59C24×C13—22no—
60C24×C13—41no—
61C24×C13—42no—
62C24×C13—81no—
63C24×C13C22⋊C411yescharacteristic
64C24×C13C22⋊C411yescharacteristic
65C24×C13C2×D411yescharacteristic
66C2×Q8×C13—41no—
67C2×Q8×C13—81no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—42no—
77C22×C4×C13—42no—
78C22×C4×C13—81no—
79C22×C4×C13C22⋊C411yescharacteristic
80C22×C4×C13C22⋊C411yescharacteristic
81C22×C4×C13C22×C411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C2×C8×C13—42no—
84C2×C8×C13—82no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—42no—
87C13×C22⋊C4—41no—
88C13×C22⋊C4—41no—
89C13×C22⋊C4—41no—
90C13×C22⋊C4—41no—
91C13×C22⋊C4—42no—
92C13×C22⋊C4—42no—
93C13×C22⋊C4—41no—
94C13×C22⋊C4—41no—
95C13×C22⋊C4—42no—
96C13×C22⋊C4—42no—
97C13×C22⋊C4—42no—
98C13×C22⋊C4—81no—
99C13×C22⋊C4—81no—
100C13×C22⋊C4—82no—
101C13×C22⋊C4—82no—
102C42×C13—81no—
103#2561C2×C1311yescharacteristic
104#1819C2×C1311yescharacteristic
105C2×#323C2×C1311yescharacteristic
106#1351C2×C1312yescomplemented
107#1344C2×C1312yescomplemented
108C23×C13—22no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—41no—
117C23×C13—42no—
118C23×C13—42no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13—42no—
124C23×C13—42no—
125C23×C13—81no—
126C23×C13—81no—
127C23×C13—84no—
128C23×C13—84no—
129C23×C13#9911yescharacteristic
130C23×C13#9911yescharacteristic
131C23×C13C2×C22⋊C411yescharacteristic
132C23×C13#13512yes—
133Q8×C13—82no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—42no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—81no—
156C2×C4×C13—81no—
157C2×C4×C13—81no—
158C2×C4×C13—82no—
159C2×C4×C13—82no—
160C2×C4×C13—82no—
161C8×C13—82no—
162C2×C22⋊Q8C4×C1311yescharacteristic, complemented
163C22×C22⋊C4C22×C1311yescharacteristic
164C2×C22⋊C8—21no—
165#397C4×C1311yescharacteristic, complemented
166#397C22×C1311yescharacteristic
167#393C4×C1311yescharacteristic, complemented
168#393C22×C1311yescharacteristic
169#388—21no—
170#388—21no—
171#381—21no—
172#379—21no—
173#379—21no—
174C4×C22⋊C4C4×C1311yescharacteristic, complemented
175#342—21no—
176#342C22×C1312yes—
177#323—21no—
178#323C22×C1312yes—
179C22×C13—21no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—22no—
186C22×C13—21no—
187C22×C13—42no—
188C22×C13—42no—
189C22×C13—42no—
190C22×C13—42no—
191C22×C13—41no—
192C22×C13—41no—
193C22×C13—41no—
194C22×C13—41no—
195C22×C13—41no—
196C22×C13—81no—
197C22×C13—84no—
198C22×C13—81no—
199C22×C13—84no—
200C22×C13#35412yes—
201C22×C13C2×#9911yescharacteristic
202C22×C13#41611yescharacteristic
203C22×C13#42111yescharacteristic
204C4×C13—41no—
205C4×C13—41no—
206C4×C13—41no—
207C4×C13—41no—
208C4×C13—81no—
209C4×C13—81no—
210C4×C13—81no—
211C4×C13—81no—
212C4×C13—162no—
213C25D4×C1311yescharacteristic
214C22×Q8C2×C4×C1311yescharacteristic
215C23×C4C2×C4×C1311yescharacteristic
216C23×C4D4×C1311yescharacteristic
217C22×C8—41no—
218C22⋊Q8—41no—
219C22⋊Q8—41no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4C2×C4×C1311yescharacteristic
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—22no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—41no—
230C2×C22⋊C4—41no—
231C2×C22⋊C4—41no—
232C2×C22⋊C4—41no—
233C2×C22⋊C4C2×C4×C1311yescharacteristic
234C2×C22⋊C4D4×C1311yescharacteristic
235C2×C22⋊C4D4×C1311yescharacteristic
236C2×C22⋊C4C23×C1311yescharacteristic
237C2×C42—21no—
238C22⋊C8—22no—
239C22⋊C8—41no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—21no—
244#95C2×C4×C1311yescharacteristic
245#95C2×C4×C1311yescharacteristic
246C2×C13—21no—
247C2×C13—21no—
248C2×C13—22no—
249C2×C13—42no—
250C2×C13—41no—
251C2×C13—81no—
252C2×C13#151611yescharacteristic
253C2×C13#212111yescharacteristic
254C2×C13C2×#35411yescharacteristic
255C24—21no—
256C24—21no—
257C24—22no—
258C24—41no—
259C24—42no—
260C24—81no—
261C24C13×C22⋊C411yescharacteristic
262C24C13×C22⋊C411yescharacteristic
263C24C2×D4×C1311yescharacteristic
264C2×Q8—41no—
265C2×Q8—81no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—81no—
277C22×C4C13×C22⋊C411yescharacteristic
278C22×C4C13×C22⋊C411yescharacteristic
279C22×C4C22×C4×C1311yescharacteristic
280C22×C4C2×D4×C1311yescharacteristic
281C2×C8—42no—
282C2×C8—82no—
283C4⋊C4—41no—
284C4⋊C4—42no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—42no—
290C22⋊C4—42no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—42no—
294C22⋊C4—42no—
295C22⋊C4—42no—
296C22⋊C4—81no—
297C22⋊C4—81no—
298C22⋊C4—82no—
299C22⋊C4—82no—
300C42—81no—
301C13#1184511yescharacteristic, direct product factor, Sylow
302C23—21no—
303C23—21no—
304C23—21no—
305C23—22no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—41no—
311C23—42no—
312C23—42no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—42no—
318C23—42no—
319C23—81no—
320C23—81no—
321C23—84no—
322C23—84no—
323C23C13×#9911yescharacteristic
324C23C13×#9911yescharacteristic
325C23C2×C13×C22⋊C411yescharacteristic
326C23C13×#13512yes—
327Q8—82no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—82no—
353C2×C4—82no—
354C2×C4—82no—
355C8—82no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—22no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—42no—
365C22—42no—
366C22—42no—
367C22—42no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—81no—
374C22—84no—
375C22—81no—
376C22—84no—
377C22C13×#35412yes—
378C22C2×C13×#9911yescharacteristic
379C22C13×#41611yescharacteristic
380C22C13×#42111yescharacteristic
381C4—41no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—81no—
386C4—81no—
387C4—81no—
388C4—81no—
389C4—162no—
390C2—21no—
391C2—21no—
392C2—22no—
393C2—42no—
394C2—41no—
395C2—81no—
396C2C13×#151611yescharacteristic
397C2C13×#212111yescharacteristic
398C2C2×C13×#35411yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC25×C13D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C24×C13 ◁ C22×C13×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
4. C13×#1351C2semidirect
5. C13×#1344C2semidirect
6. C2×C13×C22⋊Q8C4semidirect
9. C13×#397C4semidirect
11. C13×#393C4semidirect
18. C4×C13×C22⋊C4C4semidirect
56. #11845C13direct (N × H)
106. #1351C2×C13semidirect
107. #1344C2×C13semidirect
162. C2×C22⋊Q8C4×C13semidirect
165. #397C4×C13semidirect
167. #393C4×C13semidirect
174. C4×C22⋊C4C4×C13semidirect
301. C13#11845direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25612
C13×#18192
C2×C13×#3232
C13×#13512
C13×#13442
#1184513