Finite Group Databasebeta

← C13×#10335 #15696674

Subgroups — C13×#10335 #15696674

Order 3328.

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

normal subgroups only

This group has 574 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×#3195C211yesmaximal, characteristic
2C13×#2503C211yesmaximal, characteristic
3C13×#2502C211yesmaximal, characteristic
4C13×#1821C211yesmaximal, characteristic
5C13×#1508C211yesmaximal, characteristic
6C13×#1508C211yesmaximal, characteristic
7C13×#1297C211yesmaximal, characteristic
8C2×C13×C22⋊Q8C2211yescharacteristic
9C2×C13×C22⋊Q8C2211yescharacteristic
10C22×C13×C4⋊C4C2211yescharacteristic
11C13×#483—21no—
12C13×#483—21no—
13C13×#470—22no—
14C13×#451—21no—
15C13×#451—21no—
16C13×#407C2211yescharacteristic
17C13×#407C2211yescharacteristic
18C13×#400—22no—
19C13×#398—22no—
20C13×#391—21no—
21C13×#391—21no—
22C13×#385—22no—
23C13×#384—21no—
24C13×#382—21no—
25C13×#381—22no—
26C4×C13×C22⋊C4C2211yescharacteristic
27C4×C13×C22⋊C4C2211yescharacteristic
28C13×#343—22no—
29C13×#328—22no—
30C13×#328—22no—
31C22×Q8×C13D411yescharacteristic
32C22×Q8×C13D411yescharacteristic
33C23×C4×C13D412yes—
34C23×C4×C13C2311yescharacteristic
35C2×C13×Q16—22no—
36C2×C13×M16—21no—
37C2×C13×M16D412yes—
38C13×C22⋊Q8—21no—
39C13×C22⋊Q8—21no—
40C13×C22⋊Q8—21no—
41C13×C22⋊Q8—21no—
42C13×C22⋊Q8—21no—
43C13×C22⋊Q8—21no—
44C13×C22⋊Q8—21no—
45C13×C22⋊Q8—21no—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4—24no—
55C2×C13×C4⋊C4D411yescharacteristic
56C2×C13×C4⋊C4D411yescharacteristic
57C2×C13×C22⋊C4—21no—
58C2×C13×C22⋊C4—21no—
59C2×C13×C22⋊C4—21no—
60C2×C13×C22⋊C4—21no—
61C2×C42×C13—21no—
62C2×C42×C13—21no—
63C13×#106—22no—
64C13×#103—22no—
65C13×#103—22no—
66C13×C22⋊C8—21no—
67C13×C22⋊C8—21no—
68C13×C22⋊C8—21no—
69C13×C22⋊C8—21no—
70C13×#95—24no—
71C13×#95—24no—
72C13×#95—24no—
73C13×#95D412yes—
74C13×#95D412yes—
75#10335C1311yesmaximal, characteristic, direct product factor, Sylow
76C24×C13C2×D411yescharacteristic
77C2×Q8×C13—21no—
78C2×Q8×C13—21no—
79C2×Q8×C13—21no—
80C2×Q8×C13—21no—
81C2×Q8×C13—42no—
82C2×Q8×C13—42no—
83C22×C4×C13—22no—
84C22×C4×C13—22no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—22no—
89C22×C4×C13—22no—
90C22×C4×C13—21no—
91C22×C4×C13—22no—
92C22×C4×C13—42no—
93C22×C4×C13—44no—
94C22×C4×C13C2×D411yescharacteristic
95C22×C4×C13C2×D411yescharacteristic
96C22×C4×C13C2×D411yescharacteristic
97C22×C4×C13C2×D411yescharacteristic
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13#4111yescharacteristic
100C13×Q16—82no—
101C13×M16—42no—
102C13×M16—42no—
103C2×C8×C13—22no—
104C2×C8×C13—41no—
105C13×C4⋊C4—21no—
106C13×C4⋊C4—21no—
107C13×C4⋊C4—21no—
108C13×C4⋊C4—21no—
109C13×C4⋊C4—41no—
110C13×C4⋊C4—41no—
111C13×C4⋊C4—41no—
112C13×C4⋊C4—41no—
113C13×C4⋊C4—41no—
114C13×C4⋊C4—41no—
115C13×C4⋊C4—41no—
116C13×C4⋊C4—41no—
117C13×C4⋊C4—84no—
118C13×C22⋊C4—24no—
119C13×C22⋊C4—42no—
120C13×C22⋊C4—41no—
121C13×C22⋊C4—41no—
122C13×C22⋊C4—41no—
123C13×C22⋊C4—41no—
124C42×C13—42no—
125C42×C13—42no—
126#3195C2×C1311yescharacteristic
127#2503C2×C1311yescharacteristic
128#2502C2×C1311yescharacteristic
129#1821C2×C1311yescharacteristic
130#1508C2×C1311yescharacteristic
131#1508C2×C1311yescharacteristic
132#1297C2×C1311yescharacteristic
133C23×C13—22no—
134C23×C13—22no—
135C23×C13—41no—
136C23×C13#12011yescharacteristic
137C23×C13#12011yescharacteristic
138C23×C13#12111yescharacteristic
139Q8×C13—42no—
140Q8×C13—42no—
141Q8×C13—81no—
142Q8×C13—81no—
143C2×C4×C13—22no—
144C2×C4×C13—22no—
145C2×C4×C13—22no—
146C2×C4×C13—24no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—42no—
151C2×C4×C13—42no—
152C2×C4×C13—42no—
153C2×C4×C13—42no—
154C2×C4×C13—44no—
155C2×C4×C13—42no—
156C2×C4×C13—42no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—42no—
162C2×C4×C13—42no—
163C2×C4×C13—44no—
164C2×C4×C13—42no—
165C2×C4×C13—42no—
166C2×C4×C13—82no—
167C2×C4×C13#12011yescharacteristic
168C2×C4×C13#12111yescharacteristic
169C2×C4×C13#12111yescharacteristic
170C2×C4×C13#12711yescharacteristic
171C8×C13—42no—
172C8×C13—81no—
173C2×C22⋊Q8C22×C1311yescharacteristic
174C2×C22⋊Q8C22×C1311yescharacteristic
175C22×C4⋊C4C22×C1311yescharacteristic
176#483—21no—
177#483—21no—
178#470—22no—
179#451—21no—
180#451—21no—
181#407C22×C1311yescharacteristic
182#407C22×C1311yescharacteristic
183#400—22no—
184#398—22no—
185#391—21no—
186#391—21no—
187#385—22no—
188#384—21no—
189#382—21no—
190#381—22no—
191C4×C22⋊C4C22×C1311yescharacteristic
192C4×C22⋊C4C22×C1311yescharacteristic
193#343—22no—
194#328—22no—
195#328—22no—
196C22×C13—21no—
197C22×C13—21no—
198C22×C13—21no—
199C22×C13—21no—
200C22×C13—21no—
201C22×C13—21no—
202C22×C13—21no—
203C22×C13—44no—
204C22×C13#39211yescharacteristic
205C22×C13#45512yes—
206C22×C13#45612yes—
207C4×C13—21no—
208C4×C13—21no—
209C4×C13—21no—
210C4×C13—44no—
211C4×C13—82no—
212C4×C13—81no—
213C4×C13—82no—
214C4×C13—81no—
215C4×C13—81no—
216C4×C13—81no—
217C4×C13#45812yes—
218C22×Q8D4×C1311yescharacteristic
219C22×Q8D4×C1311yescharacteristic
220C23×C4D4×C1312yes—
221C23×C4C23×C1311yescharacteristic
222C2×Q16—22no—
223C2×M16—21no—
224C2×M16D4×C1312yes—
225C22⋊Q8—21no—
226C22⋊Q8—21no—
227C22⋊Q8—21no—
228C22⋊Q8—21no—
229C22⋊Q8—21no—
230C22⋊Q8—21no—
231C22⋊Q8—21no—
232C22⋊Q8—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—24no—
242C2×C4⋊C4D4×C1311yescharacteristic
243C2×C4⋊C4D4×C1311yescharacteristic
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—21no—
248C2×C42—21no—
249C2×C42—21no—
250#106—22no—
251#103—22no—
252#103—22no—
253C22⋊C8—21no—
254C22⋊C8—21no—
255C22⋊C8—21no—
256C22⋊C8—21no—
257#95—24no—
258#95—24no—
259#95—24no—
260#95D4×C1312yes—
261#95D4×C1312yes—
262C2×C13—22no—
263C2×C13—22no—
264C2×C13—41no—
265C2×C13#200411yescharacteristic
266C2×C13#200511yescharacteristic
267C2×C13#202211yescharacteristic
268C24C2×D4×C1311yescharacteristic
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—21no—
273C2×Q8—42no—
274C2×Q8—42no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—21no—
283C22×C4—22no—
284C22×C4—42no—
285C22×C4—44no—
286C22×C4C2×D4×C1311yescharacteristic
287C22×C4C2×D4×C1311yescharacteristic
288C22×C4C2×D4×C1311yescharacteristic
289C22×C4C2×D4×C1311yescharacteristic
290C22×C4C2×D4×C1311yescharacteristic
291C22×C4C13×#4111yescharacteristic
292Q16—82no—
293M16—42no—
294M16—42no—
295C2×C8—22no—
296C2×C8—41no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—84no—
310C22⋊C4—24no—
311C22⋊C4—42no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C42—42no—
317C42—42no—
318C13#1033511yescharacteristic, direct product factor, Sylow
319C23—22no—
320C23—22no—
321C23—41no—
322C23C13×#12011yescharacteristic
323C23C13×#12011yescharacteristic
324C23C13×#12111yescharacteristic
325Q8—42no—
326Q8—42no—
327Q8—81no—
328Q8—81no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—24no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—44no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—44no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—82no—
353C2×C4C13×#12011yescharacteristic
354C2×C4C13×#12111yescharacteristic
355C2×C4C13×#12111yescharacteristic
356C2×C4C13×#12711yescharacteristic
357C8—42no—
358C8—81no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—44no—
367C22C13×#39211yescharacteristic
368C22C13×#45512yes—
369C22C13×#45612yes—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—44no—
374C4—82no—
375C4—81no—
376C4—82no—
377C4—81no—
378C4—81no—
379C4—81no—
380C4C13×#45812yes—
381C2—22no—
382C2—22no—
383C2—41no—
384C2C13×#200411yescharacteristic
385C2C13×#200511yescharacteristic
386C2C13×#202211yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC24×C13C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
75. #10335C13direct (N × H)
318. C13#10335direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31952
C13×#25032
C13×#25022
C13×#18212
C13×#15082
C13×#12972
#1033513