Finite Group Databasebeta

← C13×#9459 #15695798

Subgroups — C13×#9459 #15695798

Order 3328.

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

normal subgroups only

This group has 904 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×#2435C211yesmaximal, characteristic
2C13×#2308C211yesmaximal, characteristic
3C13×#1783C211yesmaximal, characteristic
4C13×#1511C212yesmaximal, complemented
5C13×#1284C212yesmaximal, complemented
6C23×D4×C13C2211yescharacteristic
7C2×C13×#124C412yescomplemented
8C2×C13×C22⋊Q8C2211yescharacteristic
9C22×C13×C22⋊C4—21no—
10C2×C13×#100—22no—
11C13×#407C2212yes—
12C13×#394—22no—
13C13×#390C412yescomplemented
14C13×#386—24no—
15C13×#381C2212yes—
16C13×#379—21no—
17C13×#379—21no—
18C13×#379—21no—
19C4×C13×C22⋊C4C2211yescharacteristic
20C13×#328—24no—
21C25×C13D411yescharacteristic
22C25×C13D411yescharacteristic
23C22×Q8×C13C2×C411yescharacteristic, complemented
24C22×D4×C13—22no—
25C22×D4×C13—22no—
26C22×D4×C13—44no—
27C22×D4×C13C2×C412yes—
28C22×D4×C13D412yes—
29C23×C4×C13—22no—
30C23×C4×C13C2311yescharacteristic
31C2×C13×M16—22no—
32C13×#124—44no—
33C13×C22⋊Q8—22no—
34C13×C22⋊Q8—22no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4C2×C411yescharacteristic, complemented
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4—22no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
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—44no—
48C2×C42×C13C2×C412yescomplemented
49C13×#100—44no—
50C13×C22⋊C8—22no—
51C13×C22⋊C8—22no—
52C13×#95—21no—
53C13×#95—22no—
54C13×#95D414yes—
55#9459C1311yesmaximal, characteristic, direct product factor, Sylow
56C24×C13—21no—
57C24×C13—24no—
58C24×C13—21no—
59C24×C13—21no—
60C24×C13—21no—
61C24×C13—42no—
62C24×C13—42no—
63C24×C13—42no—
64C24×C13—81no—
65C24×C13—81no—
66C24×C13C22⋊C412yes—
67C24×C13C22⋊C412yes—
68C24×C13C2×D411yescharacteristic
69C2×Q8×C13—22no—
70C2×Q8×C13—42no—
71C2×D4×C13—24no—
72C2×D4×C13—24no—
73C2×D4×C13—24no—
74C2×D4×C13—24no—
75C2×D4×C13—42no—
76C2×D4×C13—42no—
77C2×D4×C13—44no—
78C2×D4×C13—44no—
79C2×D4×C13—48no—
80C22×C4×C13—22no—
81C22×C4×C13—21no—
82C22×C4×C13—21no—
83C22×C4×C13—24no—
84C22×C4×C13—42no—
85C22×C4×C13—44no—
86C22×C4×C13—82no—
87C22×C4×C13—82no—
88C22×C4×C13C22×C411yescharacteristic
89C22×C4×C13C2×D411yescharacteristic
90C22×C4×C13C2×D412yes—
91C22×C4×C13#4112yes—
92C13×M16—44no—
93C2×C8×C13—42no—
94C13×C4⋊C4—22no—
95C13×C4⋊C4—42no—
96C13×C22⋊C4—42no—
97C13×C22⋊C4—44no—
98C13×C22⋊C4—44no—
99C13×C22⋊C4—44no—
100C13×C22⋊C4—44no—
101C13×C22⋊C4—41no—
102C13×C22⋊C4—41no—
103C13×C22⋊C4—82no—
104C13×C22⋊C4—82no—
105C13×C22⋊C4—82no—
106C13×C22⋊C4—82no—
107C42×C13—42no—
108#2435C2×C1311yescharacteristic
109#2308C2×C1311yescharacteristic
110#1783C2×C1311yescharacteristic
111#1511C2×C1312yescomplemented
112#1284C2×C1312yescomplemented
113C23×C13—22no—
114C23×C13—22no—
115C23×C13—24no—
116C23×C13—22no—
117C23×C13—22no—
118C23×C13—22no—
119C23×C13—22no—
120C23×C13—22no—
121C23×C13—22no—
122C23×C13—22no—
123C23×C13—41no—
124C23×C13—42no—
125C23×C13—42no—
126C23×C13—42no—
127C23×C13—42no—
128C23×C13—42no—
129C23×C13—42no—
130C23×C13—42no—
131C23×C13—42no—
132C23×C13—42no—
133C23×C13—42no—
134C23×C13—81no—
135C23×C13—81no—
136C23×C13—81no—
137C23×C13—81no—
138C23×C13—88no—
139C23×C13—88no—
140C23×C13#9914yes—
141C23×C13C2×C22⋊C411yescharacteristic
142C23×C13#12011yescharacteristic
143C23×C13#12311yescharacteristic
144Q8×C13—82no—
145D4×C13—48no—
146D4×C13—48no—
147C2×C4×C13—22no—
148C2×C4×C13—22no—
149C2×C4×C13—42no—
150C2×C4×C13—42no—
151C2×C4×C13—44no—
152C2×C4×C13—42no—
153C2×C4×C13—42no—
154C2×C4×C13—42no—
155C2×C4×C13—44no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—42no—
159C2×C4×C13—42no—
160C2×C4×C13—44no—
161C2×C4×C13—88no—
162C2×C4×C13C4×D412yes—
163C2×C4×C13#12112yes—
164C8×C13—82no—
165C23×D4C22×C1311yescharacteristic
166C2×#124C4×C1312yescomplemented
167C2×C22⋊Q8C22×C1311yescharacteristic
168C22×C22⋊C4—21no—
169C2×#100—22no—
170#407C22×C1312yes—
171#394—22no—
172#390C4×C1312yescomplemented
173#386—24no—
174#381C22×C1312yes—
175#379—21no—
176#379—21no—
177#379—21no—
178C4×C22⋊C4C22×C1311yescharacteristic
179#328—24no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—24no—
187C22×C13—21no—
188C22×C13—44no—
189C22×C13—44no—
190C22×C13—44no—
191C22×C13—44no—
192C22×C13—44no—
193C22×C13—42no—
194C22×C13—42no—
195C22×C13—42no—
196C22×C13—42no—
197C22×C13—42no—
198C22×C13—82no—
199C22×C13—82no—
200C22×C13—84no—
201C22×C13—84no—
202C22×C13—84no—
203C22×C13#38611yescharacteristic
204C22×C13C2×#9912yes—
205C22×C13#45512yes—
206C4×C13—22no—
207C4×C13—22no—
208C4×C13—82no—
209C4×C13—84no—
210C4×C13—81no—
211C4×C13—81no—
212C25D4×C1311yescharacteristic
213C25D4×C1311yescharacteristic
214C22×Q8C2×C4×C1311yescharacteristic, complemented
215C22×D4—22no—
216C22×D4—22no—
217C22×D4—44no—
218C22×D4C2×C4×C1312yes—
219C22×D4D4×C1312yes—
220C23×C4—22no—
221C23×C4C23×C1311yescharacteristic
222C2×M16—22no—
223#124—44no—
224C22⋊Q8—22no—
225C22⋊Q8—22no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4C2×C4×C1311yescharacteristic, complemented
228C2×C22⋊C4—22no—
229C2×C22⋊C4—22no—
230C2×C22⋊C4—22no—
231C2×C22⋊C4—22no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—22no—
235C2×C22⋊C4—22no—
236C2×C22⋊C4—22no—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—44no—
239C2×C42C2×C4×C1312yescomplemented
240#100—44no—
241C22⋊C8—22no—
242C22⋊C8—22no—
243#95—21no—
244#95—22no—
245#95D4×C1314yes—
246C2×C13—22no—
247C2×C13—22no—
248C2×C13—41no—
249C2×C13—44no—
250C2×C13—82no—
251C2×C13#188511yescharacteristic
252C2×C13#189811yescharacteristic
253C2×C13#191111yescharacteristic
254C24—21no—
255C24—24no—
256C24—21no—
257C24—21no—
258C24—21no—
259C24—42no—
260C24—42no—
261C24—42no—
262C24—81no—
263C24—81no—
264C24C13×C22⋊C412yes—
265C24C13×C22⋊C412yes—
266C24C2×D4×C1311yescharacteristic
267C2×Q8—22no—
268C2×Q8—42no—
269C2×D4—24no—
270C2×D4—24no—
271C2×D4—24no—
272C2×D4—24no—
273C2×D4—42no—
274C2×D4—42no—
275C2×D4—44no—
276C2×D4—44no—
277C2×D4—48no—
278C22×C4—22no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—24no—
282C22×C4—42no—
283C22×C4—44no—
284C22×C4—82no—
285C22×C4—82no—
286C22×C4C22×C4×C1311yescharacteristic
287C22×C4C2×D4×C1311yescharacteristic
288C22×C4C2×D4×C1312yes—
289C22×C4C13×#4112yes—
290M16—44no—
291C2×C8—42no—
292C4⋊C4—22no—
293C4⋊C4—42no—
294C22⋊C4—44no—
295C22⋊C4—44no—
296C22⋊C4—44no—
297C22⋊C4—42no—
298C22⋊C4—44no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—82no—
302C22⋊C4—82no—
303C22⋊C4—82no—
304C22⋊C4—82no—
305C42—42no—
306C13#945911yescharacteristic, direct product factor, Sylow
307C23—22no—
308C23—22no—
309C23—24no—
310C23—22no—
311C23—22no—
312C23—22no—
313C23—22no—
314C23—22no—
315C23—22no—
316C23—22no—
317C23—41no—
318C23—42no—
319C23—42no—
320C23—42no—
321C23—42no—
322C23—42no—
323C23—42no—
324C23—42no—
325C23—42no—
326C23—42no—
327C23—42no—
328C23—81no—
329C23—81no—
330C23—81no—
331C23—81no—
332C23—88no—
333C23—88no—
334C23C13×#9914yes—
335C23C2×C13×C22⋊C411yescharacteristic
336C23C13×#12011yescharacteristic
337C23C13×#12311yescharacteristic
338Q8—82no—
339D4—48no—
340D4—48no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—44no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—44no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—44no—
355C2×C4—88no—
356C2×C4C4×D4×C1312yes—
357C2×C4C13×#12112yes—
358C8—82no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—24no—
366C22—21no—
367C22—44no—
368C22—44no—
369C22—44no—
370C22—44no—
371C22—44no—
372C22—42no—
373C22—42no—
374C22—42no—
375C22—42no—
376C22—42no—
377C22—82no—
378C22—82no—
379C22—84no—
380C22—84no—
381C22—84no—
382C22C13×#38611yescharacteristic
383C22C2×C13×#9912yes—
384C22C13×#45512yes—
385C4—22no—
386C4—22no—
387C4—82no—
388C4—84no—
389C4—81no—
390C4—81no—
391C2—22no—
392C2—22no—
393C2—41no—
394C2—44no—
395C2—82no—
396C2C13×#188511yescharacteristic
397C2C13×#189811yescharacteristic
398C2C13×#191111yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC22×C4C22×C4×C13
Frattini, cosocleC23×C4C23×C13
prime radicalC23×D4×C13C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
4. C13×#1511C2semidirect
5. C13×#1284C2semidirect
7. C2×C13×#124C4semidirect
13. C13×#390C4semidirect
23. C22×Q8×C13C2×C4semidirect
36. C2×C13×C4⋊C4C2×C4semidirect
48. C2×C42×C13C2×C4semidirect
55. #9459C13direct (N × H)
111. #1511C2×C13semidirect
112. #1284C2×C13semidirect
166. C2×#124C4×C13semidirect
172. #390C4×C13semidirect
214. C22×Q8C2×C4×C13semidirect
227. C2×C4⋊C4C2×C4×C13semidirect
239. C2×C42C2×C4×C13semidirect
306. C13#9459direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#24352
C13×#23082
C13×#17832
C13×#15112
C13×#12842
#945913